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169,809 | import numpy as np
import numpy.linalg as la
from numpy.core.multiarray import normalize_axis_index
from . import polyutils as pu
from ._polybase import ABCPolyBase
def polyvander(x, deg):
"""Vandermonde matrix of given degree.
Returns the Vandermonde matrix of degree `deg` and sample points
`x`. The Vandermonde matrix is defined by
.. math:: V[..., i] = x^i,
where `0 <= i <= deg`. The leading indices of `V` index the elements of
`x` and the last index is the power of `x`.
If `c` is a 1-D array of coefficients of length `n + 1` and `V` is the
matrix ``V = polyvander(x, n)``, then ``np.dot(V, c)`` and
``polyval(x, c)`` are the same up to roundoff. This equivalence is
useful both for least squares fitting and for the evaluation of a large
number of polynomials of the same degree and sample points.
Parameters
----------
x : array_like
Array of points. The dtype is converted to float64 or complex128
depending on whether any of the elements are complex. If `x` is
scalar it is converted to a 1-D array.
deg : int
Degree of the resulting matrix.
Returns
-------
vander : ndarray.
The Vandermonde matrix. The shape of the returned matrix is
``x.shape + (deg + 1,)``, where the last index is the power of `x`.
The dtype will be the same as the converted `x`.
See Also
--------
polyvander2d, polyvander3d
"""
ideg = pu._deprecate_as_int(deg, "deg")
if ideg < 0:
raise ValueError("deg must be non-negative")
x = np.array(x, copy=False, ndmin=1) + 0.0
dims = (ideg + 1,) + x.shape
dtyp = x.dtype
v = np.empty(dims, dtype=dtyp)
v[0] = x*0 + 1
if ideg > 0:
v[1] = x
for i in range(2, ideg + 1):
v[i] = v[i-1]*x
return np.moveaxis(v, 0, -1)
The provided code snippet includes necessary dependencies for implementing the `polyfit` function. Write a Python function `def polyfit(x, y, deg, rcond=None, full=False, w=None)` to solve the following problem:
Least-squares fit of a polynomial to data. Return the coefficients of a polynomial of degree `deg` that is the least squares fit to the data values `y` given at points `x`. If `y` is 1-D the returned coefficients will also be 1-D. If `y` is 2-D multiple fits are done, one for each column of `y`, and the resulting coefficients are stored in the corresponding columns of a 2-D return. The fitted polynomial(s) are in the form .. math:: p(x) = c_0 + c_1 * x + ... + c_n * x^n, where `n` is `deg`. Parameters ---------- x : array_like, shape (`M`,) x-coordinates of the `M` sample (data) points ``(x[i], y[i])``. y : array_like, shape (`M`,) or (`M`, `K`) y-coordinates of the sample points. Several sets of sample points sharing the same x-coordinates can be (independently) fit with one call to `polyfit` by passing in for `y` a 2-D array that contains one data set per column. deg : int or 1-D array_like Degree(s) of the fitting polynomials. If `deg` is a single integer all terms up to and including the `deg`'th term are included in the fit. For NumPy versions >= 1.11.0 a list of integers specifying the degrees of the terms to include may be used instead. rcond : float, optional Relative condition number of the fit. Singular values smaller than `rcond`, relative to the largest singular value, will be ignored. The default value is ``len(x)*eps``, where `eps` is the relative precision of the platform's float type, about 2e-16 in most cases. full : bool, optional Switch determining the nature of the return value. When ``False`` (the default) just the coefficients are returned; when ``True``, diagnostic information from the singular value decomposition (used to solve the fit's matrix equation) is also returned. w : array_like, shape (`M`,), optional Weights. If not None, the weight ``w[i]`` applies to the unsquared residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are chosen so that the errors of the products ``w[i]*y[i]`` all have the same variance. When using inverse-variance weighting, use ``w[i] = 1/sigma(y[i])``. The default value is None. .. versionadded:: 1.5.0 Returns ------- coef : ndarray, shape (`deg` + 1,) or (`deg` + 1, `K`) Polynomial coefficients ordered from low to high. If `y` was 2-D, the coefficients in column `k` of `coef` represent the polynomial fit to the data in `y`'s `k`-th column. [residuals, rank, singular_values, rcond] : list These values are only returned if ``full == True`` - residuals -- sum of squared residuals of the least squares fit - rank -- the numerical rank of the scaled Vandermonde matrix - singular_values -- singular values of the scaled Vandermonde matrix - rcond -- value of `rcond`. For more details, see `numpy.linalg.lstsq`. Raises ------ RankWarning Raised if the matrix in the least-squares fit is rank deficient. The warning is only raised if ``full == False``. The warnings can be turned off by: >>> import warnings >>> warnings.simplefilter('ignore', np.RankWarning) See Also -------- numpy.polynomial.chebyshev.chebfit numpy.polynomial.legendre.legfit numpy.polynomial.laguerre.lagfit numpy.polynomial.hermite.hermfit numpy.polynomial.hermite_e.hermefit polyval : Evaluates a polynomial. polyvander : Vandermonde matrix for powers. numpy.linalg.lstsq : Computes a least-squares fit from the matrix. scipy.interpolate.UnivariateSpline : Computes spline fits. Notes ----- The solution is the coefficients of the polynomial `p` that minimizes the sum of the weighted squared errors .. math:: E = \\sum_j w_j^2 * |y_j - p(x_j)|^2, where the :math:`w_j` are the weights. This problem is solved by setting up the (typically) over-determined matrix equation: .. math:: V(x) * c = w * y, where `V` is the weighted pseudo Vandermonde matrix of `x`, `c` are the coefficients to be solved for, `w` are the weights, and `y` are the observed values. This equation is then solved using the singular value decomposition of `V`. If some of the singular values of `V` are so small that they are neglected (and `full` == ``False``), a `RankWarning` will be raised. This means that the coefficient values may be poorly determined. Fitting to a lower order polynomial will usually get rid of the warning (but may not be what you want, of course; if you have independent reason(s) for choosing the degree which isn't working, you may have to: a) reconsider those reasons, and/or b) reconsider the quality of your data). The `rcond` parameter can also be set to a value smaller than its default, but the resulting fit may be spurious and have large contributions from roundoff error. Polynomial fits using double precision tend to "fail" at about (polynomial) degree 20. Fits using Chebyshev or Legendre series are generally better conditioned, but much can still depend on the distribution of the sample points and the smoothness of the data. If the quality of the fit is inadequate, splines may be a good alternative. Examples -------- >>> np.random.seed(123) >>> from numpy.polynomial import polynomial as P >>> x = np.linspace(-1,1,51) # x "data": [-1, -0.96, ..., 0.96, 1] >>> y = x**3 - x + np.random.randn(len(x)) # x^3 - x + Gaussian noise >>> c, stats = P.polyfit(x,y,3,full=True) >>> np.random.seed(123) >>> c # c[0], c[2] should be approx. 0, c[1] approx. -1, c[3] approx. 1 array([ 0.01909725, -1.30598256, -0.00577963, 1.02644286]) # may vary >>> stats # note the large SSR, explaining the rather poor results [array([ 38.06116253]), 4, array([ 1.38446749, 1.32119158, 0.50443316, # may vary 0.28853036]), 1.1324274851176597e-014] Same thing without the added noise >>> y = x**3 - x >>> c, stats = P.polyfit(x,y,3,full=True) >>> c # c[0], c[2] should be "very close to 0", c[1] ~= -1, c[3] ~= 1 array([-6.36925336e-18, -1.00000000e+00, -4.08053781e-16, 1.00000000e+00]) >>> stats # note the minuscule SSR [array([ 7.46346754e-31]), 4, array([ 1.38446749, 1.32119158, # may vary 0.50443316, 0.28853036]), 1.1324274851176597e-014]
Here is the function:
def polyfit(x, y, deg, rcond=None, full=False, w=None):
"""
Least-squares fit of a polynomial to data.
Return the coefficients of a polynomial of degree `deg` that is the
least squares fit to the data values `y` given at points `x`. If `y` is
1-D the returned coefficients will also be 1-D. If `y` is 2-D multiple
fits are done, one for each column of `y`, and the resulting
coefficients are stored in the corresponding columns of a 2-D return.
The fitted polynomial(s) are in the form
.. math:: p(x) = c_0 + c_1 * x + ... + c_n * x^n,
where `n` is `deg`.
Parameters
----------
x : array_like, shape (`M`,)
x-coordinates of the `M` sample (data) points ``(x[i], y[i])``.
y : array_like, shape (`M`,) or (`M`, `K`)
y-coordinates of the sample points. Several sets of sample points
sharing the same x-coordinates can be (independently) fit with one
call to `polyfit` by passing in for `y` a 2-D array that contains
one data set per column.
deg : int or 1-D array_like
Degree(s) of the fitting polynomials. If `deg` is a single integer
all terms up to and including the `deg`'th term are included in the
fit. For NumPy versions >= 1.11.0 a list of integers specifying the
degrees of the terms to include may be used instead.
rcond : float, optional
Relative condition number of the fit. Singular values smaller
than `rcond`, relative to the largest singular value, will be
ignored. The default value is ``len(x)*eps``, where `eps` is the
relative precision of the platform's float type, about 2e-16 in
most cases.
full : bool, optional
Switch determining the nature of the return value. When ``False``
(the default) just the coefficients are returned; when ``True``,
diagnostic information from the singular value decomposition (used
to solve the fit's matrix equation) is also returned.
w : array_like, shape (`M`,), optional
Weights. If not None, the weight ``w[i]`` applies to the unsquared
residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are
chosen so that the errors of the products ``w[i]*y[i]`` all have the
same variance. When using inverse-variance weighting, use
``w[i] = 1/sigma(y[i])``. The default value is None.
.. versionadded:: 1.5.0
Returns
-------
coef : ndarray, shape (`deg` + 1,) or (`deg` + 1, `K`)
Polynomial coefficients ordered from low to high. If `y` was 2-D,
the coefficients in column `k` of `coef` represent the polynomial
fit to the data in `y`'s `k`-th column.
[residuals, rank, singular_values, rcond] : list
These values are only returned if ``full == True``
- residuals -- sum of squared residuals of the least squares fit
- rank -- the numerical rank of the scaled Vandermonde matrix
- singular_values -- singular values of the scaled Vandermonde matrix
- rcond -- value of `rcond`.
For more details, see `numpy.linalg.lstsq`.
Raises
------
RankWarning
Raised if the matrix in the least-squares fit is rank deficient.
The warning is only raised if ``full == False``. The warnings can
be turned off by:
>>> import warnings
>>> warnings.simplefilter('ignore', np.RankWarning)
See Also
--------
numpy.polynomial.chebyshev.chebfit
numpy.polynomial.legendre.legfit
numpy.polynomial.laguerre.lagfit
numpy.polynomial.hermite.hermfit
numpy.polynomial.hermite_e.hermefit
polyval : Evaluates a polynomial.
polyvander : Vandermonde matrix for powers.
numpy.linalg.lstsq : Computes a least-squares fit from the matrix.
scipy.interpolate.UnivariateSpline : Computes spline fits.
Notes
-----
The solution is the coefficients of the polynomial `p` that minimizes
the sum of the weighted squared errors
.. math:: E = \\sum_j w_j^2 * |y_j - p(x_j)|^2,
where the :math:`w_j` are the weights. This problem is solved by
setting up the (typically) over-determined matrix equation:
.. math:: V(x) * c = w * y,
where `V` is the weighted pseudo Vandermonde matrix of `x`, `c` are the
coefficients to be solved for, `w` are the weights, and `y` are the
observed values. This equation is then solved using the singular value
decomposition of `V`.
If some of the singular values of `V` are so small that they are
neglected (and `full` == ``False``), a `RankWarning` will be raised.
This means that the coefficient values may be poorly determined.
Fitting to a lower order polynomial will usually get rid of the warning
(but may not be what you want, of course; if you have independent
reason(s) for choosing the degree which isn't working, you may have to:
a) reconsider those reasons, and/or b) reconsider the quality of your
data). The `rcond` parameter can also be set to a value smaller than
its default, but the resulting fit may be spurious and have large
contributions from roundoff error.
Polynomial fits using double precision tend to "fail" at about
(polynomial) degree 20. Fits using Chebyshev or Legendre series are
generally better conditioned, but much can still depend on the
distribution of the sample points and the smoothness of the data. If
the quality of the fit is inadequate, splines may be a good
alternative.
Examples
--------
>>> np.random.seed(123)
>>> from numpy.polynomial import polynomial as P
>>> x = np.linspace(-1,1,51) # x "data": [-1, -0.96, ..., 0.96, 1]
>>> y = x**3 - x + np.random.randn(len(x)) # x^3 - x + Gaussian noise
>>> c, stats = P.polyfit(x,y,3,full=True)
>>> np.random.seed(123)
>>> c # c[0], c[2] should be approx. 0, c[1] approx. -1, c[3] approx. 1
array([ 0.01909725, -1.30598256, -0.00577963, 1.02644286]) # may vary
>>> stats # note the large SSR, explaining the rather poor results
[array([ 38.06116253]), 4, array([ 1.38446749, 1.32119158, 0.50443316, # may vary
0.28853036]), 1.1324274851176597e-014]
Same thing without the added noise
>>> y = x**3 - x
>>> c, stats = P.polyfit(x,y,3,full=True)
>>> c # c[0], c[2] should be "very close to 0", c[1] ~= -1, c[3] ~= 1
array([-6.36925336e-18, -1.00000000e+00, -4.08053781e-16, 1.00000000e+00])
>>> stats # note the minuscule SSR
[array([ 7.46346754e-31]), 4, array([ 1.38446749, 1.32119158, # may vary
0.50443316, 0.28853036]), 1.1324274851176597e-014]
"""
return pu._fit(polyvander, x, y, deg, rcond, full, w) | Least-squares fit of a polynomial to data. Return the coefficients of a polynomial of degree `deg` that is the least squares fit to the data values `y` given at points `x`. If `y` is 1-D the returned coefficients will also be 1-D. If `y` is 2-D multiple fits are done, one for each column of `y`, and the resulting coefficients are stored in the corresponding columns of a 2-D return. The fitted polynomial(s) are in the form .. math:: p(x) = c_0 + c_1 * x + ... + c_n * x^n, where `n` is `deg`. Parameters ---------- x : array_like, shape (`M`,) x-coordinates of the `M` sample (data) points ``(x[i], y[i])``. y : array_like, shape (`M`,) or (`M`, `K`) y-coordinates of the sample points. Several sets of sample points sharing the same x-coordinates can be (independently) fit with one call to `polyfit` by passing in for `y` a 2-D array that contains one data set per column. deg : int or 1-D array_like Degree(s) of the fitting polynomials. If `deg` is a single integer all terms up to and including the `deg`'th term are included in the fit. For NumPy versions >= 1.11.0 a list of integers specifying the degrees of the terms to include may be used instead. rcond : float, optional Relative condition number of the fit. Singular values smaller than `rcond`, relative to the largest singular value, will be ignored. The default value is ``len(x)*eps``, where `eps` is the relative precision of the platform's float type, about 2e-16 in most cases. full : bool, optional Switch determining the nature of the return value. When ``False`` (the default) just the coefficients are returned; when ``True``, diagnostic information from the singular value decomposition (used to solve the fit's matrix equation) is also returned. w : array_like, shape (`M`,), optional Weights. If not None, the weight ``w[i]`` applies to the unsquared residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are chosen so that the errors of the products ``w[i]*y[i]`` all have the same variance. When using inverse-variance weighting, use ``w[i] = 1/sigma(y[i])``. The default value is None. .. versionadded:: 1.5.0 Returns ------- coef : ndarray, shape (`deg` + 1,) or (`deg` + 1, `K`) Polynomial coefficients ordered from low to high. If `y` was 2-D, the coefficients in column `k` of `coef` represent the polynomial fit to the data in `y`'s `k`-th column. [residuals, rank, singular_values, rcond] : list These values are only returned if ``full == True`` - residuals -- sum of squared residuals of the least squares fit - rank -- the numerical rank of the scaled Vandermonde matrix - singular_values -- singular values of the scaled Vandermonde matrix - rcond -- value of `rcond`. For more details, see `numpy.linalg.lstsq`. Raises ------ RankWarning Raised if the matrix in the least-squares fit is rank deficient. The warning is only raised if ``full == False``. The warnings can be turned off by: >>> import warnings >>> warnings.simplefilter('ignore', np.RankWarning) See Also -------- numpy.polynomial.chebyshev.chebfit numpy.polynomial.legendre.legfit numpy.polynomial.laguerre.lagfit numpy.polynomial.hermite.hermfit numpy.polynomial.hermite_e.hermefit polyval : Evaluates a polynomial. polyvander : Vandermonde matrix for powers. numpy.linalg.lstsq : Computes a least-squares fit from the matrix. scipy.interpolate.UnivariateSpline : Computes spline fits. Notes ----- The solution is the coefficients of the polynomial `p` that minimizes the sum of the weighted squared errors .. math:: E = \\sum_j w_j^2 * |y_j - p(x_j)|^2, where the :math:`w_j` are the weights. This problem is solved by setting up the (typically) over-determined matrix equation: .. math:: V(x) * c = w * y, where `V` is the weighted pseudo Vandermonde matrix of `x`, `c` are the coefficients to be solved for, `w` are the weights, and `y` are the observed values. This equation is then solved using the singular value decomposition of `V`. If some of the singular values of `V` are so small that they are neglected (and `full` == ``False``), a `RankWarning` will be raised. This means that the coefficient values may be poorly determined. Fitting to a lower order polynomial will usually get rid of the warning (but may not be what you want, of course; if you have independent reason(s) for choosing the degree which isn't working, you may have to: a) reconsider those reasons, and/or b) reconsider the quality of your data). The `rcond` parameter can also be set to a value smaller than its default, but the resulting fit may be spurious and have large contributions from roundoff error. Polynomial fits using double precision tend to "fail" at about (polynomial) degree 20. Fits using Chebyshev or Legendre series are generally better conditioned, but much can still depend on the distribution of the sample points and the smoothness of the data. If the quality of the fit is inadequate, splines may be a good alternative. Examples -------- >>> np.random.seed(123) >>> from numpy.polynomial import polynomial as P >>> x = np.linspace(-1,1,51) # x "data": [-1, -0.96, ..., 0.96, 1] >>> y = x**3 - x + np.random.randn(len(x)) # x^3 - x + Gaussian noise >>> c, stats = P.polyfit(x,y,3,full=True) >>> np.random.seed(123) >>> c # c[0], c[2] should be approx. 0, c[1] approx. -1, c[3] approx. 1 array([ 0.01909725, -1.30598256, -0.00577963, 1.02644286]) # may vary >>> stats # note the large SSR, explaining the rather poor results [array([ 38.06116253]), 4, array([ 1.38446749, 1.32119158, 0.50443316, # may vary 0.28853036]), 1.1324274851176597e-014] Same thing without the added noise >>> y = x**3 - x >>> c, stats = P.polyfit(x,y,3,full=True) >>> c # c[0], c[2] should be "very close to 0", c[1] ~= -1, c[3] ~= 1 array([-6.36925336e-18, -1.00000000e+00, -4.08053781e-16, 1.00000000e+00]) >>> stats # note the minuscule SSR [array([ 7.46346754e-31]), 4, array([ 1.38446749, 1.32119158, # may vary 0.50443316, 0.28853036]), 1.1324274851176597e-014] |
169,810 | import numpy as np
import numpy.linalg as la
from numpy.core.multiarray import normalize_axis_index
from . import polyutils as pu
from ._polybase import ABCPolyBase
def polycompanion(c):
"""
Return the companion matrix of c.
The companion matrix for power series cannot be made symmetric by
scaling the basis, so this function differs from those for the
orthogonal polynomials.
Parameters
----------
c : array_like
1-D array of polynomial coefficients ordered from low to high
degree.
Returns
-------
mat : ndarray
Companion matrix of dimensions (deg, deg).
Notes
-----
.. versionadded:: 1.7.0
"""
# c is a trimmed copy
[c] = pu.as_series([c])
if len(c) < 2:
raise ValueError('Series must have maximum degree of at least 1.')
if len(c) == 2:
return np.array([[-c[0]/c[1]]])
n = len(c) - 1
mat = np.zeros((n, n), dtype=c.dtype)
bot = mat.reshape(-1)[n::n+1]
bot[...] = 1
mat[:, -1] -= c[:-1]/c[-1]
return mat
The provided code snippet includes necessary dependencies for implementing the `polyroots` function. Write a Python function `def polyroots(c)` to solve the following problem:
Compute the roots of a polynomial. Return the roots (a.k.a. "zeros") of the polynomial .. math:: p(x) = \\sum_i c[i] * x^i. Parameters ---------- c : 1-D array_like 1-D array of polynomial coefficients. Returns ------- out : ndarray Array of the roots of the polynomial. If all the roots are real, then `out` is also real, otherwise it is complex. See Also -------- numpy.polynomial.chebyshev.chebroots numpy.polynomial.legendre.legroots numpy.polynomial.laguerre.lagroots numpy.polynomial.hermite.hermroots numpy.polynomial.hermite_e.hermeroots Notes ----- The root estimates are obtained as the eigenvalues of the companion matrix, Roots far from the origin of the complex plane may have large errors due to the numerical instability of the power series for such values. Roots with multiplicity greater than 1 will also show larger errors as the value of the series near such points is relatively insensitive to errors in the roots. Isolated roots near the origin can be improved by a few iterations of Newton's method. Examples -------- >>> import numpy.polynomial.polynomial as poly >>> poly.polyroots(poly.polyfromroots((-1,0,1))) array([-1., 0., 1.]) >>> poly.polyroots(poly.polyfromroots((-1,0,1))).dtype dtype('float64') >>> j = complex(0,1) >>> poly.polyroots(poly.polyfromroots((-j,0,j))) array([ 0.00000000e+00+0.j, 0.00000000e+00+1.j, 2.77555756e-17-1.j]) # may vary
Here is the function:
def polyroots(c):
"""
Compute the roots of a polynomial.
Return the roots (a.k.a. "zeros") of the polynomial
.. math:: p(x) = \\sum_i c[i] * x^i.
Parameters
----------
c : 1-D array_like
1-D array of polynomial coefficients.
Returns
-------
out : ndarray
Array of the roots of the polynomial. If all the roots are real,
then `out` is also real, otherwise it is complex.
See Also
--------
numpy.polynomial.chebyshev.chebroots
numpy.polynomial.legendre.legroots
numpy.polynomial.laguerre.lagroots
numpy.polynomial.hermite.hermroots
numpy.polynomial.hermite_e.hermeroots
Notes
-----
The root estimates are obtained as the eigenvalues of the companion
matrix, Roots far from the origin of the complex plane may have large
errors due to the numerical instability of the power series for such
values. Roots with multiplicity greater than 1 will also show larger
errors as the value of the series near such points is relatively
insensitive to errors in the roots. Isolated roots near the origin can
be improved by a few iterations of Newton's method.
Examples
--------
>>> import numpy.polynomial.polynomial as poly
>>> poly.polyroots(poly.polyfromroots((-1,0,1)))
array([-1., 0., 1.])
>>> poly.polyroots(poly.polyfromroots((-1,0,1))).dtype
dtype('float64')
>>> j = complex(0,1)
>>> poly.polyroots(poly.polyfromroots((-j,0,j)))
array([ 0.00000000e+00+0.j, 0.00000000e+00+1.j, 2.77555756e-17-1.j]) # may vary
"""
# c is a trimmed copy
[c] = pu.as_series([c])
if len(c) < 2:
return np.array([], dtype=c.dtype)
if len(c) == 2:
return np.array([-c[0]/c[1]])
# rotated companion matrix reduces error
m = polycompanion(c)[::-1,::-1]
r = la.eigvals(m)
r.sort()
return r | Compute the roots of a polynomial. Return the roots (a.k.a. "zeros") of the polynomial .. math:: p(x) = \\sum_i c[i] * x^i. Parameters ---------- c : 1-D array_like 1-D array of polynomial coefficients. Returns ------- out : ndarray Array of the roots of the polynomial. If all the roots are real, then `out` is also real, otherwise it is complex. See Also -------- numpy.polynomial.chebyshev.chebroots numpy.polynomial.legendre.legroots numpy.polynomial.laguerre.lagroots numpy.polynomial.hermite.hermroots numpy.polynomial.hermite_e.hermeroots Notes ----- The root estimates are obtained as the eigenvalues of the companion matrix, Roots far from the origin of the complex plane may have large errors due to the numerical instability of the power series for such values. Roots with multiplicity greater than 1 will also show larger errors as the value of the series near such points is relatively insensitive to errors in the roots. Isolated roots near the origin can be improved by a few iterations of Newton's method. Examples -------- >>> import numpy.polynomial.polynomial as poly >>> poly.polyroots(poly.polyfromroots((-1,0,1))) array([-1., 0., 1.]) >>> poly.polyroots(poly.polyfromroots((-1,0,1))).dtype dtype('float64') >>> j = complex(0,1) >>> poly.polyroots(poly.polyfromroots((-j,0,j))) array([ 0.00000000e+00+0.j, 0.00000000e+00+1.j, 2.77555756e-17-1.j]) # may vary |
169,827 | import numpy as np
import numpy.linalg as la
from numpy.core.multiarray import normalize_axis_index
from . import polyutils as pu
from ._polybase import ABCPolyBase
def hermeadd(c1, c2):
"""
Add one Hermite series to another.
Returns the sum of two Hermite series `c1` + `c2`. The arguments
are sequences of coefficients ordered from lowest order term to
highest, i.e., [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``.
Parameters
----------
c1, c2 : array_like
1-D arrays of Hermite series coefficients ordered from low to
high.
Returns
-------
out : ndarray
Array representing the Hermite series of their sum.
See Also
--------
hermesub, hermemulx, hermemul, hermediv, hermepow
Notes
-----
Unlike multiplication, division, etc., the sum of two Hermite series
is a Hermite series (without having to "reproject" the result onto
the basis set) so addition, just like that of "standard" polynomials,
is simply "component-wise."
Examples
--------
>>> from numpy.polynomial.hermite_e import hermeadd
>>> hermeadd([1, 2, 3], [1, 2, 3, 4])
array([2., 4., 6., 4.])
"""
return pu._add(c1, c2)
def hermemulx(c):
"""Multiply a Hermite series by x.
Multiply the Hermite series `c` by x, where x is the independent
variable.
Parameters
----------
c : array_like
1-D array of Hermite series coefficients ordered from low to
high.
Returns
-------
out : ndarray
Array representing the result of the multiplication.
Notes
-----
The multiplication uses the recursion relationship for Hermite
polynomials in the form
.. math::
xP_i(x) = (P_{i + 1}(x) + iP_{i - 1}(x)))
Examples
--------
>>> from numpy.polynomial.hermite_e import hermemulx
>>> hermemulx([1, 2, 3])
array([2., 7., 2., 3.])
"""
# c is a trimmed copy
[c] = pu.as_series([c])
# The zero series needs special treatment
if len(c) == 1 and c[0] == 0:
return c
prd = np.empty(len(c) + 1, dtype=c.dtype)
prd[0] = c[0]*0
prd[1] = c[0]
for i in range(1, len(c)):
prd[i + 1] = c[i]
prd[i - 1] += c[i]*i
return prd
The provided code snippet includes necessary dependencies for implementing the `poly2herme` function. Write a Python function `def poly2herme(pol)` to solve the following problem:
poly2herme(pol) Convert a polynomial to a Hermite series. Convert an array representing the coefficients of a polynomial (relative to the "standard" basis) ordered from lowest degree to highest, to an array of the coefficients of the equivalent Hermite series, ordered from lowest to highest degree. Parameters ---------- pol : array_like 1-D array containing the polynomial coefficients Returns ------- c : ndarray 1-D array containing the coefficients of the equivalent Hermite series. See Also -------- herme2poly Notes ----- The easy way to do conversions between polynomial basis sets is to use the convert method of a class instance. Examples -------- >>> from numpy.polynomial.hermite_e import poly2herme >>> poly2herme(np.arange(4)) array([ 2., 10., 2., 3.])
Here is the function:
def poly2herme(pol):
"""
poly2herme(pol)
Convert a polynomial to a Hermite series.
Convert an array representing the coefficients of a polynomial (relative
to the "standard" basis) ordered from lowest degree to highest, to an
array of the coefficients of the equivalent Hermite series, ordered
from lowest to highest degree.
Parameters
----------
pol : array_like
1-D array containing the polynomial coefficients
Returns
-------
c : ndarray
1-D array containing the coefficients of the equivalent Hermite
series.
See Also
--------
herme2poly
Notes
-----
The easy way to do conversions between polynomial basis sets
is to use the convert method of a class instance.
Examples
--------
>>> from numpy.polynomial.hermite_e import poly2herme
>>> poly2herme(np.arange(4))
array([ 2., 10., 2., 3.])
"""
[pol] = pu.as_series([pol])
deg = len(pol) - 1
res = 0
for i in range(deg, -1, -1):
res = hermeadd(hermemulx(res), pol[i])
return res | poly2herme(pol) Convert a polynomial to a Hermite series. Convert an array representing the coefficients of a polynomial (relative to the "standard" basis) ordered from lowest degree to highest, to an array of the coefficients of the equivalent Hermite series, ordered from lowest to highest degree. Parameters ---------- pol : array_like 1-D array containing the polynomial coefficients Returns ------- c : ndarray 1-D array containing the coefficients of the equivalent Hermite series. See Also -------- herme2poly Notes ----- The easy way to do conversions between polynomial basis sets is to use the convert method of a class instance. Examples -------- >>> from numpy.polynomial.hermite_e import poly2herme >>> poly2herme(np.arange(4)) array([ 2., 10., 2., 3.]) |
169,828 | import numpy as np
import numpy.linalg as la
from numpy.core.multiarray import normalize_axis_index
from . import polyutils as pu
from ._polybase import ABCPolyBase
def polyadd(c1, c2):
"""
Add one polynomial to another.
Returns the sum of two polynomials `c1` + `c2`. The arguments are
sequences of coefficients from lowest order term to highest, i.e.,
[1,2,3] represents the polynomial ``1 + 2*x + 3*x**2``.
Parameters
----------
c1, c2 : array_like
1-D arrays of polynomial coefficients ordered from low to high.
Returns
-------
out : ndarray
The coefficient array representing their sum.
See Also
--------
polysub, polymulx, polymul, polydiv, polypow
Examples
--------
>>> from numpy.polynomial import polynomial as P
>>> c1 = (1,2,3)
>>> c2 = (3,2,1)
>>> sum = P.polyadd(c1,c2); sum
array([4., 4., 4.])
>>> P.polyval(2, sum) # 4 + 4(2) + 4(2**2)
28.0
"""
return pu._add(c1, c2)
def polysub(c1, c2):
"""
Subtract one polynomial from another.
Returns the difference of two polynomials `c1` - `c2`. The arguments
are sequences of coefficients from lowest order term to highest, i.e.,
[1,2,3] represents the polynomial ``1 + 2*x + 3*x**2``.
Parameters
----------
c1, c2 : array_like
1-D arrays of polynomial coefficients ordered from low to
high.
Returns
-------
out : ndarray
Of coefficients representing their difference.
See Also
--------
polyadd, polymulx, polymul, polydiv, polypow
Examples
--------
>>> from numpy.polynomial import polynomial as P
>>> c1 = (1,2,3)
>>> c2 = (3,2,1)
>>> P.polysub(c1,c2)
array([-2., 0., 2.])
>>> P.polysub(c2,c1) # -P.polysub(c1,c2)
array([ 2., 0., -2.])
"""
return pu._sub(c1, c2)
def polymulx(c):
"""Multiply a polynomial by x.
Multiply the polynomial `c` by x, where x is the independent
variable.
Parameters
----------
c : array_like
1-D array of polynomial coefficients ordered from low to
high.
Returns
-------
out : ndarray
Array representing the result of the multiplication.
See Also
--------
polyadd, polysub, polymul, polydiv, polypow
Notes
-----
.. versionadded:: 1.5.0
"""
# c is a trimmed copy
[c] = pu.as_series([c])
# The zero series needs special treatment
if len(c) == 1 and c[0] == 0:
return c
prd = np.empty(len(c) + 1, dtype=c.dtype)
prd[0] = c[0]*0
prd[1:] = c
return prd
The provided code snippet includes necessary dependencies for implementing the `herme2poly` function. Write a Python function `def herme2poly(c)` to solve the following problem:
Convert a Hermite series to a polynomial. Convert an array representing the coefficients of a Hermite series, ordered from lowest degree to highest, to an array of the coefficients of the equivalent polynomial (relative to the "standard" basis) ordered from lowest to highest degree. Parameters ---------- c : array_like 1-D array containing the Hermite series coefficients, ordered from lowest order term to highest. Returns ------- pol : ndarray 1-D array containing the coefficients of the equivalent polynomial (relative to the "standard" basis) ordered from lowest order term to highest. See Also -------- poly2herme Notes ----- The easy way to do conversions between polynomial basis sets is to use the convert method of a class instance. Examples -------- >>> from numpy.polynomial.hermite_e import herme2poly >>> herme2poly([ 2., 10., 2., 3.]) array([0., 1., 2., 3.])
Here is the function:
def herme2poly(c):
"""
Convert a Hermite series to a polynomial.
Convert an array representing the coefficients of a Hermite series,
ordered from lowest degree to highest, to an array of the coefficients
of the equivalent polynomial (relative to the "standard" basis) ordered
from lowest to highest degree.
Parameters
----------
c : array_like
1-D array containing the Hermite series coefficients, ordered
from lowest order term to highest.
Returns
-------
pol : ndarray
1-D array containing the coefficients of the equivalent polynomial
(relative to the "standard" basis) ordered from lowest order term
to highest.
See Also
--------
poly2herme
Notes
-----
The easy way to do conversions between polynomial basis sets
is to use the convert method of a class instance.
Examples
--------
>>> from numpy.polynomial.hermite_e import herme2poly
>>> herme2poly([ 2., 10., 2., 3.])
array([0., 1., 2., 3.])
"""
from .polynomial import polyadd, polysub, polymulx
[c] = pu.as_series([c])
n = len(c)
if n == 1:
return c
if n == 2:
return c
else:
c0 = c[-2]
c1 = c[-1]
# i is the current degree of c1
for i in range(n - 1, 1, -1):
tmp = c0
c0 = polysub(c[i - 2], c1*(i - 1))
c1 = polyadd(tmp, polymulx(c1))
return polyadd(c0, polymulx(c1)) | Convert a Hermite series to a polynomial. Convert an array representing the coefficients of a Hermite series, ordered from lowest degree to highest, to an array of the coefficients of the equivalent polynomial (relative to the "standard" basis) ordered from lowest to highest degree. Parameters ---------- c : array_like 1-D array containing the Hermite series coefficients, ordered from lowest order term to highest. Returns ------- pol : ndarray 1-D array containing the coefficients of the equivalent polynomial (relative to the "standard" basis) ordered from lowest order term to highest. See Also -------- poly2herme Notes ----- The easy way to do conversions between polynomial basis sets is to use the convert method of a class instance. Examples -------- >>> from numpy.polynomial.hermite_e import herme2poly >>> herme2poly([ 2., 10., 2., 3.]) array([0., 1., 2., 3.]) |
169,829 | import numpy as np
import numpy.linalg as la
from numpy.core.multiarray import normalize_axis_index
from . import polyutils as pu
from ._polybase import ABCPolyBase
def hermeline(off, scl):
"""
Hermite series whose graph is a straight line.
Parameters
----------
off, scl : scalars
The specified line is given by ``off + scl*x``.
Returns
-------
y : ndarray
This module's representation of the Hermite series for
``off + scl*x``.
See Also
--------
numpy.polynomial.polynomial.polyline
numpy.polynomial.chebyshev.chebline
numpy.polynomial.legendre.legline
numpy.polynomial.laguerre.lagline
numpy.polynomial.hermite.hermline
Examples
--------
>>> from numpy.polynomial.hermite_e import hermeline
>>> from numpy.polynomial.hermite_e import hermeline, hermeval
>>> hermeval(0,hermeline(3, 2))
3.0
>>> hermeval(1,hermeline(3, 2))
5.0
"""
if scl != 0:
return np.array([off, scl])
else:
return np.array([off])
def hermemul(c1, c2):
"""
Multiply one Hermite series by another.
Returns the product of two Hermite series `c1` * `c2`. The arguments
are sequences of coefficients, from lowest order "term" to highest,
e.g., [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``.
Parameters
----------
c1, c2 : array_like
1-D arrays of Hermite series coefficients ordered from low to
high.
Returns
-------
out : ndarray
Of Hermite series coefficients representing their product.
See Also
--------
hermeadd, hermesub, hermemulx, hermediv, hermepow
Notes
-----
In general, the (polynomial) product of two C-series results in terms
that are not in the Hermite polynomial basis set. Thus, to express
the product as a Hermite series, it is necessary to "reproject" the
product onto said basis set, which may produce "unintuitive" (but
correct) results; see Examples section below.
Examples
--------
>>> from numpy.polynomial.hermite_e import hermemul
>>> hermemul([1, 2, 3], [0, 1, 2])
array([14., 15., 28., 7., 6.])
"""
# s1, s2 are trimmed copies
[c1, c2] = pu.as_series([c1, c2])
if len(c1) > len(c2):
c = c2
xs = c1
else:
c = c1
xs = c2
if len(c) == 1:
c0 = c[0]*xs
c1 = 0
elif len(c) == 2:
c0 = c[0]*xs
c1 = c[1]*xs
else:
nd = len(c)
c0 = c[-2]*xs
c1 = c[-1]*xs
for i in range(3, len(c) + 1):
tmp = c0
nd = nd - 1
c0 = hermesub(c[-i]*xs, c1*(nd - 1))
c1 = hermeadd(tmp, hermemulx(c1))
return hermeadd(c0, hermemulx(c1))
The provided code snippet includes necessary dependencies for implementing the `hermefromroots` function. Write a Python function `def hermefromroots(roots)` to solve the following problem:
Generate a HermiteE series with given roots. The function returns the coefficients of the polynomial .. math:: p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n), in HermiteE form, where the `r_n` are the roots specified in `roots`. If a zero has multiplicity n, then it must appear in `roots` n times. For instance, if 2 is a root of multiplicity three and 3 is a root of multiplicity 2, then `roots` looks something like [2, 2, 2, 3, 3]. The roots can appear in any order. If the returned coefficients are `c`, then .. math:: p(x) = c_0 + c_1 * He_1(x) + ... + c_n * He_n(x) The coefficient of the last term is not generally 1 for monic polynomials in HermiteE form. Parameters ---------- roots : array_like Sequence containing the roots. Returns ------- out : ndarray 1-D array of coefficients. If all roots are real then `out` is a real array, if some of the roots are complex, then `out` is complex even if all the coefficients in the result are real (see Examples below). See Also -------- numpy.polynomial.polynomial.polyfromroots numpy.polynomial.legendre.legfromroots numpy.polynomial.laguerre.lagfromroots numpy.polynomial.hermite.hermfromroots numpy.polynomial.chebyshev.chebfromroots Examples -------- >>> from numpy.polynomial.hermite_e import hermefromroots, hermeval >>> coef = hermefromroots((-1, 0, 1)) >>> hermeval((-1, 0, 1), coef) array([0., 0., 0.]) >>> coef = hermefromroots((-1j, 1j)) >>> hermeval((-1j, 1j), coef) array([0.+0.j, 0.+0.j])
Here is the function:
def hermefromroots(roots):
"""
Generate a HermiteE series with given roots.
The function returns the coefficients of the polynomial
.. math:: p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n),
in HermiteE form, where the `r_n` are the roots specified in `roots`.
If a zero has multiplicity n, then it must appear in `roots` n times.
For instance, if 2 is a root of multiplicity three and 3 is a root of
multiplicity 2, then `roots` looks something like [2, 2, 2, 3, 3]. The
roots can appear in any order.
If the returned coefficients are `c`, then
.. math:: p(x) = c_0 + c_1 * He_1(x) + ... + c_n * He_n(x)
The coefficient of the last term is not generally 1 for monic
polynomials in HermiteE form.
Parameters
----------
roots : array_like
Sequence containing the roots.
Returns
-------
out : ndarray
1-D array of coefficients. If all roots are real then `out` is a
real array, if some of the roots are complex, then `out` is complex
even if all the coefficients in the result are real (see Examples
below).
See Also
--------
numpy.polynomial.polynomial.polyfromroots
numpy.polynomial.legendre.legfromroots
numpy.polynomial.laguerre.lagfromroots
numpy.polynomial.hermite.hermfromroots
numpy.polynomial.chebyshev.chebfromroots
Examples
--------
>>> from numpy.polynomial.hermite_e import hermefromroots, hermeval
>>> coef = hermefromroots((-1, 0, 1))
>>> hermeval((-1, 0, 1), coef)
array([0., 0., 0.])
>>> coef = hermefromroots((-1j, 1j))
>>> hermeval((-1j, 1j), coef)
array([0.+0.j, 0.+0.j])
"""
return pu._fromroots(hermeline, hermemul, roots) | Generate a HermiteE series with given roots. The function returns the coefficients of the polynomial .. math:: p(x) = (x - r_0) * (x - r_1) * ... * (x - r_n), in HermiteE form, where the `r_n` are the roots specified in `roots`. If a zero has multiplicity n, then it must appear in `roots` n times. For instance, if 2 is a root of multiplicity three and 3 is a root of multiplicity 2, then `roots` looks something like [2, 2, 2, 3, 3]. The roots can appear in any order. If the returned coefficients are `c`, then .. math:: p(x) = c_0 + c_1 * He_1(x) + ... + c_n * He_n(x) The coefficient of the last term is not generally 1 for monic polynomials in HermiteE form. Parameters ---------- roots : array_like Sequence containing the roots. Returns ------- out : ndarray 1-D array of coefficients. If all roots are real then `out` is a real array, if some of the roots are complex, then `out` is complex even if all the coefficients in the result are real (see Examples below). See Also -------- numpy.polynomial.polynomial.polyfromroots numpy.polynomial.legendre.legfromroots numpy.polynomial.laguerre.lagfromroots numpy.polynomial.hermite.hermfromroots numpy.polynomial.chebyshev.chebfromroots Examples -------- >>> from numpy.polynomial.hermite_e import hermefromroots, hermeval >>> coef = hermefromroots((-1, 0, 1)) >>> hermeval((-1, 0, 1), coef) array([0., 0., 0.]) >>> coef = hermefromroots((-1j, 1j)) >>> hermeval((-1j, 1j), coef) array([0.+0.j, 0.+0.j]) |
169,830 | import numpy as np
import numpy.linalg as la
from numpy.core.multiarray import normalize_axis_index
from . import polyutils as pu
from ._polybase import ABCPolyBase
def hermemul(c1, c2):
"""
Multiply one Hermite series by another.
Returns the product of two Hermite series `c1` * `c2`. The arguments
are sequences of coefficients, from lowest order "term" to highest,
e.g., [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``.
Parameters
----------
c1, c2 : array_like
1-D arrays of Hermite series coefficients ordered from low to
high.
Returns
-------
out : ndarray
Of Hermite series coefficients representing their product.
See Also
--------
hermeadd, hermesub, hermemulx, hermediv, hermepow
Notes
-----
In general, the (polynomial) product of two C-series results in terms
that are not in the Hermite polynomial basis set. Thus, to express
the product as a Hermite series, it is necessary to "reproject" the
product onto said basis set, which may produce "unintuitive" (but
correct) results; see Examples section below.
Examples
--------
>>> from numpy.polynomial.hermite_e import hermemul
>>> hermemul([1, 2, 3], [0, 1, 2])
array([14., 15., 28., 7., 6.])
"""
# s1, s2 are trimmed copies
[c1, c2] = pu.as_series([c1, c2])
if len(c1) > len(c2):
c = c2
xs = c1
else:
c = c1
xs = c2
if len(c) == 1:
c0 = c[0]*xs
c1 = 0
elif len(c) == 2:
c0 = c[0]*xs
c1 = c[1]*xs
else:
nd = len(c)
c0 = c[-2]*xs
c1 = c[-1]*xs
for i in range(3, len(c) + 1):
tmp = c0
nd = nd - 1
c0 = hermesub(c[-i]*xs, c1*(nd - 1))
c1 = hermeadd(tmp, hermemulx(c1))
return hermeadd(c0, hermemulx(c1))
The provided code snippet includes necessary dependencies for implementing the `hermediv` function. Write a Python function `def hermediv(c1, c2)` to solve the following problem:
Divide one Hermite series by another. Returns the quotient-with-remainder of two Hermite series `c1` / `c2`. The arguments are sequences of coefficients from lowest order "term" to highest, e.g., [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``. Parameters ---------- c1, c2 : array_like 1-D arrays of Hermite series coefficients ordered from low to high. Returns ------- [quo, rem] : ndarrays Of Hermite series coefficients representing the quotient and remainder. See Also -------- hermeadd, hermesub, hermemulx, hermemul, hermepow Notes ----- In general, the (polynomial) division of one Hermite series by another results in quotient and remainder terms that are not in the Hermite polynomial basis set. Thus, to express these results as a Hermite series, it is necessary to "reproject" the results onto the Hermite basis set, which may produce "unintuitive" (but correct) results; see Examples section below. Examples -------- >>> from numpy.polynomial.hermite_e import hermediv >>> hermediv([ 14., 15., 28., 7., 6.], [0, 1, 2]) (array([1., 2., 3.]), array([0.])) >>> hermediv([ 15., 17., 28., 7., 6.], [0, 1, 2]) (array([1., 2., 3.]), array([1., 2.]))
Here is the function:
def hermediv(c1, c2):
"""
Divide one Hermite series by another.
Returns the quotient-with-remainder of two Hermite series
`c1` / `c2`. The arguments are sequences of coefficients from lowest
order "term" to highest, e.g., [1,2,3] represents the series
``P_0 + 2*P_1 + 3*P_2``.
Parameters
----------
c1, c2 : array_like
1-D arrays of Hermite series coefficients ordered from low to
high.
Returns
-------
[quo, rem] : ndarrays
Of Hermite series coefficients representing the quotient and
remainder.
See Also
--------
hermeadd, hermesub, hermemulx, hermemul, hermepow
Notes
-----
In general, the (polynomial) division of one Hermite series by another
results in quotient and remainder terms that are not in the Hermite
polynomial basis set. Thus, to express these results as a Hermite
series, it is necessary to "reproject" the results onto the Hermite
basis set, which may produce "unintuitive" (but correct) results; see
Examples section below.
Examples
--------
>>> from numpy.polynomial.hermite_e import hermediv
>>> hermediv([ 14., 15., 28., 7., 6.], [0, 1, 2])
(array([1., 2., 3.]), array([0.]))
>>> hermediv([ 15., 17., 28., 7., 6.], [0, 1, 2])
(array([1., 2., 3.]), array([1., 2.]))
"""
return pu._div(hermemul, c1, c2) | Divide one Hermite series by another. Returns the quotient-with-remainder of two Hermite series `c1` / `c2`. The arguments are sequences of coefficients from lowest order "term" to highest, e.g., [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``. Parameters ---------- c1, c2 : array_like 1-D arrays of Hermite series coefficients ordered from low to high. Returns ------- [quo, rem] : ndarrays Of Hermite series coefficients representing the quotient and remainder. See Also -------- hermeadd, hermesub, hermemulx, hermemul, hermepow Notes ----- In general, the (polynomial) division of one Hermite series by another results in quotient and remainder terms that are not in the Hermite polynomial basis set. Thus, to express these results as a Hermite series, it is necessary to "reproject" the results onto the Hermite basis set, which may produce "unintuitive" (but correct) results; see Examples section below. Examples -------- >>> from numpy.polynomial.hermite_e import hermediv >>> hermediv([ 14., 15., 28., 7., 6.], [0, 1, 2]) (array([1., 2., 3.]), array([0.])) >>> hermediv([ 15., 17., 28., 7., 6.], [0, 1, 2]) (array([1., 2., 3.]), array([1., 2.])) |
169,831 | import numpy as np
import numpy.linalg as la
from numpy.core.multiarray import normalize_axis_index
from . import polyutils as pu
from ._polybase import ABCPolyBase
def hermemul(c1, c2):
"""
Multiply one Hermite series by another.
Returns the product of two Hermite series `c1` * `c2`. The arguments
are sequences of coefficients, from lowest order "term" to highest,
e.g., [1,2,3] represents the series ``P_0 + 2*P_1 + 3*P_2``.
Parameters
----------
c1, c2 : array_like
1-D arrays of Hermite series coefficients ordered from low to
high.
Returns
-------
out : ndarray
Of Hermite series coefficients representing their product.
See Also
--------
hermeadd, hermesub, hermemulx, hermediv, hermepow
Notes
-----
In general, the (polynomial) product of two C-series results in terms
that are not in the Hermite polynomial basis set. Thus, to express
the product as a Hermite series, it is necessary to "reproject" the
product onto said basis set, which may produce "unintuitive" (but
correct) results; see Examples section below.
Examples
--------
>>> from numpy.polynomial.hermite_e import hermemul
>>> hermemul([1, 2, 3], [0, 1, 2])
array([14., 15., 28., 7., 6.])
"""
# s1, s2 are trimmed copies
[c1, c2] = pu.as_series([c1, c2])
if len(c1) > len(c2):
c = c2
xs = c1
else:
c = c1
xs = c2
if len(c) == 1:
c0 = c[0]*xs
c1 = 0
elif len(c) == 2:
c0 = c[0]*xs
c1 = c[1]*xs
else:
nd = len(c)
c0 = c[-2]*xs
c1 = c[-1]*xs
for i in range(3, len(c) + 1):
tmp = c0
nd = nd - 1
c0 = hermesub(c[-i]*xs, c1*(nd - 1))
c1 = hermeadd(tmp, hermemulx(c1))
return hermeadd(c0, hermemulx(c1))
The provided code snippet includes necessary dependencies for implementing the `hermepow` function. Write a Python function `def hermepow(c, pow, maxpower=16)` to solve the following problem:
Raise a Hermite series to a power. Returns the Hermite series `c` raised to the power `pow`. The argument `c` is a sequence of coefficients ordered from low to high. i.e., [1,2,3] is the series ``P_0 + 2*P_1 + 3*P_2.`` Parameters ---------- c : array_like 1-D array of Hermite series coefficients ordered from low to high. pow : integer Power to which the series will be raised maxpower : integer, optional Maximum power allowed. This is mainly to limit growth of the series to unmanageable size. Default is 16 Returns ------- coef : ndarray Hermite series of power. See Also -------- hermeadd, hermesub, hermemulx, hermemul, hermediv Examples -------- >>> from numpy.polynomial.hermite_e import hermepow >>> hermepow([1, 2, 3], 2) array([23., 28., 46., 12., 9.])
Here is the function:
def hermepow(c, pow, maxpower=16):
"""Raise a Hermite series to a power.
Returns the Hermite series `c` raised to the power `pow`. The
argument `c` is a sequence of coefficients ordered from low to high.
i.e., [1,2,3] is the series ``P_0 + 2*P_1 + 3*P_2.``
Parameters
----------
c : array_like
1-D array of Hermite series coefficients ordered from low to
high.
pow : integer
Power to which the series will be raised
maxpower : integer, optional
Maximum power allowed. This is mainly to limit growth of the series
to unmanageable size. Default is 16
Returns
-------
coef : ndarray
Hermite series of power.
See Also
--------
hermeadd, hermesub, hermemulx, hermemul, hermediv
Examples
--------
>>> from numpy.polynomial.hermite_e import hermepow
>>> hermepow([1, 2, 3], 2)
array([23., 28., 46., 12., 9.])
"""
return pu._pow(hermemul, c, pow, maxpower) | Raise a Hermite series to a power. Returns the Hermite series `c` raised to the power `pow`. The argument `c` is a sequence of coefficients ordered from low to high. i.e., [1,2,3] is the series ``P_0 + 2*P_1 + 3*P_2.`` Parameters ---------- c : array_like 1-D array of Hermite series coefficients ordered from low to high. pow : integer Power to which the series will be raised maxpower : integer, optional Maximum power allowed. This is mainly to limit growth of the series to unmanageable size. Default is 16 Returns ------- coef : ndarray Hermite series of power. See Also -------- hermeadd, hermesub, hermemulx, hermemul, hermediv Examples -------- >>> from numpy.polynomial.hermite_e import hermepow >>> hermepow([1, 2, 3], 2) array([23., 28., 46., 12., 9.]) |
169,832 | import numpy as np
import numpy.linalg as la
from numpy.core.multiarray import normalize_axis_index
from . import polyutils as pu
from ._polybase import ABCPolyBase
The provided code snippet includes necessary dependencies for implementing the `hermeder` function. Write a Python function `def hermeder(c, m=1, scl=1, axis=0)` to solve the following problem:
Differentiate a Hermite_e series. Returns the series coefficients `c` differentiated `m` times along `axis`. At each iteration the result is multiplied by `scl` (the scaling factor is for use in a linear change of variable). The argument `c` is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the series ``1*He_0 + 2*He_1 + 3*He_2`` while [[1,2],[1,2]] represents ``1*He_0(x)*He_0(y) + 1*He_1(x)*He_0(y) + 2*He_0(x)*He_1(y) + 2*He_1(x)*He_1(y)`` if axis=0 is ``x`` and axis=1 is ``y``. Parameters ---------- c : array_like Array of Hermite_e series coefficients. If `c` is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index. m : int, optional Number of derivatives taken, must be non-negative. (Default: 1) scl : scalar, optional Each differentiation is multiplied by `scl`. The end result is multiplication by ``scl**m``. This is for use in a linear change of variable. (Default: 1) axis : int, optional Axis over which the derivative is taken. (Default: 0). .. versionadded:: 1.7.0 Returns ------- der : ndarray Hermite series of the derivative. See Also -------- hermeint Notes ----- In general, the result of differentiating a Hermite series does not resemble the same operation on a power series. Thus the result of this function may be "unintuitive," albeit correct; see Examples section below. Examples -------- >>> from numpy.polynomial.hermite_e import hermeder >>> hermeder([ 1., 1., 1., 1.]) array([1., 2., 3.]) >>> hermeder([-0.25, 1., 1./2., 1./3., 1./4 ], m=2) array([1., 2., 3.])
Here is the function:
def hermeder(c, m=1, scl=1, axis=0):
"""
Differentiate a Hermite_e series.
Returns the series coefficients `c` differentiated `m` times along
`axis`. At each iteration the result is multiplied by `scl` (the
scaling factor is for use in a linear change of variable). The argument
`c` is an array of coefficients from low to high degree along each
axis, e.g., [1,2,3] represents the series ``1*He_0 + 2*He_1 + 3*He_2``
while [[1,2],[1,2]] represents ``1*He_0(x)*He_0(y) + 1*He_1(x)*He_0(y)
+ 2*He_0(x)*He_1(y) + 2*He_1(x)*He_1(y)`` if axis=0 is ``x`` and axis=1
is ``y``.
Parameters
----------
c : array_like
Array of Hermite_e series coefficients. If `c` is multidimensional
the different axis correspond to different variables with the
degree in each axis given by the corresponding index.
m : int, optional
Number of derivatives taken, must be non-negative. (Default: 1)
scl : scalar, optional
Each differentiation is multiplied by `scl`. The end result is
multiplication by ``scl**m``. This is for use in a linear change of
variable. (Default: 1)
axis : int, optional
Axis over which the derivative is taken. (Default: 0).
.. versionadded:: 1.7.0
Returns
-------
der : ndarray
Hermite series of the derivative.
See Also
--------
hermeint
Notes
-----
In general, the result of differentiating a Hermite series does not
resemble the same operation on a power series. Thus the result of this
function may be "unintuitive," albeit correct; see Examples section
below.
Examples
--------
>>> from numpy.polynomial.hermite_e import hermeder
>>> hermeder([ 1., 1., 1., 1.])
array([1., 2., 3.])
>>> hermeder([-0.25, 1., 1./2., 1./3., 1./4 ], m=2)
array([1., 2., 3.])
"""
c = np.array(c, ndmin=1, copy=True)
if c.dtype.char in '?bBhHiIlLqQpP':
c = c.astype(np.double)
cnt = pu._deprecate_as_int(m, "the order of derivation")
iaxis = pu._deprecate_as_int(axis, "the axis")
if cnt < 0:
raise ValueError("The order of derivation must be non-negative")
iaxis = normalize_axis_index(iaxis, c.ndim)
if cnt == 0:
return c
c = np.moveaxis(c, iaxis, 0)
n = len(c)
if cnt >= n:
return c[:1]*0
else:
for i in range(cnt):
n = n - 1
c *= scl
der = np.empty((n,) + c.shape[1:], dtype=c.dtype)
for j in range(n, 0, -1):
der[j - 1] = j*c[j]
c = der
c = np.moveaxis(c, 0, iaxis)
return c | Differentiate a Hermite_e series. Returns the series coefficients `c` differentiated `m` times along `axis`. At each iteration the result is multiplied by `scl` (the scaling factor is for use in a linear change of variable). The argument `c` is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the series ``1*He_0 + 2*He_1 + 3*He_2`` while [[1,2],[1,2]] represents ``1*He_0(x)*He_0(y) + 1*He_1(x)*He_0(y) + 2*He_0(x)*He_1(y) + 2*He_1(x)*He_1(y)`` if axis=0 is ``x`` and axis=1 is ``y``. Parameters ---------- c : array_like Array of Hermite_e series coefficients. If `c` is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index. m : int, optional Number of derivatives taken, must be non-negative. (Default: 1) scl : scalar, optional Each differentiation is multiplied by `scl`. The end result is multiplication by ``scl**m``. This is for use in a linear change of variable. (Default: 1) axis : int, optional Axis over which the derivative is taken. (Default: 0). .. versionadded:: 1.7.0 Returns ------- der : ndarray Hermite series of the derivative. See Also -------- hermeint Notes ----- In general, the result of differentiating a Hermite series does not resemble the same operation on a power series. Thus the result of this function may be "unintuitive," albeit correct; see Examples section below. Examples -------- >>> from numpy.polynomial.hermite_e import hermeder >>> hermeder([ 1., 1., 1., 1.]) array([1., 2., 3.]) >>> hermeder([-0.25, 1., 1./2., 1./3., 1./4 ], m=2) array([1., 2., 3.]) |
169,833 | import numpy as np
import numpy.linalg as la
from numpy.core.multiarray import normalize_axis_index
from . import polyutils as pu
from ._polybase import ABCPolyBase
def hermeval(x, c, tensor=True):
"""
Evaluate an HermiteE series at points x.
If `c` is of length `n + 1`, this function returns the value:
.. math:: p(x) = c_0 * He_0(x) + c_1 * He_1(x) + ... + c_n * He_n(x)
The parameter `x` is converted to an array only if it is a tuple or a
list, otherwise it is treated as a scalar. In either case, either `x`
or its elements must support multiplication and addition both with
themselves and with the elements of `c`.
If `c` is a 1-D array, then `p(x)` will have the same shape as `x`. If
`c` is multidimensional, then the shape of the result depends on the
value of `tensor`. If `tensor` is true the shape will be c.shape[1:] +
x.shape. If `tensor` is false the shape will be c.shape[1:]. Note that
scalars have shape (,).
Trailing zeros in the coefficients will be used in the evaluation, so
they should be avoided if efficiency is a concern.
Parameters
----------
x : array_like, compatible object
If `x` is a list or tuple, it is converted to an ndarray, otherwise
it is left unchanged and treated as a scalar. In either case, `x`
or its elements must support addition and multiplication with
with themselves and with the elements of `c`.
c : array_like
Array of coefficients ordered so that the coefficients for terms of
degree n are contained in c[n]. If `c` is multidimensional the
remaining indices enumerate multiple polynomials. In the two
dimensional case the coefficients may be thought of as stored in
the columns of `c`.
tensor : boolean, optional
If True, the shape of the coefficient array is extended with ones
on the right, one for each dimension of `x`. Scalars have dimension 0
for this action. The result is that every column of coefficients in
`c` is evaluated for every element of `x`. If False, `x` is broadcast
over the columns of `c` for the evaluation. This keyword is useful
when `c` is multidimensional. The default value is True.
.. versionadded:: 1.7.0
Returns
-------
values : ndarray, algebra_like
The shape of the return value is described above.
See Also
--------
hermeval2d, hermegrid2d, hermeval3d, hermegrid3d
Notes
-----
The evaluation uses Clenshaw recursion, aka synthetic division.
Examples
--------
>>> from numpy.polynomial.hermite_e import hermeval
>>> coef = [1,2,3]
>>> hermeval(1, coef)
3.0
>>> hermeval([[1,2],[3,4]], coef)
array([[ 3., 14.],
[31., 54.]])
"""
c = np.array(c, ndmin=1, copy=False)
if c.dtype.char in '?bBhHiIlLqQpP':
c = c.astype(np.double)
if isinstance(x, (tuple, list)):
x = np.asarray(x)
if isinstance(x, np.ndarray) and tensor:
c = c.reshape(c.shape + (1,)*x.ndim)
if len(c) == 1:
c0 = c[0]
c1 = 0
elif len(c) == 2:
c0 = c[0]
c1 = c[1]
else:
nd = len(c)
c0 = c[-2]
c1 = c[-1]
for i in range(3, len(c) + 1):
tmp = c0
nd = nd - 1
c0 = c[-i] - c1*(nd - 1)
c1 = tmp + c1*x
return c0 + c1*x
The provided code snippet includes necessary dependencies for implementing the `hermeint` function. Write a Python function `def hermeint(c, m=1, k=[], lbnd=0, scl=1, axis=0)` to solve the following problem:
Integrate a Hermite_e series. Returns the Hermite_e series coefficients `c` integrated `m` times from `lbnd` along `axis`. At each iteration the resulting series is **multiplied** by `scl` and an integration constant, `k`, is added. The scaling factor is for use in a linear change of variable. ("Buyer beware": note that, depending on what one is doing, one may want `scl` to be the reciprocal of what one might expect; for more information, see the Notes section below.) The argument `c` is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the series ``H_0 + 2*H_1 + 3*H_2`` while [[1,2],[1,2]] represents ``1*H_0(x)*H_0(y) + 1*H_1(x)*H_0(y) + 2*H_0(x)*H_1(y) + 2*H_1(x)*H_1(y)`` if axis=0 is ``x`` and axis=1 is ``y``. Parameters ---------- c : array_like Array of Hermite_e series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index. m : int, optional Order of integration, must be positive. (Default: 1) k : {[], list, scalar}, optional Integration constant(s). The value of the first integral at ``lbnd`` is the first value in the list, the value of the second integral at ``lbnd`` is the second value, etc. If ``k == []`` (the default), all constants are set to zero. If ``m == 1``, a single scalar can be given instead of a list. lbnd : scalar, optional The lower bound of the integral. (Default: 0) scl : scalar, optional Following each integration the result is *multiplied* by `scl` before the integration constant is added. (Default: 1) axis : int, optional Axis over which the integral is taken. (Default: 0). .. versionadded:: 1.7.0 Returns ------- S : ndarray Hermite_e series coefficients of the integral. Raises ------ ValueError If ``m < 0``, ``len(k) > m``, ``np.ndim(lbnd) != 0``, or ``np.ndim(scl) != 0``. See Also -------- hermeder Notes ----- Note that the result of each integration is *multiplied* by `scl`. Why is this important to note? Say one is making a linear change of variable :math:`u = ax + b` in an integral relative to `x`. Then :math:`dx = du/a`, so one will need to set `scl` equal to :math:`1/a` - perhaps not what one would have first thought. Also note that, in general, the result of integrating a C-series needs to be "reprojected" onto the C-series basis set. Thus, typically, the result of this function is "unintuitive," albeit correct; see Examples section below. Examples -------- >>> from numpy.polynomial.hermite_e import hermeint >>> hermeint([1, 2, 3]) # integrate once, value 0 at 0. array([1., 1., 1., 1.]) >>> hermeint([1, 2, 3], m=2) # integrate twice, value & deriv 0 at 0 array([-0.25 , 1. , 0.5 , 0.33333333, 0.25 ]) # may vary >>> hermeint([1, 2, 3], k=1) # integrate once, value 1 at 0. array([2., 1., 1., 1.]) >>> hermeint([1, 2, 3], lbnd=-1) # integrate once, value 0 at -1 array([-1., 1., 1., 1.]) >>> hermeint([1, 2, 3], m=2, k=[1, 2], lbnd=-1) array([ 1.83333333, 0. , 0.5 , 0.33333333, 0.25 ]) # may vary
Here is the function:
def hermeint(c, m=1, k=[], lbnd=0, scl=1, axis=0):
"""
Integrate a Hermite_e series.
Returns the Hermite_e series coefficients `c` integrated `m` times from
`lbnd` along `axis`. At each iteration the resulting series is
**multiplied** by `scl` and an integration constant, `k`, is added.
The scaling factor is for use in a linear change of variable. ("Buyer
beware": note that, depending on what one is doing, one may want `scl`
to be the reciprocal of what one might expect; for more information,
see the Notes section below.) The argument `c` is an array of
coefficients from low to high degree along each axis, e.g., [1,2,3]
represents the series ``H_0 + 2*H_1 + 3*H_2`` while [[1,2],[1,2]]
represents ``1*H_0(x)*H_0(y) + 1*H_1(x)*H_0(y) + 2*H_0(x)*H_1(y) +
2*H_1(x)*H_1(y)`` if axis=0 is ``x`` and axis=1 is ``y``.
Parameters
----------
c : array_like
Array of Hermite_e series coefficients. If c is multidimensional
the different axis correspond to different variables with the
degree in each axis given by the corresponding index.
m : int, optional
Order of integration, must be positive. (Default: 1)
k : {[], list, scalar}, optional
Integration constant(s). The value of the first integral at
``lbnd`` is the first value in the list, the value of the second
integral at ``lbnd`` is the second value, etc. If ``k == []`` (the
default), all constants are set to zero. If ``m == 1``, a single
scalar can be given instead of a list.
lbnd : scalar, optional
The lower bound of the integral. (Default: 0)
scl : scalar, optional
Following each integration the result is *multiplied* by `scl`
before the integration constant is added. (Default: 1)
axis : int, optional
Axis over which the integral is taken. (Default: 0).
.. versionadded:: 1.7.0
Returns
-------
S : ndarray
Hermite_e series coefficients of the integral.
Raises
------
ValueError
If ``m < 0``, ``len(k) > m``, ``np.ndim(lbnd) != 0``, or
``np.ndim(scl) != 0``.
See Also
--------
hermeder
Notes
-----
Note that the result of each integration is *multiplied* by `scl`.
Why is this important to note? Say one is making a linear change of
variable :math:`u = ax + b` in an integral relative to `x`. Then
:math:`dx = du/a`, so one will need to set `scl` equal to
:math:`1/a` - perhaps not what one would have first thought.
Also note that, in general, the result of integrating a C-series needs
to be "reprojected" onto the C-series basis set. Thus, typically,
the result of this function is "unintuitive," albeit correct; see
Examples section below.
Examples
--------
>>> from numpy.polynomial.hermite_e import hermeint
>>> hermeint([1, 2, 3]) # integrate once, value 0 at 0.
array([1., 1., 1., 1.])
>>> hermeint([1, 2, 3], m=2) # integrate twice, value & deriv 0 at 0
array([-0.25 , 1. , 0.5 , 0.33333333, 0.25 ]) # may vary
>>> hermeint([1, 2, 3], k=1) # integrate once, value 1 at 0.
array([2., 1., 1., 1.])
>>> hermeint([1, 2, 3], lbnd=-1) # integrate once, value 0 at -1
array([-1., 1., 1., 1.])
>>> hermeint([1, 2, 3], m=2, k=[1, 2], lbnd=-1)
array([ 1.83333333, 0. , 0.5 , 0.33333333, 0.25 ]) # may vary
"""
c = np.array(c, ndmin=1, copy=True)
if c.dtype.char in '?bBhHiIlLqQpP':
c = c.astype(np.double)
if not np.iterable(k):
k = [k]
cnt = pu._deprecate_as_int(m, "the order of integration")
iaxis = pu._deprecate_as_int(axis, "the axis")
if cnt < 0:
raise ValueError("The order of integration must be non-negative")
if len(k) > cnt:
raise ValueError("Too many integration constants")
if np.ndim(lbnd) != 0:
raise ValueError("lbnd must be a scalar.")
if np.ndim(scl) != 0:
raise ValueError("scl must be a scalar.")
iaxis = normalize_axis_index(iaxis, c.ndim)
if cnt == 0:
return c
c = np.moveaxis(c, iaxis, 0)
k = list(k) + [0]*(cnt - len(k))
for i in range(cnt):
n = len(c)
c *= scl
if n == 1 and np.all(c[0] == 0):
c[0] += k[i]
else:
tmp = np.empty((n + 1,) + c.shape[1:], dtype=c.dtype)
tmp[0] = c[0]*0
tmp[1] = c[0]
for j in range(1, n):
tmp[j + 1] = c[j]/(j + 1)
tmp[0] += k[i] - hermeval(lbnd, tmp)
c = tmp
c = np.moveaxis(c, 0, iaxis)
return c | Integrate a Hermite_e series. Returns the Hermite_e series coefficients `c` integrated `m` times from `lbnd` along `axis`. At each iteration the resulting series is **multiplied** by `scl` and an integration constant, `k`, is added. The scaling factor is for use in a linear change of variable. ("Buyer beware": note that, depending on what one is doing, one may want `scl` to be the reciprocal of what one might expect; for more information, see the Notes section below.) The argument `c` is an array of coefficients from low to high degree along each axis, e.g., [1,2,3] represents the series ``H_0 + 2*H_1 + 3*H_2`` while [[1,2],[1,2]] represents ``1*H_0(x)*H_0(y) + 1*H_1(x)*H_0(y) + 2*H_0(x)*H_1(y) + 2*H_1(x)*H_1(y)`` if axis=0 is ``x`` and axis=1 is ``y``. Parameters ---------- c : array_like Array of Hermite_e series coefficients. If c is multidimensional the different axis correspond to different variables with the degree in each axis given by the corresponding index. m : int, optional Order of integration, must be positive. (Default: 1) k : {[], list, scalar}, optional Integration constant(s). The value of the first integral at ``lbnd`` is the first value in the list, the value of the second integral at ``lbnd`` is the second value, etc. If ``k == []`` (the default), all constants are set to zero. If ``m == 1``, a single scalar can be given instead of a list. lbnd : scalar, optional The lower bound of the integral. (Default: 0) scl : scalar, optional Following each integration the result is *multiplied* by `scl` before the integration constant is added. (Default: 1) axis : int, optional Axis over which the integral is taken. (Default: 0). .. versionadded:: 1.7.0 Returns ------- S : ndarray Hermite_e series coefficients of the integral. Raises ------ ValueError If ``m < 0``, ``len(k) > m``, ``np.ndim(lbnd) != 0``, or ``np.ndim(scl) != 0``. See Also -------- hermeder Notes ----- Note that the result of each integration is *multiplied* by `scl`. Why is this important to note? Say one is making a linear change of variable :math:`u = ax + b` in an integral relative to `x`. Then :math:`dx = du/a`, so one will need to set `scl` equal to :math:`1/a` - perhaps not what one would have first thought. Also note that, in general, the result of integrating a C-series needs to be "reprojected" onto the C-series basis set. Thus, typically, the result of this function is "unintuitive," albeit correct; see Examples section below. Examples -------- >>> from numpy.polynomial.hermite_e import hermeint >>> hermeint([1, 2, 3]) # integrate once, value 0 at 0. array([1., 1., 1., 1.]) >>> hermeint([1, 2, 3], m=2) # integrate twice, value & deriv 0 at 0 array([-0.25 , 1. , 0.5 , 0.33333333, 0.25 ]) # may vary >>> hermeint([1, 2, 3], k=1) # integrate once, value 1 at 0. array([2., 1., 1., 1.]) >>> hermeint([1, 2, 3], lbnd=-1) # integrate once, value 0 at -1 array([-1., 1., 1., 1.]) >>> hermeint([1, 2, 3], m=2, k=[1, 2], lbnd=-1) array([ 1.83333333, 0. , 0.5 , 0.33333333, 0.25 ]) # may vary |
169,834 | import numpy as np
import numpy.linalg as la
from numpy.core.multiarray import normalize_axis_index
from . import polyutils as pu
from ._polybase import ABCPolyBase
def hermeval(x, c, tensor=True):
"""
Evaluate an HermiteE series at points x.
If `c` is of length `n + 1`, this function returns the value:
.. math:: p(x) = c_0 * He_0(x) + c_1 * He_1(x) + ... + c_n * He_n(x)
The parameter `x` is converted to an array only if it is a tuple or a
list, otherwise it is treated as a scalar. In either case, either `x`
or its elements must support multiplication and addition both with
themselves and with the elements of `c`.
If `c` is a 1-D array, then `p(x)` will have the same shape as `x`. If
`c` is multidimensional, then the shape of the result depends on the
value of `tensor`. If `tensor` is true the shape will be c.shape[1:] +
x.shape. If `tensor` is false the shape will be c.shape[1:]. Note that
scalars have shape (,).
Trailing zeros in the coefficients will be used in the evaluation, so
they should be avoided if efficiency is a concern.
Parameters
----------
x : array_like, compatible object
If `x` is a list or tuple, it is converted to an ndarray, otherwise
it is left unchanged and treated as a scalar. In either case, `x`
or its elements must support addition and multiplication with
with themselves and with the elements of `c`.
c : array_like
Array of coefficients ordered so that the coefficients for terms of
degree n are contained in c[n]. If `c` is multidimensional the
remaining indices enumerate multiple polynomials. In the two
dimensional case the coefficients may be thought of as stored in
the columns of `c`.
tensor : boolean, optional
If True, the shape of the coefficient array is extended with ones
on the right, one for each dimension of `x`. Scalars have dimension 0
for this action. The result is that every column of coefficients in
`c` is evaluated for every element of `x`. If False, `x` is broadcast
over the columns of `c` for the evaluation. This keyword is useful
when `c` is multidimensional. The default value is True.
.. versionadded:: 1.7.0
Returns
-------
values : ndarray, algebra_like
The shape of the return value is described above.
See Also
--------
hermeval2d, hermegrid2d, hermeval3d, hermegrid3d
Notes
-----
The evaluation uses Clenshaw recursion, aka synthetic division.
Examples
--------
>>> from numpy.polynomial.hermite_e import hermeval
>>> coef = [1,2,3]
>>> hermeval(1, coef)
3.0
>>> hermeval([[1,2],[3,4]], coef)
array([[ 3., 14.],
[31., 54.]])
"""
c = np.array(c, ndmin=1, copy=False)
if c.dtype.char in '?bBhHiIlLqQpP':
c = c.astype(np.double)
if isinstance(x, (tuple, list)):
x = np.asarray(x)
if isinstance(x, np.ndarray) and tensor:
c = c.reshape(c.shape + (1,)*x.ndim)
if len(c) == 1:
c0 = c[0]
c1 = 0
elif len(c) == 2:
c0 = c[0]
c1 = c[1]
else:
nd = len(c)
c0 = c[-2]
c1 = c[-1]
for i in range(3, len(c) + 1):
tmp = c0
nd = nd - 1
c0 = c[-i] - c1*(nd - 1)
c1 = tmp + c1*x
return c0 + c1*x
The provided code snippet includes necessary dependencies for implementing the `hermeval2d` function. Write a Python function `def hermeval2d(x, y, c)` to solve the following problem:
Evaluate a 2-D HermiteE series at points (x, y). This function returns the values: .. math:: p(x,y) = \\sum_{i,j} c_{i,j} * He_i(x) * He_j(y) The parameters `x` and `y` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars and they must have the same shape after conversion. In either case, either `x` and `y` or their elements must support multiplication and addition both with themselves and with the elements of `c`. If `c` is a 1-D array a one is implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape. Parameters ---------- x, y : array_like, compatible objects The two dimensional series is evaluated at the points `(x, y)`, where `x` and `y` must have the same shape. If `x` or `y` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and if it isn't an ndarray it is treated as a scalar. c : array_like Array of coefficients ordered so that the coefficient of the term of multi-degree i,j is contained in ``c[i,j]``. If `c` has dimension greater than two the remaining indices enumerate multiple sets of coefficients. Returns ------- values : ndarray, compatible object The values of the two dimensional polynomial at points formed with pairs of corresponding values from `x` and `y`. See Also -------- hermeval, hermegrid2d, hermeval3d, hermegrid3d Notes ----- .. versionadded:: 1.7.0
Here is the function:
def hermeval2d(x, y, c):
"""
Evaluate a 2-D HermiteE series at points (x, y).
This function returns the values:
.. math:: p(x,y) = \\sum_{i,j} c_{i,j} * He_i(x) * He_j(y)
The parameters `x` and `y` are converted to arrays only if they are
tuples or a lists, otherwise they are treated as a scalars and they
must have the same shape after conversion. In either case, either `x`
and `y` or their elements must support multiplication and addition both
with themselves and with the elements of `c`.
If `c` is a 1-D array a one is implicitly appended to its shape to make
it 2-D. The shape of the result will be c.shape[2:] + x.shape.
Parameters
----------
x, y : array_like, compatible objects
The two dimensional series is evaluated at the points `(x, y)`,
where `x` and `y` must have the same shape. If `x` or `y` is a list
or tuple, it is first converted to an ndarray, otherwise it is left
unchanged and if it isn't an ndarray it is treated as a scalar.
c : array_like
Array of coefficients ordered so that the coefficient of the term
of multi-degree i,j is contained in ``c[i,j]``. If `c` has
dimension greater than two the remaining indices enumerate multiple
sets of coefficients.
Returns
-------
values : ndarray, compatible object
The values of the two dimensional polynomial at points formed with
pairs of corresponding values from `x` and `y`.
See Also
--------
hermeval, hermegrid2d, hermeval3d, hermegrid3d
Notes
-----
.. versionadded:: 1.7.0
"""
return pu._valnd(hermeval, c, x, y) | Evaluate a 2-D HermiteE series at points (x, y). This function returns the values: .. math:: p(x,y) = \\sum_{i,j} c_{i,j} * He_i(x) * He_j(y) The parameters `x` and `y` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars and they must have the same shape after conversion. In either case, either `x` and `y` or their elements must support multiplication and addition both with themselves and with the elements of `c`. If `c` is a 1-D array a one is implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape. Parameters ---------- x, y : array_like, compatible objects The two dimensional series is evaluated at the points `(x, y)`, where `x` and `y` must have the same shape. If `x` or `y` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and if it isn't an ndarray it is treated as a scalar. c : array_like Array of coefficients ordered so that the coefficient of the term of multi-degree i,j is contained in ``c[i,j]``. If `c` has dimension greater than two the remaining indices enumerate multiple sets of coefficients. Returns ------- values : ndarray, compatible object The values of the two dimensional polynomial at points formed with pairs of corresponding values from `x` and `y`. See Also -------- hermeval, hermegrid2d, hermeval3d, hermegrid3d Notes ----- .. versionadded:: 1.7.0 |
169,835 | import numpy as np
import numpy.linalg as la
from numpy.core.multiarray import normalize_axis_index
from . import polyutils as pu
from ._polybase import ABCPolyBase
def hermeval(x, c, tensor=True):
"""
Evaluate an HermiteE series at points x.
If `c` is of length `n + 1`, this function returns the value:
.. math:: p(x) = c_0 * He_0(x) + c_1 * He_1(x) + ... + c_n * He_n(x)
The parameter `x` is converted to an array only if it is a tuple or a
list, otherwise it is treated as a scalar. In either case, either `x`
or its elements must support multiplication and addition both with
themselves and with the elements of `c`.
If `c` is a 1-D array, then `p(x)` will have the same shape as `x`. If
`c` is multidimensional, then the shape of the result depends on the
value of `tensor`. If `tensor` is true the shape will be c.shape[1:] +
x.shape. If `tensor` is false the shape will be c.shape[1:]. Note that
scalars have shape (,).
Trailing zeros in the coefficients will be used in the evaluation, so
they should be avoided if efficiency is a concern.
Parameters
----------
x : array_like, compatible object
If `x` is a list or tuple, it is converted to an ndarray, otherwise
it is left unchanged and treated as a scalar. In either case, `x`
or its elements must support addition and multiplication with
with themselves and with the elements of `c`.
c : array_like
Array of coefficients ordered so that the coefficients for terms of
degree n are contained in c[n]. If `c` is multidimensional the
remaining indices enumerate multiple polynomials. In the two
dimensional case the coefficients may be thought of as stored in
the columns of `c`.
tensor : boolean, optional
If True, the shape of the coefficient array is extended with ones
on the right, one for each dimension of `x`. Scalars have dimension 0
for this action. The result is that every column of coefficients in
`c` is evaluated for every element of `x`. If False, `x` is broadcast
over the columns of `c` for the evaluation. This keyword is useful
when `c` is multidimensional. The default value is True.
.. versionadded:: 1.7.0
Returns
-------
values : ndarray, algebra_like
The shape of the return value is described above.
See Also
--------
hermeval2d, hermegrid2d, hermeval3d, hermegrid3d
Notes
-----
The evaluation uses Clenshaw recursion, aka synthetic division.
Examples
--------
>>> from numpy.polynomial.hermite_e import hermeval
>>> coef = [1,2,3]
>>> hermeval(1, coef)
3.0
>>> hermeval([[1,2],[3,4]], coef)
array([[ 3., 14.],
[31., 54.]])
"""
c = np.array(c, ndmin=1, copy=False)
if c.dtype.char in '?bBhHiIlLqQpP':
c = c.astype(np.double)
if isinstance(x, (tuple, list)):
x = np.asarray(x)
if isinstance(x, np.ndarray) and tensor:
c = c.reshape(c.shape + (1,)*x.ndim)
if len(c) == 1:
c0 = c[0]
c1 = 0
elif len(c) == 2:
c0 = c[0]
c1 = c[1]
else:
nd = len(c)
c0 = c[-2]
c1 = c[-1]
for i in range(3, len(c) + 1):
tmp = c0
nd = nd - 1
c0 = c[-i] - c1*(nd - 1)
c1 = tmp + c1*x
return c0 + c1*x
The provided code snippet includes necessary dependencies for implementing the `hermegrid2d` function. Write a Python function `def hermegrid2d(x, y, c)` to solve the following problem:
Evaluate a 2-D HermiteE series on the Cartesian product of x and y. This function returns the values: .. math:: p(a,b) = \\sum_{i,j} c_{i,j} * H_i(a) * H_j(b) where the points `(a, b)` consist of all pairs formed by taking `a` from `x` and `b` from `y`. The resulting points form a grid with `x` in the first dimension and `y` in the second. The parameters `x` and `y` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars. In either case, either `x` and `y` or their elements must support multiplication and addition both with themselves and with the elements of `c`. If `c` has fewer than two dimensions, ones are implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape. Parameters ---------- x, y : array_like, compatible objects The two dimensional series is evaluated at the points in the Cartesian product of `x` and `y`. If `x` or `y` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if it isn't an ndarray, it is treated as a scalar. c : array_like Array of coefficients ordered so that the coefficients for terms of degree i,j are contained in ``c[i,j]``. If `c` has dimension greater than two the remaining indices enumerate multiple sets of coefficients. Returns ------- values : ndarray, compatible object The values of the two dimensional polynomial at points in the Cartesian product of `x` and `y`. See Also -------- hermeval, hermeval2d, hermeval3d, hermegrid3d Notes ----- .. versionadded:: 1.7.0
Here is the function:
def hermegrid2d(x, y, c):
"""
Evaluate a 2-D HermiteE series on the Cartesian product of x and y.
This function returns the values:
.. math:: p(a,b) = \\sum_{i,j} c_{i,j} * H_i(a) * H_j(b)
where the points `(a, b)` consist of all pairs formed by taking
`a` from `x` and `b` from `y`. The resulting points form a grid with
`x` in the first dimension and `y` in the second.
The parameters `x` and `y` are converted to arrays only if they are
tuples or a lists, otherwise they are treated as a scalars. In either
case, either `x` and `y` or their elements must support multiplication
and addition both with themselves and with the elements of `c`.
If `c` has fewer than two dimensions, ones are implicitly appended to
its shape to make it 2-D. The shape of the result will be c.shape[2:] +
x.shape.
Parameters
----------
x, y : array_like, compatible objects
The two dimensional series is evaluated at the points in the
Cartesian product of `x` and `y`. If `x` or `y` is a list or
tuple, it is first converted to an ndarray, otherwise it is left
unchanged and, if it isn't an ndarray, it is treated as a scalar.
c : array_like
Array of coefficients ordered so that the coefficients for terms of
degree i,j are contained in ``c[i,j]``. If `c` has dimension
greater than two the remaining indices enumerate multiple sets of
coefficients.
Returns
-------
values : ndarray, compatible object
The values of the two dimensional polynomial at points in the Cartesian
product of `x` and `y`.
See Also
--------
hermeval, hermeval2d, hermeval3d, hermegrid3d
Notes
-----
.. versionadded:: 1.7.0
"""
return pu._gridnd(hermeval, c, x, y) | Evaluate a 2-D HermiteE series on the Cartesian product of x and y. This function returns the values: .. math:: p(a,b) = \\sum_{i,j} c_{i,j} * H_i(a) * H_j(b) where the points `(a, b)` consist of all pairs formed by taking `a` from `x` and `b` from `y`. The resulting points form a grid with `x` in the first dimension and `y` in the second. The parameters `x` and `y` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars. In either case, either `x` and `y` or their elements must support multiplication and addition both with themselves and with the elements of `c`. If `c` has fewer than two dimensions, ones are implicitly appended to its shape to make it 2-D. The shape of the result will be c.shape[2:] + x.shape. Parameters ---------- x, y : array_like, compatible objects The two dimensional series is evaluated at the points in the Cartesian product of `x` and `y`. If `x` or `y` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if it isn't an ndarray, it is treated as a scalar. c : array_like Array of coefficients ordered so that the coefficients for terms of degree i,j are contained in ``c[i,j]``. If `c` has dimension greater than two the remaining indices enumerate multiple sets of coefficients. Returns ------- values : ndarray, compatible object The values of the two dimensional polynomial at points in the Cartesian product of `x` and `y`. See Also -------- hermeval, hermeval2d, hermeval3d, hermegrid3d Notes ----- .. versionadded:: 1.7.0 |
169,836 | import numpy as np
import numpy.linalg as la
from numpy.core.multiarray import normalize_axis_index
from . import polyutils as pu
from ._polybase import ABCPolyBase
def hermeval(x, c, tensor=True):
"""
Evaluate an HermiteE series at points x.
If `c` is of length `n + 1`, this function returns the value:
.. math:: p(x) = c_0 * He_0(x) + c_1 * He_1(x) + ... + c_n * He_n(x)
The parameter `x` is converted to an array only if it is a tuple or a
list, otherwise it is treated as a scalar. In either case, either `x`
or its elements must support multiplication and addition both with
themselves and with the elements of `c`.
If `c` is a 1-D array, then `p(x)` will have the same shape as `x`. If
`c` is multidimensional, then the shape of the result depends on the
value of `tensor`. If `tensor` is true the shape will be c.shape[1:] +
x.shape. If `tensor` is false the shape will be c.shape[1:]. Note that
scalars have shape (,).
Trailing zeros in the coefficients will be used in the evaluation, so
they should be avoided if efficiency is a concern.
Parameters
----------
x : array_like, compatible object
If `x` is a list or tuple, it is converted to an ndarray, otherwise
it is left unchanged and treated as a scalar. In either case, `x`
or its elements must support addition and multiplication with
with themselves and with the elements of `c`.
c : array_like
Array of coefficients ordered so that the coefficients for terms of
degree n are contained in c[n]. If `c` is multidimensional the
remaining indices enumerate multiple polynomials. In the two
dimensional case the coefficients may be thought of as stored in
the columns of `c`.
tensor : boolean, optional
If True, the shape of the coefficient array is extended with ones
on the right, one for each dimension of `x`. Scalars have dimension 0
for this action. The result is that every column of coefficients in
`c` is evaluated for every element of `x`. If False, `x` is broadcast
over the columns of `c` for the evaluation. This keyword is useful
when `c` is multidimensional. The default value is True.
.. versionadded:: 1.7.0
Returns
-------
values : ndarray, algebra_like
The shape of the return value is described above.
See Also
--------
hermeval2d, hermegrid2d, hermeval3d, hermegrid3d
Notes
-----
The evaluation uses Clenshaw recursion, aka synthetic division.
Examples
--------
>>> from numpy.polynomial.hermite_e import hermeval
>>> coef = [1,2,3]
>>> hermeval(1, coef)
3.0
>>> hermeval([[1,2],[3,4]], coef)
array([[ 3., 14.],
[31., 54.]])
"""
c = np.array(c, ndmin=1, copy=False)
if c.dtype.char in '?bBhHiIlLqQpP':
c = c.astype(np.double)
if isinstance(x, (tuple, list)):
x = np.asarray(x)
if isinstance(x, np.ndarray) and tensor:
c = c.reshape(c.shape + (1,)*x.ndim)
if len(c) == 1:
c0 = c[0]
c1 = 0
elif len(c) == 2:
c0 = c[0]
c1 = c[1]
else:
nd = len(c)
c0 = c[-2]
c1 = c[-1]
for i in range(3, len(c) + 1):
tmp = c0
nd = nd - 1
c0 = c[-i] - c1*(nd - 1)
c1 = tmp + c1*x
return c0 + c1*x
The provided code snippet includes necessary dependencies for implementing the `hermeval3d` function. Write a Python function `def hermeval3d(x, y, z, c)` to solve the following problem:
Evaluate a 3-D Hermite_e series at points (x, y, z). This function returns the values: .. math:: p(x,y,z) = \\sum_{i,j,k} c_{i,j,k} * He_i(x) * He_j(y) * He_k(z) The parameters `x`, `y`, and `z` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars and they must have the same shape after conversion. In either case, either `x`, `y`, and `z` or their elements must support multiplication and addition both with themselves and with the elements of `c`. If `c` has fewer than 3 dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape. Parameters ---------- x, y, z : array_like, compatible object The three dimensional series is evaluated at the points `(x, y, z)`, where `x`, `y`, and `z` must have the same shape. If any of `x`, `y`, or `z` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and if it isn't an ndarray it is treated as a scalar. c : array_like Array of coefficients ordered so that the coefficient of the term of multi-degree i,j,k is contained in ``c[i,j,k]``. If `c` has dimension greater than 3 the remaining indices enumerate multiple sets of coefficients. Returns ------- values : ndarray, compatible object The values of the multidimensional polynomial on points formed with triples of corresponding values from `x`, `y`, and `z`. See Also -------- hermeval, hermeval2d, hermegrid2d, hermegrid3d Notes ----- .. versionadded:: 1.7.0
Here is the function:
def hermeval3d(x, y, z, c):
"""
Evaluate a 3-D Hermite_e series at points (x, y, z).
This function returns the values:
.. math:: p(x,y,z) = \\sum_{i,j,k} c_{i,j,k} * He_i(x) * He_j(y) * He_k(z)
The parameters `x`, `y`, and `z` are converted to arrays only if
they are tuples or a lists, otherwise they are treated as a scalars and
they must have the same shape after conversion. In either case, either
`x`, `y`, and `z` or their elements must support multiplication and
addition both with themselves and with the elements of `c`.
If `c` has fewer than 3 dimensions, ones are implicitly appended to its
shape to make it 3-D. The shape of the result will be c.shape[3:] +
x.shape.
Parameters
----------
x, y, z : array_like, compatible object
The three dimensional series is evaluated at the points
`(x, y, z)`, where `x`, `y`, and `z` must have the same shape. If
any of `x`, `y`, or `z` is a list or tuple, it is first converted
to an ndarray, otherwise it is left unchanged and if it isn't an
ndarray it is treated as a scalar.
c : array_like
Array of coefficients ordered so that the coefficient of the term of
multi-degree i,j,k is contained in ``c[i,j,k]``. If `c` has dimension
greater than 3 the remaining indices enumerate multiple sets of
coefficients.
Returns
-------
values : ndarray, compatible object
The values of the multidimensional polynomial on points formed with
triples of corresponding values from `x`, `y`, and `z`.
See Also
--------
hermeval, hermeval2d, hermegrid2d, hermegrid3d
Notes
-----
.. versionadded:: 1.7.0
"""
return pu._valnd(hermeval, c, x, y, z) | Evaluate a 3-D Hermite_e series at points (x, y, z). This function returns the values: .. math:: p(x,y,z) = \\sum_{i,j,k} c_{i,j,k} * He_i(x) * He_j(y) * He_k(z) The parameters `x`, `y`, and `z` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars and they must have the same shape after conversion. In either case, either `x`, `y`, and `z` or their elements must support multiplication and addition both with themselves and with the elements of `c`. If `c` has fewer than 3 dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape. Parameters ---------- x, y, z : array_like, compatible object The three dimensional series is evaluated at the points `(x, y, z)`, where `x`, `y`, and `z` must have the same shape. If any of `x`, `y`, or `z` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and if it isn't an ndarray it is treated as a scalar. c : array_like Array of coefficients ordered so that the coefficient of the term of multi-degree i,j,k is contained in ``c[i,j,k]``. If `c` has dimension greater than 3 the remaining indices enumerate multiple sets of coefficients. Returns ------- values : ndarray, compatible object The values of the multidimensional polynomial on points formed with triples of corresponding values from `x`, `y`, and `z`. See Also -------- hermeval, hermeval2d, hermegrid2d, hermegrid3d Notes ----- .. versionadded:: 1.7.0 |
169,837 | import numpy as np
import numpy.linalg as la
from numpy.core.multiarray import normalize_axis_index
from . import polyutils as pu
from ._polybase import ABCPolyBase
def hermeval(x, c, tensor=True):
"""
Evaluate an HermiteE series at points x.
If `c` is of length `n + 1`, this function returns the value:
.. math:: p(x) = c_0 * He_0(x) + c_1 * He_1(x) + ... + c_n * He_n(x)
The parameter `x` is converted to an array only if it is a tuple or a
list, otherwise it is treated as a scalar. In either case, either `x`
or its elements must support multiplication and addition both with
themselves and with the elements of `c`.
If `c` is a 1-D array, then `p(x)` will have the same shape as `x`. If
`c` is multidimensional, then the shape of the result depends on the
value of `tensor`. If `tensor` is true the shape will be c.shape[1:] +
x.shape. If `tensor` is false the shape will be c.shape[1:]. Note that
scalars have shape (,).
Trailing zeros in the coefficients will be used in the evaluation, so
they should be avoided if efficiency is a concern.
Parameters
----------
x : array_like, compatible object
If `x` is a list or tuple, it is converted to an ndarray, otherwise
it is left unchanged and treated as a scalar. In either case, `x`
or its elements must support addition and multiplication with
with themselves and with the elements of `c`.
c : array_like
Array of coefficients ordered so that the coefficients for terms of
degree n are contained in c[n]. If `c` is multidimensional the
remaining indices enumerate multiple polynomials. In the two
dimensional case the coefficients may be thought of as stored in
the columns of `c`.
tensor : boolean, optional
If True, the shape of the coefficient array is extended with ones
on the right, one for each dimension of `x`. Scalars have dimension 0
for this action. The result is that every column of coefficients in
`c` is evaluated for every element of `x`. If False, `x` is broadcast
over the columns of `c` for the evaluation. This keyword is useful
when `c` is multidimensional. The default value is True.
.. versionadded:: 1.7.0
Returns
-------
values : ndarray, algebra_like
The shape of the return value is described above.
See Also
--------
hermeval2d, hermegrid2d, hermeval3d, hermegrid3d
Notes
-----
The evaluation uses Clenshaw recursion, aka synthetic division.
Examples
--------
>>> from numpy.polynomial.hermite_e import hermeval
>>> coef = [1,2,3]
>>> hermeval(1, coef)
3.0
>>> hermeval([[1,2],[3,4]], coef)
array([[ 3., 14.],
[31., 54.]])
"""
c = np.array(c, ndmin=1, copy=False)
if c.dtype.char in '?bBhHiIlLqQpP':
c = c.astype(np.double)
if isinstance(x, (tuple, list)):
x = np.asarray(x)
if isinstance(x, np.ndarray) and tensor:
c = c.reshape(c.shape + (1,)*x.ndim)
if len(c) == 1:
c0 = c[0]
c1 = 0
elif len(c) == 2:
c0 = c[0]
c1 = c[1]
else:
nd = len(c)
c0 = c[-2]
c1 = c[-1]
for i in range(3, len(c) + 1):
tmp = c0
nd = nd - 1
c0 = c[-i] - c1*(nd - 1)
c1 = tmp + c1*x
return c0 + c1*x
The provided code snippet includes necessary dependencies for implementing the `hermegrid3d` function. Write a Python function `def hermegrid3d(x, y, z, c)` to solve the following problem:
Evaluate a 3-D HermiteE series on the Cartesian product of x, y, and z. This function returns the values: .. math:: p(a,b,c) = \\sum_{i,j,k} c_{i,j,k} * He_i(a) * He_j(b) * He_k(c) where the points `(a, b, c)` consist of all triples formed by taking `a` from `x`, `b` from `y`, and `c` from `z`. The resulting points form a grid with `x` in the first dimension, `y` in the second, and `z` in the third. The parameters `x`, `y`, and `z` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars. In either case, either `x`, `y`, and `z` or their elements must support multiplication and addition both with themselves and with the elements of `c`. If `c` has fewer than three dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape + y.shape + z.shape. Parameters ---------- x, y, z : array_like, compatible objects The three dimensional series is evaluated at the points in the Cartesian product of `x`, `y`, and `z`. If `x`,`y`, or `z` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if it isn't an ndarray, it is treated as a scalar. c : array_like Array of coefficients ordered so that the coefficients for terms of degree i,j are contained in ``c[i,j]``. If `c` has dimension greater than two the remaining indices enumerate multiple sets of coefficients. Returns ------- values : ndarray, compatible object The values of the two dimensional polynomial at points in the Cartesian product of `x` and `y`. See Also -------- hermeval, hermeval2d, hermegrid2d, hermeval3d Notes ----- .. versionadded:: 1.7.0
Here is the function:
def hermegrid3d(x, y, z, c):
"""
Evaluate a 3-D HermiteE series on the Cartesian product of x, y, and z.
This function returns the values:
.. math:: p(a,b,c) = \\sum_{i,j,k} c_{i,j,k} * He_i(a) * He_j(b) * He_k(c)
where the points `(a, b, c)` consist of all triples formed by taking
`a` from `x`, `b` from `y`, and `c` from `z`. The resulting points form
a grid with `x` in the first dimension, `y` in the second, and `z` in
the third.
The parameters `x`, `y`, and `z` are converted to arrays only if they
are tuples or a lists, otherwise they are treated as a scalars. In
either case, either `x`, `y`, and `z` or their elements must support
multiplication and addition both with themselves and with the elements
of `c`.
If `c` has fewer than three dimensions, ones are implicitly appended to
its shape to make it 3-D. The shape of the result will be c.shape[3:] +
x.shape + y.shape + z.shape.
Parameters
----------
x, y, z : array_like, compatible objects
The three dimensional series is evaluated at the points in the
Cartesian product of `x`, `y`, and `z`. If `x`,`y`, or `z` is a
list or tuple, it is first converted to an ndarray, otherwise it is
left unchanged and, if it isn't an ndarray, it is treated as a
scalar.
c : array_like
Array of coefficients ordered so that the coefficients for terms of
degree i,j are contained in ``c[i,j]``. If `c` has dimension
greater than two the remaining indices enumerate multiple sets of
coefficients.
Returns
-------
values : ndarray, compatible object
The values of the two dimensional polynomial at points in the Cartesian
product of `x` and `y`.
See Also
--------
hermeval, hermeval2d, hermegrid2d, hermeval3d
Notes
-----
.. versionadded:: 1.7.0
"""
return pu._gridnd(hermeval, c, x, y, z) | Evaluate a 3-D HermiteE series on the Cartesian product of x, y, and z. This function returns the values: .. math:: p(a,b,c) = \\sum_{i,j,k} c_{i,j,k} * He_i(a) * He_j(b) * He_k(c) where the points `(a, b, c)` consist of all triples formed by taking `a` from `x`, `b` from `y`, and `c` from `z`. The resulting points form a grid with `x` in the first dimension, `y` in the second, and `z` in the third. The parameters `x`, `y`, and `z` are converted to arrays only if they are tuples or a lists, otherwise they are treated as a scalars. In either case, either `x`, `y`, and `z` or their elements must support multiplication and addition both with themselves and with the elements of `c`. If `c` has fewer than three dimensions, ones are implicitly appended to its shape to make it 3-D. The shape of the result will be c.shape[3:] + x.shape + y.shape + z.shape. Parameters ---------- x, y, z : array_like, compatible objects The three dimensional series is evaluated at the points in the Cartesian product of `x`, `y`, and `z`. If `x`,`y`, or `z` is a list or tuple, it is first converted to an ndarray, otherwise it is left unchanged and, if it isn't an ndarray, it is treated as a scalar. c : array_like Array of coefficients ordered so that the coefficients for terms of degree i,j are contained in ``c[i,j]``. If `c` has dimension greater than two the remaining indices enumerate multiple sets of coefficients. Returns ------- values : ndarray, compatible object The values of the two dimensional polynomial at points in the Cartesian product of `x` and `y`. See Also -------- hermeval, hermeval2d, hermegrid2d, hermeval3d Notes ----- .. versionadded:: 1.7.0 |
169,838 | import numpy as np
import numpy.linalg as la
from numpy.core.multiarray import normalize_axis_index
from . import polyutils as pu
from ._polybase import ABCPolyBase
def hermevander(x, deg):
"""Pseudo-Vandermonde matrix of given degree.
Returns the pseudo-Vandermonde matrix of degree `deg` and sample points
`x`. The pseudo-Vandermonde matrix is defined by
.. math:: V[..., i] = He_i(x),
where `0 <= i <= deg`. The leading indices of `V` index the elements of
`x` and the last index is the degree of the HermiteE polynomial.
If `c` is a 1-D array of coefficients of length `n + 1` and `V` is the
array ``V = hermevander(x, n)``, then ``np.dot(V, c)`` and
``hermeval(x, c)`` are the same up to roundoff. This equivalence is
useful both for least squares fitting and for the evaluation of a large
number of HermiteE series of the same degree and sample points.
Parameters
----------
x : array_like
Array of points. The dtype is converted to float64 or complex128
depending on whether any of the elements are complex. If `x` is
scalar it is converted to a 1-D array.
deg : int
Degree of the resulting matrix.
Returns
-------
vander : ndarray
The pseudo-Vandermonde matrix. The shape of the returned matrix is
``x.shape + (deg + 1,)``, where The last index is the degree of the
corresponding HermiteE polynomial. The dtype will be the same as
the converted `x`.
Examples
--------
>>> from numpy.polynomial.hermite_e import hermevander
>>> x = np.array([-1, 0, 1])
>>> hermevander(x, 3)
array([[ 1., -1., 0., 2.],
[ 1., 0., -1., -0.],
[ 1., 1., 0., -2.]])
"""
ideg = pu._deprecate_as_int(deg, "deg")
if ideg < 0:
raise ValueError("deg must be non-negative")
x = np.array(x, copy=False, ndmin=1) + 0.0
dims = (ideg + 1,) + x.shape
dtyp = x.dtype
v = np.empty(dims, dtype=dtyp)
v[0] = x*0 + 1
if ideg > 0:
v[1] = x
for i in range(2, ideg + 1):
v[i] = (v[i-1]*x - v[i-2]*(i - 1))
return np.moveaxis(v, 0, -1)
The provided code snippet includes necessary dependencies for implementing the `hermevander2d` function. Write a Python function `def hermevander2d(x, y, deg)` to solve the following problem:
Pseudo-Vandermonde matrix of given degrees. Returns the pseudo-Vandermonde matrix of degrees `deg` and sample points `(x, y)`. The pseudo-Vandermonde matrix is defined by .. math:: V[..., (deg[1] + 1)*i + j] = He_i(x) * He_j(y), where `0 <= i <= deg[0]` and `0 <= j <= deg[1]`. The leading indices of `V` index the points `(x, y)` and the last index encodes the degrees of the HermiteE polynomials. If ``V = hermevander2d(x, y, [xdeg, ydeg])``, then the columns of `V` correspond to the elements of a 2-D coefficient array `c` of shape (xdeg + 1, ydeg + 1) in the order .. math:: c_{00}, c_{01}, c_{02} ... , c_{10}, c_{11}, c_{12} ... and ``np.dot(V, c.flat)`` and ``hermeval2d(x, y, c)`` will be the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of 2-D HermiteE series of the same degrees and sample points. Parameters ---------- x, y : array_like Arrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays. deg : list of ints List of maximum degrees of the form [x_deg, y_deg]. Returns ------- vander2d : ndarray The shape of the returned matrix is ``x.shape + (order,)``, where :math:`order = (deg[0]+1)*(deg[1]+1)`. The dtype will be the same as the converted `x` and `y`. See Also -------- hermevander, hermevander3d, hermeval2d, hermeval3d Notes ----- .. versionadded:: 1.7.0
Here is the function:
def hermevander2d(x, y, deg):
"""Pseudo-Vandermonde matrix of given degrees.
Returns the pseudo-Vandermonde matrix of degrees `deg` and sample
points `(x, y)`. The pseudo-Vandermonde matrix is defined by
.. math:: V[..., (deg[1] + 1)*i + j] = He_i(x) * He_j(y),
where `0 <= i <= deg[0]` and `0 <= j <= deg[1]`. The leading indices of
`V` index the points `(x, y)` and the last index encodes the degrees of
the HermiteE polynomials.
If ``V = hermevander2d(x, y, [xdeg, ydeg])``, then the columns of `V`
correspond to the elements of a 2-D coefficient array `c` of shape
(xdeg + 1, ydeg + 1) in the order
.. math:: c_{00}, c_{01}, c_{02} ... , c_{10}, c_{11}, c_{12} ...
and ``np.dot(V, c.flat)`` and ``hermeval2d(x, y, c)`` will be the same
up to roundoff. This equivalence is useful both for least squares
fitting and for the evaluation of a large number of 2-D HermiteE
series of the same degrees and sample points.
Parameters
----------
x, y : array_like
Arrays of point coordinates, all of the same shape. The dtypes
will be converted to either float64 or complex128 depending on
whether any of the elements are complex. Scalars are converted to
1-D arrays.
deg : list of ints
List of maximum degrees of the form [x_deg, y_deg].
Returns
-------
vander2d : ndarray
The shape of the returned matrix is ``x.shape + (order,)``, where
:math:`order = (deg[0]+1)*(deg[1]+1)`. The dtype will be the same
as the converted `x` and `y`.
See Also
--------
hermevander, hermevander3d, hermeval2d, hermeval3d
Notes
-----
.. versionadded:: 1.7.0
"""
return pu._vander_nd_flat((hermevander, hermevander), (x, y), deg) | Pseudo-Vandermonde matrix of given degrees. Returns the pseudo-Vandermonde matrix of degrees `deg` and sample points `(x, y)`. The pseudo-Vandermonde matrix is defined by .. math:: V[..., (deg[1] + 1)*i + j] = He_i(x) * He_j(y), where `0 <= i <= deg[0]` and `0 <= j <= deg[1]`. The leading indices of `V` index the points `(x, y)` and the last index encodes the degrees of the HermiteE polynomials. If ``V = hermevander2d(x, y, [xdeg, ydeg])``, then the columns of `V` correspond to the elements of a 2-D coefficient array `c` of shape (xdeg + 1, ydeg + 1) in the order .. math:: c_{00}, c_{01}, c_{02} ... , c_{10}, c_{11}, c_{12} ... and ``np.dot(V, c.flat)`` and ``hermeval2d(x, y, c)`` will be the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of 2-D HermiteE series of the same degrees and sample points. Parameters ---------- x, y : array_like Arrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays. deg : list of ints List of maximum degrees of the form [x_deg, y_deg]. Returns ------- vander2d : ndarray The shape of the returned matrix is ``x.shape + (order,)``, where :math:`order = (deg[0]+1)*(deg[1]+1)`. The dtype will be the same as the converted `x` and `y`. See Also -------- hermevander, hermevander3d, hermeval2d, hermeval3d Notes ----- .. versionadded:: 1.7.0 |
169,839 | import numpy as np
import numpy.linalg as la
from numpy.core.multiarray import normalize_axis_index
from . import polyutils as pu
from ._polybase import ABCPolyBase
def hermevander(x, deg):
"""Pseudo-Vandermonde matrix of given degree.
Returns the pseudo-Vandermonde matrix of degree `deg` and sample points
`x`. The pseudo-Vandermonde matrix is defined by
.. math:: V[..., i] = He_i(x),
where `0 <= i <= deg`. The leading indices of `V` index the elements of
`x` and the last index is the degree of the HermiteE polynomial.
If `c` is a 1-D array of coefficients of length `n + 1` and `V` is the
array ``V = hermevander(x, n)``, then ``np.dot(V, c)`` and
``hermeval(x, c)`` are the same up to roundoff. This equivalence is
useful both for least squares fitting and for the evaluation of a large
number of HermiteE series of the same degree and sample points.
Parameters
----------
x : array_like
Array of points. The dtype is converted to float64 or complex128
depending on whether any of the elements are complex. If `x` is
scalar it is converted to a 1-D array.
deg : int
Degree of the resulting matrix.
Returns
-------
vander : ndarray
The pseudo-Vandermonde matrix. The shape of the returned matrix is
``x.shape + (deg + 1,)``, where The last index is the degree of the
corresponding HermiteE polynomial. The dtype will be the same as
the converted `x`.
Examples
--------
>>> from numpy.polynomial.hermite_e import hermevander
>>> x = np.array([-1, 0, 1])
>>> hermevander(x, 3)
array([[ 1., -1., 0., 2.],
[ 1., 0., -1., -0.],
[ 1., 1., 0., -2.]])
"""
ideg = pu._deprecate_as_int(deg, "deg")
if ideg < 0:
raise ValueError("deg must be non-negative")
x = np.array(x, copy=False, ndmin=1) + 0.0
dims = (ideg + 1,) + x.shape
dtyp = x.dtype
v = np.empty(dims, dtype=dtyp)
v[0] = x*0 + 1
if ideg > 0:
v[1] = x
for i in range(2, ideg + 1):
v[i] = (v[i-1]*x - v[i-2]*(i - 1))
return np.moveaxis(v, 0, -1)
The provided code snippet includes necessary dependencies for implementing the `hermevander3d` function. Write a Python function `def hermevander3d(x, y, z, deg)` to solve the following problem:
Pseudo-Vandermonde matrix of given degrees. Returns the pseudo-Vandermonde matrix of degrees `deg` and sample points `(x, y, z)`. If `l, m, n` are the given degrees in `x, y, z`, then Hehe pseudo-Vandermonde matrix is defined by .. math:: V[..., (m+1)(n+1)i + (n+1)j + k] = He_i(x)*He_j(y)*He_k(z), where `0 <= i <= l`, `0 <= j <= m`, and `0 <= j <= n`. The leading indices of `V` index the points `(x, y, z)` and the last index encodes the degrees of the HermiteE polynomials. If ``V = hermevander3d(x, y, z, [xdeg, ydeg, zdeg])``, then the columns of `V` correspond to the elements of a 3-D coefficient array `c` of shape (xdeg + 1, ydeg + 1, zdeg + 1) in the order .. math:: c_{000}, c_{001}, c_{002},... , c_{010}, c_{011}, c_{012},... and ``np.dot(V, c.flat)`` and ``hermeval3d(x, y, z, c)`` will be the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of 3-D HermiteE series of the same degrees and sample points. Parameters ---------- x, y, z : array_like Arrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays. deg : list of ints List of maximum degrees of the form [x_deg, y_deg, z_deg]. Returns ------- vander3d : ndarray The shape of the returned matrix is ``x.shape + (order,)``, where :math:`order = (deg[0]+1)*(deg[1]+1)*(deg[2]+1)`. The dtype will be the same as the converted `x`, `y`, and `z`. See Also -------- hermevander, hermevander3d, hermeval2d, hermeval3d Notes ----- .. versionadded:: 1.7.0
Here is the function:
def hermevander3d(x, y, z, deg):
"""Pseudo-Vandermonde matrix of given degrees.
Returns the pseudo-Vandermonde matrix of degrees `deg` and sample
points `(x, y, z)`. If `l, m, n` are the given degrees in `x, y, z`,
then Hehe pseudo-Vandermonde matrix is defined by
.. math:: V[..., (m+1)(n+1)i + (n+1)j + k] = He_i(x)*He_j(y)*He_k(z),
where `0 <= i <= l`, `0 <= j <= m`, and `0 <= j <= n`. The leading
indices of `V` index the points `(x, y, z)` and the last index encodes
the degrees of the HermiteE polynomials.
If ``V = hermevander3d(x, y, z, [xdeg, ydeg, zdeg])``, then the columns
of `V` correspond to the elements of a 3-D coefficient array `c` of
shape (xdeg + 1, ydeg + 1, zdeg + 1) in the order
.. math:: c_{000}, c_{001}, c_{002},... , c_{010}, c_{011}, c_{012},...
and ``np.dot(V, c.flat)`` and ``hermeval3d(x, y, z, c)`` will be the
same up to roundoff. This equivalence is useful both for least squares
fitting and for the evaluation of a large number of 3-D HermiteE
series of the same degrees and sample points.
Parameters
----------
x, y, z : array_like
Arrays of point coordinates, all of the same shape. The dtypes will
be converted to either float64 or complex128 depending on whether
any of the elements are complex. Scalars are converted to 1-D
arrays.
deg : list of ints
List of maximum degrees of the form [x_deg, y_deg, z_deg].
Returns
-------
vander3d : ndarray
The shape of the returned matrix is ``x.shape + (order,)``, where
:math:`order = (deg[0]+1)*(deg[1]+1)*(deg[2]+1)`. The dtype will
be the same as the converted `x`, `y`, and `z`.
See Also
--------
hermevander, hermevander3d, hermeval2d, hermeval3d
Notes
-----
.. versionadded:: 1.7.0
"""
return pu._vander_nd_flat((hermevander, hermevander, hermevander), (x, y, z), deg) | Pseudo-Vandermonde matrix of given degrees. Returns the pseudo-Vandermonde matrix of degrees `deg` and sample points `(x, y, z)`. If `l, m, n` are the given degrees in `x, y, z`, then Hehe pseudo-Vandermonde matrix is defined by .. math:: V[..., (m+1)(n+1)i + (n+1)j + k] = He_i(x)*He_j(y)*He_k(z), where `0 <= i <= l`, `0 <= j <= m`, and `0 <= j <= n`. The leading indices of `V` index the points `(x, y, z)` and the last index encodes the degrees of the HermiteE polynomials. If ``V = hermevander3d(x, y, z, [xdeg, ydeg, zdeg])``, then the columns of `V` correspond to the elements of a 3-D coefficient array `c` of shape (xdeg + 1, ydeg + 1, zdeg + 1) in the order .. math:: c_{000}, c_{001}, c_{002},... , c_{010}, c_{011}, c_{012},... and ``np.dot(V, c.flat)`` and ``hermeval3d(x, y, z, c)`` will be the same up to roundoff. This equivalence is useful both for least squares fitting and for the evaluation of a large number of 3-D HermiteE series of the same degrees and sample points. Parameters ---------- x, y, z : array_like Arrays of point coordinates, all of the same shape. The dtypes will be converted to either float64 or complex128 depending on whether any of the elements are complex. Scalars are converted to 1-D arrays. deg : list of ints List of maximum degrees of the form [x_deg, y_deg, z_deg]. Returns ------- vander3d : ndarray The shape of the returned matrix is ``x.shape + (order,)``, where :math:`order = (deg[0]+1)*(deg[1]+1)*(deg[2]+1)`. The dtype will be the same as the converted `x`, `y`, and `z`. See Also -------- hermevander, hermevander3d, hermeval2d, hermeval3d Notes ----- .. versionadded:: 1.7.0 |
169,840 | import numpy as np
import numpy.linalg as la
from numpy.core.multiarray import normalize_axis_index
from . import polyutils as pu
from ._polybase import ABCPolyBase
def hermevander(x, deg):
"""Pseudo-Vandermonde matrix of given degree.
Returns the pseudo-Vandermonde matrix of degree `deg` and sample points
`x`. The pseudo-Vandermonde matrix is defined by
.. math:: V[..., i] = He_i(x),
where `0 <= i <= deg`. The leading indices of `V` index the elements of
`x` and the last index is the degree of the HermiteE polynomial.
If `c` is a 1-D array of coefficients of length `n + 1` and `V` is the
array ``V = hermevander(x, n)``, then ``np.dot(V, c)`` and
``hermeval(x, c)`` are the same up to roundoff. This equivalence is
useful both for least squares fitting and for the evaluation of a large
number of HermiteE series of the same degree and sample points.
Parameters
----------
x : array_like
Array of points. The dtype is converted to float64 or complex128
depending on whether any of the elements are complex. If `x` is
scalar it is converted to a 1-D array.
deg : int
Degree of the resulting matrix.
Returns
-------
vander : ndarray
The pseudo-Vandermonde matrix. The shape of the returned matrix is
``x.shape + (deg + 1,)``, where The last index is the degree of the
corresponding HermiteE polynomial. The dtype will be the same as
the converted `x`.
Examples
--------
>>> from numpy.polynomial.hermite_e import hermevander
>>> x = np.array([-1, 0, 1])
>>> hermevander(x, 3)
array([[ 1., -1., 0., 2.],
[ 1., 0., -1., -0.],
[ 1., 1., 0., -2.]])
"""
ideg = pu._deprecate_as_int(deg, "deg")
if ideg < 0:
raise ValueError("deg must be non-negative")
x = np.array(x, copy=False, ndmin=1) + 0.0
dims = (ideg + 1,) + x.shape
dtyp = x.dtype
v = np.empty(dims, dtype=dtyp)
v[0] = x*0 + 1
if ideg > 0:
v[1] = x
for i in range(2, ideg + 1):
v[i] = (v[i-1]*x - v[i-2]*(i - 1))
return np.moveaxis(v, 0, -1)
The provided code snippet includes necessary dependencies for implementing the `hermefit` function. Write a Python function `def hermefit(x, y, deg, rcond=None, full=False, w=None)` to solve the following problem:
Least squares fit of Hermite series to data. Return the coefficients of a HermiteE series of degree `deg` that is the least squares fit to the data values `y` given at points `x`. If `y` is 1-D the returned coefficients will also be 1-D. If `y` is 2-D multiple fits are done, one for each column of `y`, and the resulting coefficients are stored in the corresponding columns of a 2-D return. The fitted polynomial(s) are in the form .. math:: p(x) = c_0 + c_1 * He_1(x) + ... + c_n * He_n(x), where `n` is `deg`. Parameters ---------- x : array_like, shape (M,) x-coordinates of the M sample points ``(x[i], y[i])``. y : array_like, shape (M,) or (M, K) y-coordinates of the sample points. Several data sets of sample points sharing the same x-coordinates can be fitted at once by passing in a 2D-array that contains one dataset per column. deg : int or 1-D array_like Degree(s) of the fitting polynomials. If `deg` is a single integer all terms up to and including the `deg`'th term are included in the fit. For NumPy versions >= 1.11.0 a list of integers specifying the degrees of the terms to include may be used instead. rcond : float, optional Relative condition number of the fit. Singular values smaller than this relative to the largest singular value will be ignored. The default value is len(x)*eps, where eps is the relative precision of the float type, about 2e-16 in most cases. full : bool, optional Switch determining nature of return value. When it is False (the default) just the coefficients are returned, when True diagnostic information from the singular value decomposition is also returned. w : array_like, shape (`M`,), optional Weights. If not None, the weight ``w[i]`` applies to the unsquared residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are chosen so that the errors of the products ``w[i]*y[i]`` all have the same variance. When using inverse-variance weighting, use ``w[i] = 1/sigma(y[i])``. The default value is None. Returns ------- coef : ndarray, shape (M,) or (M, K) Hermite coefficients ordered from low to high. If `y` was 2-D, the coefficients for the data in column k of `y` are in column `k`. [residuals, rank, singular_values, rcond] : list These values are only returned if ``full == True`` - residuals -- sum of squared residuals of the least squares fit - rank -- the numerical rank of the scaled Vandermonde matrix - singular_values -- singular values of the scaled Vandermonde matrix - rcond -- value of `rcond`. For more details, see `numpy.linalg.lstsq`. Warns ----- RankWarning The rank of the coefficient matrix in the least-squares fit is deficient. The warning is only raised if ``full = False``. The warnings can be turned off by >>> import warnings >>> warnings.simplefilter('ignore', np.RankWarning) See Also -------- numpy.polynomial.chebyshev.chebfit numpy.polynomial.legendre.legfit numpy.polynomial.polynomial.polyfit numpy.polynomial.hermite.hermfit numpy.polynomial.laguerre.lagfit hermeval : Evaluates a Hermite series. hermevander : pseudo Vandermonde matrix of Hermite series. hermeweight : HermiteE weight function. numpy.linalg.lstsq : Computes a least-squares fit from the matrix. scipy.interpolate.UnivariateSpline : Computes spline fits. Notes ----- The solution is the coefficients of the HermiteE series `p` that minimizes the sum of the weighted squared errors .. math:: E = \\sum_j w_j^2 * |y_j - p(x_j)|^2, where the :math:`w_j` are the weights. This problem is solved by setting up the (typically) overdetermined matrix equation .. math:: V(x) * c = w * y, where `V` is the pseudo Vandermonde matrix of `x`, the elements of `c` are the coefficients to be solved for, and the elements of `y` are the observed values. This equation is then solved using the singular value decomposition of `V`. If some of the singular values of `V` are so small that they are neglected, then a `RankWarning` will be issued. This means that the coefficient values may be poorly determined. Using a lower order fit will usually get rid of the warning. The `rcond` parameter can also be set to a value smaller than its default, but the resulting fit may be spurious and have large contributions from roundoff error. Fits using HermiteE series are probably most useful when the data can be approximated by ``sqrt(w(x)) * p(x)``, where `w(x)` is the HermiteE weight. In that case the weight ``sqrt(w(x[i]))`` should be used together with data values ``y[i]/sqrt(w(x[i]))``. The weight function is available as `hermeweight`. References ---------- .. [1] Wikipedia, "Curve fitting", https://en.wikipedia.org/wiki/Curve_fitting Examples -------- >>> from numpy.polynomial.hermite_e import hermefit, hermeval >>> x = np.linspace(-10, 10) >>> np.random.seed(123) >>> err = np.random.randn(len(x))/10 >>> y = hermeval(x, [1, 2, 3]) + err >>> hermefit(x, y, 2) array([ 1.01690445, 1.99951418, 2.99948696]) # may vary
Here is the function:
def hermefit(x, y, deg, rcond=None, full=False, w=None):
"""
Least squares fit of Hermite series to data.
Return the coefficients of a HermiteE series of degree `deg` that is
the least squares fit to the data values `y` given at points `x`. If
`y` is 1-D the returned coefficients will also be 1-D. If `y` is 2-D
multiple fits are done, one for each column of `y`, and the resulting
coefficients are stored in the corresponding columns of a 2-D return.
The fitted polynomial(s) are in the form
.. math:: p(x) = c_0 + c_1 * He_1(x) + ... + c_n * He_n(x),
where `n` is `deg`.
Parameters
----------
x : array_like, shape (M,)
x-coordinates of the M sample points ``(x[i], y[i])``.
y : array_like, shape (M,) or (M, K)
y-coordinates of the sample points. Several data sets of sample
points sharing the same x-coordinates can be fitted at once by
passing in a 2D-array that contains one dataset per column.
deg : int or 1-D array_like
Degree(s) of the fitting polynomials. If `deg` is a single integer
all terms up to and including the `deg`'th term are included in the
fit. For NumPy versions >= 1.11.0 a list of integers specifying the
degrees of the terms to include may be used instead.
rcond : float, optional
Relative condition number of the fit. Singular values smaller than
this relative to the largest singular value will be ignored. The
default value is len(x)*eps, where eps is the relative precision of
the float type, about 2e-16 in most cases.
full : bool, optional
Switch determining nature of return value. When it is False (the
default) just the coefficients are returned, when True diagnostic
information from the singular value decomposition is also returned.
w : array_like, shape (`M`,), optional
Weights. If not None, the weight ``w[i]`` applies to the unsquared
residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are
chosen so that the errors of the products ``w[i]*y[i]`` all have the
same variance. When using inverse-variance weighting, use
``w[i] = 1/sigma(y[i])``. The default value is None.
Returns
-------
coef : ndarray, shape (M,) or (M, K)
Hermite coefficients ordered from low to high. If `y` was 2-D,
the coefficients for the data in column k of `y` are in column
`k`.
[residuals, rank, singular_values, rcond] : list
These values are only returned if ``full == True``
- residuals -- sum of squared residuals of the least squares fit
- rank -- the numerical rank of the scaled Vandermonde matrix
- singular_values -- singular values of the scaled Vandermonde matrix
- rcond -- value of `rcond`.
For more details, see `numpy.linalg.lstsq`.
Warns
-----
RankWarning
The rank of the coefficient matrix in the least-squares fit is
deficient. The warning is only raised if ``full = False``. The
warnings can be turned off by
>>> import warnings
>>> warnings.simplefilter('ignore', np.RankWarning)
See Also
--------
numpy.polynomial.chebyshev.chebfit
numpy.polynomial.legendre.legfit
numpy.polynomial.polynomial.polyfit
numpy.polynomial.hermite.hermfit
numpy.polynomial.laguerre.lagfit
hermeval : Evaluates a Hermite series.
hermevander : pseudo Vandermonde matrix of Hermite series.
hermeweight : HermiteE weight function.
numpy.linalg.lstsq : Computes a least-squares fit from the matrix.
scipy.interpolate.UnivariateSpline : Computes spline fits.
Notes
-----
The solution is the coefficients of the HermiteE series `p` that
minimizes the sum of the weighted squared errors
.. math:: E = \\sum_j w_j^2 * |y_j - p(x_j)|^2,
where the :math:`w_j` are the weights. This problem is solved by
setting up the (typically) overdetermined matrix equation
.. math:: V(x) * c = w * y,
where `V` is the pseudo Vandermonde matrix of `x`, the elements of `c`
are the coefficients to be solved for, and the elements of `y` are the
observed values. This equation is then solved using the singular value
decomposition of `V`.
If some of the singular values of `V` are so small that they are
neglected, then a `RankWarning` will be issued. This means that the
coefficient values may be poorly determined. Using a lower order fit
will usually get rid of the warning. The `rcond` parameter can also be
set to a value smaller than its default, but the resulting fit may be
spurious and have large contributions from roundoff error.
Fits using HermiteE series are probably most useful when the data can
be approximated by ``sqrt(w(x)) * p(x)``, where `w(x)` is the HermiteE
weight. In that case the weight ``sqrt(w(x[i]))`` should be used
together with data values ``y[i]/sqrt(w(x[i]))``. The weight function is
available as `hermeweight`.
References
----------
.. [1] Wikipedia, "Curve fitting",
https://en.wikipedia.org/wiki/Curve_fitting
Examples
--------
>>> from numpy.polynomial.hermite_e import hermefit, hermeval
>>> x = np.linspace(-10, 10)
>>> np.random.seed(123)
>>> err = np.random.randn(len(x))/10
>>> y = hermeval(x, [1, 2, 3]) + err
>>> hermefit(x, y, 2)
array([ 1.01690445, 1.99951418, 2.99948696]) # may vary
"""
return pu._fit(hermevander, x, y, deg, rcond, full, w) | Least squares fit of Hermite series to data. Return the coefficients of a HermiteE series of degree `deg` that is the least squares fit to the data values `y` given at points `x`. If `y` is 1-D the returned coefficients will also be 1-D. If `y` is 2-D multiple fits are done, one for each column of `y`, and the resulting coefficients are stored in the corresponding columns of a 2-D return. The fitted polynomial(s) are in the form .. math:: p(x) = c_0 + c_1 * He_1(x) + ... + c_n * He_n(x), where `n` is `deg`. Parameters ---------- x : array_like, shape (M,) x-coordinates of the M sample points ``(x[i], y[i])``. y : array_like, shape (M,) or (M, K) y-coordinates of the sample points. Several data sets of sample points sharing the same x-coordinates can be fitted at once by passing in a 2D-array that contains one dataset per column. deg : int or 1-D array_like Degree(s) of the fitting polynomials. If `deg` is a single integer all terms up to and including the `deg`'th term are included in the fit. For NumPy versions >= 1.11.0 a list of integers specifying the degrees of the terms to include may be used instead. rcond : float, optional Relative condition number of the fit. Singular values smaller than this relative to the largest singular value will be ignored. The default value is len(x)*eps, where eps is the relative precision of the float type, about 2e-16 in most cases. full : bool, optional Switch determining nature of return value. When it is False (the default) just the coefficients are returned, when True diagnostic information from the singular value decomposition is also returned. w : array_like, shape (`M`,), optional Weights. If not None, the weight ``w[i]`` applies to the unsquared residual ``y[i] - y_hat[i]`` at ``x[i]``. Ideally the weights are chosen so that the errors of the products ``w[i]*y[i]`` all have the same variance. When using inverse-variance weighting, use ``w[i] = 1/sigma(y[i])``. The default value is None. Returns ------- coef : ndarray, shape (M,) or (M, K) Hermite coefficients ordered from low to high. If `y` was 2-D, the coefficients for the data in column k of `y` are in column `k`. [residuals, rank, singular_values, rcond] : list These values are only returned if ``full == True`` - residuals -- sum of squared residuals of the least squares fit - rank -- the numerical rank of the scaled Vandermonde matrix - singular_values -- singular values of the scaled Vandermonde matrix - rcond -- value of `rcond`. For more details, see `numpy.linalg.lstsq`. Warns ----- RankWarning The rank of the coefficient matrix in the least-squares fit is deficient. The warning is only raised if ``full = False``. The warnings can be turned off by >>> import warnings >>> warnings.simplefilter('ignore', np.RankWarning) See Also -------- numpy.polynomial.chebyshev.chebfit numpy.polynomial.legendre.legfit numpy.polynomial.polynomial.polyfit numpy.polynomial.hermite.hermfit numpy.polynomial.laguerre.lagfit hermeval : Evaluates a Hermite series. hermevander : pseudo Vandermonde matrix of Hermite series. hermeweight : HermiteE weight function. numpy.linalg.lstsq : Computes a least-squares fit from the matrix. scipy.interpolate.UnivariateSpline : Computes spline fits. Notes ----- The solution is the coefficients of the HermiteE series `p` that minimizes the sum of the weighted squared errors .. math:: E = \\sum_j w_j^2 * |y_j - p(x_j)|^2, where the :math:`w_j` are the weights. This problem is solved by setting up the (typically) overdetermined matrix equation .. math:: V(x) * c = w * y, where `V` is the pseudo Vandermonde matrix of `x`, the elements of `c` are the coefficients to be solved for, and the elements of `y` are the observed values. This equation is then solved using the singular value decomposition of `V`. If some of the singular values of `V` are so small that they are neglected, then a `RankWarning` will be issued. This means that the coefficient values may be poorly determined. Using a lower order fit will usually get rid of the warning. The `rcond` parameter can also be set to a value smaller than its default, but the resulting fit may be spurious and have large contributions from roundoff error. Fits using HermiteE series are probably most useful when the data can be approximated by ``sqrt(w(x)) * p(x)``, where `w(x)` is the HermiteE weight. In that case the weight ``sqrt(w(x[i]))`` should be used together with data values ``y[i]/sqrt(w(x[i]))``. The weight function is available as `hermeweight`. References ---------- .. [1] Wikipedia, "Curve fitting", https://en.wikipedia.org/wiki/Curve_fitting Examples -------- >>> from numpy.polynomial.hermite_e import hermefit, hermeval >>> x = np.linspace(-10, 10) >>> np.random.seed(123) >>> err = np.random.randn(len(x))/10 >>> y = hermeval(x, [1, 2, 3]) + err >>> hermefit(x, y, 2) array([ 1.01690445, 1.99951418, 2.99948696]) # may vary |
169,841 | import numpy as np
import numpy.linalg as la
from numpy.core.multiarray import normalize_axis_index
from . import polyutils as pu
from ._polybase import ABCPolyBase
def hermecompanion(c):
"""
Return the scaled companion matrix of c.
The basis polynomials are scaled so that the companion matrix is
symmetric when `c` is an HermiteE basis polynomial. This provides
better eigenvalue estimates than the unscaled case and for basis
polynomials the eigenvalues are guaranteed to be real if
`numpy.linalg.eigvalsh` is used to obtain them.
Parameters
----------
c : array_like
1-D array of HermiteE series coefficients ordered from low to high
degree.
Returns
-------
mat : ndarray
Scaled companion matrix of dimensions (deg, deg).
Notes
-----
.. versionadded:: 1.7.0
"""
# c is a trimmed copy
[c] = pu.as_series([c])
if len(c) < 2:
raise ValueError('Series must have maximum degree of at least 1.')
if len(c) == 2:
return np.array([[-c[0]/c[1]]])
n = len(c) - 1
mat = np.zeros((n, n), dtype=c.dtype)
scl = np.hstack((1., 1./np.sqrt(np.arange(n - 1, 0, -1))))
scl = np.multiply.accumulate(scl)[::-1]
top = mat.reshape(-1)[1::n+1]
bot = mat.reshape(-1)[n::n+1]
top[...] = np.sqrt(np.arange(1, n))
bot[...] = top
mat[:, -1] -= scl*c[:-1]/c[-1]
return mat
The provided code snippet includes necessary dependencies for implementing the `hermeroots` function. Write a Python function `def hermeroots(c)` to solve the following problem:
Compute the roots of a HermiteE series. Return the roots (a.k.a. "zeros") of the polynomial .. math:: p(x) = \\sum_i c[i] * He_i(x). Parameters ---------- c : 1-D array_like 1-D array of coefficients. Returns ------- out : ndarray Array of the roots of the series. If all the roots are real, then `out` is also real, otherwise it is complex. See Also -------- numpy.polynomial.polynomial.polyroots numpy.polynomial.legendre.legroots numpy.polynomial.laguerre.lagroots numpy.polynomial.hermite.hermroots numpy.polynomial.chebyshev.chebroots Notes ----- The root estimates are obtained as the eigenvalues of the companion matrix, Roots far from the origin of the complex plane may have large errors due to the numerical instability of the series for such values. Roots with multiplicity greater than 1 will also show larger errors as the value of the series near such points is relatively insensitive to errors in the roots. Isolated roots near the origin can be improved by a few iterations of Newton's method. The HermiteE series basis polynomials aren't powers of `x` so the results of this function may seem unintuitive. Examples -------- >>> from numpy.polynomial.hermite_e import hermeroots, hermefromroots >>> coef = hermefromroots([-1, 0, 1]) >>> coef array([0., 2., 0., 1.]) >>> hermeroots(coef) array([-1., 0., 1.]) # may vary
Here is the function:
def hermeroots(c):
"""
Compute the roots of a HermiteE series.
Return the roots (a.k.a. "zeros") of the polynomial
.. math:: p(x) = \\sum_i c[i] * He_i(x).
Parameters
----------
c : 1-D array_like
1-D array of coefficients.
Returns
-------
out : ndarray
Array of the roots of the series. If all the roots are real,
then `out` is also real, otherwise it is complex.
See Also
--------
numpy.polynomial.polynomial.polyroots
numpy.polynomial.legendre.legroots
numpy.polynomial.laguerre.lagroots
numpy.polynomial.hermite.hermroots
numpy.polynomial.chebyshev.chebroots
Notes
-----
The root estimates are obtained as the eigenvalues of the companion
matrix, Roots far from the origin of the complex plane may have large
errors due to the numerical instability of the series for such
values. Roots with multiplicity greater than 1 will also show larger
errors as the value of the series near such points is relatively
insensitive to errors in the roots. Isolated roots near the origin can
be improved by a few iterations of Newton's method.
The HermiteE series basis polynomials aren't powers of `x` so the
results of this function may seem unintuitive.
Examples
--------
>>> from numpy.polynomial.hermite_e import hermeroots, hermefromroots
>>> coef = hermefromroots([-1, 0, 1])
>>> coef
array([0., 2., 0., 1.])
>>> hermeroots(coef)
array([-1., 0., 1.]) # may vary
"""
# c is a trimmed copy
[c] = pu.as_series([c])
if len(c) <= 1:
return np.array([], dtype=c.dtype)
if len(c) == 2:
return np.array([-c[0]/c[1]])
# rotated companion matrix reduces error
m = hermecompanion(c)[::-1,::-1]
r = la.eigvals(m)
r.sort()
return r | Compute the roots of a HermiteE series. Return the roots (a.k.a. "zeros") of the polynomial .. math:: p(x) = \\sum_i c[i] * He_i(x). Parameters ---------- c : 1-D array_like 1-D array of coefficients. Returns ------- out : ndarray Array of the roots of the series. If all the roots are real, then `out` is also real, otherwise it is complex. See Also -------- numpy.polynomial.polynomial.polyroots numpy.polynomial.legendre.legroots numpy.polynomial.laguerre.lagroots numpy.polynomial.hermite.hermroots numpy.polynomial.chebyshev.chebroots Notes ----- The root estimates are obtained as the eigenvalues of the companion matrix, Roots far from the origin of the complex plane may have large errors due to the numerical instability of the series for such values. Roots with multiplicity greater than 1 will also show larger errors as the value of the series near such points is relatively insensitive to errors in the roots. Isolated roots near the origin can be improved by a few iterations of Newton's method. The HermiteE series basis polynomials aren't powers of `x` so the results of this function may seem unintuitive. Examples -------- >>> from numpy.polynomial.hermite_e import hermeroots, hermefromroots >>> coef = hermefromroots([-1, 0, 1]) >>> coef array([0., 2., 0., 1.]) >>> hermeroots(coef) array([-1., 0., 1.]) # may vary |
169,842 | import numpy as np
import numpy.linalg as la
from numpy.core.multiarray import normalize_axis_index
from . import polyutils as pu
from ._polybase import ABCPolyBase
def hermecompanion(c):
"""
Return the scaled companion matrix of c.
The basis polynomials are scaled so that the companion matrix is
symmetric when `c` is an HermiteE basis polynomial. This provides
better eigenvalue estimates than the unscaled case and for basis
polynomials the eigenvalues are guaranteed to be real if
`numpy.linalg.eigvalsh` is used to obtain them.
Parameters
----------
c : array_like
1-D array of HermiteE series coefficients ordered from low to high
degree.
Returns
-------
mat : ndarray
Scaled companion matrix of dimensions (deg, deg).
Notes
-----
.. versionadded:: 1.7.0
"""
# c is a trimmed copy
[c] = pu.as_series([c])
if len(c) < 2:
raise ValueError('Series must have maximum degree of at least 1.')
if len(c) == 2:
return np.array([[-c[0]/c[1]]])
n = len(c) - 1
mat = np.zeros((n, n), dtype=c.dtype)
scl = np.hstack((1., 1./np.sqrt(np.arange(n - 1, 0, -1))))
scl = np.multiply.accumulate(scl)[::-1]
top = mat.reshape(-1)[1::n+1]
bot = mat.reshape(-1)[n::n+1]
top[...] = np.sqrt(np.arange(1, n))
bot[...] = top
mat[:, -1] -= scl*c[:-1]/c[-1]
return mat
def _normed_hermite_e_n(x, n):
"""
Evaluate a normalized HermiteE polynomial.
Compute the value of the normalized HermiteE polynomial of degree ``n``
at the points ``x``.
Parameters
----------
x : ndarray of double.
Points at which to evaluate the function
n : int
Degree of the normalized HermiteE function to be evaluated.
Returns
-------
values : ndarray
The shape of the return value is described above.
Notes
-----
.. versionadded:: 1.10.0
This function is needed for finding the Gauss points and integration
weights for high degrees. The values of the standard HermiteE functions
overflow when n >= 207.
"""
if n == 0:
return np.full(x.shape, 1/np.sqrt(np.sqrt(2*np.pi)))
c0 = 0.
c1 = 1./np.sqrt(np.sqrt(2*np.pi))
nd = float(n)
for i in range(n - 1):
tmp = c0
c0 = -c1*np.sqrt((nd - 1.)/nd)
c1 = tmp + c1*x*np.sqrt(1./nd)
nd = nd - 1.0
return c0 + c1*x
The provided code snippet includes necessary dependencies for implementing the `hermegauss` function. Write a Python function `def hermegauss(deg)` to solve the following problem:
Gauss-HermiteE quadrature. Computes the sample points and weights for Gauss-HermiteE quadrature. These sample points and weights will correctly integrate polynomials of degree :math:`2*deg - 1` or less over the interval :math:`[-\\inf, \\inf]` with the weight function :math:`f(x) = \\exp(-x^2/2)`. Parameters ---------- deg : int Number of sample points and weights. It must be >= 1. Returns ------- x : ndarray 1-D ndarray containing the sample points. y : ndarray 1-D ndarray containing the weights. Notes ----- .. versionadded:: 1.7.0 The results have only been tested up to degree 100, higher degrees may be problematic. The weights are determined by using the fact that .. math:: w_k = c / (He'_n(x_k) * He_{n-1}(x_k)) where :math:`c` is a constant independent of :math:`k` and :math:`x_k` is the k'th root of :math:`He_n`, and then scaling the results to get the right value when integrating 1.
Here is the function:
def hermegauss(deg):
"""
Gauss-HermiteE quadrature.
Computes the sample points and weights for Gauss-HermiteE quadrature.
These sample points and weights will correctly integrate polynomials of
degree :math:`2*deg - 1` or less over the interval :math:`[-\\inf, \\inf]`
with the weight function :math:`f(x) = \\exp(-x^2/2)`.
Parameters
----------
deg : int
Number of sample points and weights. It must be >= 1.
Returns
-------
x : ndarray
1-D ndarray containing the sample points.
y : ndarray
1-D ndarray containing the weights.
Notes
-----
.. versionadded:: 1.7.0
The results have only been tested up to degree 100, higher degrees may
be problematic. The weights are determined by using the fact that
.. math:: w_k = c / (He'_n(x_k) * He_{n-1}(x_k))
where :math:`c` is a constant independent of :math:`k` and :math:`x_k`
is the k'th root of :math:`He_n`, and then scaling the results to get
the right value when integrating 1.
"""
ideg = pu._deprecate_as_int(deg, "deg")
if ideg <= 0:
raise ValueError("deg must be a positive integer")
# first approximation of roots. We use the fact that the companion
# matrix is symmetric in this case in order to obtain better zeros.
c = np.array([0]*deg + [1])
m = hermecompanion(c)
x = la.eigvalsh(m)
# improve roots by one application of Newton
dy = _normed_hermite_e_n(x, ideg)
df = _normed_hermite_e_n(x, ideg - 1) * np.sqrt(ideg)
x -= dy/df
# compute the weights. We scale the factor to avoid possible numerical
# overflow.
fm = _normed_hermite_e_n(x, ideg - 1)
fm /= np.abs(fm).max()
w = 1/(fm * fm)
# for Hermite_e we can also symmetrize
w = (w + w[::-1])/2
x = (x - x[::-1])/2
# scale w to get the right value
w *= np.sqrt(2*np.pi) / w.sum()
return x, w | Gauss-HermiteE quadrature. Computes the sample points and weights for Gauss-HermiteE quadrature. These sample points and weights will correctly integrate polynomials of degree :math:`2*deg - 1` or less over the interval :math:`[-\\inf, \\inf]` with the weight function :math:`f(x) = \\exp(-x^2/2)`. Parameters ---------- deg : int Number of sample points and weights. It must be >= 1. Returns ------- x : ndarray 1-D ndarray containing the sample points. y : ndarray 1-D ndarray containing the weights. Notes ----- .. versionadded:: 1.7.0 The results have only been tested up to degree 100, higher degrees may be problematic. The weights are determined by using the fact that .. math:: w_k = c / (He'_n(x_k) * He_{n-1}(x_k)) where :math:`c` is a constant independent of :math:`k` and :math:`x_k` is the k'th root of :math:`He_n`, and then scaling the results to get the right value when integrating 1. |
169,843 | import numpy as np
import numpy.linalg as la
from numpy.core.multiarray import normalize_axis_index
from . import polyutils as pu
from ._polybase import ABCPolyBase
The provided code snippet includes necessary dependencies for implementing the `hermeweight` function. Write a Python function `def hermeweight(x)` to solve the following problem:
Weight function of the Hermite_e polynomials. The weight function is :math:`\\exp(-x^2/2)` and the interval of integration is :math:`[-\\inf, \\inf]`. the HermiteE polynomials are orthogonal, but not normalized, with respect to this weight function. Parameters ---------- x : array_like Values at which the weight function will be computed. Returns ------- w : ndarray The weight function at `x`. Notes ----- .. versionadded:: 1.7.0
Here is the function:
def hermeweight(x):
"""Weight function of the Hermite_e polynomials.
The weight function is :math:`\\exp(-x^2/2)` and the interval of
integration is :math:`[-\\inf, \\inf]`. the HermiteE polynomials are
orthogonal, but not normalized, with respect to this weight function.
Parameters
----------
x : array_like
Values at which the weight function will be computed.
Returns
-------
w : ndarray
The weight function at `x`.
Notes
-----
.. versionadded:: 1.7.0
"""
w = np.exp(-.5*x**2)
return w | Weight function of the Hermite_e polynomials. The weight function is :math:`\\exp(-x^2/2)` and the interval of integration is :math:`[-\\inf, \\inf]`. the HermiteE polynomials are orthogonal, but not normalized, with respect to this weight function. Parameters ---------- x : array_like Values at which the weight function will be computed. Returns ------- w : ndarray The weight function at `x`. Notes ----- .. versionadded:: 1.7.0 |
169,897 | import operator
import functools
import warnings
import numpy as np
from numpy.core.multiarray import dragon4_positional, dragon4_scientific
from numpy.core.umath import absolute
def as_series(alist, trim=True):
"""
Return argument as a list of 1-d arrays.
The returned list contains array(s) of dtype double, complex double, or
object. A 1-d argument of shape ``(N,)`` is parsed into ``N`` arrays of
size one; a 2-d argument of shape ``(M,N)`` is parsed into ``M`` arrays
of size ``N`` (i.e., is "parsed by row"); and a higher dimensional array
raises a Value Error if it is not first reshaped into either a 1-d or 2-d
array.
Parameters
----------
alist : array_like
A 1- or 2-d array_like
trim : boolean, optional
When True, trailing zeros are removed from the inputs.
When False, the inputs are passed through intact.
Returns
-------
[a1, a2,...] : list of 1-D arrays
A copy of the input data as a list of 1-d arrays.
Raises
------
ValueError
Raised when `as_series` cannot convert its input to 1-d arrays, or at
least one of the resulting arrays is empty.
Examples
--------
>>> from numpy.polynomial import polyutils as pu
>>> a = np.arange(4)
>>> pu.as_series(a)
[array([0.]), array([1.]), array([2.]), array([3.])]
>>> b = np.arange(6).reshape((2,3))
>>> pu.as_series(b)
[array([0., 1., 2.]), array([3., 4., 5.])]
>>> pu.as_series((1, np.arange(3), np.arange(2, dtype=np.float16)))
[array([1.]), array([0., 1., 2.]), array([0., 1.])]
>>> pu.as_series([2, [1.1, 0.]])
[array([2.]), array([1.1])]
>>> pu.as_series([2, [1.1, 0.]], trim=False)
[array([2.]), array([1.1, 0. ])]
"""
arrays = [np.array(a, ndmin=1, copy=False) for a in alist]
if min([a.size for a in arrays]) == 0:
raise ValueError("Coefficient array is empty")
if any(a.ndim != 1 for a in arrays):
raise ValueError("Coefficient array is not 1-d")
if trim:
arrays = [trimseq(a) for a in arrays]
if any(a.dtype == np.dtype(object) for a in arrays):
ret = []
for a in arrays:
if a.dtype != np.dtype(object):
tmp = np.empty(len(a), dtype=np.dtype(object))
tmp[:] = a[:]
ret.append(tmp)
else:
ret.append(a.copy())
else:
try:
dtype = np.common_type(*arrays)
except Exception as e:
raise ValueError("Coefficient arrays have no common type") from e
ret = [np.array(a, copy=True, dtype=dtype) for a in arrays]
return ret
The provided code snippet includes necessary dependencies for implementing the `trimcoef` function. Write a Python function `def trimcoef(c, tol=0)` to solve the following problem:
Remove "small" "trailing" coefficients from a polynomial. "Small" means "small in absolute value" and is controlled by the parameter `tol`; "trailing" means highest order coefficient(s), e.g., in ``[0, 1, 1, 0, 0]`` (which represents ``0 + x + x**2 + 0*x**3 + 0*x**4``) both the 3-rd and 4-th order coefficients would be "trimmed." Parameters ---------- c : array_like 1-d array of coefficients, ordered from lowest order to highest. tol : number, optional Trailing (i.e., highest order) elements with absolute value less than or equal to `tol` (default value is zero) are removed. Returns ------- trimmed : ndarray 1-d array with trailing zeros removed. If the resulting series would be empty, a series containing a single zero is returned. Raises ------ ValueError If `tol` < 0 See Also -------- trimseq Examples -------- >>> from numpy.polynomial import polyutils as pu >>> pu.trimcoef((0,0,3,0,5,0,0)) array([0., 0., 3., 0., 5.]) >>> pu.trimcoef((0,0,1e-3,0,1e-5,0,0),1e-3) # item == tol is trimmed array([0.]) >>> i = complex(0,1) # works for complex >>> pu.trimcoef((3e-4,1e-3*(1-i),5e-4,2e-5*(1+i)), 1e-3) array([0.0003+0.j , 0.001 -0.001j])
Here is the function:
def trimcoef(c, tol=0):
"""
Remove "small" "trailing" coefficients from a polynomial.
"Small" means "small in absolute value" and is controlled by the
parameter `tol`; "trailing" means highest order coefficient(s), e.g., in
``[0, 1, 1, 0, 0]`` (which represents ``0 + x + x**2 + 0*x**3 + 0*x**4``)
both the 3-rd and 4-th order coefficients would be "trimmed."
Parameters
----------
c : array_like
1-d array of coefficients, ordered from lowest order to highest.
tol : number, optional
Trailing (i.e., highest order) elements with absolute value less
than or equal to `tol` (default value is zero) are removed.
Returns
-------
trimmed : ndarray
1-d array with trailing zeros removed. If the resulting series
would be empty, a series containing a single zero is returned.
Raises
------
ValueError
If `tol` < 0
See Also
--------
trimseq
Examples
--------
>>> from numpy.polynomial import polyutils as pu
>>> pu.trimcoef((0,0,3,0,5,0,0))
array([0., 0., 3., 0., 5.])
>>> pu.trimcoef((0,0,1e-3,0,1e-5,0,0),1e-3) # item == tol is trimmed
array([0.])
>>> i = complex(0,1) # works for complex
>>> pu.trimcoef((3e-4,1e-3*(1-i),5e-4,2e-5*(1+i)), 1e-3)
array([0.0003+0.j , 0.001 -0.001j])
"""
if tol < 0:
raise ValueError("tol must be non-negative")
[c] = as_series([c])
[ind] = np.nonzero(np.abs(c) > tol)
if len(ind) == 0:
return c[:1]*0
else:
return c[:ind[-1] + 1].copy() | Remove "small" "trailing" coefficients from a polynomial. "Small" means "small in absolute value" and is controlled by the parameter `tol`; "trailing" means highest order coefficient(s), e.g., in ``[0, 1, 1, 0, 0]`` (which represents ``0 + x + x**2 + 0*x**3 + 0*x**4``) both the 3-rd and 4-th order coefficients would be "trimmed." Parameters ---------- c : array_like 1-d array of coefficients, ordered from lowest order to highest. tol : number, optional Trailing (i.e., highest order) elements with absolute value less than or equal to `tol` (default value is zero) are removed. Returns ------- trimmed : ndarray 1-d array with trailing zeros removed. If the resulting series would be empty, a series containing a single zero is returned. Raises ------ ValueError If `tol` < 0 See Also -------- trimseq Examples -------- >>> from numpy.polynomial import polyutils as pu >>> pu.trimcoef((0,0,3,0,5,0,0)) array([0., 0., 3., 0., 5.]) >>> pu.trimcoef((0,0,1e-3,0,1e-5,0,0),1e-3) # item == tol is trimmed array([0.]) >>> i = complex(0,1) # works for complex >>> pu.trimcoef((3e-4,1e-3*(1-i),5e-4,2e-5*(1+i)), 1e-3) array([0.0003+0.j , 0.001 -0.001j]) |
169,898 | import operator
import functools
import warnings
import numpy as np
from numpy.core.multiarray import dragon4_positional, dragon4_scientific
from numpy.core.umath import absolute
def as_series(alist, trim=True):
"""
Return argument as a list of 1-d arrays.
The returned list contains array(s) of dtype double, complex double, or
object. A 1-d argument of shape ``(N,)`` is parsed into ``N`` arrays of
size one; a 2-d argument of shape ``(M,N)`` is parsed into ``M`` arrays
of size ``N`` (i.e., is "parsed by row"); and a higher dimensional array
raises a Value Error if it is not first reshaped into either a 1-d or 2-d
array.
Parameters
----------
alist : array_like
A 1- or 2-d array_like
trim : boolean, optional
When True, trailing zeros are removed from the inputs.
When False, the inputs are passed through intact.
Returns
-------
[a1, a2,...] : list of 1-D arrays
A copy of the input data as a list of 1-d arrays.
Raises
------
ValueError
Raised when `as_series` cannot convert its input to 1-d arrays, or at
least one of the resulting arrays is empty.
Examples
--------
>>> from numpy.polynomial import polyutils as pu
>>> a = np.arange(4)
>>> pu.as_series(a)
[array([0.]), array([1.]), array([2.]), array([3.])]
>>> b = np.arange(6).reshape((2,3))
>>> pu.as_series(b)
[array([0., 1., 2.]), array([3., 4., 5.])]
>>> pu.as_series((1, np.arange(3), np.arange(2, dtype=np.float16)))
[array([1.]), array([0., 1., 2.]), array([0., 1.])]
>>> pu.as_series([2, [1.1, 0.]])
[array([2.]), array([1.1])]
>>> pu.as_series([2, [1.1, 0.]], trim=False)
[array([2.]), array([1.1, 0. ])]
"""
arrays = [np.array(a, ndmin=1, copy=False) for a in alist]
if min([a.size for a in arrays]) == 0:
raise ValueError("Coefficient array is empty")
if any(a.ndim != 1 for a in arrays):
raise ValueError("Coefficient array is not 1-d")
if trim:
arrays = [trimseq(a) for a in arrays]
if any(a.dtype == np.dtype(object) for a in arrays):
ret = []
for a in arrays:
if a.dtype != np.dtype(object):
tmp = np.empty(len(a), dtype=np.dtype(object))
tmp[:] = a[:]
ret.append(tmp)
else:
ret.append(a.copy())
else:
try:
dtype = np.common_type(*arrays)
except Exception as e:
raise ValueError("Coefficient arrays have no common type") from e
ret = [np.array(a, copy=True, dtype=dtype) for a in arrays]
return ret
The provided code snippet includes necessary dependencies for implementing the `getdomain` function. Write a Python function `def getdomain(x)` to solve the following problem:
Return a domain suitable for given abscissae. Find a domain suitable for a polynomial or Chebyshev series defined at the values supplied. Parameters ---------- x : array_like 1-d array of abscissae whose domain will be determined. Returns ------- domain : ndarray 1-d array containing two values. If the inputs are complex, then the two returned points are the lower left and upper right corners of the smallest rectangle (aligned with the axes) in the complex plane containing the points `x`. If the inputs are real, then the two points are the ends of the smallest interval containing the points `x`. See Also -------- mapparms, mapdomain Examples -------- >>> from numpy.polynomial import polyutils as pu >>> points = np.arange(4)**2 - 5; points array([-5, -4, -1, 4]) >>> pu.getdomain(points) array([-5., 4.]) >>> c = np.exp(complex(0,1)*np.pi*np.arange(12)/6) # unit circle >>> pu.getdomain(c) array([-1.-1.j, 1.+1.j])
Here is the function:
def getdomain(x):
"""
Return a domain suitable for given abscissae.
Find a domain suitable for a polynomial or Chebyshev series
defined at the values supplied.
Parameters
----------
x : array_like
1-d array of abscissae whose domain will be determined.
Returns
-------
domain : ndarray
1-d array containing two values. If the inputs are complex, then
the two returned points are the lower left and upper right corners
of the smallest rectangle (aligned with the axes) in the complex
plane containing the points `x`. If the inputs are real, then the
two points are the ends of the smallest interval containing the
points `x`.
See Also
--------
mapparms, mapdomain
Examples
--------
>>> from numpy.polynomial import polyutils as pu
>>> points = np.arange(4)**2 - 5; points
array([-5, -4, -1, 4])
>>> pu.getdomain(points)
array([-5., 4.])
>>> c = np.exp(complex(0,1)*np.pi*np.arange(12)/6) # unit circle
>>> pu.getdomain(c)
array([-1.-1.j, 1.+1.j])
"""
[x] = as_series([x], trim=False)
if x.dtype.char in np.typecodes['Complex']:
rmin, rmax = x.real.min(), x.real.max()
imin, imax = x.imag.min(), x.imag.max()
return np.array((complex(rmin, imin), complex(rmax, imax)))
else:
return np.array((x.min(), x.max())) | Return a domain suitable for given abscissae. Find a domain suitable for a polynomial or Chebyshev series defined at the values supplied. Parameters ---------- x : array_like 1-d array of abscissae whose domain will be determined. Returns ------- domain : ndarray 1-d array containing two values. If the inputs are complex, then the two returned points are the lower left and upper right corners of the smallest rectangle (aligned with the axes) in the complex plane containing the points `x`. If the inputs are real, then the two points are the ends of the smallest interval containing the points `x`. See Also -------- mapparms, mapdomain Examples -------- >>> from numpy.polynomial import polyutils as pu >>> points = np.arange(4)**2 - 5; points array([-5, -4, -1, 4]) >>> pu.getdomain(points) array([-5., 4.]) >>> c = np.exp(complex(0,1)*np.pi*np.arange(12)/6) # unit circle >>> pu.getdomain(c) array([-1.-1.j, 1.+1.j]) |
169,899 | import operator
import functools
import warnings
import numpy as np
from numpy.core.multiarray import dragon4_positional, dragon4_scientific
from numpy.core.umath import absolute
def mapparms(old, new):
"""
Linear map parameters between domains.
Return the parameters of the linear map ``offset + scale*x`` that maps
`old` to `new` such that ``old[i] -> new[i]``, ``i = 0, 1``.
Parameters
----------
old, new : array_like
Domains. Each domain must (successfully) convert to a 1-d array
containing precisely two values.
Returns
-------
offset, scale : scalars
The map ``L(x) = offset + scale*x`` maps the first domain to the
second.
See Also
--------
getdomain, mapdomain
Notes
-----
Also works for complex numbers, and thus can be used to calculate the
parameters required to map any line in the complex plane to any other
line therein.
Examples
--------
>>> from numpy.polynomial import polyutils as pu
>>> pu.mapparms((-1,1),(-1,1))
(0.0, 1.0)
>>> pu.mapparms((1,-1),(-1,1))
(-0.0, -1.0)
>>> i = complex(0,1)
>>> pu.mapparms((-i,-1),(1,i))
((1+1j), (1-0j))
"""
oldlen = old[1] - old[0]
newlen = new[1] - new[0]
off = (old[1]*new[0] - old[0]*new[1])/oldlen
scl = newlen/oldlen
return off, scl
The provided code snippet includes necessary dependencies for implementing the `mapdomain` function. Write a Python function `def mapdomain(x, old, new)` to solve the following problem:
Apply linear map to input points. The linear map ``offset + scale*x`` that maps the domain `old` to the domain `new` is applied to the points `x`. Parameters ---------- x : array_like Points to be mapped. If `x` is a subtype of ndarray the subtype will be preserved. old, new : array_like The two domains that determine the map. Each must (successfully) convert to 1-d arrays containing precisely two values. Returns ------- x_out : ndarray Array of points of the same shape as `x`, after application of the linear map between the two domains. See Also -------- getdomain, mapparms Notes ----- Effectively, this implements: .. math:: x\\_out = new[0] + m(x - old[0]) where .. math:: m = \\frac{new[1]-new[0]}{old[1]-old[0]} Examples -------- >>> from numpy.polynomial import polyutils as pu >>> old_domain = (-1,1) >>> new_domain = (0,2*np.pi) >>> x = np.linspace(-1,1,6); x array([-1. , -0.6, -0.2, 0.2, 0.6, 1. ]) >>> x_out = pu.mapdomain(x, old_domain, new_domain); x_out array([ 0. , 1.25663706, 2.51327412, 3.76991118, 5.02654825, # may vary 6.28318531]) >>> x - pu.mapdomain(x_out, new_domain, old_domain) array([0., 0., 0., 0., 0., 0.]) Also works for complex numbers (and thus can be used to map any line in the complex plane to any other line therein). >>> i = complex(0,1) >>> old = (-1 - i, 1 + i) >>> new = (-1 + i, 1 - i) >>> z = np.linspace(old[0], old[1], 6); z array([-1. -1.j , -0.6-0.6j, -0.2-0.2j, 0.2+0.2j, 0.6+0.6j, 1. +1.j ]) >>> new_z = pu.mapdomain(z, old, new); new_z array([-1.0+1.j , -0.6+0.6j, -0.2+0.2j, 0.2-0.2j, 0.6-0.6j, 1.0-1.j ]) # may vary
Here is the function:
def mapdomain(x, old, new):
"""
Apply linear map to input points.
The linear map ``offset + scale*x`` that maps the domain `old` to
the domain `new` is applied to the points `x`.
Parameters
----------
x : array_like
Points to be mapped. If `x` is a subtype of ndarray the subtype
will be preserved.
old, new : array_like
The two domains that determine the map. Each must (successfully)
convert to 1-d arrays containing precisely two values.
Returns
-------
x_out : ndarray
Array of points of the same shape as `x`, after application of the
linear map between the two domains.
See Also
--------
getdomain, mapparms
Notes
-----
Effectively, this implements:
.. math::
x\\_out = new[0] + m(x - old[0])
where
.. math::
m = \\frac{new[1]-new[0]}{old[1]-old[0]}
Examples
--------
>>> from numpy.polynomial import polyutils as pu
>>> old_domain = (-1,1)
>>> new_domain = (0,2*np.pi)
>>> x = np.linspace(-1,1,6); x
array([-1. , -0.6, -0.2, 0.2, 0.6, 1. ])
>>> x_out = pu.mapdomain(x, old_domain, new_domain); x_out
array([ 0. , 1.25663706, 2.51327412, 3.76991118, 5.02654825, # may vary
6.28318531])
>>> x - pu.mapdomain(x_out, new_domain, old_domain)
array([0., 0., 0., 0., 0., 0.])
Also works for complex numbers (and thus can be used to map any line in
the complex plane to any other line therein).
>>> i = complex(0,1)
>>> old = (-1 - i, 1 + i)
>>> new = (-1 + i, 1 - i)
>>> z = np.linspace(old[0], old[1], 6); z
array([-1. -1.j , -0.6-0.6j, -0.2-0.2j, 0.2+0.2j, 0.6+0.6j, 1. +1.j ])
>>> new_z = pu.mapdomain(z, old, new); new_z
array([-1.0+1.j , -0.6+0.6j, -0.2+0.2j, 0.2-0.2j, 0.6-0.6j, 1.0-1.j ]) # may vary
"""
x = np.asanyarray(x)
off, scl = mapparms(old, new)
return off + scl*x | Apply linear map to input points. The linear map ``offset + scale*x`` that maps the domain `old` to the domain `new` is applied to the points `x`. Parameters ---------- x : array_like Points to be mapped. If `x` is a subtype of ndarray the subtype will be preserved. old, new : array_like The two domains that determine the map. Each must (successfully) convert to 1-d arrays containing precisely two values. Returns ------- x_out : ndarray Array of points of the same shape as `x`, after application of the linear map between the two domains. See Also -------- getdomain, mapparms Notes ----- Effectively, this implements: .. math:: x\\_out = new[0] + m(x - old[0]) where .. math:: m = \\frac{new[1]-new[0]}{old[1]-old[0]} Examples -------- >>> from numpy.polynomial import polyutils as pu >>> old_domain = (-1,1) >>> new_domain = (0,2*np.pi) >>> x = np.linspace(-1,1,6); x array([-1. , -0.6, -0.2, 0.2, 0.6, 1. ]) >>> x_out = pu.mapdomain(x, old_domain, new_domain); x_out array([ 0. , 1.25663706, 2.51327412, 3.76991118, 5.02654825, # may vary 6.28318531]) >>> x - pu.mapdomain(x_out, new_domain, old_domain) array([0., 0., 0., 0., 0., 0.]) Also works for complex numbers (and thus can be used to map any line in the complex plane to any other line therein). >>> i = complex(0,1) >>> old = (-1 - i, 1 + i) >>> new = (-1 + i, 1 - i) >>> z = np.linspace(old[0], old[1], 6); z array([-1. -1.j , -0.6-0.6j, -0.2-0.2j, 0.2+0.2j, 0.6+0.6j, 1. +1.j ]) >>> new_z = pu.mapdomain(z, old, new); new_z array([-1.0+1.j , -0.6+0.6j, -0.2+0.2j, 0.2-0.2j, 0.6-0.6j, 1.0-1.j ]) # may vary |
169,900 | import operator
import functools
import warnings
import numpy as np
from numpy.core.multiarray import dragon4_positional, dragon4_scientific
from numpy.core.umath import absolute
def format_float(x, parens=False):
if not np.issubdtype(type(x), np.floating):
return str(x)
opts = np.get_printoptions()
if np.isnan(x):
return opts['nanstr']
elif np.isinf(x):
return opts['infstr']
exp_format = False
if x != 0:
a = absolute(x)
if a >= 1.e8 or a < 10**min(0, -(opts['precision']-1)//2):
exp_format = True
trim, unique = '0', True
if opts['floatmode'] == 'fixed':
trim, unique = 'k', False
if exp_format:
s = dragon4_scientific(x, precision=opts['precision'],
unique=unique, trim=trim,
sign=opts['sign'] == '+')
if parens:
s = '(' + s + ')'
else:
s = dragon4_positional(x, precision=opts['precision'],
fractional=True,
unique=unique, trim=trim,
sign=opts['sign'] == '+')
return s | null |
169,938 | import os
from numpy import (
integer, ndarray, dtype as _dtype, asarray, frombuffer
)
from numpy.core.multiarray import _flagdict, flagsobj
The provided code snippet includes necessary dependencies for implementing the `_dummy` function. Write a Python function `def _dummy(*args, **kwds)` to solve the following problem:
Dummy object that raises an ImportError if ctypes is not available. Raises ------ ImportError If ctypes is not available.
Here is the function:
def _dummy(*args, **kwds):
"""
Dummy object that raises an ImportError if ctypes is not available.
Raises
------
ImportError
If ctypes is not available.
"""
raise ImportError("ctypes is not available.") | Dummy object that raises an ImportError if ctypes is not available. Raises ------ ImportError If ctypes is not available. |
169,939 | import os
from numpy import (
integer, ndarray, dtype as _dtype, asarray, frombuffer
)
from numpy.core.multiarray import _flagdict, flagsobj
try:
import ctypes
except ImportError:
ctypes = None
if ctypes is None:
load_library = _dummy
as_ctypes = _dummy
as_array = _dummy
from numpy import intp as c_intp
_ndptr_base = object
else:
import numpy.core._internal as nic
c_intp = nic._getintp_ctype()
del nic
_ndptr_base = ctypes.c_void_p
# Adapted from Albert Strasheim
if ctypes is not None:
_scalar_type_map = _get_scalar_type_map()
def get_shared_lib_extension(is_python_ext=False):
"""Return the correct file extension for shared libraries.
Parameters
----------
is_python_ext : bool, optional
Whether the shared library is a Python extension. Default is False.
Returns
-------
so_ext : str
The shared library extension.
Notes
-----
For Python shared libs, `so_ext` will typically be '.so' on Linux and OS X,
and '.pyd' on Windows. For Python >= 3.2 `so_ext` has a tag prepended on
POSIX systems according to PEP 3149.
"""
confvars = distutils.sysconfig.get_config_vars()
so_ext = confvars.get('EXT_SUFFIX', '')
if not is_python_ext:
# hardcode known values, config vars (including SHLIB_SUFFIX) are
# unreliable (see #3182)
# darwin, windows and debug linux are wrong in 3.3.1 and older
if (sys.platform.startswith('linux') or
sys.platform.startswith('gnukfreebsd')):
so_ext = '.so'
elif sys.platform.startswith('darwin'):
so_ext = '.dylib'
elif sys.platform.startswith('win'):
so_ext = '.dll'
else:
# fall back to config vars for unknown platforms
# fix long extension for Python >=3.2, see PEP 3149.
if 'SOABI' in confvars:
# Does nothing unless SOABI config var exists
so_ext = so_ext.replace('.' + confvars.get('SOABI'), '', 1)
return so_ext
The provided code snippet includes necessary dependencies for implementing the `load_library` function. Write a Python function `def load_library(libname, loader_path)` to solve the following problem:
It is possible to load a library using >>> lib = ctypes.cdll[<full_path_name>] # doctest: +SKIP But there are cross-platform considerations, such as library file extensions, plus the fact Windows will just load the first library it finds with that name. NumPy supplies the load_library function as a convenience. .. versionchanged:: 1.20.0 Allow libname and loader_path to take any :term:`python:path-like object`. Parameters ---------- libname : path-like Name of the library, which can have 'lib' as a prefix, but without an extension. loader_path : path-like Where the library can be found. Returns ------- ctypes.cdll[libpath] : library object A ctypes library object Raises ------ OSError If there is no library with the expected extension, or the library is defective and cannot be loaded.
Here is the function:
def load_library(libname, loader_path):
"""
It is possible to load a library using
>>> lib = ctypes.cdll[<full_path_name>] # doctest: +SKIP
But there are cross-platform considerations, such as library file extensions,
plus the fact Windows will just load the first library it finds with that name.
NumPy supplies the load_library function as a convenience.
.. versionchanged:: 1.20.0
Allow libname and loader_path to take any
:term:`python:path-like object`.
Parameters
----------
libname : path-like
Name of the library, which can have 'lib' as a prefix,
but without an extension.
loader_path : path-like
Where the library can be found.
Returns
-------
ctypes.cdll[libpath] : library object
A ctypes library object
Raises
------
OSError
If there is no library with the expected extension, or the
library is defective and cannot be loaded.
"""
if ctypes.__version__ < '1.0.1':
import warnings
warnings.warn("All features of ctypes interface may not work "
"with ctypes < 1.0.1", stacklevel=2)
# Convert path-like objects into strings
libname = os.fsdecode(libname)
loader_path = os.fsdecode(loader_path)
ext = os.path.splitext(libname)[1]
if not ext:
# Try to load library with platform-specific name, otherwise
# default to libname.[so|pyd]. Sometimes, these files are built
# erroneously on non-linux platforms.
from numpy.distutils.misc_util import get_shared_lib_extension
so_ext = get_shared_lib_extension()
libname_ext = [libname + so_ext]
# mac, windows and linux >= py3.2 shared library and loadable
# module have different extensions so try both
so_ext2 = get_shared_lib_extension(is_python_ext=True)
if not so_ext2 == so_ext:
libname_ext.insert(0, libname + so_ext2)
else:
libname_ext = [libname]
loader_path = os.path.abspath(loader_path)
if not os.path.isdir(loader_path):
libdir = os.path.dirname(loader_path)
else:
libdir = loader_path
for ln in libname_ext:
libpath = os.path.join(libdir, ln)
if os.path.exists(libpath):
try:
return ctypes.cdll[libpath]
except OSError:
## defective lib file
raise
## if no successful return in the libname_ext loop:
raise OSError("no file with expected extension") | It is possible to load a library using >>> lib = ctypes.cdll[<full_path_name>] # doctest: +SKIP But there are cross-platform considerations, such as library file extensions, plus the fact Windows will just load the first library it finds with that name. NumPy supplies the load_library function as a convenience. .. versionchanged:: 1.20.0 Allow libname and loader_path to take any :term:`python:path-like object`. Parameters ---------- libname : path-like Name of the library, which can have 'lib' as a prefix, but without an extension. loader_path : path-like Where the library can be found. Returns ------- ctypes.cdll[libpath] : library object A ctypes library object Raises ------ OSError If there is no library with the expected extension, or the library is defective and cannot be loaded. |
169,940 | import os
from numpy import (
integer, ndarray, dtype as _dtype, asarray, frombuffer
)
from numpy.core.multiarray import _flagdict, flagsobj
def _num_fromflags(flaglist):
num = 0
for val in flaglist:
num += _flagdict[val]
return num
def _flags_fromnum(num):
res = []
for key in _flagnames:
value = _flagdict[key]
if (num & value):
res.append(key)
return res
class _ndptr(_ndptr_base):
def from_param(cls, obj):
if not isinstance(obj, ndarray):
raise TypeError("argument must be an ndarray")
if cls._dtype_ is not None \
and obj.dtype != cls._dtype_:
raise TypeError("array must have data type %s" % cls._dtype_)
if cls._ndim_ is not None \
and obj.ndim != cls._ndim_:
raise TypeError("array must have %d dimension(s)" % cls._ndim_)
if cls._shape_ is not None \
and obj.shape != cls._shape_:
raise TypeError("array must have shape %s" % str(cls._shape_))
if cls._flags_ is not None \
and ((obj.flags.num & cls._flags_) != cls._flags_):
raise TypeError("array must have flags %s" %
_flags_fromnum(cls._flags_))
return obj.ctypes
class _concrete_ndptr(_ndptr):
"""
Like _ndptr, but with `_shape_` and `_dtype_` specified.
Notably, this means the pointer has enough information to reconstruct
the array, which is not generally true.
"""
def _check_retval_(self):
"""
This method is called when this class is used as the .restype
attribute for a shared-library function, to automatically wrap the
pointer into an array.
"""
return self.contents
def contents(self):
"""
Get an ndarray viewing the data pointed to by this pointer.
This mirrors the `contents` attribute of a normal ctypes pointer
"""
full_dtype = _dtype((self._dtype_, self._shape_))
full_ctype = ctypes.c_char * full_dtype.itemsize
buffer = ctypes.cast(self, ctypes.POINTER(full_ctype)).contents
return frombuffer(buffer, dtype=full_dtype).squeeze(axis=0)
_pointer_type_cache = {}
The provided code snippet includes necessary dependencies for implementing the `ndpointer` function. Write a Python function `def ndpointer(dtype=None, ndim=None, shape=None, flags=None)` to solve the following problem:
Array-checking restype/argtypes. An ndpointer instance is used to describe an ndarray in restypes and argtypes specifications. This approach is more flexible than using, for example, ``POINTER(c_double)``, since several restrictions can be specified, which are verified upon calling the ctypes function. These include data type, number of dimensions, shape and flags. If a given array does not satisfy the specified restrictions, a ``TypeError`` is raised. Parameters ---------- dtype : data-type, optional Array data-type. ndim : int, optional Number of array dimensions. shape : tuple of ints, optional Array shape. flags : str or tuple of str Array flags; may be one or more of: - C_CONTIGUOUS / C / CONTIGUOUS - F_CONTIGUOUS / F / FORTRAN - OWNDATA / O - WRITEABLE / W - ALIGNED / A - WRITEBACKIFCOPY / X Returns ------- klass : ndpointer type object A type object, which is an ``_ndtpr`` instance containing dtype, ndim, shape and flags information. Raises ------ TypeError If a given array does not satisfy the specified restrictions. Examples -------- >>> clib.somefunc.argtypes = [np.ctypeslib.ndpointer(dtype=np.float64, ... ndim=1, ... flags='C_CONTIGUOUS')] ... #doctest: +SKIP >>> clib.somefunc(np.array([1, 2, 3], dtype=np.float64)) ... #doctest: +SKIP
Here is the function:
def ndpointer(dtype=None, ndim=None, shape=None, flags=None):
"""
Array-checking restype/argtypes.
An ndpointer instance is used to describe an ndarray in restypes
and argtypes specifications. This approach is more flexible than
using, for example, ``POINTER(c_double)``, since several restrictions
can be specified, which are verified upon calling the ctypes function.
These include data type, number of dimensions, shape and flags. If a
given array does not satisfy the specified restrictions,
a ``TypeError`` is raised.
Parameters
----------
dtype : data-type, optional
Array data-type.
ndim : int, optional
Number of array dimensions.
shape : tuple of ints, optional
Array shape.
flags : str or tuple of str
Array flags; may be one or more of:
- C_CONTIGUOUS / C / CONTIGUOUS
- F_CONTIGUOUS / F / FORTRAN
- OWNDATA / O
- WRITEABLE / W
- ALIGNED / A
- WRITEBACKIFCOPY / X
Returns
-------
klass : ndpointer type object
A type object, which is an ``_ndtpr`` instance containing
dtype, ndim, shape and flags information.
Raises
------
TypeError
If a given array does not satisfy the specified restrictions.
Examples
--------
>>> clib.somefunc.argtypes = [np.ctypeslib.ndpointer(dtype=np.float64,
... ndim=1,
... flags='C_CONTIGUOUS')]
... #doctest: +SKIP
>>> clib.somefunc(np.array([1, 2, 3], dtype=np.float64))
... #doctest: +SKIP
"""
# normalize dtype to an Optional[dtype]
if dtype is not None:
dtype = _dtype(dtype)
# normalize flags to an Optional[int]
num = None
if flags is not None:
if isinstance(flags, str):
flags = flags.split(',')
elif isinstance(flags, (int, integer)):
num = flags
flags = _flags_fromnum(num)
elif isinstance(flags, flagsobj):
num = flags.num
flags = _flags_fromnum(num)
if num is None:
try:
flags = [x.strip().upper() for x in flags]
except Exception as e:
raise TypeError("invalid flags specification") from e
num = _num_fromflags(flags)
# normalize shape to an Optional[tuple]
if shape is not None:
try:
shape = tuple(shape)
except TypeError:
# single integer -> 1-tuple
shape = (shape,)
cache_key = (dtype, ndim, shape, num)
try:
return _pointer_type_cache[cache_key]
except KeyError:
pass
# produce a name for the new type
if dtype is None:
name = 'any'
elif dtype.names is not None:
name = str(id(dtype))
else:
name = dtype.str
if ndim is not None:
name += "_%dd" % ndim
if shape is not None:
name += "_"+"x".join(str(x) for x in shape)
if flags is not None:
name += "_"+"_".join(flags)
if dtype is not None and shape is not None:
base = _concrete_ndptr
else:
base = _ndptr
klass = type("ndpointer_%s"%name, (base,),
{"_dtype_": dtype,
"_shape_" : shape,
"_ndim_" : ndim,
"_flags_" : num})
_pointer_type_cache[cache_key] = klass
return klass | Array-checking restype/argtypes. An ndpointer instance is used to describe an ndarray in restypes and argtypes specifications. This approach is more flexible than using, for example, ``POINTER(c_double)``, since several restrictions can be specified, which are verified upon calling the ctypes function. These include data type, number of dimensions, shape and flags. If a given array does not satisfy the specified restrictions, a ``TypeError`` is raised. Parameters ---------- dtype : data-type, optional Array data-type. ndim : int, optional Number of array dimensions. shape : tuple of ints, optional Array shape. flags : str or tuple of str Array flags; may be one or more of: - C_CONTIGUOUS / C / CONTIGUOUS - F_CONTIGUOUS / F / FORTRAN - OWNDATA / O - WRITEABLE / W - ALIGNED / A - WRITEBACKIFCOPY / X Returns ------- klass : ndpointer type object A type object, which is an ``_ndtpr`` instance containing dtype, ndim, shape and flags information. Raises ------ TypeError If a given array does not satisfy the specified restrictions. Examples -------- >>> clib.somefunc.argtypes = [np.ctypeslib.ndpointer(dtype=np.float64, ... ndim=1, ... flags='C_CONTIGUOUS')] ... #doctest: +SKIP >>> clib.somefunc(np.array([1, 2, 3], dtype=np.float64)) ... #doctest: +SKIP |
169,941 | import os
from numpy import (
integer, ndarray, dtype as _dtype, asarray, frombuffer
)
from numpy.core.multiarray import _flagdict, flagsobj
try:
import ctypes
except ImportError:
ctypes = None
if ctypes is None:
load_library = _dummy
as_ctypes = _dummy
as_array = _dummy
from numpy import intp as c_intp
_ndptr_base = object
else:
import numpy.core._internal as nic
c_intp = nic._getintp_ctype()
del nic
_ndptr_base = ctypes.c_void_p
# Adapted from Albert Strasheim
if ctypes is not None:
_scalar_type_map = _get_scalar_type_map()
The provided code snippet includes necessary dependencies for implementing the `_get_scalar_type_map` function. Write a Python function `def _get_scalar_type_map()` to solve the following problem:
Return a dictionary mapping native endian scalar dtype to ctypes types
Here is the function:
def _get_scalar_type_map():
"""
Return a dictionary mapping native endian scalar dtype to ctypes types
"""
ct = ctypes
simple_types = [
ct.c_byte, ct.c_short, ct.c_int, ct.c_long, ct.c_longlong,
ct.c_ubyte, ct.c_ushort, ct.c_uint, ct.c_ulong, ct.c_ulonglong,
ct.c_float, ct.c_double,
ct.c_bool,
]
return {_dtype(ctype): ctype for ctype in simple_types} | Return a dictionary mapping native endian scalar dtype to ctypes types |
169,942 | import os
from numpy import (
integer, ndarray, dtype as _dtype, asarray, frombuffer
)
from numpy.core.multiarray import _flagdict, flagsobj
try:
import ctypes
except ImportError:
ctypes = None
if ctypes is None:
load_library = _dummy
as_ctypes = _dummy
as_array = _dummy
from numpy import intp as c_intp
_ndptr_base = object
else:
import numpy.core._internal as nic
c_intp = nic._getintp_ctype()
del nic
_ndptr_base = ctypes.c_void_p
# Adapted from Albert Strasheim
if ctypes is not None:
def _ctype_ndarray(element_type, shape):
""" Create an ndarray of the given element type and shape """
for dim in shape[::-1]:
element_type = dim * element_type
# prevent the type name include np.ctypeslib
element_type.__module__ = None
return element_type
_scalar_type_map = _get_scalar_type_map()
The provided code snippet includes necessary dependencies for implementing the `as_array` function. Write a Python function `def as_array(obj, shape=None)` to solve the following problem:
Create a numpy array from a ctypes array or POINTER. The numpy array shares the memory with the ctypes object. The shape parameter must be given if converting from a ctypes POINTER. The shape parameter is ignored if converting from a ctypes array
Here is the function:
def as_array(obj, shape=None):
"""
Create a numpy array from a ctypes array or POINTER.
The numpy array shares the memory with the ctypes object.
The shape parameter must be given if converting from a ctypes POINTER.
The shape parameter is ignored if converting from a ctypes array
"""
if isinstance(obj, ctypes._Pointer):
# convert pointers to an array of the desired shape
if shape is None:
raise TypeError(
'as_array() requires a shape argument when called on a '
'pointer')
p_arr_type = ctypes.POINTER(_ctype_ndarray(obj._type_, shape))
obj = ctypes.cast(obj, p_arr_type).contents
return asarray(obj) | Create a numpy array from a ctypes array or POINTER. The numpy array shares the memory with the ctypes object. The shape parameter must be given if converting from a ctypes POINTER. The shape parameter is ignored if converting from a ctypes array |
169,943 | import os
from numpy import (
integer, ndarray, dtype as _dtype, asarray, frombuffer
)
from numpy.core.multiarray import _flagdict, flagsobj
if ctypes is not None:
def _ctype_ndarray(element_type, shape):
""" Create an ndarray of the given element type and shape """
for dim in shape[::-1]:
element_type = dim * element_type
# prevent the type name include np.ctypeslib
element_type.__module__ = None
return element_type
_scalar_type_map = _get_scalar_type_map()
def as_ctypes_type(dtype):
r"""
Convert a dtype into a ctypes type.
Parameters
----------
dtype : dtype
The dtype to convert
Returns
-------
ctype
A ctype scalar, union, array, or struct
Raises
------
NotImplementedError
If the conversion is not possible
Notes
-----
This function does not losslessly round-trip in either direction.
``np.dtype(as_ctypes_type(dt))`` will:
- insert padding fields
- reorder fields to be sorted by offset
- discard field titles
``as_ctypes_type(np.dtype(ctype))`` will:
- discard the class names of `ctypes.Structure`\ s and
`ctypes.Union`\ s
- convert single-element `ctypes.Union`\ s into single-element
`ctypes.Structure`\ s
- insert padding fields
"""
return _ctype_from_dtype(_dtype(dtype))
The provided code snippet includes necessary dependencies for implementing the `as_ctypes` function. Write a Python function `def as_ctypes(obj)` to solve the following problem:
Create and return a ctypes object from a numpy array. Actually anything that exposes the __array_interface__ is accepted.
Here is the function:
def as_ctypes(obj):
"""Create and return a ctypes object from a numpy array. Actually
anything that exposes the __array_interface__ is accepted."""
ai = obj.__array_interface__
if ai["strides"]:
raise TypeError("strided arrays not supported")
if ai["version"] != 3:
raise TypeError("only __array_interface__ version 3 supported")
addr, readonly = ai["data"]
if readonly:
raise TypeError("readonly arrays unsupported")
# can't use `_dtype((ai["typestr"], ai["shape"]))` here, as it overflows
# dtype.itemsize (gh-14214)
ctype_scalar = as_ctypes_type(ai["typestr"])
result_type = _ctype_ndarray(ctype_scalar, ai["shape"])
result = result_type.from_address(addr)
result.__keep = obj
return result | Create and return a ctypes object from a numpy array. Actually anything that exposes the __array_interface__ is accepted. |
169,944 | import os
import sys
from os.path import join
from numpy.distutils.system_info import platform_bits
from numpy.distutils.msvccompiler import lib_opts_if_msvc
import sys
if sys.version_info >= (3, 9):
def randbytes(n: int) -> bytes:
if sys.version_info >= (3, 9):
def sample(population: Union[Sequence[_T], AbstractSet[_T]], k: int, *, counts: Optional[Iterable[_T]] = ...) -> List[_T]:
else:
def sample(population: Union[Sequence[_T], AbstractSet[_T]], k: int) -> List[_T]:
def lib_opts_if_msvc(build_cmd):
def get_mathlibs(path=None):
class Configuration:
def __init__(self,
package_name=None,
parent_name=None,
top_path=None,
package_path=None,
caller_level=1,
setup_name='setup.py',
**attrs):
def todict(self):
def info(self, message):
def warn(self, message):
def set_options(self, **options):
def get_distribution(self):
def _wildcard_get_subpackage(self, subpackage_name,
parent_name,
caller_level = 1):
def _get_configuration_from_setup_py(self, setup_py,
subpackage_name,
subpackage_path,
parent_name,
caller_level = 1):
def get_subpackage(self,subpackage_name,
subpackage_path=None,
parent_name=None,
caller_level = 1):
def add_subpackage(self,subpackage_name,
subpackage_path=None,
standalone = False):
def add_data_dir(self, data_path):
def _optimize_data_files(self):
def add_data_files(self,*files):
def add_define_macros(self, macros):
def add_include_dirs(self,*paths):
def add_headers(self,*files):
def paths(self,*paths,**kws):
def _fix_paths_dict(self, kw):
def add_extension(self,name,sources,**kw):
def add_library(self,name,sources,**build_info):
def _add_library(self, name, sources, install_dir, build_info):
def add_installed_library(self, name, sources, install_dir, build_info=None):
def add_npy_pkg_config(self, template, install_dir, subst_dict=None):
def add_scripts(self,*files):
def dict_append(self,**dict):
def __str__(self):
def get_config_cmd(self):
def get_build_temp_dir(self):
def have_f77c(self):
def have_f90c(self):
def append_to(self, extlib):
def _get_svn_revision(self, path):
def _get_hg_revision(self, path):
def get_version(self, version_file=None, version_variable=None):
def make_svn_version_py(self, delete=True):
def generate_svn_version_py():
def rm_file(f=target,p=self.info):
def make_hg_version_py(self, delete=True):
def generate_hg_version_py():
def rm_file(f=target,p=self.info):
def make_config_py(self,name='__config__'):
def get_info(self,*names):
def configuration(parent_package='', top_path=None):
from numpy.distutils.misc_util import Configuration, get_mathlibs
config = Configuration('random', parent_package, top_path)
def generate_libraries(ext, build_dir):
config_cmd = config.get_config_cmd()
libs = get_mathlibs()
if sys.platform == 'win32':
libs.extend(['Advapi32', 'Kernel32'])
ext.libraries.extend(libs)
return None
# enable unix large file support on 32 bit systems
# (64 bit off_t, lseek -> lseek64 etc.)
if sys.platform[:3] == 'aix':
defs = [('_LARGE_FILES', None)]
else:
defs = [('_FILE_OFFSET_BITS', '64'),
('_LARGEFILE_SOURCE', '1'),
('_LARGEFILE64_SOURCE', '1')]
defs.append(('NPY_NO_DEPRECATED_API', 0))
config.add_subpackage('tests')
config.add_data_dir('tests/data')
config.add_data_dir('_examples')
EXTRA_LINK_ARGS = []
EXTRA_LIBRARIES = ['npyrandom']
if os.name != 'nt':
# Math lib
EXTRA_LIBRARIES.append('m')
# Some bit generators exclude GCC inlining
EXTRA_COMPILE_ARGS = ['-U__GNUC_GNU_INLINE__']
if sys.platform == 'cygwin':
# Export symbols without __declspec(dllexport) for using by cython.
# Using __declspec(dllexport) does not export other necessary symbols
# in Cygwin package's Cython environment, making it impossible to
# import modules.
EXTRA_LINK_ARGS += ['-Wl,--export-all-symbols']
# Use legacy integer variable sizes
LEGACY_DEFS = [('NP_RANDOM_LEGACY', '1')]
PCG64_DEFS = []
# One can force emulated 128-bit arithmetic if one wants.
#PCG64_DEFS += [('PCG_FORCE_EMULATED_128BIT_MATH', '1')]
depends = ['__init__.pxd', 'c_distributions.pxd', 'bit_generator.pxd']
# npyrandom - a library like npymath
npyrandom_sources = [
'src/distributions/logfactorial.c',
'src/distributions/distributions.c',
'src/distributions/random_mvhg_count.c',
'src/distributions/random_mvhg_marginals.c',
'src/distributions/random_hypergeometric.c',
]
def lib_opts(build_cmd):
""" Add flags that depend on the compiler.
We can't see which compiler we are using in our scope, because we have
not initialized the distutils build command, so use this deferred
calculation to run when we are building the library.
"""
opts = lib_opts_if_msvc(build_cmd)
if build_cmd.compiler.compiler_type != 'msvc':
# Some bit generators require c99
opts.append('-std=c99')
return opts
config.add_installed_library('npyrandom',
sources=npyrandom_sources,
install_dir='lib',
build_info={
'include_dirs' : [], # empty list required for creating npyrandom.h
'extra_compiler_args': [lib_opts],
})
for gen in ['mt19937']:
# gen.pyx, src/gen/gen.c, src/gen/gen-jump.c
config.add_extension(f'_{gen}',
sources=[f'_{gen}.c',
f'src/{gen}/{gen}.c',
f'src/{gen}/{gen}-jump.c'],
include_dirs=['.', 'src', join('src', gen)],
libraries=EXTRA_LIBRARIES,
extra_compile_args=EXTRA_COMPILE_ARGS,
extra_link_args=EXTRA_LINK_ARGS,
depends=depends + [f'_{gen}.pyx'],
define_macros=defs,
)
for gen in ['philox', 'pcg64', 'sfc64']:
# gen.pyx, src/gen/gen.c
_defs = defs + PCG64_DEFS if gen == 'pcg64' else defs
config.add_extension(f'_{gen}',
sources=[f'_{gen}.c',
f'src/{gen}/{gen}.c'],
include_dirs=['.', 'src', join('src', gen)],
libraries=EXTRA_LIBRARIES,
extra_compile_args=EXTRA_COMPILE_ARGS,
extra_link_args=EXTRA_LINK_ARGS,
depends=depends + [f'_{gen}.pyx',
'bit_generator.pyx', 'bit_generator.pxd'],
define_macros=_defs,
)
for gen in ['_common', 'bit_generator']:
# gen.pyx
config.add_extension(gen,
sources=[f'{gen}.c'],
libraries=EXTRA_LIBRARIES,
extra_compile_args=EXTRA_COMPILE_ARGS,
extra_link_args=EXTRA_LINK_ARGS,
include_dirs=['.', 'src'],
depends=depends + [f'{gen}.pyx', f'{gen}.pxd',],
define_macros=defs,
)
config.add_data_files(f'{gen}.pxd')
for gen in ['_generator', '_bounded_integers']:
# gen.pyx, src/distributions/distributions.c
config.add_extension(gen,
sources=[f'{gen}.c'],
libraries=EXTRA_LIBRARIES + ['npymath'],
extra_compile_args=EXTRA_COMPILE_ARGS,
include_dirs=['.', 'src'],
extra_link_args=EXTRA_LINK_ARGS,
depends=depends + [f'{gen}.pyx'],
define_macros=defs,
)
config.add_data_files('_bounded_integers.pxd')
mtrand_libs = ['m', 'npymath'] if os.name != 'nt' else ['npymath']
config.add_extension('mtrand',
sources=['mtrand.c',
'src/legacy/legacy-distributions.c',
'src/distributions/distributions.c',
],
include_dirs=['.', 'src', 'src/legacy'],
libraries=mtrand_libs,
extra_compile_args=EXTRA_COMPILE_ARGS,
extra_link_args=EXTRA_LINK_ARGS,
depends=depends + ['mtrand.pyx'],
define_macros=defs + LEGACY_DEFS,
)
config.add_data_files(*depends)
config.add_data_files('*.pyi')
return config | null |
169,945 | from .mtrand import RandomState
from ._philox import Philox
from ._pcg64 import PCG64, PCG64DXSM
from ._sfc64 import SFC64
from ._generator import Generator
from ._mt19937 import MT19937
def __bit_generator_ctor(bit_generator_name='MT19937'):
"""
Pickling helper function that returns a bit generator object
Parameters
----------
bit_generator_name : str
String containing the name of the BitGenerator
Returns
-------
bit_generator : BitGenerator
BitGenerator instance
"""
if bit_generator_name in BitGenerators:
bit_generator = BitGenerators[bit_generator_name]
else:
raise ValueError(str(bit_generator_name) + ' is not a known '
'BitGenerator module.')
return bit_generator()
class Generator:
def __init__(self, bit_generator: BitGenerator) -> None: ...
def __repr__(self) -> str: ...
def __str__(self) -> str: ...
def __getstate__(self) -> dict[str, Any]: ...
def __setstate__(self, state: dict[str, Any]) -> None: ...
def __reduce__(self) -> tuple[Callable[[str], Generator], tuple[str], dict[str, Any]]: ...
def bit_generator(self) -> BitGenerator: ...
def bytes(self, length: int) -> bytes: ...
def standard_normal( # type: ignore[misc]
self,
size: None = ...,
dtype: _DTypeLikeFloat32 | _DTypeLikeFloat64 = ...,
out: None = ...,
) -> float: ...
def standard_normal( # type: ignore[misc]
self,
size: _ShapeLike = ...,
) -> ndarray[Any, dtype[float64]]: ...
def standard_normal( # type: ignore[misc]
self,
*,
out: ndarray[Any, dtype[float64]] = ...,
) -> ndarray[Any, dtype[float64]]: ...
def standard_normal( # type: ignore[misc]
self,
size: _ShapeLike = ...,
dtype: _DTypeLikeFloat32 = ...,
out: None | ndarray[Any, dtype[float32]] = ...,
) -> ndarray[Any, dtype[float32]]: ...
def standard_normal( # type: ignore[misc]
self,
size: _ShapeLike = ...,
dtype: _DTypeLikeFloat64 = ...,
out: None | ndarray[Any, dtype[float64]] = ...,
) -> ndarray[Any, dtype[float64]]: ...
def permutation(self, x: int, axis: int = ...) -> ndarray[Any, dtype[int64]]: ...
def permutation(self, x: ArrayLike, axis: int = ...) -> ndarray[Any, Any]: ...
def standard_exponential( # type: ignore[misc]
self,
size: None = ...,
dtype: _DTypeLikeFloat32 | _DTypeLikeFloat64 = ...,
method: Literal["zig", "inv"] = ...,
out: None = ...,
) -> float: ...
def standard_exponential(
self,
size: _ShapeLike = ...,
) -> ndarray[Any, dtype[float64]]: ...
def standard_exponential(
self,
*,
out: ndarray[Any, dtype[float64]] = ...,
) -> ndarray[Any, dtype[float64]]: ...
def standard_exponential(
self,
size: _ShapeLike = ...,
*,
method: Literal["zig", "inv"] = ...,
out: None | ndarray[Any, dtype[float64]] = ...,
) -> ndarray[Any, dtype[float64]]: ...
def standard_exponential(
self,
size: _ShapeLike = ...,
dtype: _DTypeLikeFloat32 = ...,
method: Literal["zig", "inv"] = ...,
out: None | ndarray[Any, dtype[float32]] = ...,
) -> ndarray[Any, dtype[float32]]: ...
def standard_exponential(
self,
size: _ShapeLike = ...,
dtype: _DTypeLikeFloat64 = ...,
method: Literal["zig", "inv"] = ...,
out: None | ndarray[Any, dtype[float64]] = ...,
) -> ndarray[Any, dtype[float64]]: ...
def random( # type: ignore[misc]
self,
size: None = ...,
dtype: _DTypeLikeFloat32 | _DTypeLikeFloat64 = ...,
out: None = ...,
) -> float: ...
def random(
self,
*,
out: ndarray[Any, dtype[float64]] = ...,
) -> ndarray[Any, dtype[float64]]: ...
def random(
self,
size: _ShapeLike = ...,
*,
out: None | ndarray[Any, dtype[float64]] = ...,
) -> ndarray[Any, dtype[float64]]: ...
def random(
self,
size: _ShapeLike = ...,
dtype: _DTypeLikeFloat32 = ...,
out: None | ndarray[Any, dtype[float32]] = ...,
) -> ndarray[Any, dtype[float32]]: ...
def random(
self,
size: _ShapeLike = ...,
dtype: _DTypeLikeFloat64 = ...,
out: None | ndarray[Any, dtype[float64]] = ...,
) -> ndarray[Any, dtype[float64]]: ...
def beta(self, a: float, b: float, size: None = ...) -> float: ... # type: ignore[misc]
def beta(
self, a: _ArrayLikeFloat_co, b: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def exponential(self, scale: float = ..., size: None = ...) -> float: ... # type: ignore[misc]
def exponential(
self, scale: _ArrayLikeFloat_co = ..., size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def integers( # type: ignore[misc]
self,
low: int,
high: None | int = ...,
) -> int: ...
def integers( # type: ignore[misc]
self,
low: int,
high: None | int = ...,
size: None = ...,
dtype: _DTypeLikeBool = ...,
endpoint: bool = ...,
) -> bool: ...
def integers( # type: ignore[misc]
self,
low: int,
high: None | int = ...,
size: None = ...,
dtype: _DTypeLikeInt | _DTypeLikeUInt = ...,
endpoint: bool = ...,
) -> int: ...
def integers( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[int64]]: ...
def integers( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
dtype: _DTypeLikeBool = ...,
endpoint: bool = ...,
) -> ndarray[Any, dtype[bool_]]: ...
def integers( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
dtype: dtype[int8] | type[int8] | _Int8Codes | _SupportsDType[dtype[int8]] = ...,
endpoint: bool = ...,
) -> ndarray[Any, dtype[int8]]: ...
def integers( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
dtype: dtype[int16] | type[int16] | _Int16Codes | _SupportsDType[dtype[int16]] = ...,
endpoint: bool = ...,
) -> ndarray[Any, dtype[int16]]: ...
def integers( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
dtype: dtype[int32] | type[int32] | _Int32Codes | _SupportsDType[dtype[int32]] = ...,
endpoint: bool = ...,
) -> ndarray[Any, dtype[int32]]: ...
def integers( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
dtype: None | dtype[int64] | type[int64] | _Int64Codes | _SupportsDType[dtype[int64]] = ...,
endpoint: bool = ...,
) -> ndarray[Any, dtype[int64]]: ...
def integers( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
dtype: dtype[uint8] | type[uint8] | _UInt8Codes | _SupportsDType[dtype[uint8]] = ...,
endpoint: bool = ...,
) -> ndarray[Any, dtype[uint8]]: ...
def integers( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
dtype: dtype[uint16] | type[uint16] | _UInt16Codes | _SupportsDType[dtype[uint16]] = ...,
endpoint: bool = ...,
) -> ndarray[Any, dtype[uint16]]: ...
def integers( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
dtype: dtype[uint32] | type[uint32] | _UInt32Codes | _SupportsDType[dtype[uint32]] = ...,
endpoint: bool = ...,
) -> ndarray[Any, dtype[uint32]]: ...
def integers( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
dtype: dtype[uint64] | type[uint64] | _UInt64Codes | _SupportsDType[dtype[uint64]] = ...,
endpoint: bool = ...,
) -> ndarray[Any, dtype[uint64]]: ...
def integers( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
dtype: dtype[int_] | type[int] | type[int_] | _IntCodes | _SupportsDType[dtype[int_]] = ...,
endpoint: bool = ...,
) -> ndarray[Any, dtype[int_]]: ...
def integers( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
dtype: dtype[uint] | type[uint] | _UIntCodes | _SupportsDType[dtype[uint]] = ...,
endpoint: bool = ...,
) -> ndarray[Any, dtype[uint]]: ...
# TODO: Use a TypeVar _T here to get away from Any output? Should be int->ndarray[Any,dtype[int64]], ArrayLike[_T] -> _T | ndarray[Any,Any]
def choice(
self,
a: int,
size: None = ...,
replace: bool = ...,
p: None | _ArrayLikeFloat_co = ...,
axis: int = ...,
shuffle: bool = ...,
) -> int: ...
def choice(
self,
a: int,
size: _ShapeLike = ...,
replace: bool = ...,
p: None | _ArrayLikeFloat_co = ...,
axis: int = ...,
shuffle: bool = ...,
) -> ndarray[Any, dtype[int64]]: ...
def choice(
self,
a: ArrayLike,
size: None = ...,
replace: bool = ...,
p: None | _ArrayLikeFloat_co = ...,
axis: int = ...,
shuffle: bool = ...,
) -> Any: ...
def choice(
self,
a: ArrayLike,
size: _ShapeLike = ...,
replace: bool = ...,
p: None | _ArrayLikeFloat_co = ...,
axis: int = ...,
shuffle: bool = ...,
) -> ndarray[Any, Any]: ...
def uniform(self, low: float = ..., high: float = ..., size: None = ...) -> float: ... # type: ignore[misc]
def uniform(
self,
low: _ArrayLikeFloat_co = ...,
high: _ArrayLikeFloat_co = ...,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[float64]]: ...
def normal(self, loc: float = ..., scale: float = ..., size: None = ...) -> float: ... # type: ignore[misc]
def normal(
self,
loc: _ArrayLikeFloat_co = ...,
scale: _ArrayLikeFloat_co = ...,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[float64]]: ...
def standard_gamma( # type: ignore[misc]
self,
shape: float,
size: None = ...,
dtype: _DTypeLikeFloat32 | _DTypeLikeFloat64 = ...,
out: None = ...,
) -> float: ...
def standard_gamma(
self,
shape: _ArrayLikeFloat_co,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[float64]]: ...
def standard_gamma(
self,
shape: _ArrayLikeFloat_co,
*,
out: ndarray[Any, dtype[float64]] = ...,
) -> ndarray[Any, dtype[float64]]: ...
def standard_gamma(
self,
shape: _ArrayLikeFloat_co,
size: None | _ShapeLike = ...,
dtype: _DTypeLikeFloat32 = ...,
out: None | ndarray[Any, dtype[float32]] = ...,
) -> ndarray[Any, dtype[float32]]: ...
def standard_gamma(
self,
shape: _ArrayLikeFloat_co,
size: None | _ShapeLike = ...,
dtype: _DTypeLikeFloat64 = ...,
out: None | ndarray[Any, dtype[float64]] = ...,
) -> ndarray[Any, dtype[float64]]: ...
def gamma(self, shape: float, scale: float = ..., size: None = ...) -> float: ... # type: ignore[misc]
def gamma(
self,
shape: _ArrayLikeFloat_co,
scale: _ArrayLikeFloat_co = ...,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[float64]]: ...
def f(self, dfnum: float, dfden: float, size: None = ...) -> float: ... # type: ignore[misc]
def f(
self, dfnum: _ArrayLikeFloat_co, dfden: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def noncentral_f(self, dfnum: float, dfden: float, nonc: float, size: None = ...) -> float: ... # type: ignore[misc]
def noncentral_f(
self,
dfnum: _ArrayLikeFloat_co,
dfden: _ArrayLikeFloat_co,
nonc: _ArrayLikeFloat_co,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[float64]]: ...
def chisquare(self, df: float, size: None = ...) -> float: ... # type: ignore[misc]
def chisquare(
self, df: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def noncentral_chisquare(self, df: float, nonc: float, size: None = ...) -> float: ... # type: ignore[misc]
def noncentral_chisquare(
self, df: _ArrayLikeFloat_co, nonc: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def standard_t(self, df: float, size: None = ...) -> float: ... # type: ignore[misc]
def standard_t(
self, df: _ArrayLikeFloat_co, size: None = ...
) -> ndarray[Any, dtype[float64]]: ...
def standard_t(
self, df: _ArrayLikeFloat_co, size: _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def vonmises(self, mu: float, kappa: float, size: None = ...) -> float: ... # type: ignore[misc]
def vonmises(
self, mu: _ArrayLikeFloat_co, kappa: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def pareto(self, a: float, size: None = ...) -> float: ... # type: ignore[misc]
def pareto(
self, a: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def weibull(self, a: float, size: None = ...) -> float: ... # type: ignore[misc]
def weibull(
self, a: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def power(self, a: float, size: None = ...) -> float: ... # type: ignore[misc]
def power(
self, a: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def standard_cauchy(self, size: None = ...) -> float: ... # type: ignore[misc]
def standard_cauchy(self, size: _ShapeLike = ...) -> ndarray[Any, dtype[float64]]: ...
def laplace(self, loc: float = ..., scale: float = ..., size: None = ...) -> float: ... # type: ignore[misc]
def laplace(
self,
loc: _ArrayLikeFloat_co = ...,
scale: _ArrayLikeFloat_co = ...,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[float64]]: ...
def gumbel(self, loc: float = ..., scale: float = ..., size: None = ...) -> float: ... # type: ignore[misc]
def gumbel(
self,
loc: _ArrayLikeFloat_co = ...,
scale: _ArrayLikeFloat_co = ...,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[float64]]: ...
def logistic(self, loc: float = ..., scale: float = ..., size: None = ...) -> float: ... # type: ignore[misc]
def logistic(
self,
loc: _ArrayLikeFloat_co = ...,
scale: _ArrayLikeFloat_co = ...,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[float64]]: ...
def lognormal(self, mean: float = ..., sigma: float = ..., size: None = ...) -> float: ... # type: ignore[misc]
def lognormal(
self,
mean: _ArrayLikeFloat_co = ...,
sigma: _ArrayLikeFloat_co = ...,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[float64]]: ...
def rayleigh(self, scale: float = ..., size: None = ...) -> float: ... # type: ignore[misc]
def rayleigh(
self, scale: _ArrayLikeFloat_co = ..., size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def wald(self, mean: float, scale: float, size: None = ...) -> float: ... # type: ignore[misc]
def wald(
self, mean: _ArrayLikeFloat_co, scale: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def triangular(self, left: float, mode: float, right: float, size: None = ...) -> float: ... # type: ignore[misc]
def triangular(
self,
left: _ArrayLikeFloat_co,
mode: _ArrayLikeFloat_co,
right: _ArrayLikeFloat_co,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[float64]]: ...
def binomial(self, n: int, p: float, size: None = ...) -> int: ... # type: ignore[misc]
def binomial(
self, n: _ArrayLikeInt_co, p: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[int64]]: ...
def negative_binomial(self, n: float, p: float, size: None = ...) -> int: ... # type: ignore[misc]
def negative_binomial(
self, n: _ArrayLikeFloat_co, p: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[int64]]: ...
def poisson(self, lam: float = ..., size: None = ...) -> int: ... # type: ignore[misc]
def poisson(
self, lam: _ArrayLikeFloat_co = ..., size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[int64]]: ...
def zipf(self, a: float, size: None = ...) -> int: ... # type: ignore[misc]
def zipf(
self, a: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[int64]]: ...
def geometric(self, p: float, size: None = ...) -> int: ... # type: ignore[misc]
def geometric(
self, p: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[int64]]: ...
def hypergeometric(self, ngood: int, nbad: int, nsample: int, size: None = ...) -> int: ... # type: ignore[misc]
def hypergeometric(
self,
ngood: _ArrayLikeInt_co,
nbad: _ArrayLikeInt_co,
nsample: _ArrayLikeInt_co,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[int64]]: ...
def logseries(self, p: float, size: None = ...) -> int: ... # type: ignore[misc]
def logseries(
self, p: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[int64]]: ...
def multivariate_normal(
self,
mean: _ArrayLikeFloat_co,
cov: _ArrayLikeFloat_co,
size: None | _ShapeLike = ...,
check_valid: Literal["warn", "raise", "ignore"] = ...,
tol: float = ...,
*,
method: Literal["svd", "eigh", "cholesky"] = ...,
) -> ndarray[Any, dtype[float64]]: ...
def multinomial(
self, n: _ArrayLikeInt_co,
pvals: _ArrayLikeFloat_co,
size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[int64]]: ...
def multivariate_hypergeometric(
self,
colors: _ArrayLikeInt_co,
nsample: int,
size: None | _ShapeLike = ...,
method: Literal["marginals", "count"] = ...,
) -> ndarray[Any, dtype[int64]]: ...
def dirichlet(
self, alpha: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def permuted(
self, x: ArrayLike, *, axis: None | int = ..., out: None | ndarray[Any, Any] = ...
) -> ndarray[Any, Any]: ...
def shuffle(self, x: ArrayLike, axis: int = ...) -> None: ...
The provided code snippet includes necessary dependencies for implementing the `__generator_ctor` function. Write a Python function `def __generator_ctor(bit_generator_name="MT19937", bit_generator_ctor=__bit_generator_ctor)` to solve the following problem:
Pickling helper function that returns a Generator object Parameters ---------- bit_generator_name : str String containing the core BitGenerator's name bit_generator_ctor : callable, optional Callable function that takes bit_generator_name as its only argument and returns an instantized bit generator. Returns ------- rg : Generator Generator using the named core BitGenerator
Here is the function:
def __generator_ctor(bit_generator_name="MT19937",
bit_generator_ctor=__bit_generator_ctor):
"""
Pickling helper function that returns a Generator object
Parameters
----------
bit_generator_name : str
String containing the core BitGenerator's name
bit_generator_ctor : callable, optional
Callable function that takes bit_generator_name as its only argument
and returns an instantized bit generator.
Returns
-------
rg : Generator
Generator using the named core BitGenerator
"""
return Generator(bit_generator_ctor(bit_generator_name)) | Pickling helper function that returns a Generator object Parameters ---------- bit_generator_name : str String containing the core BitGenerator's name bit_generator_ctor : callable, optional Callable function that takes bit_generator_name as its only argument and returns an instantized bit generator. Returns ------- rg : Generator Generator using the named core BitGenerator |
169,946 | from .mtrand import RandomState
from ._philox import Philox
from ._pcg64 import PCG64, PCG64DXSM
from ._sfc64 import SFC64
from ._generator import Generator
from ._mt19937 import MT19937
def __bit_generator_ctor(bit_generator_name='MT19937'):
"""
Pickling helper function that returns a bit generator object
Parameters
----------
bit_generator_name : str
String containing the name of the BitGenerator
Returns
-------
bit_generator : BitGenerator
BitGenerator instance
"""
if bit_generator_name in BitGenerators:
bit_generator = BitGenerators[bit_generator_name]
else:
raise ValueError(str(bit_generator_name) + ' is not a known '
'BitGenerator module.')
return bit_generator()
class RandomState:
_bit_generator: BitGenerator
def __init__(self, seed: None | _ArrayLikeInt_co | BitGenerator = ...) -> None: ...
def __repr__(self) -> str: ...
def __str__(self) -> str: ...
def __getstate__(self) -> dict[str, Any]: ...
def __setstate__(self, state: dict[str, Any]) -> None: ...
def __reduce__(self) -> tuple[Callable[[str], RandomState], tuple[str], dict[str, Any]]: ...
def seed(self, seed: None | _ArrayLikeFloat_co = ...) -> None: ...
def get_state(self, legacy: Literal[False] = ...) -> dict[str, Any]: ...
def get_state(
self, legacy: Literal[True] = ...
) -> dict[str, Any] | tuple[str, ndarray[Any, dtype[uint32]], int, int, float]: ...
def set_state(
self, state: dict[str, Any] | tuple[str, ndarray[Any, dtype[uint32]], int, int, float]
) -> None: ...
def random_sample(self, size: None = ...) -> float: ... # type: ignore[misc]
def random_sample(self, size: _ShapeLike = ...) -> ndarray[Any, dtype[float64]]: ...
def random(self, size: None = ...) -> float: ... # type: ignore[misc]
def random(self, size: _ShapeLike = ...) -> ndarray[Any, dtype[float64]]: ...
def beta(self, a: float, b: float, size: None = ...) -> float: ... # type: ignore[misc]
def beta(
self, a: _ArrayLikeFloat_co, b: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def exponential(self, scale: float = ..., size: None = ...) -> float: ... # type: ignore[misc]
def exponential(
self, scale: _ArrayLikeFloat_co = ..., size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def standard_exponential(self, size: None = ...) -> float: ... # type: ignore[misc]
def standard_exponential(self, size: _ShapeLike = ...) -> ndarray[Any, dtype[float64]]: ...
def tomaxint(self, size: None = ...) -> int: ... # type: ignore[misc]
def tomaxint(self, size: _ShapeLike = ...) -> ndarray[Any, dtype[int_]]: ...
def randint( # type: ignore[misc]
self,
low: int,
high: None | int = ...,
) -> int: ...
def randint( # type: ignore[misc]
self,
low: int,
high: None | int = ...,
size: None = ...,
dtype: _DTypeLikeBool = ...,
) -> bool: ...
def randint( # type: ignore[misc]
self,
low: int,
high: None | int = ...,
size: None = ...,
dtype: _DTypeLikeInt | _DTypeLikeUInt = ...,
) -> int: ...
def randint( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[int_]]: ...
def randint( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
dtype: _DTypeLikeBool = ...,
) -> ndarray[Any, dtype[bool_]]: ...
def randint( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
dtype: dtype[int8] | type[int8] | _Int8Codes | _SupportsDType[dtype[int8]] = ...,
) -> ndarray[Any, dtype[int8]]: ...
def randint( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
dtype: dtype[int16] | type[int16] | _Int16Codes | _SupportsDType[dtype[int16]] = ...,
) -> ndarray[Any, dtype[int16]]: ...
def randint( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
dtype: dtype[int32] | type[int32] | _Int32Codes | _SupportsDType[dtype[int32]] = ...,
) -> ndarray[Any, dtype[int32]]: ...
def randint( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
dtype: None | dtype[int64] | type[int64] | _Int64Codes | _SupportsDType[dtype[int64]] = ...,
) -> ndarray[Any, dtype[int64]]: ...
def randint( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
dtype: dtype[uint8] | type[uint8] | _UInt8Codes | _SupportsDType[dtype[uint8]] = ...,
) -> ndarray[Any, dtype[uint8]]: ...
def randint( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
dtype: dtype[uint16] | type[uint16] | _UInt16Codes | _SupportsDType[dtype[uint16]] = ...,
) -> ndarray[Any, dtype[uint16]]: ...
def randint( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
dtype: dtype[uint32] | type[uint32] | _UInt32Codes | _SupportsDType[dtype[uint32]] = ...,
) -> ndarray[Any, dtype[uint32]]: ...
def randint( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
dtype: dtype[uint64] | type[uint64] | _UInt64Codes | _SupportsDType[dtype[uint64]] = ...,
) -> ndarray[Any, dtype[uint64]]: ...
def randint( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
dtype: dtype[int_] | type[int] | type[int_] | _IntCodes | _SupportsDType[dtype[int_]] = ...,
) -> ndarray[Any, dtype[int_]]: ...
def randint( # type: ignore[misc]
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
dtype: dtype[uint] | type[uint] | _UIntCodes | _SupportsDType[dtype[uint]] = ...,
) -> ndarray[Any, dtype[uint]]: ...
def bytes(self, length: int) -> bytes: ...
def choice(
self,
a: int,
size: None = ...,
replace: bool = ...,
p: None | _ArrayLikeFloat_co = ...,
) -> int: ...
def choice(
self,
a: int,
size: _ShapeLike = ...,
replace: bool = ...,
p: None | _ArrayLikeFloat_co = ...,
) -> ndarray[Any, dtype[int_]]: ...
def choice(
self,
a: ArrayLike,
size: None = ...,
replace: bool = ...,
p: None | _ArrayLikeFloat_co = ...,
) -> Any: ...
def choice(
self,
a: ArrayLike,
size: _ShapeLike = ...,
replace: bool = ...,
p: None | _ArrayLikeFloat_co = ...,
) -> ndarray[Any, Any]: ...
def uniform(self, low: float = ..., high: float = ..., size: None = ...) -> float: ... # type: ignore[misc]
def uniform(
self,
low: _ArrayLikeFloat_co = ...,
high: _ArrayLikeFloat_co = ...,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[float64]]: ...
def rand(self) -> float: ...
def rand(self, *args: int) -> ndarray[Any, dtype[float64]]: ...
def randn(self) -> float: ...
def randn(self, *args: int) -> ndarray[Any, dtype[float64]]: ...
def random_integers(self, low: int, high: None | int = ..., size: None = ...) -> int: ... # type: ignore[misc]
def random_integers(
self,
low: _ArrayLikeInt_co,
high: None | _ArrayLikeInt_co = ...,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[int_]]: ...
def standard_normal(self, size: None = ...) -> float: ... # type: ignore[misc]
def standard_normal( # type: ignore[misc]
self, size: _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def normal(self, loc: float = ..., scale: float = ..., size: None = ...) -> float: ... # type: ignore[misc]
def normal(
self,
loc: _ArrayLikeFloat_co = ...,
scale: _ArrayLikeFloat_co = ...,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[float64]]: ...
def standard_gamma( # type: ignore[misc]
self,
shape: float,
size: None = ...,
) -> float: ...
def standard_gamma(
self,
shape: _ArrayLikeFloat_co,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[float64]]: ...
def gamma(self, shape: float, scale: float = ..., size: None = ...) -> float: ... # type: ignore[misc]
def gamma(
self,
shape: _ArrayLikeFloat_co,
scale: _ArrayLikeFloat_co = ...,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[float64]]: ...
def f(self, dfnum: float, dfden: float, size: None = ...) -> float: ... # type: ignore[misc]
def f(
self, dfnum: _ArrayLikeFloat_co, dfden: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def noncentral_f(self, dfnum: float, dfden: float, nonc: float, size: None = ...) -> float: ... # type: ignore[misc]
def noncentral_f(
self,
dfnum: _ArrayLikeFloat_co,
dfden: _ArrayLikeFloat_co,
nonc: _ArrayLikeFloat_co,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[float64]]: ...
def chisquare(self, df: float, size: None = ...) -> float: ... # type: ignore[misc]
def chisquare(
self, df: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def noncentral_chisquare(self, df: float, nonc: float, size: None = ...) -> float: ... # type: ignore[misc]
def noncentral_chisquare(
self, df: _ArrayLikeFloat_co, nonc: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def standard_t(self, df: float, size: None = ...) -> float: ... # type: ignore[misc]
def standard_t(
self, df: _ArrayLikeFloat_co, size: None = ...
) -> ndarray[Any, dtype[float64]]: ...
def standard_t(
self, df: _ArrayLikeFloat_co, size: _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def vonmises(self, mu: float, kappa: float, size: None = ...) -> float: ... # type: ignore[misc]
def vonmises(
self, mu: _ArrayLikeFloat_co, kappa: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def pareto(self, a: float, size: None = ...) -> float: ... # type: ignore[misc]
def pareto(
self, a: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def weibull(self, a: float, size: None = ...) -> float: ... # type: ignore[misc]
def weibull(
self, a: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def power(self, a: float, size: None = ...) -> float: ... # type: ignore[misc]
def power(
self, a: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def standard_cauchy(self, size: None = ...) -> float: ... # type: ignore[misc]
def standard_cauchy(self, size: _ShapeLike = ...) -> ndarray[Any, dtype[float64]]: ...
def laplace(self, loc: float = ..., scale: float = ..., size: None = ...) -> float: ... # type: ignore[misc]
def laplace(
self,
loc: _ArrayLikeFloat_co = ...,
scale: _ArrayLikeFloat_co = ...,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[float64]]: ...
def gumbel(self, loc: float = ..., scale: float = ..., size: None = ...) -> float: ... # type: ignore[misc]
def gumbel(
self,
loc: _ArrayLikeFloat_co = ...,
scale: _ArrayLikeFloat_co = ...,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[float64]]: ...
def logistic(self, loc: float = ..., scale: float = ..., size: None = ...) -> float: ... # type: ignore[misc]
def logistic(
self,
loc: _ArrayLikeFloat_co = ...,
scale: _ArrayLikeFloat_co = ...,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[float64]]: ...
def lognormal(self, mean: float = ..., sigma: float = ..., size: None = ...) -> float: ... # type: ignore[misc]
def lognormal(
self,
mean: _ArrayLikeFloat_co = ...,
sigma: _ArrayLikeFloat_co = ...,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[float64]]: ...
def rayleigh(self, scale: float = ..., size: None = ...) -> float: ... # type: ignore[misc]
def rayleigh(
self, scale: _ArrayLikeFloat_co = ..., size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def wald(self, mean: float, scale: float, size: None = ...) -> float: ... # type: ignore[misc]
def wald(
self, mean: _ArrayLikeFloat_co, scale: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def triangular(self, left: float, mode: float, right: float, size: None = ...) -> float: ... # type: ignore[misc]
def triangular(
self,
left: _ArrayLikeFloat_co,
mode: _ArrayLikeFloat_co,
right: _ArrayLikeFloat_co,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[float64]]: ...
def binomial(self, n: int, p: float, size: None = ...) -> int: ... # type: ignore[misc]
def binomial(
self, n: _ArrayLikeInt_co, p: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[int_]]: ...
def negative_binomial(self, n: float, p: float, size: None = ...) -> int: ... # type: ignore[misc]
def negative_binomial(
self, n: _ArrayLikeFloat_co, p: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[int_]]: ...
def poisson(self, lam: float = ..., size: None = ...) -> int: ... # type: ignore[misc]
def poisson(
self, lam: _ArrayLikeFloat_co = ..., size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[int_]]: ...
def zipf(self, a: float, size: None = ...) -> int: ... # type: ignore[misc]
def zipf(
self, a: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[int_]]: ...
def geometric(self, p: float, size: None = ...) -> int: ... # type: ignore[misc]
def geometric(
self, p: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[int_]]: ...
def hypergeometric(self, ngood: int, nbad: int, nsample: int, size: None = ...) -> int: ... # type: ignore[misc]
def hypergeometric(
self,
ngood: _ArrayLikeInt_co,
nbad: _ArrayLikeInt_co,
nsample: _ArrayLikeInt_co,
size: None | _ShapeLike = ...,
) -> ndarray[Any, dtype[int_]]: ...
def logseries(self, p: float, size: None = ...) -> int: ... # type: ignore[misc]
def logseries(
self, p: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[int_]]: ...
def multivariate_normal(
self,
mean: _ArrayLikeFloat_co,
cov: _ArrayLikeFloat_co,
size: None | _ShapeLike = ...,
check_valid: Literal["warn", "raise", "ignore"] = ...,
tol: float = ...,
) -> ndarray[Any, dtype[float64]]: ...
def multinomial(
self, n: _ArrayLikeInt_co, pvals: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[int_]]: ...
def dirichlet(
self, alpha: _ArrayLikeFloat_co, size: None | _ShapeLike = ...
) -> ndarray[Any, dtype[float64]]: ...
def shuffle(self, x: ArrayLike) -> None: ...
def permutation(self, x: int) -> ndarray[Any, dtype[int_]]: ...
def permutation(self, x: ArrayLike) -> ndarray[Any, Any]: ...
The provided code snippet includes necessary dependencies for implementing the `__randomstate_ctor` function. Write a Python function `def __randomstate_ctor(bit_generator_name="MT19937", bit_generator_ctor=__bit_generator_ctor)` to solve the following problem:
Pickling helper function that returns a legacy RandomState-like object Parameters ---------- bit_generator_name : str String containing the core BitGenerator's name bit_generator_ctor : callable, optional Callable function that takes bit_generator_name as its only argument and returns an instantized bit generator. Returns ------- rs : RandomState Legacy RandomState using the named core BitGenerator
Here is the function:
def __randomstate_ctor(bit_generator_name="MT19937",
bit_generator_ctor=__bit_generator_ctor):
"""
Pickling helper function that returns a legacy RandomState-like object
Parameters
----------
bit_generator_name : str
String containing the core BitGenerator's name
bit_generator_ctor : callable, optional
Callable function that takes bit_generator_name as its only argument
and returns an instantized bit generator.
Returns
-------
rs : RandomState
Legacy RandomState using the named core BitGenerator
"""
return RandomState(bit_generator_ctor(bit_generator_name)) | Pickling helper function that returns a legacy RandomState-like object Parameters ---------- bit_generator_name : str String containing the core BitGenerator's name bit_generator_ctor : callable, optional Callable function that takes bit_generator_name as its only argument and returns an instantized bit generator. Returns ------- rs : RandomState Legacy RandomState using the named core BitGenerator |
169,947 | import os
The provided code snippet includes necessary dependencies for implementing the `parse_distributions_h` function. Write a Python function `def parse_distributions_h(ffi, inc_dir)` to solve the following problem:
Parse distributions.h located in inc_dir for CFFI, filling in the ffi.cdef Read the function declarations without the "#define ..." macros that will be filled in when loading the library.
Here is the function:
def parse_distributions_h(ffi, inc_dir):
"""
Parse distributions.h located in inc_dir for CFFI, filling in the ffi.cdef
Read the function declarations without the "#define ..." macros that will
be filled in when loading the library.
"""
with open(os.path.join(inc_dir, 'random', 'bitgen.h')) as fid:
s = []
for line in fid:
# massage the include file
if line.strip().startswith('#'):
continue
s.append(line)
ffi.cdef('\n'.join(s))
with open(os.path.join(inc_dir, 'random', 'distributions.h')) as fid:
s = []
in_skip = 0
ignoring = False
for line in fid:
# check for and remove extern "C" guards
if ignoring:
if line.strip().startswith('#endif'):
ignoring = False
continue
if line.strip().startswith('#ifdef __cplusplus'):
ignoring = True
# massage the include file
if line.strip().startswith('#'):
continue
# skip any inlined function definition
# which starts with 'static NPY_INLINE xxx(...) {'
# and ends with a closing '}'
if line.strip().startswith('static NPY_INLINE'):
in_skip += line.count('{')
continue
elif in_skip > 0:
in_skip += line.count('{')
in_skip -= line.count('}')
continue
# replace defines with their value or remove them
line = line.replace('DECLDIR', '')
line = line.replace('NPY_INLINE', '')
line = line.replace('RAND_INT_TYPE', 'int64_t')
s.append(line)
ffi.cdef('\n'.join(s)) | Parse distributions.h located in inc_dir for CFFI, filling in the ffi.cdef Read the function declarations without the "#define ..." macros that will be filled in when loading the library. |
169,948 | import numpy as np
import numba as nb
from numpy.random import PCG64
from timeit import timeit
next_d = bit_gen.cffi.next_double
r2 = numpycall()
def normals(n, state):
out = np.empty(n)
for i in range((n + 1) // 2):
x1 = 2.0 * next_d(state) - 1.0
x2 = 2.0 * next_d(state) - 1.0
r2 = x1 * x1 + x2 * x2
while r2 >= 1.0 or r2 == 0.0:
x1 = 2.0 * next_d(state) - 1.0
x2 = 2.0 * next_d(state) - 1.0
r2 = x1 * x1 + x2 * x2
f = np.sqrt(-2.0 * np.log(r2) / r2)
out[2 * i] = f * x1
if 2 * i + 1 < n:
out[2 * i + 1] = f * x2
return out | null |
169,949 | import numpy as np
import numba as nb
from numpy.random import PCG64
from timeit import timeit
state_addr = bit_gen.cffi.state_address
normalsj = nb.jit(normals, nopython=True)
n = 10000
def numbacall():
return normalsj(n, state_addr) | null |
169,950 | import numpy as np
import numba as nb
from numpy.random import PCG64
from timeit import timeit
n = 10000
rg = np.random.Generator(PCG64())
def numpycall():
return rg.normal(size=n) | null |
169,951 | import numpy as np
import numba as nb
from numpy.random import PCG64
from timeit import timeit
def bounded_uint(lb, ub, state):
mask = delta = ub - lb
mask |= mask >> 1
mask |= mask >> 2
mask |= mask >> 4
mask |= mask >> 8
mask |= mask >> 16
val = next_u32(state) & mask
while val > delta:
val = next_u32(state) & mask
return lb + val
def bounded_uints(lb, ub, n, state):
out = np.empty(n, dtype=np.uint32)
for i in range(n):
out[i] = bounded_uint(lb, ub, state) | null |
169,952 | import os
import numba as nb
import numpy as np
from cffi import FFI
from numpy.random import PCG64
random_standard_normal = lib.random_standard_normal
def normals(n, bit_generator):
out = np.empty(n)
for i in range(n):
out[i] = random_standard_normal(bit_generator)
return out | null |
169,953 | import warnings
import numpy as np
from numpy.matrixlib.defmatrix import matrix, asmatrix
from numpy import *
class matrix(N.ndarray):
"""
matrix(data, dtype=None, copy=True)
.. note:: It is no longer recommended to use this class, even for linear
algebra. Instead use regular arrays. The class may be removed
in the future.
Returns a matrix from an array-like object, or from a string of data.
A matrix is a specialized 2-D array that retains its 2-D nature
through operations. It has certain special operators, such as ``*``
(matrix multiplication) and ``**`` (matrix power).
Parameters
----------
data : array_like or string
If `data` is a string, it is interpreted as a matrix with commas
or spaces separating columns, and semicolons separating rows.
dtype : data-type
Data-type of the output matrix.
copy : bool
If `data` is already an `ndarray`, then this flag determines
whether the data is copied (the default), or whether a view is
constructed.
See Also
--------
array
Examples
--------
>>> a = np.matrix('1 2; 3 4')
>>> a
matrix([[1, 2],
[3, 4]])
>>> np.matrix([[1, 2], [3, 4]])
matrix([[1, 2],
[3, 4]])
"""
__array_priority__ = 10.0
def __new__(subtype, data, dtype=None, copy=True):
warnings.warn('the matrix subclass is not the recommended way to '
'represent matrices or deal with linear algebra (see '
'https://docs.scipy.org/doc/numpy/user/'
'numpy-for-matlab-users.html). '
'Please adjust your code to use regular ndarray.',
PendingDeprecationWarning, stacklevel=2)
if isinstance(data, matrix):
dtype2 = data.dtype
if (dtype is None):
dtype = dtype2
if (dtype2 == dtype) and (not copy):
return data
return data.astype(dtype)
if isinstance(data, N.ndarray):
if dtype is None:
intype = data.dtype
else:
intype = N.dtype(dtype)
new = data.view(subtype)
if intype != data.dtype:
return new.astype(intype)
if copy: return new.copy()
else: return new
if isinstance(data, str):
data = _convert_from_string(data)
# now convert data to an array
arr = N.array(data, dtype=dtype, copy=copy)
ndim = arr.ndim
shape = arr.shape
if (ndim > 2):
raise ValueError("matrix must be 2-dimensional")
elif ndim == 0:
shape = (1, 1)
elif ndim == 1:
shape = (1, shape[0])
order = 'C'
if (ndim == 2) and arr.flags.fortran:
order = 'F'
if not (order or arr.flags.contiguous):
arr = arr.copy()
ret = N.ndarray.__new__(subtype, shape, arr.dtype,
buffer=arr,
order=order)
return ret
def __array_finalize__(self, obj):
self._getitem = False
if (isinstance(obj, matrix) and obj._getitem): return
ndim = self.ndim
if (ndim == 2):
return
if (ndim > 2):
newshape = tuple([x for x in self.shape if x > 1])
ndim = len(newshape)
if ndim == 2:
self.shape = newshape
return
elif (ndim > 2):
raise ValueError("shape too large to be a matrix.")
else:
newshape = self.shape
if ndim == 0:
self.shape = (1, 1)
elif ndim == 1:
self.shape = (1, newshape[0])
return
def __getitem__(self, index):
self._getitem = True
try:
out = N.ndarray.__getitem__(self, index)
finally:
self._getitem = False
if not isinstance(out, N.ndarray):
return out
if out.ndim == 0:
return out[()]
if out.ndim == 1:
sh = out.shape[0]
# Determine when we should have a column array
try:
n = len(index)
except Exception:
n = 0
if n > 1 and isscalar(index[1]):
out.shape = (sh, 1)
else:
out.shape = (1, sh)
return out
def __mul__(self, other):
if isinstance(other, (N.ndarray, list, tuple)) :
# This promotes 1-D vectors to row vectors
return N.dot(self, asmatrix(other))
if isscalar(other) or not hasattr(other, '__rmul__') :
return N.dot(self, other)
return NotImplemented
def __rmul__(self, other):
return N.dot(other, self)
def __imul__(self, other):
self[:] = self * other
return self
def __pow__(self, other):
return matrix_power(self, other)
def __ipow__(self, other):
self[:] = self ** other
return self
def __rpow__(self, other):
return NotImplemented
def _align(self, axis):
"""A convenience function for operations that need to preserve axis
orientation.
"""
if axis is None:
return self[0, 0]
elif axis==0:
return self
elif axis==1:
return self.transpose()
else:
raise ValueError("unsupported axis")
def _collapse(self, axis):
"""A convenience function for operations that want to collapse
to a scalar like _align, but are using keepdims=True
"""
if axis is None:
return self[0, 0]
else:
return self
# Necessary because base-class tolist expects dimension
# reduction by x[0]
def tolist(self):
"""
Return the matrix as a (possibly nested) list.
See `ndarray.tolist` for full documentation.
See Also
--------
ndarray.tolist
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.tolist()
[[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11]]
"""
return self.__array__().tolist()
# To preserve orientation of result...
def sum(self, axis=None, dtype=None, out=None):
"""
Returns the sum of the matrix elements, along the given axis.
Refer to `numpy.sum` for full documentation.
See Also
--------
numpy.sum
Notes
-----
This is the same as `ndarray.sum`, except that where an `ndarray` would
be returned, a `matrix` object is returned instead.
Examples
--------
>>> x = np.matrix([[1, 2], [4, 3]])
>>> x.sum()
10
>>> x.sum(axis=1)
matrix([[3],
[7]])
>>> x.sum(axis=1, dtype='float')
matrix([[3.],
[7.]])
>>> out = np.zeros((2, 1), dtype='float')
>>> x.sum(axis=1, dtype='float', out=np.asmatrix(out))
matrix([[3.],
[7.]])
"""
return N.ndarray.sum(self, axis, dtype, out, keepdims=True)._collapse(axis)
# To update docstring from array to matrix...
def squeeze(self, axis=None):
"""
Return a possibly reshaped matrix.
Refer to `numpy.squeeze` for more documentation.
Parameters
----------
axis : None or int or tuple of ints, optional
Selects a subset of the axes of length one in the shape.
If an axis is selected with shape entry greater than one,
an error is raised.
Returns
-------
squeezed : matrix
The matrix, but as a (1, N) matrix if it had shape (N, 1).
See Also
--------
numpy.squeeze : related function
Notes
-----
If `m` has a single column then that column is returned
as the single row of a matrix. Otherwise `m` is returned.
The returned matrix is always either `m` itself or a view into `m`.
Supplying an axis keyword argument will not affect the returned matrix
but it may cause an error to be raised.
Examples
--------
>>> c = np.matrix([[1], [2]])
>>> c
matrix([[1],
[2]])
>>> c.squeeze()
matrix([[1, 2]])
>>> r = c.T
>>> r
matrix([[1, 2]])
>>> r.squeeze()
matrix([[1, 2]])
>>> m = np.matrix([[1, 2], [3, 4]])
>>> m.squeeze()
matrix([[1, 2],
[3, 4]])
"""
return N.ndarray.squeeze(self, axis=axis)
# To update docstring from array to matrix...
def flatten(self, order='C'):
"""
Return a flattened copy of the matrix.
All `N` elements of the matrix are placed into a single row.
Parameters
----------
order : {'C', 'F', 'A', 'K'}, optional
'C' means to flatten in row-major (C-style) order. 'F' means to
flatten in column-major (Fortran-style) order. 'A' means to
flatten in column-major order if `m` is Fortran *contiguous* in
memory, row-major order otherwise. 'K' means to flatten `m` in
the order the elements occur in memory. The default is 'C'.
Returns
-------
y : matrix
A copy of the matrix, flattened to a `(1, N)` matrix where `N`
is the number of elements in the original matrix.
See Also
--------
ravel : Return a flattened array.
flat : A 1-D flat iterator over the matrix.
Examples
--------
>>> m = np.matrix([[1,2], [3,4]])
>>> m.flatten()
matrix([[1, 2, 3, 4]])
>>> m.flatten('F')
matrix([[1, 3, 2, 4]])
"""
return N.ndarray.flatten(self, order=order)
def mean(self, axis=None, dtype=None, out=None):
"""
Returns the average of the matrix elements along the given axis.
Refer to `numpy.mean` for full documentation.
See Also
--------
numpy.mean
Notes
-----
Same as `ndarray.mean` except that, where that returns an `ndarray`,
this returns a `matrix` object.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3, 4)))
>>> x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.mean()
5.5
>>> x.mean(0)
matrix([[4., 5., 6., 7.]])
>>> x.mean(1)
matrix([[ 1.5],
[ 5.5],
[ 9.5]])
"""
return N.ndarray.mean(self, axis, dtype, out, keepdims=True)._collapse(axis)
def std(self, axis=None, dtype=None, out=None, ddof=0):
"""
Return the standard deviation of the array elements along the given axis.
Refer to `numpy.std` for full documentation.
See Also
--------
numpy.std
Notes
-----
This is the same as `ndarray.std`, except that where an `ndarray` would
be returned, a `matrix` object is returned instead.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3, 4)))
>>> x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.std()
3.4520525295346629 # may vary
>>> x.std(0)
matrix([[ 3.26598632, 3.26598632, 3.26598632, 3.26598632]]) # may vary
>>> x.std(1)
matrix([[ 1.11803399],
[ 1.11803399],
[ 1.11803399]])
"""
return N.ndarray.std(self, axis, dtype, out, ddof, keepdims=True)._collapse(axis)
def var(self, axis=None, dtype=None, out=None, ddof=0):
"""
Returns the variance of the matrix elements, along the given axis.
Refer to `numpy.var` for full documentation.
See Also
--------
numpy.var
Notes
-----
This is the same as `ndarray.var`, except that where an `ndarray` would
be returned, a `matrix` object is returned instead.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3, 4)))
>>> x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.var()
11.916666666666666
>>> x.var(0)
matrix([[ 10.66666667, 10.66666667, 10.66666667, 10.66666667]]) # may vary
>>> x.var(1)
matrix([[1.25],
[1.25],
[1.25]])
"""
return N.ndarray.var(self, axis, dtype, out, ddof, keepdims=True)._collapse(axis)
def prod(self, axis=None, dtype=None, out=None):
"""
Return the product of the array elements over the given axis.
Refer to `prod` for full documentation.
See Also
--------
prod, ndarray.prod
Notes
-----
Same as `ndarray.prod`, except, where that returns an `ndarray`, this
returns a `matrix` object instead.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.prod()
0
>>> x.prod(0)
matrix([[ 0, 45, 120, 231]])
>>> x.prod(1)
matrix([[ 0],
[ 840],
[7920]])
"""
return N.ndarray.prod(self, axis, dtype, out, keepdims=True)._collapse(axis)
def any(self, axis=None, out=None):
"""
Test whether any array element along a given axis evaluates to True.
Refer to `numpy.any` for full documentation.
Parameters
----------
axis : int, optional
Axis along which logical OR is performed
out : ndarray, optional
Output to existing array instead of creating new one, must have
same shape as expected output
Returns
-------
any : bool, ndarray
Returns a single bool if `axis` is ``None``; otherwise,
returns `ndarray`
"""
return N.ndarray.any(self, axis, out, keepdims=True)._collapse(axis)
def all(self, axis=None, out=None):
"""
Test whether all matrix elements along a given axis evaluate to True.
Parameters
----------
See `numpy.all` for complete descriptions
See Also
--------
numpy.all
Notes
-----
This is the same as `ndarray.all`, but it returns a `matrix` object.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> y = x[0]; y
matrix([[0, 1, 2, 3]])
>>> (x == y)
matrix([[ True, True, True, True],
[False, False, False, False],
[False, False, False, False]])
>>> (x == y).all()
False
>>> (x == y).all(0)
matrix([[False, False, False, False]])
>>> (x == y).all(1)
matrix([[ True],
[False],
[False]])
"""
return N.ndarray.all(self, axis, out, keepdims=True)._collapse(axis)
def max(self, axis=None, out=None):
"""
Return the maximum value along an axis.
Parameters
----------
See `amax` for complete descriptions
See Also
--------
amax, ndarray.max
Notes
-----
This is the same as `ndarray.max`, but returns a `matrix` object
where `ndarray.max` would return an ndarray.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.max()
11
>>> x.max(0)
matrix([[ 8, 9, 10, 11]])
>>> x.max(1)
matrix([[ 3],
[ 7],
[11]])
"""
return N.ndarray.max(self, axis, out, keepdims=True)._collapse(axis)
def argmax(self, axis=None, out=None):
"""
Indexes of the maximum values along an axis.
Return the indexes of the first occurrences of the maximum values
along the specified axis. If axis is None, the index is for the
flattened matrix.
Parameters
----------
See `numpy.argmax` for complete descriptions
See Also
--------
numpy.argmax
Notes
-----
This is the same as `ndarray.argmax`, but returns a `matrix` object
where `ndarray.argmax` would return an `ndarray`.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.argmax()
11
>>> x.argmax(0)
matrix([[2, 2, 2, 2]])
>>> x.argmax(1)
matrix([[3],
[3],
[3]])
"""
return N.ndarray.argmax(self, axis, out)._align(axis)
def min(self, axis=None, out=None):
"""
Return the minimum value along an axis.
Parameters
----------
See `amin` for complete descriptions.
See Also
--------
amin, ndarray.min
Notes
-----
This is the same as `ndarray.min`, but returns a `matrix` object
where `ndarray.min` would return an ndarray.
Examples
--------
>>> x = -np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, -1, -2, -3],
[ -4, -5, -6, -7],
[ -8, -9, -10, -11]])
>>> x.min()
-11
>>> x.min(0)
matrix([[ -8, -9, -10, -11]])
>>> x.min(1)
matrix([[ -3],
[ -7],
[-11]])
"""
return N.ndarray.min(self, axis, out, keepdims=True)._collapse(axis)
def argmin(self, axis=None, out=None):
"""
Indexes of the minimum values along an axis.
Return the indexes of the first occurrences of the minimum values
along the specified axis. If axis is None, the index is for the
flattened matrix.
Parameters
----------
See `numpy.argmin` for complete descriptions.
See Also
--------
numpy.argmin
Notes
-----
This is the same as `ndarray.argmin`, but returns a `matrix` object
where `ndarray.argmin` would return an `ndarray`.
Examples
--------
>>> x = -np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, -1, -2, -3],
[ -4, -5, -6, -7],
[ -8, -9, -10, -11]])
>>> x.argmin()
11
>>> x.argmin(0)
matrix([[2, 2, 2, 2]])
>>> x.argmin(1)
matrix([[3],
[3],
[3]])
"""
return N.ndarray.argmin(self, axis, out)._align(axis)
def ptp(self, axis=None, out=None):
"""
Peak-to-peak (maximum - minimum) value along the given axis.
Refer to `numpy.ptp` for full documentation.
See Also
--------
numpy.ptp
Notes
-----
Same as `ndarray.ptp`, except, where that would return an `ndarray` object,
this returns a `matrix` object.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.ptp()
11
>>> x.ptp(0)
matrix([[8, 8, 8, 8]])
>>> x.ptp(1)
matrix([[3],
[3],
[3]])
"""
return N.ndarray.ptp(self, axis, out)._align(axis)
def I(self):
"""
Returns the (multiplicative) inverse of invertible `self`.
Parameters
----------
None
Returns
-------
ret : matrix object
If `self` is non-singular, `ret` is such that ``ret * self`` ==
``self * ret`` == ``np.matrix(np.eye(self[0,:].size))`` all return
``True``.
Raises
------
numpy.linalg.LinAlgError: Singular matrix
If `self` is singular.
See Also
--------
linalg.inv
Examples
--------
>>> m = np.matrix('[1, 2; 3, 4]'); m
matrix([[1, 2],
[3, 4]])
>>> m.getI()
matrix([[-2. , 1. ],
[ 1.5, -0.5]])
>>> m.getI() * m
matrix([[ 1., 0.], # may vary
[ 0., 1.]])
"""
M, N = self.shape
if M == N:
from numpy.linalg import inv as func
else:
from numpy.linalg import pinv as func
return asmatrix(func(self))
def A(self):
"""
Return `self` as an `ndarray` object.
Equivalent to ``np.asarray(self)``.
Parameters
----------
None
Returns
-------
ret : ndarray
`self` as an `ndarray`
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.getA()
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
"""
return self.__array__()
def A1(self):
"""
Return `self` as a flattened `ndarray`.
Equivalent to ``np.asarray(x).ravel()``
Parameters
----------
None
Returns
-------
ret : ndarray
`self`, 1-D, as an `ndarray`
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.getA1()
array([ 0, 1, 2, ..., 9, 10, 11])
"""
return self.__array__().ravel()
def ravel(self, order='C'):
"""
Return a flattened matrix.
Refer to `numpy.ravel` for more documentation.
Parameters
----------
order : {'C', 'F', 'A', 'K'}, optional
The elements of `m` are read using this index order. 'C' means to
index the elements in C-like order, with the last axis index
changing fastest, back to the first axis index changing slowest.
'F' means to index the elements in Fortran-like index order, with
the first index changing fastest, and the last index changing
slowest. Note that the 'C' and 'F' options take no account of the
memory layout of the underlying array, and only refer to the order
of axis indexing. 'A' means to read the elements in Fortran-like
index order if `m` is Fortran *contiguous* in memory, C-like order
otherwise. 'K' means to read the elements in the order they occur
in memory, except for reversing the data when strides are negative.
By default, 'C' index order is used.
Returns
-------
ret : matrix
Return the matrix flattened to shape `(1, N)` where `N`
is the number of elements in the original matrix.
A copy is made only if necessary.
See Also
--------
matrix.flatten : returns a similar output matrix but always a copy
matrix.flat : a flat iterator on the array.
numpy.ravel : related function which returns an ndarray
"""
return N.ndarray.ravel(self, order=order)
def T(self):
"""
Returns the transpose of the matrix.
Does *not* conjugate! For the complex conjugate transpose, use ``.H``.
Parameters
----------
None
Returns
-------
ret : matrix object
The (non-conjugated) transpose of the matrix.
See Also
--------
transpose, getH
Examples
--------
>>> m = np.matrix('[1, 2; 3, 4]')
>>> m
matrix([[1, 2],
[3, 4]])
>>> m.getT()
matrix([[1, 3],
[2, 4]])
"""
return self.transpose()
def H(self):
"""
Returns the (complex) conjugate transpose of `self`.
Equivalent to ``np.transpose(self)`` if `self` is real-valued.
Parameters
----------
None
Returns
-------
ret : matrix object
complex conjugate transpose of `self`
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4)))
>>> z = x - 1j*x; z
matrix([[ 0. +0.j, 1. -1.j, 2. -2.j, 3. -3.j],
[ 4. -4.j, 5. -5.j, 6. -6.j, 7. -7.j],
[ 8. -8.j, 9. -9.j, 10.-10.j, 11.-11.j]])
>>> z.getH()
matrix([[ 0. -0.j, 4. +4.j, 8. +8.j],
[ 1. +1.j, 5. +5.j, 9. +9.j],
[ 2. +2.j, 6. +6.j, 10.+10.j],
[ 3. +3.j, 7. +7.j, 11.+11.j]])
"""
if issubclass(self.dtype.type, N.complexfloating):
return self.transpose().conjugate()
else:
return self.transpose()
# kept for compatibility
getT = T.fget
getA = A.fget
getA1 = A1.fget
getH = H.fget
getI = I.fget
The provided code snippet includes necessary dependencies for implementing the `ones` function. Write a Python function `def ones(shape, dtype=None, order='C')` to solve the following problem:
Matrix of ones. Return a matrix of given shape and type, filled with ones. Parameters ---------- shape : {sequence of ints, int} Shape of the matrix dtype : data-type, optional The desired data-type for the matrix, default is np.float64. order : {'C', 'F'}, optional Whether to store matrix in C- or Fortran-contiguous order, default is 'C'. Returns ------- out : matrix Matrix of ones of given shape, dtype, and order. See Also -------- ones : Array of ones. matlib.zeros : Zero matrix. Notes ----- If `shape` has length one i.e. ``(N,)``, or is a scalar ``N``, `out` becomes a single row matrix of shape ``(1,N)``. Examples -------- >>> np.matlib.ones((2,3)) matrix([[1., 1., 1.], [1., 1., 1.]]) >>> np.matlib.ones(2) matrix([[1., 1.]])
Here is the function:
def ones(shape, dtype=None, order='C'):
"""
Matrix of ones.
Return a matrix of given shape and type, filled with ones.
Parameters
----------
shape : {sequence of ints, int}
Shape of the matrix
dtype : data-type, optional
The desired data-type for the matrix, default is np.float64.
order : {'C', 'F'}, optional
Whether to store matrix in C- or Fortran-contiguous order,
default is 'C'.
Returns
-------
out : matrix
Matrix of ones of given shape, dtype, and order.
See Also
--------
ones : Array of ones.
matlib.zeros : Zero matrix.
Notes
-----
If `shape` has length one i.e. ``(N,)``, or is a scalar ``N``,
`out` becomes a single row matrix of shape ``(1,N)``.
Examples
--------
>>> np.matlib.ones((2,3))
matrix([[1., 1., 1.],
[1., 1., 1.]])
>>> np.matlib.ones(2)
matrix([[1., 1.]])
"""
a = ndarray.__new__(matrix, shape, dtype, order=order)
a.fill(1)
return a | Matrix of ones. Return a matrix of given shape and type, filled with ones. Parameters ---------- shape : {sequence of ints, int} Shape of the matrix dtype : data-type, optional The desired data-type for the matrix, default is np.float64. order : {'C', 'F'}, optional Whether to store matrix in C- or Fortran-contiguous order, default is 'C'. Returns ------- out : matrix Matrix of ones of given shape, dtype, and order. See Also -------- ones : Array of ones. matlib.zeros : Zero matrix. Notes ----- If `shape` has length one i.e. ``(N,)``, or is a scalar ``N``, `out` becomes a single row matrix of shape ``(1,N)``. Examples -------- >>> np.matlib.ones((2,3)) matrix([[1., 1., 1.], [1., 1., 1.]]) >>> np.matlib.ones(2) matrix([[1., 1.]]) |
169,954 | import warnings
import numpy as np
from numpy.matrixlib.defmatrix import matrix, asmatrix
from numpy import *
class matrix(N.ndarray):
"""
matrix(data, dtype=None, copy=True)
.. note:: It is no longer recommended to use this class, even for linear
algebra. Instead use regular arrays. The class may be removed
in the future.
Returns a matrix from an array-like object, or from a string of data.
A matrix is a specialized 2-D array that retains its 2-D nature
through operations. It has certain special operators, such as ``*``
(matrix multiplication) and ``**`` (matrix power).
Parameters
----------
data : array_like or string
If `data` is a string, it is interpreted as a matrix with commas
or spaces separating columns, and semicolons separating rows.
dtype : data-type
Data-type of the output matrix.
copy : bool
If `data` is already an `ndarray`, then this flag determines
whether the data is copied (the default), or whether a view is
constructed.
See Also
--------
array
Examples
--------
>>> a = np.matrix('1 2; 3 4')
>>> a
matrix([[1, 2],
[3, 4]])
>>> np.matrix([[1, 2], [3, 4]])
matrix([[1, 2],
[3, 4]])
"""
__array_priority__ = 10.0
def __new__(subtype, data, dtype=None, copy=True):
warnings.warn('the matrix subclass is not the recommended way to '
'represent matrices or deal with linear algebra (see '
'https://docs.scipy.org/doc/numpy/user/'
'numpy-for-matlab-users.html). '
'Please adjust your code to use regular ndarray.',
PendingDeprecationWarning, stacklevel=2)
if isinstance(data, matrix):
dtype2 = data.dtype
if (dtype is None):
dtype = dtype2
if (dtype2 == dtype) and (not copy):
return data
return data.astype(dtype)
if isinstance(data, N.ndarray):
if dtype is None:
intype = data.dtype
else:
intype = N.dtype(dtype)
new = data.view(subtype)
if intype != data.dtype:
return new.astype(intype)
if copy: return new.copy()
else: return new
if isinstance(data, str):
data = _convert_from_string(data)
# now convert data to an array
arr = N.array(data, dtype=dtype, copy=copy)
ndim = arr.ndim
shape = arr.shape
if (ndim > 2):
raise ValueError("matrix must be 2-dimensional")
elif ndim == 0:
shape = (1, 1)
elif ndim == 1:
shape = (1, shape[0])
order = 'C'
if (ndim == 2) and arr.flags.fortran:
order = 'F'
if not (order or arr.flags.contiguous):
arr = arr.copy()
ret = N.ndarray.__new__(subtype, shape, arr.dtype,
buffer=arr,
order=order)
return ret
def __array_finalize__(self, obj):
self._getitem = False
if (isinstance(obj, matrix) and obj._getitem): return
ndim = self.ndim
if (ndim == 2):
return
if (ndim > 2):
newshape = tuple([x for x in self.shape if x > 1])
ndim = len(newshape)
if ndim == 2:
self.shape = newshape
return
elif (ndim > 2):
raise ValueError("shape too large to be a matrix.")
else:
newshape = self.shape
if ndim == 0:
self.shape = (1, 1)
elif ndim == 1:
self.shape = (1, newshape[0])
return
def __getitem__(self, index):
self._getitem = True
try:
out = N.ndarray.__getitem__(self, index)
finally:
self._getitem = False
if not isinstance(out, N.ndarray):
return out
if out.ndim == 0:
return out[()]
if out.ndim == 1:
sh = out.shape[0]
# Determine when we should have a column array
try:
n = len(index)
except Exception:
n = 0
if n > 1 and isscalar(index[1]):
out.shape = (sh, 1)
else:
out.shape = (1, sh)
return out
def __mul__(self, other):
if isinstance(other, (N.ndarray, list, tuple)) :
# This promotes 1-D vectors to row vectors
return N.dot(self, asmatrix(other))
if isscalar(other) or not hasattr(other, '__rmul__') :
return N.dot(self, other)
return NotImplemented
def __rmul__(self, other):
return N.dot(other, self)
def __imul__(self, other):
self[:] = self * other
return self
def __pow__(self, other):
return matrix_power(self, other)
def __ipow__(self, other):
self[:] = self ** other
return self
def __rpow__(self, other):
return NotImplemented
def _align(self, axis):
"""A convenience function for operations that need to preserve axis
orientation.
"""
if axis is None:
return self[0, 0]
elif axis==0:
return self
elif axis==1:
return self.transpose()
else:
raise ValueError("unsupported axis")
def _collapse(self, axis):
"""A convenience function for operations that want to collapse
to a scalar like _align, but are using keepdims=True
"""
if axis is None:
return self[0, 0]
else:
return self
# Necessary because base-class tolist expects dimension
# reduction by x[0]
def tolist(self):
"""
Return the matrix as a (possibly nested) list.
See `ndarray.tolist` for full documentation.
See Also
--------
ndarray.tolist
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.tolist()
[[0, 1, 2, 3], [4, 5, 6, 7], [8, 9, 10, 11]]
"""
return self.__array__().tolist()
# To preserve orientation of result...
def sum(self, axis=None, dtype=None, out=None):
"""
Returns the sum of the matrix elements, along the given axis.
Refer to `numpy.sum` for full documentation.
See Also
--------
numpy.sum
Notes
-----
This is the same as `ndarray.sum`, except that where an `ndarray` would
be returned, a `matrix` object is returned instead.
Examples
--------
>>> x = np.matrix([[1, 2], [4, 3]])
>>> x.sum()
10
>>> x.sum(axis=1)
matrix([[3],
[7]])
>>> x.sum(axis=1, dtype='float')
matrix([[3.],
[7.]])
>>> out = np.zeros((2, 1), dtype='float')
>>> x.sum(axis=1, dtype='float', out=np.asmatrix(out))
matrix([[3.],
[7.]])
"""
return N.ndarray.sum(self, axis, dtype, out, keepdims=True)._collapse(axis)
# To update docstring from array to matrix...
def squeeze(self, axis=None):
"""
Return a possibly reshaped matrix.
Refer to `numpy.squeeze` for more documentation.
Parameters
----------
axis : None or int or tuple of ints, optional
Selects a subset of the axes of length one in the shape.
If an axis is selected with shape entry greater than one,
an error is raised.
Returns
-------
squeezed : matrix
The matrix, but as a (1, N) matrix if it had shape (N, 1).
See Also
--------
numpy.squeeze : related function
Notes
-----
If `m` has a single column then that column is returned
as the single row of a matrix. Otherwise `m` is returned.
The returned matrix is always either `m` itself or a view into `m`.
Supplying an axis keyword argument will not affect the returned matrix
but it may cause an error to be raised.
Examples
--------
>>> c = np.matrix([[1], [2]])
>>> c
matrix([[1],
[2]])
>>> c.squeeze()
matrix([[1, 2]])
>>> r = c.T
>>> r
matrix([[1, 2]])
>>> r.squeeze()
matrix([[1, 2]])
>>> m = np.matrix([[1, 2], [3, 4]])
>>> m.squeeze()
matrix([[1, 2],
[3, 4]])
"""
return N.ndarray.squeeze(self, axis=axis)
# To update docstring from array to matrix...
def flatten(self, order='C'):
"""
Return a flattened copy of the matrix.
All `N` elements of the matrix are placed into a single row.
Parameters
----------
order : {'C', 'F', 'A', 'K'}, optional
'C' means to flatten in row-major (C-style) order. 'F' means to
flatten in column-major (Fortran-style) order. 'A' means to
flatten in column-major order if `m` is Fortran *contiguous* in
memory, row-major order otherwise. 'K' means to flatten `m` in
the order the elements occur in memory. The default is 'C'.
Returns
-------
y : matrix
A copy of the matrix, flattened to a `(1, N)` matrix where `N`
is the number of elements in the original matrix.
See Also
--------
ravel : Return a flattened array.
flat : A 1-D flat iterator over the matrix.
Examples
--------
>>> m = np.matrix([[1,2], [3,4]])
>>> m.flatten()
matrix([[1, 2, 3, 4]])
>>> m.flatten('F')
matrix([[1, 3, 2, 4]])
"""
return N.ndarray.flatten(self, order=order)
def mean(self, axis=None, dtype=None, out=None):
"""
Returns the average of the matrix elements along the given axis.
Refer to `numpy.mean` for full documentation.
See Also
--------
numpy.mean
Notes
-----
Same as `ndarray.mean` except that, where that returns an `ndarray`,
this returns a `matrix` object.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3, 4)))
>>> x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.mean()
5.5
>>> x.mean(0)
matrix([[4., 5., 6., 7.]])
>>> x.mean(1)
matrix([[ 1.5],
[ 5.5],
[ 9.5]])
"""
return N.ndarray.mean(self, axis, dtype, out, keepdims=True)._collapse(axis)
def std(self, axis=None, dtype=None, out=None, ddof=0):
"""
Return the standard deviation of the array elements along the given axis.
Refer to `numpy.std` for full documentation.
See Also
--------
numpy.std
Notes
-----
This is the same as `ndarray.std`, except that where an `ndarray` would
be returned, a `matrix` object is returned instead.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3, 4)))
>>> x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.std()
3.4520525295346629 # may vary
>>> x.std(0)
matrix([[ 3.26598632, 3.26598632, 3.26598632, 3.26598632]]) # may vary
>>> x.std(1)
matrix([[ 1.11803399],
[ 1.11803399],
[ 1.11803399]])
"""
return N.ndarray.std(self, axis, dtype, out, ddof, keepdims=True)._collapse(axis)
def var(self, axis=None, dtype=None, out=None, ddof=0):
"""
Returns the variance of the matrix elements, along the given axis.
Refer to `numpy.var` for full documentation.
See Also
--------
numpy.var
Notes
-----
This is the same as `ndarray.var`, except that where an `ndarray` would
be returned, a `matrix` object is returned instead.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3, 4)))
>>> x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.var()
11.916666666666666
>>> x.var(0)
matrix([[ 10.66666667, 10.66666667, 10.66666667, 10.66666667]]) # may vary
>>> x.var(1)
matrix([[1.25],
[1.25],
[1.25]])
"""
return N.ndarray.var(self, axis, dtype, out, ddof, keepdims=True)._collapse(axis)
def prod(self, axis=None, dtype=None, out=None):
"""
Return the product of the array elements over the given axis.
Refer to `prod` for full documentation.
See Also
--------
prod, ndarray.prod
Notes
-----
Same as `ndarray.prod`, except, where that returns an `ndarray`, this
returns a `matrix` object instead.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.prod()
0
>>> x.prod(0)
matrix([[ 0, 45, 120, 231]])
>>> x.prod(1)
matrix([[ 0],
[ 840],
[7920]])
"""
return N.ndarray.prod(self, axis, dtype, out, keepdims=True)._collapse(axis)
def any(self, axis=None, out=None):
"""
Test whether any array element along a given axis evaluates to True.
Refer to `numpy.any` for full documentation.
Parameters
----------
axis : int, optional
Axis along which logical OR is performed
out : ndarray, optional
Output to existing array instead of creating new one, must have
same shape as expected output
Returns
-------
any : bool, ndarray
Returns a single bool if `axis` is ``None``; otherwise,
returns `ndarray`
"""
return N.ndarray.any(self, axis, out, keepdims=True)._collapse(axis)
def all(self, axis=None, out=None):
"""
Test whether all matrix elements along a given axis evaluate to True.
Parameters
----------
See `numpy.all` for complete descriptions
See Also
--------
numpy.all
Notes
-----
This is the same as `ndarray.all`, but it returns a `matrix` object.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> y = x[0]; y
matrix([[0, 1, 2, 3]])
>>> (x == y)
matrix([[ True, True, True, True],
[False, False, False, False],
[False, False, False, False]])
>>> (x == y).all()
False
>>> (x == y).all(0)
matrix([[False, False, False, False]])
>>> (x == y).all(1)
matrix([[ True],
[False],
[False]])
"""
return N.ndarray.all(self, axis, out, keepdims=True)._collapse(axis)
def max(self, axis=None, out=None):
"""
Return the maximum value along an axis.
Parameters
----------
See `amax` for complete descriptions
See Also
--------
amax, ndarray.max
Notes
-----
This is the same as `ndarray.max`, but returns a `matrix` object
where `ndarray.max` would return an ndarray.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.max()
11
>>> x.max(0)
matrix([[ 8, 9, 10, 11]])
>>> x.max(1)
matrix([[ 3],
[ 7],
[11]])
"""
return N.ndarray.max(self, axis, out, keepdims=True)._collapse(axis)
def argmax(self, axis=None, out=None):
"""
Indexes of the maximum values along an axis.
Return the indexes of the first occurrences of the maximum values
along the specified axis. If axis is None, the index is for the
flattened matrix.
Parameters
----------
See `numpy.argmax` for complete descriptions
See Also
--------
numpy.argmax
Notes
-----
This is the same as `ndarray.argmax`, but returns a `matrix` object
where `ndarray.argmax` would return an `ndarray`.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.argmax()
11
>>> x.argmax(0)
matrix([[2, 2, 2, 2]])
>>> x.argmax(1)
matrix([[3],
[3],
[3]])
"""
return N.ndarray.argmax(self, axis, out)._align(axis)
def min(self, axis=None, out=None):
"""
Return the minimum value along an axis.
Parameters
----------
See `amin` for complete descriptions.
See Also
--------
amin, ndarray.min
Notes
-----
This is the same as `ndarray.min`, but returns a `matrix` object
where `ndarray.min` would return an ndarray.
Examples
--------
>>> x = -np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, -1, -2, -3],
[ -4, -5, -6, -7],
[ -8, -9, -10, -11]])
>>> x.min()
-11
>>> x.min(0)
matrix([[ -8, -9, -10, -11]])
>>> x.min(1)
matrix([[ -3],
[ -7],
[-11]])
"""
return N.ndarray.min(self, axis, out, keepdims=True)._collapse(axis)
def argmin(self, axis=None, out=None):
"""
Indexes of the minimum values along an axis.
Return the indexes of the first occurrences of the minimum values
along the specified axis. If axis is None, the index is for the
flattened matrix.
Parameters
----------
See `numpy.argmin` for complete descriptions.
See Also
--------
numpy.argmin
Notes
-----
This is the same as `ndarray.argmin`, but returns a `matrix` object
where `ndarray.argmin` would return an `ndarray`.
Examples
--------
>>> x = -np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, -1, -2, -3],
[ -4, -5, -6, -7],
[ -8, -9, -10, -11]])
>>> x.argmin()
11
>>> x.argmin(0)
matrix([[2, 2, 2, 2]])
>>> x.argmin(1)
matrix([[3],
[3],
[3]])
"""
return N.ndarray.argmin(self, axis, out)._align(axis)
def ptp(self, axis=None, out=None):
"""
Peak-to-peak (maximum - minimum) value along the given axis.
Refer to `numpy.ptp` for full documentation.
See Also
--------
numpy.ptp
Notes
-----
Same as `ndarray.ptp`, except, where that would return an `ndarray` object,
this returns a `matrix` object.
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.ptp()
11
>>> x.ptp(0)
matrix([[8, 8, 8, 8]])
>>> x.ptp(1)
matrix([[3],
[3],
[3]])
"""
return N.ndarray.ptp(self, axis, out)._align(axis)
def I(self):
"""
Returns the (multiplicative) inverse of invertible `self`.
Parameters
----------
None
Returns
-------
ret : matrix object
If `self` is non-singular, `ret` is such that ``ret * self`` ==
``self * ret`` == ``np.matrix(np.eye(self[0,:].size))`` all return
``True``.
Raises
------
numpy.linalg.LinAlgError: Singular matrix
If `self` is singular.
See Also
--------
linalg.inv
Examples
--------
>>> m = np.matrix('[1, 2; 3, 4]'); m
matrix([[1, 2],
[3, 4]])
>>> m.getI()
matrix([[-2. , 1. ],
[ 1.5, -0.5]])
>>> m.getI() * m
matrix([[ 1., 0.], # may vary
[ 0., 1.]])
"""
M, N = self.shape
if M == N:
from numpy.linalg import inv as func
else:
from numpy.linalg import pinv as func
return asmatrix(func(self))
def A(self):
"""
Return `self` as an `ndarray` object.
Equivalent to ``np.asarray(self)``.
Parameters
----------
None
Returns
-------
ret : ndarray
`self` as an `ndarray`
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.getA()
array([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
"""
return self.__array__()
def A1(self):
"""
Return `self` as a flattened `ndarray`.
Equivalent to ``np.asarray(x).ravel()``
Parameters
----------
None
Returns
-------
ret : ndarray
`self`, 1-D, as an `ndarray`
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4))); x
matrix([[ 0, 1, 2, 3],
[ 4, 5, 6, 7],
[ 8, 9, 10, 11]])
>>> x.getA1()
array([ 0, 1, 2, ..., 9, 10, 11])
"""
return self.__array__().ravel()
def ravel(self, order='C'):
"""
Return a flattened matrix.
Refer to `numpy.ravel` for more documentation.
Parameters
----------
order : {'C', 'F', 'A', 'K'}, optional
The elements of `m` are read using this index order. 'C' means to
index the elements in C-like order, with the last axis index
changing fastest, back to the first axis index changing slowest.
'F' means to index the elements in Fortran-like index order, with
the first index changing fastest, and the last index changing
slowest. Note that the 'C' and 'F' options take no account of the
memory layout of the underlying array, and only refer to the order
of axis indexing. 'A' means to read the elements in Fortran-like
index order if `m` is Fortran *contiguous* in memory, C-like order
otherwise. 'K' means to read the elements in the order they occur
in memory, except for reversing the data when strides are negative.
By default, 'C' index order is used.
Returns
-------
ret : matrix
Return the matrix flattened to shape `(1, N)` where `N`
is the number of elements in the original matrix.
A copy is made only if necessary.
See Also
--------
matrix.flatten : returns a similar output matrix but always a copy
matrix.flat : a flat iterator on the array.
numpy.ravel : related function which returns an ndarray
"""
return N.ndarray.ravel(self, order=order)
def T(self):
"""
Returns the transpose of the matrix.
Does *not* conjugate! For the complex conjugate transpose, use ``.H``.
Parameters
----------
None
Returns
-------
ret : matrix object
The (non-conjugated) transpose of the matrix.
See Also
--------
transpose, getH
Examples
--------
>>> m = np.matrix('[1, 2; 3, 4]')
>>> m
matrix([[1, 2],
[3, 4]])
>>> m.getT()
matrix([[1, 3],
[2, 4]])
"""
return self.transpose()
def H(self):
"""
Returns the (complex) conjugate transpose of `self`.
Equivalent to ``np.transpose(self)`` if `self` is real-valued.
Parameters
----------
None
Returns
-------
ret : matrix object
complex conjugate transpose of `self`
Examples
--------
>>> x = np.matrix(np.arange(12).reshape((3,4)))
>>> z = x - 1j*x; z
matrix([[ 0. +0.j, 1. -1.j, 2. -2.j, 3. -3.j],
[ 4. -4.j, 5. -5.j, 6. -6.j, 7. -7.j],
[ 8. -8.j, 9. -9.j, 10.-10.j, 11.-11.j]])
>>> z.getH()
matrix([[ 0. -0.j, 4. +4.j, 8. +8.j],
[ 1. +1.j, 5. +5.j, 9. +9.j],
[ 2. +2.j, 6. +6.j, 10.+10.j],
[ 3. +3.j, 7. +7.j, 11.+11.j]])
"""
if issubclass(self.dtype.type, N.complexfloating):
return self.transpose().conjugate()
else:
return self.transpose()
# kept for compatibility
getT = T.fget
getA = A.fget
getA1 = A1.fget
getH = H.fget
getI = I.fget
The provided code snippet includes necessary dependencies for implementing the `zeros` function. Write a Python function `def zeros(shape, dtype=None, order='C')` to solve the following problem:
Return a matrix of given shape and type, filled with zeros. Parameters ---------- shape : int or sequence of ints Shape of the matrix dtype : data-type, optional The desired data-type for the matrix, default is float. order : {'C', 'F'}, optional Whether to store the result in C- or Fortran-contiguous order, default is 'C'. Returns ------- out : matrix Zero matrix of given shape, dtype, and order. See Also -------- numpy.zeros : Equivalent array function. matlib.ones : Return a matrix of ones. Notes ----- If `shape` has length one i.e. ``(N,)``, or is a scalar ``N``, `out` becomes a single row matrix of shape ``(1,N)``. Examples -------- >>> import numpy.matlib >>> np.matlib.zeros((2, 3)) matrix([[0., 0., 0.], [0., 0., 0.]]) >>> np.matlib.zeros(2) matrix([[0., 0.]])
Here is the function:
def zeros(shape, dtype=None, order='C'):
"""
Return a matrix of given shape and type, filled with zeros.
Parameters
----------
shape : int or sequence of ints
Shape of the matrix
dtype : data-type, optional
The desired data-type for the matrix, default is float.
order : {'C', 'F'}, optional
Whether to store the result in C- or Fortran-contiguous order,
default is 'C'.
Returns
-------
out : matrix
Zero matrix of given shape, dtype, and order.
See Also
--------
numpy.zeros : Equivalent array function.
matlib.ones : Return a matrix of ones.
Notes
-----
If `shape` has length one i.e. ``(N,)``, or is a scalar ``N``,
`out` becomes a single row matrix of shape ``(1,N)``.
Examples
--------
>>> import numpy.matlib
>>> np.matlib.zeros((2, 3))
matrix([[0., 0., 0.],
[0., 0., 0.]])
>>> np.matlib.zeros(2)
matrix([[0., 0.]])
"""
a = ndarray.__new__(matrix, shape, dtype, order=order)
a.fill(0)
return a | Return a matrix of given shape and type, filled with zeros. Parameters ---------- shape : int or sequence of ints Shape of the matrix dtype : data-type, optional The desired data-type for the matrix, default is float. order : {'C', 'F'}, optional Whether to store the result in C- or Fortran-contiguous order, default is 'C'. Returns ------- out : matrix Zero matrix of given shape, dtype, and order. See Also -------- numpy.zeros : Equivalent array function. matlib.ones : Return a matrix of ones. Notes ----- If `shape` has length one i.e. ``(N,)``, or is a scalar ``N``, `out` becomes a single row matrix of shape ``(1,N)``. Examples -------- >>> import numpy.matlib >>> np.matlib.zeros((2, 3)) matrix([[0., 0., 0.], [0., 0., 0.]]) >>> np.matlib.zeros(2) matrix([[0., 0.]]) |
169,955 | import warnings
import numpy as np
from numpy.matrixlib.defmatrix import matrix, asmatrix
from numpy import *
def empty(shape, dtype=None, order='C'):
"""Return a new matrix of given shape and type, without initializing entries.
Parameters
----------
shape : int or tuple of int
Shape of the empty matrix.
dtype : data-type, optional
Desired output data-type.
order : {'C', 'F'}, optional
Whether to store multi-dimensional data in row-major
(C-style) or column-major (Fortran-style) order in
memory.
See Also
--------
empty_like, zeros
Notes
-----
`empty`, unlike `zeros`, does not set the matrix values to zero,
and may therefore be marginally faster. On the other hand, it requires
the user to manually set all the values in the array, and should be
used with caution.
Examples
--------
>>> import numpy.matlib
>>> np.matlib.empty((2, 2)) # filled with random data
matrix([[ 6.76425276e-320, 9.79033856e-307], # random
[ 7.39337286e-309, 3.22135945e-309]])
>>> np.matlib.empty((2, 2), dtype=int)
matrix([[ 6600475, 0], # random
[ 6586976, 22740995]])
"""
return ndarray.__new__(matrix, shape, dtype, order=order)
The provided code snippet includes necessary dependencies for implementing the `identity` function. Write a Python function `def identity(n,dtype=None)` to solve the following problem:
Returns the square identity matrix of given size. Parameters ---------- n : int Size of the returned identity matrix. dtype : data-type, optional Data-type of the output. Defaults to ``float``. Returns ------- out : matrix `n` x `n` matrix with its main diagonal set to one, and all other elements zero. See Also -------- numpy.identity : Equivalent array function. matlib.eye : More general matrix identity function. Examples -------- >>> import numpy.matlib >>> np.matlib.identity(3, dtype=int) matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
Here is the function:
def identity(n,dtype=None):
"""
Returns the square identity matrix of given size.
Parameters
----------
n : int
Size of the returned identity matrix.
dtype : data-type, optional
Data-type of the output. Defaults to ``float``.
Returns
-------
out : matrix
`n` x `n` matrix with its main diagonal set to one,
and all other elements zero.
See Also
--------
numpy.identity : Equivalent array function.
matlib.eye : More general matrix identity function.
Examples
--------
>>> import numpy.matlib
>>> np.matlib.identity(3, dtype=int)
matrix([[1, 0, 0],
[0, 1, 0],
[0, 0, 1]])
"""
a = array([1]+n*[0], dtype=dtype)
b = empty((n, n), dtype=dtype)
b.flat = a
return b | Returns the square identity matrix of given size. Parameters ---------- n : int Size of the returned identity matrix. dtype : data-type, optional Data-type of the output. Defaults to ``float``. Returns ------- out : matrix `n` x `n` matrix with its main diagonal set to one, and all other elements zero. See Also -------- numpy.identity : Equivalent array function. matlib.eye : More general matrix identity function. Examples -------- >>> import numpy.matlib >>> np.matlib.identity(3, dtype=int) matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]]) |
169,956 | import warnings
import numpy as np
from numpy.matrixlib.defmatrix import matrix, asmatrix
from numpy import *
def asmatrix(data, dtype=None):
"""
Interpret the input as a matrix.
Unlike `matrix`, `asmatrix` does not make a copy if the input is already
a matrix or an ndarray. Equivalent to ``matrix(data, copy=False)``.
Parameters
----------
data : array_like
Input data.
dtype : data-type
Data-type of the output matrix.
Returns
-------
mat : matrix
`data` interpreted as a matrix.
Examples
--------
>>> x = np.array([[1, 2], [3, 4]])
>>> m = np.asmatrix(x)
>>> x[0,0] = 5
>>> m
matrix([[5, 2],
[3, 4]])
"""
return matrix(data, dtype=dtype, copy=False)
The provided code snippet includes necessary dependencies for implementing the `eye` function. Write a Python function `def eye(n,M=None, k=0, dtype=float, order='C')` to solve the following problem:
Return a matrix with ones on the diagonal and zeros elsewhere. Parameters ---------- n : int Number of rows in the output. M : int, optional Number of columns in the output, defaults to `n`. k : int, optional Index of the diagonal: 0 refers to the main diagonal, a positive value refers to an upper diagonal, and a negative value to a lower diagonal. dtype : dtype, optional Data-type of the returned matrix. order : {'C', 'F'}, optional Whether the output should be stored in row-major (C-style) or column-major (Fortran-style) order in memory. .. versionadded:: 1.14.0 Returns ------- I : matrix A `n` x `M` matrix where all elements are equal to zero, except for the `k`-th diagonal, whose values are equal to one. See Also -------- numpy.eye : Equivalent array function. identity : Square identity matrix. Examples -------- >>> import numpy.matlib >>> np.matlib.eye(3, k=1, dtype=float) matrix([[0., 1., 0.], [0., 0., 1.], [0., 0., 0.]])
Here is the function:
def eye(n,M=None, k=0, dtype=float, order='C'):
"""
Return a matrix with ones on the diagonal and zeros elsewhere.
Parameters
----------
n : int
Number of rows in the output.
M : int, optional
Number of columns in the output, defaults to `n`.
k : int, optional
Index of the diagonal: 0 refers to the main diagonal,
a positive value refers to an upper diagonal,
and a negative value to a lower diagonal.
dtype : dtype, optional
Data-type of the returned matrix.
order : {'C', 'F'}, optional
Whether the output should be stored in row-major (C-style) or
column-major (Fortran-style) order in memory.
.. versionadded:: 1.14.0
Returns
-------
I : matrix
A `n` x `M` matrix where all elements are equal to zero,
except for the `k`-th diagonal, whose values are equal to one.
See Also
--------
numpy.eye : Equivalent array function.
identity : Square identity matrix.
Examples
--------
>>> import numpy.matlib
>>> np.matlib.eye(3, k=1, dtype=float)
matrix([[0., 1., 0.],
[0., 0., 1.],
[0., 0., 0.]])
"""
return asmatrix(np.eye(n, M=M, k=k, dtype=dtype, order=order)) | Return a matrix with ones on the diagonal and zeros elsewhere. Parameters ---------- n : int Number of rows in the output. M : int, optional Number of columns in the output, defaults to `n`. k : int, optional Index of the diagonal: 0 refers to the main diagonal, a positive value refers to an upper diagonal, and a negative value to a lower diagonal. dtype : dtype, optional Data-type of the returned matrix. order : {'C', 'F'}, optional Whether the output should be stored in row-major (C-style) or column-major (Fortran-style) order in memory. .. versionadded:: 1.14.0 Returns ------- I : matrix A `n` x `M` matrix where all elements are equal to zero, except for the `k`-th diagonal, whose values are equal to one. See Also -------- numpy.eye : Equivalent array function. identity : Square identity matrix. Examples -------- >>> import numpy.matlib >>> np.matlib.eye(3, k=1, dtype=float) matrix([[0., 1., 0.], [0., 0., 1.], [0., 0., 0.]]) |
169,957 | import warnings
import numpy as np
from numpy.matrixlib.defmatrix import matrix, asmatrix
from numpy import *
def asmatrix(data, dtype=None):
"""
Interpret the input as a matrix.
Unlike `matrix`, `asmatrix` does not make a copy if the input is already
a matrix or an ndarray. Equivalent to ``matrix(data, copy=False)``.
Parameters
----------
data : array_like
Input data.
dtype : data-type
Data-type of the output matrix.
Returns
-------
mat : matrix
`data` interpreted as a matrix.
Examples
--------
>>> x = np.array([[1, 2], [3, 4]])
>>> m = np.asmatrix(x)
>>> x[0,0] = 5
>>> m
matrix([[5, 2],
[3, 4]])
"""
return matrix(data, dtype=dtype, copy=False)
The provided code snippet includes necessary dependencies for implementing the `rand` function. Write a Python function `def rand(*args)` to solve the following problem:
Return a matrix of random values with given shape. Create a matrix of the given shape and propagate it with random samples from a uniform distribution over ``[0, 1)``. Parameters ---------- \\*args : Arguments Shape of the output. If given as N integers, each integer specifies the size of one dimension. If given as a tuple, this tuple gives the complete shape. Returns ------- out : ndarray The matrix of random values with shape given by `\\*args`. See Also -------- randn, numpy.random.RandomState.rand Examples -------- >>> np.random.seed(123) >>> import numpy.matlib >>> np.matlib.rand(2, 3) matrix([[0.69646919, 0.28613933, 0.22685145], [0.55131477, 0.71946897, 0.42310646]]) >>> np.matlib.rand((2, 3)) matrix([[0.9807642 , 0.68482974, 0.4809319 ], [0.39211752, 0.34317802, 0.72904971]]) If the first argument is a tuple, other arguments are ignored: >>> np.matlib.rand((2, 3), 4) matrix([[0.43857224, 0.0596779 , 0.39804426], [0.73799541, 0.18249173, 0.17545176]])
Here is the function:
def rand(*args):
"""
Return a matrix of random values with given shape.
Create a matrix of the given shape and propagate it with
random samples from a uniform distribution over ``[0, 1)``.
Parameters
----------
\\*args : Arguments
Shape of the output.
If given as N integers, each integer specifies the size of one
dimension.
If given as a tuple, this tuple gives the complete shape.
Returns
-------
out : ndarray
The matrix of random values with shape given by `\\*args`.
See Also
--------
randn, numpy.random.RandomState.rand
Examples
--------
>>> np.random.seed(123)
>>> import numpy.matlib
>>> np.matlib.rand(2, 3)
matrix([[0.69646919, 0.28613933, 0.22685145],
[0.55131477, 0.71946897, 0.42310646]])
>>> np.matlib.rand((2, 3))
matrix([[0.9807642 , 0.68482974, 0.4809319 ],
[0.39211752, 0.34317802, 0.72904971]])
If the first argument is a tuple, other arguments are ignored:
>>> np.matlib.rand((2, 3), 4)
matrix([[0.43857224, 0.0596779 , 0.39804426],
[0.73799541, 0.18249173, 0.17545176]])
"""
if isinstance(args[0], tuple):
args = args[0]
return asmatrix(np.random.rand(*args)) | Return a matrix of random values with given shape. Create a matrix of the given shape and propagate it with random samples from a uniform distribution over ``[0, 1)``. Parameters ---------- \\*args : Arguments Shape of the output. If given as N integers, each integer specifies the size of one dimension. If given as a tuple, this tuple gives the complete shape. Returns ------- out : ndarray The matrix of random values with shape given by `\\*args`. See Also -------- randn, numpy.random.RandomState.rand Examples -------- >>> np.random.seed(123) >>> import numpy.matlib >>> np.matlib.rand(2, 3) matrix([[0.69646919, 0.28613933, 0.22685145], [0.55131477, 0.71946897, 0.42310646]]) >>> np.matlib.rand((2, 3)) matrix([[0.9807642 , 0.68482974, 0.4809319 ], [0.39211752, 0.34317802, 0.72904971]]) If the first argument is a tuple, other arguments are ignored: >>> np.matlib.rand((2, 3), 4) matrix([[0.43857224, 0.0596779 , 0.39804426], [0.73799541, 0.18249173, 0.17545176]]) |
169,958 | import warnings
import numpy as np
from numpy.matrixlib.defmatrix import matrix, asmatrix
from numpy import *
def asmatrix(data, dtype=None):
"""
Interpret the input as a matrix.
Unlike `matrix`, `asmatrix` does not make a copy if the input is already
a matrix or an ndarray. Equivalent to ``matrix(data, copy=False)``.
Parameters
----------
data : array_like
Input data.
dtype : data-type
Data-type of the output matrix.
Returns
-------
mat : matrix
`data` interpreted as a matrix.
Examples
--------
>>> x = np.array([[1, 2], [3, 4]])
>>> m = np.asmatrix(x)
>>> x[0,0] = 5
>>> m
matrix([[5, 2],
[3, 4]])
"""
return matrix(data, dtype=dtype, copy=False)
The provided code snippet includes necessary dependencies for implementing the `randn` function. Write a Python function `def randn(*args)` to solve the following problem:
Return a random matrix with data from the "standard normal" distribution. `randn` generates a matrix filled with random floats sampled from a univariate "normal" (Gaussian) distribution of mean 0 and variance 1. Parameters ---------- \\*args : Arguments Shape of the output. If given as N integers, each integer specifies the size of one dimension. If given as a tuple, this tuple gives the complete shape. Returns ------- Z : matrix of floats A matrix of floating-point samples drawn from the standard normal distribution. See Also -------- rand, numpy.random.RandomState.randn Notes ----- For random samples from the normal distribution with mean ``mu`` and standard deviation ``sigma``, use:: sigma * np.matlib.randn(...) + mu Examples -------- >>> np.random.seed(123) >>> import numpy.matlib >>> np.matlib.randn(1) matrix([[-1.0856306]]) >>> np.matlib.randn(1, 2, 3) matrix([[ 0.99734545, 0.2829785 , -1.50629471], [-0.57860025, 1.65143654, -2.42667924]]) Two-by-four matrix of samples from the normal distribution with mean 3 and standard deviation 2.5: >>> 2.5 * np.matlib.randn((2, 4)) + 3 matrix([[1.92771843, 6.16484065, 0.83314899, 1.30278462], [2.76322758, 6.72847407, 1.40274501, 1.8900451 ]])
Here is the function:
def randn(*args):
"""
Return a random matrix with data from the "standard normal" distribution.
`randn` generates a matrix filled with random floats sampled from a
univariate "normal" (Gaussian) distribution of mean 0 and variance 1.
Parameters
----------
\\*args : Arguments
Shape of the output.
If given as N integers, each integer specifies the size of one
dimension. If given as a tuple, this tuple gives the complete shape.
Returns
-------
Z : matrix of floats
A matrix of floating-point samples drawn from the standard normal
distribution.
See Also
--------
rand, numpy.random.RandomState.randn
Notes
-----
For random samples from the normal distribution with mean ``mu`` and
standard deviation ``sigma``, use::
sigma * np.matlib.randn(...) + mu
Examples
--------
>>> np.random.seed(123)
>>> import numpy.matlib
>>> np.matlib.randn(1)
matrix([[-1.0856306]])
>>> np.matlib.randn(1, 2, 3)
matrix([[ 0.99734545, 0.2829785 , -1.50629471],
[-0.57860025, 1.65143654, -2.42667924]])
Two-by-four matrix of samples from the normal distribution with
mean 3 and standard deviation 2.5:
>>> 2.5 * np.matlib.randn((2, 4)) + 3
matrix([[1.92771843, 6.16484065, 0.83314899, 1.30278462],
[2.76322758, 6.72847407, 1.40274501, 1.8900451 ]])
"""
if isinstance(args[0], tuple):
args = args[0]
return asmatrix(np.random.randn(*args)) | Return a random matrix with data from the "standard normal" distribution. `randn` generates a matrix filled with random floats sampled from a univariate "normal" (Gaussian) distribution of mean 0 and variance 1. Parameters ---------- \\*args : Arguments Shape of the output. If given as N integers, each integer specifies the size of one dimension. If given as a tuple, this tuple gives the complete shape. Returns ------- Z : matrix of floats A matrix of floating-point samples drawn from the standard normal distribution. See Also -------- rand, numpy.random.RandomState.randn Notes ----- For random samples from the normal distribution with mean ``mu`` and standard deviation ``sigma``, use:: sigma * np.matlib.randn(...) + mu Examples -------- >>> np.random.seed(123) >>> import numpy.matlib >>> np.matlib.randn(1) matrix([[-1.0856306]]) >>> np.matlib.randn(1, 2, 3) matrix([[ 0.99734545, 0.2829785 , -1.50629471], [-0.57860025, 1.65143654, -2.42667924]]) Two-by-four matrix of samples from the normal distribution with mean 3 and standard deviation 2.5: >>> 2.5 * np.matlib.randn((2, 4)) + 3 matrix([[1.92771843, 6.16484065, 0.83314899, 1.30278462], [2.76322758, 6.72847407, 1.40274501, 1.8900451 ]]) |
169,959 | import warnings
import numpy as np
from numpy.matrixlib.defmatrix import matrix, asmatrix
from numpy import *
The provided code snippet includes necessary dependencies for implementing the `repmat` function. Write a Python function `def repmat(a, m, n)` to solve the following problem:
Repeat a 0-D to 2-D array or matrix MxN times. Parameters ---------- a : array_like The array or matrix to be repeated. m, n : int The number of times `a` is repeated along the first and second axes. Returns ------- out : ndarray The result of repeating `a`. Examples -------- >>> import numpy.matlib >>> a0 = np.array(1) >>> np.matlib.repmat(a0, 2, 3) array([[1, 1, 1], [1, 1, 1]]) >>> a1 = np.arange(4) >>> np.matlib.repmat(a1, 2, 2) array([[0, 1, 2, 3, 0, 1, 2, 3], [0, 1, 2, 3, 0, 1, 2, 3]]) >>> a2 = np.asmatrix(np.arange(6).reshape(2, 3)) >>> np.matlib.repmat(a2, 2, 3) matrix([[0, 1, 2, 0, 1, 2, 0, 1, 2], [3, 4, 5, 3, 4, 5, 3, 4, 5], [0, 1, 2, 0, 1, 2, 0, 1, 2], [3, 4, 5, 3, 4, 5, 3, 4, 5]])
Here is the function:
def repmat(a, m, n):
"""
Repeat a 0-D to 2-D array or matrix MxN times.
Parameters
----------
a : array_like
The array or matrix to be repeated.
m, n : int
The number of times `a` is repeated along the first and second axes.
Returns
-------
out : ndarray
The result of repeating `a`.
Examples
--------
>>> import numpy.matlib
>>> a0 = np.array(1)
>>> np.matlib.repmat(a0, 2, 3)
array([[1, 1, 1],
[1, 1, 1]])
>>> a1 = np.arange(4)
>>> np.matlib.repmat(a1, 2, 2)
array([[0, 1, 2, 3, 0, 1, 2, 3],
[0, 1, 2, 3, 0, 1, 2, 3]])
>>> a2 = np.asmatrix(np.arange(6).reshape(2, 3))
>>> np.matlib.repmat(a2, 2, 3)
matrix([[0, 1, 2, 0, 1, 2, 0, 1, 2],
[3, 4, 5, 3, 4, 5, 3, 4, 5],
[0, 1, 2, 0, 1, 2, 0, 1, 2],
[3, 4, 5, 3, 4, 5, 3, 4, 5]])
"""
a = asanyarray(a)
ndim = a.ndim
if ndim == 0:
origrows, origcols = (1, 1)
elif ndim == 1:
origrows, origcols = (1, a.shape[0])
else:
origrows, origcols = a.shape
rows = origrows * m
cols = origcols * n
c = a.reshape(1, a.size).repeat(m, 0).reshape(rows, origcols).repeat(n, 0)
return c.reshape(rows, cols) | Repeat a 0-D to 2-D array or matrix MxN times. Parameters ---------- a : array_like The array or matrix to be repeated. m, n : int The number of times `a` is repeated along the first and second axes. Returns ------- out : ndarray The result of repeating `a`. Examples -------- >>> import numpy.matlib >>> a0 = np.array(1) >>> np.matlib.repmat(a0, 2, 3) array([[1, 1, 1], [1, 1, 1]]) >>> a1 = np.arange(4) >>> np.matlib.repmat(a1, 2, 2) array([[0, 1, 2, 3, 0, 1, 2, 3], [0, 1, 2, 3, 0, 1, 2, 3]]) >>> a2 = np.asmatrix(np.arange(6).reshape(2, 3)) >>> np.matlib.repmat(a2, 2, 3) matrix([[0, 1, 2, 0, 1, 2, 0, 1, 2], [3, 4, 5, 3, 4, 5, 3, 4, 5], [0, 1, 2, 0, 1, 2, 0, 1, 2], [3, 4, 5, 3, 4, 5, 3, 4, 5]]) |
169,960 |
class Configuration:
_list_keys = ['packages', 'ext_modules', 'data_files', 'include_dirs',
'libraries', 'headers', 'scripts', 'py_modules',
'installed_libraries', 'define_macros']
_dict_keys = ['package_dir', 'installed_pkg_config']
_extra_keys = ['name', 'version']
numpy_include_dirs = []
def __init__(self,
package_name=None,
parent_name=None,
top_path=None,
package_path=None,
caller_level=1,
setup_name='setup.py',
**attrs):
"""Construct configuration instance of a package.
package_name -- name of the package
Ex.: 'distutils'
parent_name -- name of the parent package
Ex.: 'numpy'
top_path -- directory of the toplevel package
Ex.: the directory where the numpy package source sits
package_path -- directory of package. Will be computed by magic from the
directory of the caller module if not specified
Ex.: the directory where numpy.distutils is
caller_level -- frame level to caller namespace, internal parameter.
"""
self.name = dot_join(parent_name, package_name)
self.version = None
caller_frame = get_frame(caller_level)
self.local_path = get_path_from_frame(caller_frame, top_path)
# local_path -- directory of a file (usually setup.py) that
# defines a configuration() function.
# local_path -- directory of a file (usually setup.py) that
# defines a configuration() function.
if top_path is None:
top_path = self.local_path
self.local_path = ''
if package_path is None:
package_path = self.local_path
elif os.path.isdir(njoin(self.local_path, package_path)):
package_path = njoin(self.local_path, package_path)
if not os.path.isdir(package_path or '.'):
raise ValueError("%r is not a directory" % (package_path,))
self.top_path = top_path
self.package_path = package_path
# this is the relative path in the installed package
self.path_in_package = os.path.join(*self.name.split('.'))
self.list_keys = self._list_keys[:]
self.dict_keys = self._dict_keys[:]
for n in self.list_keys:
v = copy.copy(attrs.get(n, []))
setattr(self, n, as_list(v))
for n in self.dict_keys:
v = copy.copy(attrs.get(n, {}))
setattr(self, n, v)
known_keys = self.list_keys + self.dict_keys
self.extra_keys = self._extra_keys[:]
for n in attrs.keys():
if n in known_keys:
continue
a = attrs[n]
setattr(self, n, a)
if isinstance(a, list):
self.list_keys.append(n)
elif isinstance(a, dict):
self.dict_keys.append(n)
else:
self.extra_keys.append(n)
if os.path.exists(njoin(package_path, '__init__.py')):
self.packages.append(self.name)
self.package_dir[self.name] = package_path
self.options = dict(
ignore_setup_xxx_py = False,
assume_default_configuration = False,
delegate_options_to_subpackages = False,
quiet = False,
)
caller_instance = None
for i in range(1, 3):
try:
f = get_frame(i)
except ValueError:
break
try:
caller_instance = eval('self', f.f_globals, f.f_locals)
break
except NameError:
pass
if isinstance(caller_instance, self.__class__):
if caller_instance.options['delegate_options_to_subpackages']:
self.set_options(**caller_instance.options)
self.setup_name = setup_name
def todict(self):
"""
Return a dictionary compatible with the keyword arguments of distutils
setup function.
Examples
--------
>>> setup(**config.todict()) #doctest: +SKIP
"""
self._optimize_data_files()
d = {}
known_keys = self.list_keys + self.dict_keys + self.extra_keys
for n in known_keys:
a = getattr(self, n)
if a:
d[n] = a
return d
def info(self, message):
if not self.options['quiet']:
print(message)
def warn(self, message):
sys.stderr.write('Warning: %s\n' % (message,))
def set_options(self, **options):
"""
Configure Configuration instance.
The following options are available:
- ignore_setup_xxx_py
- assume_default_configuration
- delegate_options_to_subpackages
- quiet
"""
for key, value in options.items():
if key in self.options:
self.options[key] = value
else:
raise ValueError('Unknown option: '+key)
def get_distribution(self):
"""Return the distutils distribution object for self."""
from numpy.distutils.core import get_distribution
return get_distribution()
def _wildcard_get_subpackage(self, subpackage_name,
parent_name,
caller_level = 1):
l = subpackage_name.split('.')
subpackage_path = njoin([self.local_path]+l)
dirs = [_m for _m in sorted_glob(subpackage_path) if os.path.isdir(_m)]
config_list = []
for d in dirs:
if not os.path.isfile(njoin(d, '__init__.py')):
continue
if 'build' in d.split(os.sep):
continue
n = '.'.join(d.split(os.sep)[-len(l):])
c = self.get_subpackage(n,
parent_name = parent_name,
caller_level = caller_level+1)
config_list.extend(c)
return config_list
def _get_configuration_from_setup_py(self, setup_py,
subpackage_name,
subpackage_path,
parent_name,
caller_level = 1):
# In case setup_py imports local modules:
sys.path.insert(0, os.path.dirname(setup_py))
try:
setup_name = os.path.splitext(os.path.basename(setup_py))[0]
n = dot_join(self.name, subpackage_name, setup_name)
setup_module = exec_mod_from_location(
'_'.join(n.split('.')), setup_py)
if not hasattr(setup_module, 'configuration'):
if not self.options['assume_default_configuration']:
self.warn('Assuming default configuration '\
'(%s does not define configuration())'\
% (setup_module))
config = Configuration(subpackage_name, parent_name,
self.top_path, subpackage_path,
caller_level = caller_level + 1)
else:
pn = dot_join(*([parent_name] + subpackage_name.split('.')[:-1]))
args = (pn,)
if setup_module.configuration.__code__.co_argcount > 1:
args = args + (self.top_path,)
config = setup_module.configuration(*args)
if config.name!=dot_join(parent_name, subpackage_name):
self.warn('Subpackage %r configuration returned as %r' % \
(dot_join(parent_name, subpackage_name), config.name))
finally:
del sys.path[0]
return config
def get_subpackage(self,subpackage_name,
subpackage_path=None,
parent_name=None,
caller_level = 1):
"""Return list of subpackage configurations.
Parameters
----------
subpackage_name : str or None
Name of the subpackage to get the configuration. '*' in
subpackage_name is handled as a wildcard.
subpackage_path : str
If None, then the path is assumed to be the local path plus the
subpackage_name. If a setup.py file is not found in the
subpackage_path, then a default configuration is used.
parent_name : str
Parent name.
"""
if subpackage_name is None:
if subpackage_path is None:
raise ValueError(
"either subpackage_name or subpackage_path must be specified")
subpackage_name = os.path.basename(subpackage_path)
# handle wildcards
l = subpackage_name.split('.')
if subpackage_path is None and '*' in subpackage_name:
return self._wildcard_get_subpackage(subpackage_name,
parent_name,
caller_level = caller_level+1)
assert '*' not in subpackage_name, repr((subpackage_name, subpackage_path, parent_name))
if subpackage_path is None:
subpackage_path = njoin([self.local_path] + l)
else:
subpackage_path = njoin([subpackage_path] + l[:-1])
subpackage_path = self.paths([subpackage_path])[0]
setup_py = njoin(subpackage_path, self.setup_name)
if not self.options['ignore_setup_xxx_py']:
if not os.path.isfile(setup_py):
setup_py = njoin(subpackage_path,
'setup_%s.py' % (subpackage_name))
if not os.path.isfile(setup_py):
if not self.options['assume_default_configuration']:
self.warn('Assuming default configuration '\
'(%s/{setup_%s,setup}.py was not found)' \
% (os.path.dirname(setup_py), subpackage_name))
config = Configuration(subpackage_name, parent_name,
self.top_path, subpackage_path,
caller_level = caller_level+1)
else:
config = self._get_configuration_from_setup_py(
setup_py,
subpackage_name,
subpackage_path,
parent_name,
caller_level = caller_level + 1)
if config:
return [config]
else:
return []
def add_subpackage(self,subpackage_name,
subpackage_path=None,
standalone = False):
"""Add a sub-package to the current Configuration instance.
This is useful in a setup.py script for adding sub-packages to a
package.
Parameters
----------
subpackage_name : str
name of the subpackage
subpackage_path : str
if given, the subpackage path such as the subpackage is in
subpackage_path / subpackage_name. If None,the subpackage is
assumed to be located in the local path / subpackage_name.
standalone : bool
"""
if standalone:
parent_name = None
else:
parent_name = self.name
config_list = self.get_subpackage(subpackage_name, subpackage_path,
parent_name = parent_name,
caller_level = 2)
if not config_list:
self.warn('No configuration returned, assuming unavailable.')
for config in config_list:
d = config
if isinstance(config, Configuration):
d = config.todict()
assert isinstance(d, dict), repr(type(d))
self.info('Appending %s configuration to %s' \
% (d.get('name'), self.name))
self.dict_append(**d)
dist = self.get_distribution()
if dist is not None:
self.warn('distutils distribution has been initialized,'\
' it may be too late to add a subpackage '+ subpackage_name)
def add_data_dir(self, data_path):
"""Recursively add files under data_path to data_files list.
Recursively add files under data_path to the list of data_files to be
installed (and distributed). The data_path can be either a relative
path-name, or an absolute path-name, or a 2-tuple where the first
argument shows where in the install directory the data directory
should be installed to.
Parameters
----------
data_path : seq or str
Argument can be either
* 2-sequence (<datadir suffix>, <path to data directory>)
* path to data directory where python datadir suffix defaults
to package dir.
Notes
-----
Rules for installation paths::
foo/bar -> (foo/bar, foo/bar) -> parent/foo/bar
(gun, foo/bar) -> parent/gun
foo/* -> (foo/a, foo/a), (foo/b, foo/b) -> parent/foo/a, parent/foo/b
(gun, foo/*) -> (gun, foo/a), (gun, foo/b) -> gun
(gun/*, foo/*) -> parent/gun/a, parent/gun/b
/foo/bar -> (bar, /foo/bar) -> parent/bar
(gun, /foo/bar) -> parent/gun
(fun/*/gun/*, sun/foo/bar) -> parent/fun/foo/gun/bar
Examples
--------
For example suppose the source directory contains fun/foo.dat and
fun/bar/car.dat:
>>> self.add_data_dir('fun') #doctest: +SKIP
>>> self.add_data_dir(('sun', 'fun')) #doctest: +SKIP
>>> self.add_data_dir(('gun', '/full/path/to/fun'))#doctest: +SKIP
Will install data-files to the locations::
<package install directory>/
fun/
foo.dat
bar/
car.dat
sun/
foo.dat
bar/
car.dat
gun/
foo.dat
car.dat
"""
if is_sequence(data_path):
d, data_path = data_path
else:
d = None
if is_sequence(data_path):
[self.add_data_dir((d, p)) for p in data_path]
return
if not is_string(data_path):
raise TypeError("not a string: %r" % (data_path,))
if d is None:
if os.path.isabs(data_path):
return self.add_data_dir((os.path.basename(data_path), data_path))
return self.add_data_dir((data_path, data_path))
paths = self.paths(data_path, include_non_existing=False)
if is_glob_pattern(data_path):
if is_glob_pattern(d):
pattern_list = allpath(d).split(os.sep)
pattern_list.reverse()
# /a/*//b/ -> /a/*/b
rl = list(range(len(pattern_list)-1)); rl.reverse()
for i in rl:
if not pattern_list[i]:
del pattern_list[i]
#
for path in paths:
if not os.path.isdir(path):
print('Not a directory, skipping', path)
continue
rpath = rel_path(path, self.local_path)
path_list = rpath.split(os.sep)
path_list.reverse()
target_list = []
i = 0
for s in pattern_list:
if is_glob_pattern(s):
if i>=len(path_list):
raise ValueError('cannot fill pattern %r with %r' \
% (d, path))
target_list.append(path_list[i])
else:
assert s==path_list[i], repr((s, path_list[i], data_path, d, path, rpath))
target_list.append(s)
i += 1
if path_list[i:]:
self.warn('mismatch of pattern_list=%s and path_list=%s'\
% (pattern_list, path_list))
target_list.reverse()
self.add_data_dir((os.sep.join(target_list), path))
else:
for path in paths:
self.add_data_dir((d, path))
return
assert not is_glob_pattern(d), repr(d)
dist = self.get_distribution()
if dist is not None and dist.data_files is not None:
data_files = dist.data_files
else:
data_files = self.data_files
for path in paths:
for d1, f in list(general_source_directories_files(path)):
target_path = os.path.join(self.path_in_package, d, d1)
data_files.append((target_path, f))
def _optimize_data_files(self):
data_dict = {}
for p, files in self.data_files:
if p not in data_dict:
data_dict[p] = set()
for f in files:
data_dict[p].add(f)
self.data_files[:] = [(p, list(files)) for p, files in data_dict.items()]
def add_data_files(self,*files):
"""Add data files to configuration data_files.
Parameters
----------
files : sequence
Argument(s) can be either
* 2-sequence (<datadir prefix>,<path to data file(s)>)
* paths to data files where python datadir prefix defaults
to package dir.
Notes
-----
The form of each element of the files sequence is very flexible
allowing many combinations of where to get the files from the package
and where they should ultimately be installed on the system. The most
basic usage is for an element of the files argument sequence to be a
simple filename. This will cause that file from the local path to be
installed to the installation path of the self.name package (package
path). The file argument can also be a relative path in which case the
entire relative path will be installed into the package directory.
Finally, the file can be an absolute path name in which case the file
will be found at the absolute path name but installed to the package
path.
This basic behavior can be augmented by passing a 2-tuple in as the
file argument. The first element of the tuple should specify the
relative path (under the package install directory) where the
remaining sequence of files should be installed to (it has nothing to
do with the file-names in the source distribution). The second element
of the tuple is the sequence of files that should be installed. The
files in this sequence can be filenames, relative paths, or absolute
paths. For absolute paths the file will be installed in the top-level
package installation directory (regardless of the first argument).
Filenames and relative path names will be installed in the package
install directory under the path name given as the first element of
the tuple.
Rules for installation paths:
#. file.txt -> (., file.txt)-> parent/file.txt
#. foo/file.txt -> (foo, foo/file.txt) -> parent/foo/file.txt
#. /foo/bar/file.txt -> (., /foo/bar/file.txt) -> parent/file.txt
#. ``*``.txt -> parent/a.txt, parent/b.txt
#. foo/``*``.txt`` -> parent/foo/a.txt, parent/foo/b.txt
#. ``*/*.txt`` -> (``*``, ``*``/``*``.txt) -> parent/c/a.txt, parent/d/b.txt
#. (sun, file.txt) -> parent/sun/file.txt
#. (sun, bar/file.txt) -> parent/sun/file.txt
#. (sun, /foo/bar/file.txt) -> parent/sun/file.txt
#. (sun, ``*``.txt) -> parent/sun/a.txt, parent/sun/b.txt
#. (sun, bar/``*``.txt) -> parent/sun/a.txt, parent/sun/b.txt
#. (sun/``*``, ``*``/``*``.txt) -> parent/sun/c/a.txt, parent/d/b.txt
An additional feature is that the path to a data-file can actually be
a function that takes no arguments and returns the actual path(s) to
the data-files. This is useful when the data files are generated while
building the package.
Examples
--------
Add files to the list of data_files to be included with the package.
>>> self.add_data_files('foo.dat',
... ('fun', ['gun.dat', 'nun/pun.dat', '/tmp/sun.dat']),
... 'bar/cat.dat',
... '/full/path/to/can.dat') #doctest: +SKIP
will install these data files to::
<package install directory>/
foo.dat
fun/
gun.dat
nun/
pun.dat
sun.dat
bar/
car.dat
can.dat
where <package install directory> is the package (or sub-package)
directory such as '/usr/lib/python2.4/site-packages/mypackage' ('C:
\\Python2.4 \\Lib \\site-packages \\mypackage') or
'/usr/lib/python2.4/site- packages/mypackage/mysubpackage' ('C:
\\Python2.4 \\Lib \\site-packages \\mypackage \\mysubpackage').
"""
if len(files)>1:
for f in files:
self.add_data_files(f)
return
assert len(files)==1
if is_sequence(files[0]):
d, files = files[0]
else:
d = None
if is_string(files):
filepat = files
elif is_sequence(files):
if len(files)==1:
filepat = files[0]
else:
for f in files:
self.add_data_files((d, f))
return
else:
raise TypeError(repr(type(files)))
if d is None:
if hasattr(filepat, '__call__'):
d = ''
elif os.path.isabs(filepat):
d = ''
else:
d = os.path.dirname(filepat)
self.add_data_files((d, files))
return
paths = self.paths(filepat, include_non_existing=False)
if is_glob_pattern(filepat):
if is_glob_pattern(d):
pattern_list = d.split(os.sep)
pattern_list.reverse()
for path in paths:
path_list = path.split(os.sep)
path_list.reverse()
path_list.pop() # filename
target_list = []
i = 0
for s in pattern_list:
if is_glob_pattern(s):
target_list.append(path_list[i])
i += 1
else:
target_list.append(s)
target_list.reverse()
self.add_data_files((os.sep.join(target_list), path))
else:
self.add_data_files((d, paths))
return
assert not is_glob_pattern(d), repr((d, filepat))
dist = self.get_distribution()
if dist is not None and dist.data_files is not None:
data_files = dist.data_files
else:
data_files = self.data_files
data_files.append((os.path.join(self.path_in_package, d), paths))
### XXX Implement add_py_modules
def add_define_macros(self, macros):
"""Add define macros to configuration
Add the given sequence of macro name and value duples to the beginning
of the define_macros list This list will be visible to all extension
modules of the current package.
"""
dist = self.get_distribution()
if dist is not None:
if not hasattr(dist, 'define_macros'):
dist.define_macros = []
dist.define_macros.extend(macros)
else:
self.define_macros.extend(macros)
def add_include_dirs(self,*paths):
"""Add paths to configuration include directories.
Add the given sequence of paths to the beginning of the include_dirs
list. This list will be visible to all extension modules of the
current package.
"""
include_dirs = self.paths(paths)
dist = self.get_distribution()
if dist is not None:
if dist.include_dirs is None:
dist.include_dirs = []
dist.include_dirs.extend(include_dirs)
else:
self.include_dirs.extend(include_dirs)
def add_headers(self,*files):
"""Add installable headers to configuration.
Add the given sequence of files to the beginning of the headers list.
By default, headers will be installed under <python-
include>/<self.name.replace('.','/')>/ directory. If an item of files
is a tuple, then its first argument specifies the actual installation
location relative to the <python-include> path.
Parameters
----------
files : str or seq
Argument(s) can be either:
* 2-sequence (<includedir suffix>,<path to header file(s)>)
* path(s) to header file(s) where python includedir suffix will
default to package name.
"""
headers = []
for path in files:
if is_string(path):
[headers.append((self.name, p)) for p in self.paths(path)]
else:
if not isinstance(path, (tuple, list)) or len(path) != 2:
raise TypeError(repr(path))
[headers.append((path[0], p)) for p in self.paths(path[1])]
dist = self.get_distribution()
if dist is not None:
if dist.headers is None:
dist.headers = []
dist.headers.extend(headers)
else:
self.headers.extend(headers)
def paths(self,*paths,**kws):
"""Apply glob to paths and prepend local_path if needed.
Applies glob.glob(...) to each path in the sequence (if needed) and
pre-pends the local_path if needed. Because this is called on all
source lists, this allows wildcard characters to be specified in lists
of sources for extension modules and libraries and scripts and allows
path-names be relative to the source directory.
"""
include_non_existing = kws.get('include_non_existing', True)
return gpaths(paths,
local_path = self.local_path,
include_non_existing=include_non_existing)
def _fix_paths_dict(self, kw):
for k in kw.keys():
v = kw[k]
if k in ['sources', 'depends', 'include_dirs', 'library_dirs',
'module_dirs', 'extra_objects']:
new_v = self.paths(v)
kw[k] = new_v
def add_extension(self,name,sources,**kw):
"""Add extension to configuration.
Create and add an Extension instance to the ext_modules list. This
method also takes the following optional keyword arguments that are
passed on to the Extension constructor.
Parameters
----------
name : str
name of the extension
sources : seq
list of the sources. The list of sources may contain functions
(called source generators) which must take an extension instance
and a build directory as inputs and return a source file or list of
source files or None. If None is returned then no sources are
generated. If the Extension instance has no sources after
processing all source generators, then no extension module is
built.
include_dirs :
define_macros :
undef_macros :
library_dirs :
libraries :
runtime_library_dirs :
extra_objects :
extra_compile_args :
extra_link_args :
extra_f77_compile_args :
extra_f90_compile_args :
export_symbols :
swig_opts :
depends :
The depends list contains paths to files or directories that the
sources of the extension module depend on. If any path in the
depends list is newer than the extension module, then the module
will be rebuilt.
language :
f2py_options :
module_dirs :
extra_info : dict or list
dict or list of dict of keywords to be appended to keywords.
Notes
-----
The self.paths(...) method is applied to all lists that may contain
paths.
"""
ext_args = copy.copy(kw)
ext_args['name'] = dot_join(self.name, name)
ext_args['sources'] = sources
if 'extra_info' in ext_args:
extra_info = ext_args['extra_info']
del ext_args['extra_info']
if isinstance(extra_info, dict):
extra_info = [extra_info]
for info in extra_info:
assert isinstance(info, dict), repr(info)
dict_append(ext_args,**info)
self._fix_paths_dict(ext_args)
# Resolve out-of-tree dependencies
libraries = ext_args.get('libraries', [])
libnames = []
ext_args['libraries'] = []
for libname in libraries:
if isinstance(libname, tuple):
self._fix_paths_dict(libname[1])
# Handle library names of the form libname@relative/path/to/library
if '@' in libname:
lname, lpath = libname.split('@', 1)
lpath = os.path.abspath(njoin(self.local_path, lpath))
if os.path.isdir(lpath):
c = self.get_subpackage(None, lpath,
caller_level = 2)
if isinstance(c, Configuration):
c = c.todict()
for l in [l[0] for l in c.get('libraries', [])]:
llname = l.split('__OF__', 1)[0]
if llname == lname:
c.pop('name', None)
dict_append(ext_args,**c)
break
continue
libnames.append(libname)
ext_args['libraries'] = libnames + ext_args['libraries']
ext_args['define_macros'] = \
self.define_macros + ext_args.get('define_macros', [])
from numpy.distutils.core import Extension
ext = Extension(**ext_args)
self.ext_modules.append(ext)
dist = self.get_distribution()
if dist is not None:
self.warn('distutils distribution has been initialized,'\
' it may be too late to add an extension '+name)
return ext
def add_library(self,name,sources,**build_info):
"""
Add library to configuration.
Parameters
----------
name : str
Name of the extension.
sources : sequence
List of the sources. The list of sources may contain functions
(called source generators) which must take an extension instance
and a build directory as inputs and return a source file or list of
source files or None. If None is returned then no sources are
generated. If the Extension instance has no sources after
processing all source generators, then no extension module is
built.
build_info : dict, optional
The following keys are allowed:
* depends
* macros
* include_dirs
* extra_compiler_args
* extra_f77_compile_args
* extra_f90_compile_args
* f2py_options
* language
"""
self._add_library(name, sources, None, build_info)
dist = self.get_distribution()
if dist is not None:
self.warn('distutils distribution has been initialized,'\
' it may be too late to add a library '+ name)
def _add_library(self, name, sources, install_dir, build_info):
"""Common implementation for add_library and add_installed_library. Do
not use directly"""
build_info = copy.copy(build_info)
build_info['sources'] = sources
# Sometimes, depends is not set up to an empty list by default, and if
# depends is not given to add_library, distutils barfs (#1134)
if not 'depends' in build_info:
build_info['depends'] = []
self._fix_paths_dict(build_info)
# Add to libraries list so that it is build with build_clib
self.libraries.append((name, build_info))
def add_installed_library(self, name, sources, install_dir, build_info=None):
"""
Similar to add_library, but the specified library is installed.
Most C libraries used with `distutils` are only used to build python
extensions, but libraries built through this method will be installed
so that they can be reused by third-party packages.
Parameters
----------
name : str
Name of the installed library.
sources : sequence
List of the library's source files. See `add_library` for details.
install_dir : str
Path to install the library, relative to the current sub-package.
build_info : dict, optional
The following keys are allowed:
* depends
* macros
* include_dirs
* extra_compiler_args
* extra_f77_compile_args
* extra_f90_compile_args
* f2py_options
* language
Returns
-------
None
See Also
--------
add_library, add_npy_pkg_config, get_info
Notes
-----
The best way to encode the options required to link against the specified
C libraries is to use a "libname.ini" file, and use `get_info` to
retrieve the required options (see `add_npy_pkg_config` for more
information).
"""
if not build_info:
build_info = {}
install_dir = os.path.join(self.package_path, install_dir)
self._add_library(name, sources, install_dir, build_info)
self.installed_libraries.append(InstallableLib(name, build_info, install_dir))
def add_npy_pkg_config(self, template, install_dir, subst_dict=None):
"""
Generate and install a npy-pkg config file from a template.
The config file generated from `template` is installed in the
given install directory, using `subst_dict` for variable substitution.
Parameters
----------
template : str
The path of the template, relatively to the current package path.
install_dir : str
Where to install the npy-pkg config file, relatively to the current
package path.
subst_dict : dict, optional
If given, any string of the form ``@key@`` will be replaced by
``subst_dict[key]`` in the template file when installed. The install
prefix is always available through the variable ``@prefix@``, since the
install prefix is not easy to get reliably from setup.py.
See also
--------
add_installed_library, get_info
Notes
-----
This works for both standard installs and in-place builds, i.e. the
``@prefix@`` refer to the source directory for in-place builds.
Examples
--------
::
config.add_npy_pkg_config('foo.ini.in', 'lib', {'foo': bar})
Assuming the foo.ini.in file has the following content::
[meta]
Name=@foo@
Version=1.0
Description=dummy description
[default]
Cflags=-I@prefix@/include
Libs=
The generated file will have the following content::
[meta]
Name=bar
Version=1.0
Description=dummy description
[default]
Cflags=-Iprefix_dir/include
Libs=
and will be installed as foo.ini in the 'lib' subpath.
When cross-compiling with numpy distutils, it might be necessary to
use modified npy-pkg-config files. Using the default/generated files
will link with the host libraries (i.e. libnpymath.a). For
cross-compilation you of-course need to link with target libraries,
while using the host Python installation.
You can copy out the numpy/core/lib/npy-pkg-config directory, add a
pkgdir value to the .ini files and set NPY_PKG_CONFIG_PATH environment
variable to point to the directory with the modified npy-pkg-config
files.
Example npymath.ini modified for cross-compilation::
[meta]
Name=npymath
Description=Portable, core math library implementing C99 standard
Version=0.1
[variables]
pkgname=numpy.core
pkgdir=/build/arm-linux-gnueabi/sysroot/usr/lib/python3.7/site-packages/numpy/core
prefix=${pkgdir}
libdir=${prefix}/lib
includedir=${prefix}/include
[default]
Libs=-L${libdir} -lnpymath
Cflags=-I${includedir}
Requires=mlib
[msvc]
Libs=/LIBPATH:${libdir} npymath.lib
Cflags=/INCLUDE:${includedir}
Requires=mlib
"""
if subst_dict is None:
subst_dict = {}
template = os.path.join(self.package_path, template)
if self.name in self.installed_pkg_config:
self.installed_pkg_config[self.name].append((template, install_dir,
subst_dict))
else:
self.installed_pkg_config[self.name] = [(template, install_dir,
subst_dict)]
def add_scripts(self,*files):
"""Add scripts to configuration.
Add the sequence of files to the beginning of the scripts list.
Scripts will be installed under the <prefix>/bin/ directory.
"""
scripts = self.paths(files)
dist = self.get_distribution()
if dist is not None:
if dist.scripts is None:
dist.scripts = []
dist.scripts.extend(scripts)
else:
self.scripts.extend(scripts)
def dict_append(self,**dict):
for key in self.list_keys:
a = getattr(self, key)
a.extend(dict.get(key, []))
for key in self.dict_keys:
a = getattr(self, key)
a.update(dict.get(key, {}))
known_keys = self.list_keys + self.dict_keys + self.extra_keys
for key in dict.keys():
if key not in known_keys:
a = getattr(self, key, None)
if a and a==dict[key]: continue
self.warn('Inheriting attribute %r=%r from %r' \
% (key, dict[key], dict.get('name', '?')))
setattr(self, key, dict[key])
self.extra_keys.append(key)
elif key in self.extra_keys:
self.info('Ignoring attempt to set %r (from %r to %r)' \
% (key, getattr(self, key), dict[key]))
elif key in known_keys:
# key is already processed above
pass
else:
raise ValueError("Don't know about key=%r" % (key))
def __str__(self):
from pprint import pformat
known_keys = self.list_keys + self.dict_keys + self.extra_keys
s = '<'+5*'-' + '\n'
s += 'Configuration of '+self.name+':\n'
known_keys.sort()
for k in known_keys:
a = getattr(self, k, None)
if a:
s += '%s = %s\n' % (k, pformat(a))
s += 5*'-' + '>'
return s
def get_config_cmd(self):
"""
Returns the numpy.distutils config command instance.
"""
cmd = get_cmd('config')
cmd.ensure_finalized()
cmd.dump_source = 0
cmd.noisy = 0
old_path = os.environ.get('PATH')
if old_path:
path = os.pathsep.join(['.', old_path])
os.environ['PATH'] = path
return cmd
def get_build_temp_dir(self):
"""
Return a path to a temporary directory where temporary files should be
placed.
"""
cmd = get_cmd('build')
cmd.ensure_finalized()
return cmd.build_temp
def have_f77c(self):
"""Check for availability of Fortran 77 compiler.
Use it inside source generating function to ensure that
setup distribution instance has been initialized.
Notes
-----
True if a Fortran 77 compiler is available (because a simple Fortran 77
code was able to be compiled successfully).
"""
simple_fortran_subroutine = '''
subroutine simple
end
'''
config_cmd = self.get_config_cmd()
flag = config_cmd.try_compile(simple_fortran_subroutine, lang='f77')
return flag
def have_f90c(self):
"""Check for availability of Fortran 90 compiler.
Use it inside source generating function to ensure that
setup distribution instance has been initialized.
Notes
-----
True if a Fortran 90 compiler is available (because a simple Fortran
90 code was able to be compiled successfully)
"""
simple_fortran_subroutine = '''
subroutine simple
end
'''
config_cmd = self.get_config_cmd()
flag = config_cmd.try_compile(simple_fortran_subroutine, lang='f90')
return flag
def append_to(self, extlib):
"""Append libraries, include_dirs to extension or library item.
"""
if is_sequence(extlib):
lib_name, build_info = extlib
dict_append(build_info,
libraries=self.libraries,
include_dirs=self.include_dirs)
else:
from numpy.distutils.core import Extension
assert isinstance(extlib, Extension), repr(extlib)
extlib.libraries.extend(self.libraries)
extlib.include_dirs.extend(self.include_dirs)
def _get_svn_revision(self, path):
"""Return path's SVN revision number.
"""
try:
output = subprocess.check_output(['svnversion'], cwd=path)
except (subprocess.CalledProcessError, OSError):
pass
else:
m = re.match(rb'(?P<revision>\d+)', output)
if m:
return int(m.group('revision'))
if sys.platform=='win32' and os.environ.get('SVN_ASP_DOT_NET_HACK', None):
entries = njoin(path, '_svn', 'entries')
else:
entries = njoin(path, '.svn', 'entries')
if os.path.isfile(entries):
with open(entries) as f:
fstr = f.read()
if fstr[:5] == '<?xml': # pre 1.4
m = re.search(r'revision="(?P<revision>\d+)"', fstr)
if m:
return int(m.group('revision'))
else: # non-xml entries file --- check to be sure that
m = re.search(r'dir[\n\r]+(?P<revision>\d+)', fstr)
if m:
return int(m.group('revision'))
return None
def _get_hg_revision(self, path):
"""Return path's Mercurial revision number.
"""
try:
output = subprocess.check_output(
['hg', 'identify', '--num'], cwd=path)
except (subprocess.CalledProcessError, OSError):
pass
else:
m = re.match(rb'(?P<revision>\d+)', output)
if m:
return int(m.group('revision'))
branch_fn = njoin(path, '.hg', 'branch')
branch_cache_fn = njoin(path, '.hg', 'branch.cache')
if os.path.isfile(branch_fn):
branch0 = None
with open(branch_fn) as f:
revision0 = f.read().strip()
branch_map = {}
with open(branch_cache_fn, 'r') as f:
for line in f:
branch1, revision1 = line.split()[:2]
if revision1==revision0:
branch0 = branch1
try:
revision1 = int(revision1)
except ValueError:
continue
branch_map[branch1] = revision1
return branch_map.get(branch0)
return None
def get_version(self, version_file=None, version_variable=None):
"""Try to get version string of a package.
Return a version string of the current package or None if the version
information could not be detected.
Notes
-----
This method scans files named
__version__.py, <packagename>_version.py, version.py, and
__svn_version__.py for string variables version, __version__, and
<packagename>_version, until a version number is found.
"""
version = getattr(self, 'version', None)
if version is not None:
return version
# Get version from version file.
if version_file is None:
files = ['__version__.py',
self.name.split('.')[-1]+'_version.py',
'version.py',
'__svn_version__.py',
'__hg_version__.py']
else:
files = [version_file]
if version_variable is None:
version_vars = ['version',
'__version__',
self.name.split('.')[-1]+'_version']
else:
version_vars = [version_variable]
for f in files:
fn = njoin(self.local_path, f)
if os.path.isfile(fn):
info = ('.py', 'U', 1)
name = os.path.splitext(os.path.basename(fn))[0]
n = dot_join(self.name, name)
try:
version_module = exec_mod_from_location(
'_'.join(n.split('.')), fn)
except ImportError as e:
self.warn(str(e))
version_module = None
if version_module is None:
continue
for a in version_vars:
version = getattr(version_module, a, None)
if version is not None:
break
# Try if versioneer module
try:
version = version_module.get_versions()['version']
except AttributeError:
pass
if version is not None:
break
if version is not None:
self.version = version
return version
# Get version as SVN or Mercurial revision number
revision = self._get_svn_revision(self.local_path)
if revision is None:
revision = self._get_hg_revision(self.local_path)
if revision is not None:
version = str(revision)
self.version = version
return version
def make_svn_version_py(self, delete=True):
"""Appends a data function to the data_files list that will generate
__svn_version__.py file to the current package directory.
Generate package __svn_version__.py file from SVN revision number,
it will be removed after python exits but will be available
when sdist, etc commands are executed.
Notes
-----
If __svn_version__.py existed before, nothing is done.
This is
intended for working with source directories that are in an SVN
repository.
"""
target = njoin(self.local_path, '__svn_version__.py')
revision = self._get_svn_revision(self.local_path)
if os.path.isfile(target) or revision is None:
return
else:
def generate_svn_version_py():
if not os.path.isfile(target):
version = str(revision)
self.info('Creating %s (version=%r)' % (target, version))
with open(target, 'w') as f:
f.write('version = %r\n' % (version))
def rm_file(f=target,p=self.info):
if delete:
try: os.remove(f); p('removed '+f)
except OSError: pass
try: os.remove(f+'c'); p('removed '+f+'c')
except OSError: pass
atexit.register(rm_file)
return target
self.add_data_files(('', generate_svn_version_py()))
def make_hg_version_py(self, delete=True):
"""Appends a data function to the data_files list that will generate
__hg_version__.py file to the current package directory.
Generate package __hg_version__.py file from Mercurial revision,
it will be removed after python exits but will be available
when sdist, etc commands are executed.
Notes
-----
If __hg_version__.py existed before, nothing is done.
This is intended for working with source directories that are
in an Mercurial repository.
"""
target = njoin(self.local_path, '__hg_version__.py')
revision = self._get_hg_revision(self.local_path)
if os.path.isfile(target) or revision is None:
return
else:
def generate_hg_version_py():
if not os.path.isfile(target):
version = str(revision)
self.info('Creating %s (version=%r)' % (target, version))
with open(target, 'w') as f:
f.write('version = %r\n' % (version))
def rm_file(f=target,p=self.info):
if delete:
try: os.remove(f); p('removed '+f)
except OSError: pass
try: os.remove(f+'c'); p('removed '+f+'c')
except OSError: pass
atexit.register(rm_file)
return target
self.add_data_files(('', generate_hg_version_py()))
def make_config_py(self,name='__config__'):
"""Generate package __config__.py file containing system_info
information used during building the package.
This file is installed to the
package installation directory.
"""
self.py_modules.append((self.name, name, generate_config_py))
def get_info(self,*names):
"""Get resources information.
Return information (from system_info.get_info) for all of the names in
the argument list in a single dictionary.
"""
from .system_info import get_info, dict_append
info_dict = {}
for a in names:
dict_append(info_dict,**get_info(a))
return info_dict
def configuration(parent_package="", top_path=None):
from numpy.distutils.misc_util import Configuration
config = Configuration("array_api", parent_package, top_path)
config.add_subpackage("tests")
return config | null |
169,961 | from __future__ import annotations
from ._array_object import Array
from typing import NamedTuple
import numpy as np
class UniqueAllResult(NamedTuple):
values: Array
indices: Array
inverse_indices: Array
counts: Array
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `unique_all` function. Write a Python function `def unique_all(x: Array, /) -> UniqueAllResult` to solve the following problem:
Array API compatible wrapper for :py:func:`np.unique <numpy.unique>`. See its docstring for more information.
Here is the function:
def unique_all(x: Array, /) -> UniqueAllResult:
"""
Array API compatible wrapper for :py:func:`np.unique <numpy.unique>`.
See its docstring for more information.
"""
values, indices, inverse_indices, counts = np.unique(
x._array,
return_counts=True,
return_index=True,
return_inverse=True,
equal_nan=False,
)
# np.unique() flattens inverse indices, but they need to share x's shape
# See https://github.com/numpy/numpy/issues/20638
inverse_indices = inverse_indices.reshape(x.shape)
return UniqueAllResult(
Array._new(values),
Array._new(indices),
Array._new(inverse_indices),
Array._new(counts),
) | Array API compatible wrapper for :py:func:`np.unique <numpy.unique>`. See its docstring for more information. |
169,962 | from __future__ import annotations
from ._array_object import Array
from typing import NamedTuple
import numpy as np
class UniqueCountsResult(NamedTuple):
class Array:
def _new(cls, x, /):
def __new__(cls, *args, **kwargs):
def __str__(self: Array, /) -> str:
def __repr__(self: Array, /) -> str:
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
def _promote_scalar(self, scalar):
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
def _validate_index(self, key):
def __abs__(self: Array, /) -> Array:
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
def __bool__(self: Array, /) -> bool:
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
def __float__(self: Array, /) -> float:
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
def __int__(self: Array, /) -> int:
def __index__(self: Array, /) -> int:
def __invert__(self: Array, /) -> Array:
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
def __matmul__(self: Array, other: Array, /) -> Array:
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
def __neg__(self: Array, /) -> Array:
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __pos__(self: Array, /) -> Array:
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
def __imatmul__(self: Array, other: Array, /) -> Array:
def __rmatmul__(self: Array, other: Array, /) -> Array:
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
def dtype(self) -> Dtype:
def device(self) -> Device:
def mT(self) -> Array:
def ndim(self) -> int:
def shape(self) -> Tuple[int, ...]:
def size(self) -> int:
def T(self) -> Array:
def unique_counts(x: Array, /) -> UniqueCountsResult:
res = np.unique(
x._array,
return_counts=True,
return_index=False,
return_inverse=False,
equal_nan=False,
)
return UniqueCountsResult(*[Array._new(i) for i in res]) | null |
169,963 | from __future__ import annotations
from ._array_object import Array
from typing import NamedTuple
import numpy as np
class UniqueInverseResult(NamedTuple):
values: Array
inverse_indices: Array
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `unique_inverse` function. Write a Python function `def unique_inverse(x: Array, /) -> UniqueInverseResult` to solve the following problem:
Array API compatible wrapper for :py:func:`np.unique <numpy.unique>`. See its docstring for more information.
Here is the function:
def unique_inverse(x: Array, /) -> UniqueInverseResult:
"""
Array API compatible wrapper for :py:func:`np.unique <numpy.unique>`.
See its docstring for more information.
"""
values, inverse_indices = np.unique(
x._array,
return_counts=False,
return_index=False,
return_inverse=True,
equal_nan=False,
)
# np.unique() flattens inverse indices, but they need to share x's shape
# See https://github.com/numpy/numpy/issues/20638
inverse_indices = inverse_indices.reshape(x.shape)
return UniqueInverseResult(Array._new(values), Array._new(inverse_indices)) | Array API compatible wrapper for :py:func:`np.unique <numpy.unique>`. See its docstring for more information. |
169,964 | from __future__ import annotations
from ._array_object import Array
from typing import NamedTuple
import numpy as np
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `unique_values` function. Write a Python function `def unique_values(x: Array, /) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.unique <numpy.unique>`. See its docstring for more information.
Here is the function:
def unique_values(x: Array, /) -> Array:
"""
Array API compatible wrapper for :py:func:`np.unique <numpy.unique>`.
See its docstring for more information.
"""
res = np.unique(
x._array,
return_counts=False,
return_index=False,
return_inverse=False,
equal_nan=False,
)
return Array._new(res) | Array API compatible wrapper for :py:func:`np.unique <numpy.unique>`. See its docstring for more information. |
169,965 | from __future__ import annotations
from typing import TYPE_CHECKING, List, Optional, Tuple, Union
from ._dtypes import _all_dtypes
import numpy as np
def _check_valid_dtype(dtype):
# Note: Only spelling dtypes as the dtype objects is supported.
# We use this instead of "dtype in _all_dtypes" because the dtype objects
# define equality with the sorts of things we want to disallow.
for d in (None,) + _all_dtypes:
if dtype is d:
return
raise ValueError("dtype must be one of the supported dtypes")
Union: _SpecialForm = ...
Optional: _SpecialForm = ...
class NestedSequence(Protocol[_T_co]):
def __getitem__(self, key: int, /) -> _T_co | NestedSequence[_T_co]: ...
def __len__(self, /) -> int: ...
Device = Literal["cpu"]
SupportsBufferProtocol = Any
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `asarray` function. Write a Python function `def asarray( obj: Union[ Array, bool, int, float, NestedSequence[bool | int | float], SupportsBufferProtocol, ], /, *, dtype: Optional[Dtype] = None, device: Optional[Device] = None, copy: Optional[Union[bool, np._CopyMode]] = None, ) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.asarray <numpy.asarray>`. See its docstring for more information.
Here is the function:
def asarray(
obj: Union[
Array,
bool,
int,
float,
NestedSequence[bool | int | float],
SupportsBufferProtocol,
],
/,
*,
dtype: Optional[Dtype] = None,
device: Optional[Device] = None,
copy: Optional[Union[bool, np._CopyMode]] = None,
) -> Array:
"""
Array API compatible wrapper for :py:func:`np.asarray <numpy.asarray>`.
See its docstring for more information.
"""
# _array_object imports in this file are inside the functions to avoid
# circular imports
from ._array_object import Array
_check_valid_dtype(dtype)
if device not in ["cpu", None]:
raise ValueError(f"Unsupported device {device!r}")
if copy in (False, np._CopyMode.IF_NEEDED):
# Note: copy=False is not yet implemented in np.asarray
raise NotImplementedError("copy=False is not yet implemented")
if isinstance(obj, Array):
if dtype is not None and obj.dtype != dtype:
copy = True
if copy in (True, np._CopyMode.ALWAYS):
return Array._new(np.array(obj._array, copy=True, dtype=dtype))
return obj
if dtype is None and isinstance(obj, int) and (obj > 2 ** 64 or obj < -(2 ** 63)):
# Give a better error message in this case. NumPy would convert this
# to an object array. TODO: This won't handle large integers in lists.
raise OverflowError("Integer out of bounds for array dtypes")
res = np.asarray(obj, dtype=dtype)
return Array._new(res) | Array API compatible wrapper for :py:func:`np.asarray <numpy.asarray>`. See its docstring for more information. |
169,966 | from __future__ import annotations
from typing import TYPE_CHECKING, List, Optional, Tuple, Union
from ._dtypes import _all_dtypes
import numpy as np
def _check_valid_dtype(dtype):
# Note: Only spelling dtypes as the dtype objects is supported.
# We use this instead of "dtype in _all_dtypes" because the dtype objects
# define equality with the sorts of things we want to disallow.
for d in (None,) + _all_dtypes:
if dtype is d:
return
raise ValueError("dtype must be one of the supported dtypes")
Union: _SpecialForm = ...
Optional: _SpecialForm = ...
Device = Literal["cpu"]
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `arange` function. Write a Python function `def arange( start: Union[int, float], /, stop: Optional[Union[int, float]] = None, step: Union[int, float] = 1, *, dtype: Optional[Dtype] = None, device: Optional[Device] = None, ) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.arange <numpy.arange>`. See its docstring for more information.
Here is the function:
def arange(
start: Union[int, float],
/,
stop: Optional[Union[int, float]] = None,
step: Union[int, float] = 1,
*,
dtype: Optional[Dtype] = None,
device: Optional[Device] = None,
) -> Array:
"""
Array API compatible wrapper for :py:func:`np.arange <numpy.arange>`.
See its docstring for more information.
"""
from ._array_object import Array
_check_valid_dtype(dtype)
if device not in ["cpu", None]:
raise ValueError(f"Unsupported device {device!r}")
return Array._new(np.arange(start, stop=stop, step=step, dtype=dtype)) | Array API compatible wrapper for :py:func:`np.arange <numpy.arange>`. See its docstring for more information. |
169,967 | from __future__ import annotations
from typing import TYPE_CHECKING, List, Optional, Tuple, Union
from ._dtypes import _all_dtypes
import numpy as np
def _check_valid_dtype(dtype):
# Note: Only spelling dtypes as the dtype objects is supported.
# We use this instead of "dtype in _all_dtypes" because the dtype objects
# define equality with the sorts of things we want to disallow.
for d in (None,) + _all_dtypes:
if dtype is d:
return
raise ValueError("dtype must be one of the supported dtypes")
Union: _SpecialForm = ...
Optional: _SpecialForm = ...
class Tuple(BaseTypingInstance):
def _is_homogenous(self):
# To specify a variable-length tuple of homogeneous type, Tuple[T, ...]
# is used.
return self._generics_manager.is_homogenous_tuple()
def py__simple_getitem__(self, index):
if self._is_homogenous():
return self._generics_manager.get_index_and_execute(0)
else:
if isinstance(index, int):
return self._generics_manager.get_index_and_execute(index)
debug.dbg('The getitem type on Tuple was %s' % index)
return NO_VALUES
def py__iter__(self, contextualized_node=None):
if self._is_homogenous():
yield LazyKnownValues(self._generics_manager.get_index_and_execute(0))
else:
for v in self._generics_manager.to_tuple():
yield LazyKnownValues(v.execute_annotation())
def py__getitem__(self, index_value_set, contextualized_node):
if self._is_homogenous():
return self._generics_manager.get_index_and_execute(0)
return ValueSet.from_sets(
self._generics_manager.to_tuple()
).execute_annotation()
def _get_wrapped_value(self):
tuple_, = self.inference_state.builtins_module \
.py__getattribute__('tuple').execute_annotation()
return tuple_
def name(self):
return self._wrapped_value.name
def infer_type_vars(self, value_set):
# Circular
from jedi.inference.gradual.annotation import merge_pairwise_generics, merge_type_var_dicts
value_set = value_set.filter(
lambda x: x.py__name__().lower() == 'tuple',
)
if self._is_homogenous():
# The parameter annotation is of the form `Tuple[T, ...]`,
# so we treat the incoming tuple like a iterable sequence
# rather than a positional container of elements.
return self._class_value.get_generics()[0].infer_type_vars(
value_set.merge_types_of_iterate(),
)
else:
# The parameter annotation has only explicit type parameters
# (e.g: `Tuple[T]`, `Tuple[T, U]`, `Tuple[T, U, V]`, etc.) so we
# treat the incoming values as needing to match the annotation
# exactly, just as we would for non-tuple annotations.
type_var_dict = {}
for element in value_set:
try:
method = element.get_annotated_class_object
except AttributeError:
# This might still happen, because the tuple name matching
# above is not 100% correct, so just catch the remaining
# cases here.
continue
py_class = method()
merge_type_var_dicts(
type_var_dict,
merge_pairwise_generics(self._class_value, py_class),
)
return type_var_dict
Device = Literal["cpu"]
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `empty` function. Write a Python function `def empty( shape: Union[int, Tuple[int, ...]], *, dtype: Optional[Dtype] = None, device: Optional[Device] = None, ) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.empty <numpy.empty>`. See its docstring for more information.
Here is the function:
def empty(
shape: Union[int, Tuple[int, ...]],
*,
dtype: Optional[Dtype] = None,
device: Optional[Device] = None,
) -> Array:
"""
Array API compatible wrapper for :py:func:`np.empty <numpy.empty>`.
See its docstring for more information.
"""
from ._array_object import Array
_check_valid_dtype(dtype)
if device not in ["cpu", None]:
raise ValueError(f"Unsupported device {device!r}")
return Array._new(np.empty(shape, dtype=dtype)) | Array API compatible wrapper for :py:func:`np.empty <numpy.empty>`. See its docstring for more information. |
169,968 | from __future__ import annotations
from typing import TYPE_CHECKING, List, Optional, Tuple, Union
from ._dtypes import _all_dtypes
import numpy as np
def _check_valid_dtype(dtype):
# Note: Only spelling dtypes as the dtype objects is supported.
# We use this instead of "dtype in _all_dtypes" because the dtype objects
# define equality with the sorts of things we want to disallow.
for d in (None,) + _all_dtypes:
if dtype is d:
return
raise ValueError("dtype must be one of the supported dtypes")
Optional: _SpecialForm = ...
Device = Literal["cpu"]
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `empty_like` function. Write a Python function `def empty_like( x: Array, /, *, dtype: Optional[Dtype] = None, device: Optional[Device] = None ) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.empty_like <numpy.empty_like>`. See its docstring for more information.
Here is the function:
def empty_like(
x: Array, /, *, dtype: Optional[Dtype] = None, device: Optional[Device] = None
) -> Array:
"""
Array API compatible wrapper for :py:func:`np.empty_like <numpy.empty_like>`.
See its docstring for more information.
"""
from ._array_object import Array
_check_valid_dtype(dtype)
if device not in ["cpu", None]:
raise ValueError(f"Unsupported device {device!r}")
return Array._new(np.empty_like(x._array, dtype=dtype)) | Array API compatible wrapper for :py:func:`np.empty_like <numpy.empty_like>`. See its docstring for more information. |
169,969 | from __future__ import annotations
from typing import TYPE_CHECKING, List, Optional, Tuple, Union
from ._dtypes import _all_dtypes
import numpy as np
def _check_valid_dtype(dtype):
# Note: Only spelling dtypes as the dtype objects is supported.
# We use this instead of "dtype in _all_dtypes" because the dtype objects
# define equality with the sorts of things we want to disallow.
for d in (None,) + _all_dtypes:
if dtype is d:
return
raise ValueError("dtype must be one of the supported dtypes")
Optional: _SpecialForm = ...
Device = Literal["cpu"]
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `eye` function. Write a Python function `def eye( n_rows: int, n_cols: Optional[int] = None, /, *, k: int = 0, dtype: Optional[Dtype] = None, device: Optional[Device] = None, ) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.eye <numpy.eye>`. See its docstring for more information.
Here is the function:
def eye(
n_rows: int,
n_cols: Optional[int] = None,
/,
*,
k: int = 0,
dtype: Optional[Dtype] = None,
device: Optional[Device] = None,
) -> Array:
"""
Array API compatible wrapper for :py:func:`np.eye <numpy.eye>`.
See its docstring for more information.
"""
from ._array_object import Array
_check_valid_dtype(dtype)
if device not in ["cpu", None]:
raise ValueError(f"Unsupported device {device!r}")
return Array._new(np.eye(n_rows, M=n_cols, k=k, dtype=dtype)) | Array API compatible wrapper for :py:func:`np.eye <numpy.eye>`. See its docstring for more information. |
169,970 | from __future__ import annotations
from typing import TYPE_CHECKING, List, Optional, Tuple, Union
from ._dtypes import _all_dtypes
import numpy as np
class Array:
def _new(cls, x, /):
def __new__(cls, *args, **kwargs):
def __str__(self: Array, /) -> str:
def __repr__(self: Array, /) -> str:
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
def _promote_scalar(self, scalar):
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
def _validate_index(self, key):
def __abs__(self: Array, /) -> Array:
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
def __bool__(self: Array, /) -> bool:
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
def __float__(self: Array, /) -> float:
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
def __int__(self: Array, /) -> int:
def __index__(self: Array, /) -> int:
def __invert__(self: Array, /) -> Array:
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
def __matmul__(self: Array, other: Array, /) -> Array:
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
def __neg__(self: Array, /) -> Array:
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __pos__(self: Array, /) -> Array:
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
def __imatmul__(self: Array, other: Array, /) -> Array:
def __rmatmul__(self: Array, other: Array, /) -> Array:
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
def dtype(self) -> Dtype:
def device(self) -> Device:
def mT(self) -> Array:
def ndim(self) -> int:
def shape(self) -> Tuple[int, ...]:
def size(self) -> int:
def T(self) -> Array:
def from_dlpack(x: object, /) -> Array:
from ._array_object import Array
return Array._new(np.from_dlpack(x)) | null |
169,971 | from __future__ import annotations
from typing import TYPE_CHECKING, List, Optional, Tuple, Union
from ._dtypes import _all_dtypes
import numpy as np
def _check_valid_dtype(dtype):
# Note: Only spelling dtypes as the dtype objects is supported.
# We use this instead of "dtype in _all_dtypes" because the dtype objects
# define equality with the sorts of things we want to disallow.
for d in (None,) + _all_dtypes:
if dtype is d:
return
raise ValueError("dtype must be one of the supported dtypes")
Union: _SpecialForm = ...
Optional: _SpecialForm = ...
class Tuple(BaseTypingInstance):
def _is_homogenous(self):
# To specify a variable-length tuple of homogeneous type, Tuple[T, ...]
# is used.
return self._generics_manager.is_homogenous_tuple()
def py__simple_getitem__(self, index):
if self._is_homogenous():
return self._generics_manager.get_index_and_execute(0)
else:
if isinstance(index, int):
return self._generics_manager.get_index_and_execute(index)
debug.dbg('The getitem type on Tuple was %s' % index)
return NO_VALUES
def py__iter__(self, contextualized_node=None):
if self._is_homogenous():
yield LazyKnownValues(self._generics_manager.get_index_and_execute(0))
else:
for v in self._generics_manager.to_tuple():
yield LazyKnownValues(v.execute_annotation())
def py__getitem__(self, index_value_set, contextualized_node):
if self._is_homogenous():
return self._generics_manager.get_index_and_execute(0)
return ValueSet.from_sets(
self._generics_manager.to_tuple()
).execute_annotation()
def _get_wrapped_value(self):
tuple_, = self.inference_state.builtins_module \
.py__getattribute__('tuple').execute_annotation()
return tuple_
def name(self):
return self._wrapped_value.name
def infer_type_vars(self, value_set):
# Circular
from jedi.inference.gradual.annotation import merge_pairwise_generics, merge_type_var_dicts
value_set = value_set.filter(
lambda x: x.py__name__().lower() == 'tuple',
)
if self._is_homogenous():
# The parameter annotation is of the form `Tuple[T, ...]`,
# so we treat the incoming tuple like a iterable sequence
# rather than a positional container of elements.
return self._class_value.get_generics()[0].infer_type_vars(
value_set.merge_types_of_iterate(),
)
else:
# The parameter annotation has only explicit type parameters
# (e.g: `Tuple[T]`, `Tuple[T, U]`, `Tuple[T, U, V]`, etc.) so we
# treat the incoming values as needing to match the annotation
# exactly, just as we would for non-tuple annotations.
type_var_dict = {}
for element in value_set:
try:
method = element.get_annotated_class_object
except AttributeError:
# This might still happen, because the tuple name matching
# above is not 100% correct, so just catch the remaining
# cases here.
continue
py_class = method()
merge_type_var_dicts(
type_var_dict,
merge_pairwise_generics(self._class_value, py_class),
)
return type_var_dict
Device = Literal["cpu"]
_all_dtypes = (
int8,
int16,
int32,
int64,
uint8,
uint16,
uint32,
uint64,
float32,
float64,
bool,
)
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `full` function. Write a Python function `def full( shape: Union[int, Tuple[int, ...]], fill_value: Union[int, float], *, dtype: Optional[Dtype] = None, device: Optional[Device] = None, ) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.full <numpy.full>`. See its docstring for more information.
Here is the function:
def full(
shape: Union[int, Tuple[int, ...]],
fill_value: Union[int, float],
*,
dtype: Optional[Dtype] = None,
device: Optional[Device] = None,
) -> Array:
"""
Array API compatible wrapper for :py:func:`np.full <numpy.full>`.
See its docstring for more information.
"""
from ._array_object import Array
_check_valid_dtype(dtype)
if device not in ["cpu", None]:
raise ValueError(f"Unsupported device {device!r}")
if isinstance(fill_value, Array) and fill_value.ndim == 0:
fill_value = fill_value._array
res = np.full(shape, fill_value, dtype=dtype)
if res.dtype not in _all_dtypes:
# This will happen if the fill value is not something that NumPy
# coerces to one of the acceptable dtypes.
raise TypeError("Invalid input to full")
return Array._new(res) | Array API compatible wrapper for :py:func:`np.full <numpy.full>`. See its docstring for more information. |
169,972 | from __future__ import annotations
from typing import TYPE_CHECKING, List, Optional, Tuple, Union
from ._dtypes import _all_dtypes
import numpy as np
def _check_valid_dtype(dtype):
# Note: Only spelling dtypes as the dtype objects is supported.
# We use this instead of "dtype in _all_dtypes" because the dtype objects
# define equality with the sorts of things we want to disallow.
for d in (None,) + _all_dtypes:
if dtype is d:
return
raise ValueError("dtype must be one of the supported dtypes")
Union: _SpecialForm = ...
Optional: _SpecialForm = ...
Device = Literal["cpu"]
_all_dtypes = (
int8,
int16,
int32,
int64,
uint8,
uint16,
uint32,
uint64,
float32,
float64,
bool,
)
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `full_like` function. Write a Python function `def full_like( x: Array, /, fill_value: Union[int, float], *, dtype: Optional[Dtype] = None, device: Optional[Device] = None, ) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.full_like <numpy.full_like>`. See its docstring for more information.
Here is the function:
def full_like(
x: Array,
/,
fill_value: Union[int, float],
*,
dtype: Optional[Dtype] = None,
device: Optional[Device] = None,
) -> Array:
"""
Array API compatible wrapper for :py:func:`np.full_like <numpy.full_like>`.
See its docstring for more information.
"""
from ._array_object import Array
_check_valid_dtype(dtype)
if device not in ["cpu", None]:
raise ValueError(f"Unsupported device {device!r}")
res = np.full_like(x._array, fill_value, dtype=dtype)
if res.dtype not in _all_dtypes:
# This will happen if the fill value is not something that NumPy
# coerces to one of the acceptable dtypes.
raise TypeError("Invalid input to full_like")
return Array._new(res) | Array API compatible wrapper for :py:func:`np.full_like <numpy.full_like>`. See its docstring for more information. |
169,973 | from __future__ import annotations
from typing import TYPE_CHECKING, List, Optional, Tuple, Union
from ._dtypes import _all_dtypes
import numpy as np
def _check_valid_dtype(dtype):
# Note: Only spelling dtypes as the dtype objects is supported.
# We use this instead of "dtype in _all_dtypes" because the dtype objects
# define equality with the sorts of things we want to disallow.
for d in (None,) + _all_dtypes:
if dtype is d:
return
raise ValueError("dtype must be one of the supported dtypes")
Union: _SpecialForm = ...
Optional: _SpecialForm = ...
Device = Literal["cpu"]
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `linspace` function. Write a Python function `def linspace( start: Union[int, float], stop: Union[int, float], /, num: int, *, dtype: Optional[Dtype] = None, device: Optional[Device] = None, endpoint: bool = True, ) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.linspace <numpy.linspace>`. See its docstring for more information.
Here is the function:
def linspace(
start: Union[int, float],
stop: Union[int, float],
/,
num: int,
*,
dtype: Optional[Dtype] = None,
device: Optional[Device] = None,
endpoint: bool = True,
) -> Array:
"""
Array API compatible wrapper for :py:func:`np.linspace <numpy.linspace>`.
See its docstring for more information.
"""
from ._array_object import Array
_check_valid_dtype(dtype)
if device not in ["cpu", None]:
raise ValueError(f"Unsupported device {device!r}")
return Array._new(np.linspace(start, stop, num, dtype=dtype, endpoint=endpoint)) | Array API compatible wrapper for :py:func:`np.linspace <numpy.linspace>`. See its docstring for more information. |
169,974 | from __future__ import annotations
from typing import TYPE_CHECKING, List, Optional, Tuple, Union
from ._dtypes import _all_dtypes
import numpy as np
List = _Alias()
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `meshgrid` function. Write a Python function `def meshgrid(*arrays: Array, indexing: str = "xy") -> List[Array]` to solve the following problem:
Array API compatible wrapper for :py:func:`np.meshgrid <numpy.meshgrid>`. See its docstring for more information.
Here is the function:
def meshgrid(*arrays: Array, indexing: str = "xy") -> List[Array]:
"""
Array API compatible wrapper for :py:func:`np.meshgrid <numpy.meshgrid>`.
See its docstring for more information.
"""
from ._array_object import Array
# Note: unlike np.meshgrid, only inputs with all the same dtype are
# allowed
if len({a.dtype for a in arrays}) > 1:
raise ValueError("meshgrid inputs must all have the same dtype")
return [
Array._new(array)
for array in np.meshgrid(*[a._array for a in arrays], indexing=indexing)
] | Array API compatible wrapper for :py:func:`np.meshgrid <numpy.meshgrid>`. See its docstring for more information. |
169,975 | from __future__ import annotations
from typing import TYPE_CHECKING, List, Optional, Tuple, Union
from ._dtypes import _all_dtypes
import numpy as np
def _check_valid_dtype(dtype):
# Note: Only spelling dtypes as the dtype objects is supported.
# We use this instead of "dtype in _all_dtypes" because the dtype objects
# define equality with the sorts of things we want to disallow.
for d in (None,) + _all_dtypes:
if dtype is d:
return
raise ValueError("dtype must be one of the supported dtypes")
Union: _SpecialForm = ...
Optional: _SpecialForm = ...
class Tuple(BaseTypingInstance):
def _is_homogenous(self):
# To specify a variable-length tuple of homogeneous type, Tuple[T, ...]
# is used.
return self._generics_manager.is_homogenous_tuple()
def py__simple_getitem__(self, index):
if self._is_homogenous():
return self._generics_manager.get_index_and_execute(0)
else:
if isinstance(index, int):
return self._generics_manager.get_index_and_execute(index)
debug.dbg('The getitem type on Tuple was %s' % index)
return NO_VALUES
def py__iter__(self, contextualized_node=None):
if self._is_homogenous():
yield LazyKnownValues(self._generics_manager.get_index_and_execute(0))
else:
for v in self._generics_manager.to_tuple():
yield LazyKnownValues(v.execute_annotation())
def py__getitem__(self, index_value_set, contextualized_node):
if self._is_homogenous():
return self._generics_manager.get_index_and_execute(0)
return ValueSet.from_sets(
self._generics_manager.to_tuple()
).execute_annotation()
def _get_wrapped_value(self):
tuple_, = self.inference_state.builtins_module \
.py__getattribute__('tuple').execute_annotation()
return tuple_
def name(self):
return self._wrapped_value.name
def infer_type_vars(self, value_set):
# Circular
from jedi.inference.gradual.annotation import merge_pairwise_generics, merge_type_var_dicts
value_set = value_set.filter(
lambda x: x.py__name__().lower() == 'tuple',
)
if self._is_homogenous():
# The parameter annotation is of the form `Tuple[T, ...]`,
# so we treat the incoming tuple like a iterable sequence
# rather than a positional container of elements.
return self._class_value.get_generics()[0].infer_type_vars(
value_set.merge_types_of_iterate(),
)
else:
# The parameter annotation has only explicit type parameters
# (e.g: `Tuple[T]`, `Tuple[T, U]`, `Tuple[T, U, V]`, etc.) so we
# treat the incoming values as needing to match the annotation
# exactly, just as we would for non-tuple annotations.
type_var_dict = {}
for element in value_set:
try:
method = element.get_annotated_class_object
except AttributeError:
# This might still happen, because the tuple name matching
# above is not 100% correct, so just catch the remaining
# cases here.
continue
py_class = method()
merge_type_var_dicts(
type_var_dict,
merge_pairwise_generics(self._class_value, py_class),
)
return type_var_dict
Device = Literal["cpu"]
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `ones` function. Write a Python function `def ones( shape: Union[int, Tuple[int, ...]], *, dtype: Optional[Dtype] = None, device: Optional[Device] = None, ) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.ones <numpy.ones>`. See its docstring for more information.
Here is the function:
def ones(
shape: Union[int, Tuple[int, ...]],
*,
dtype: Optional[Dtype] = None,
device: Optional[Device] = None,
) -> Array:
"""
Array API compatible wrapper for :py:func:`np.ones <numpy.ones>`.
See its docstring for more information.
"""
from ._array_object import Array
_check_valid_dtype(dtype)
if device not in ["cpu", None]:
raise ValueError(f"Unsupported device {device!r}")
return Array._new(np.ones(shape, dtype=dtype)) | Array API compatible wrapper for :py:func:`np.ones <numpy.ones>`. See its docstring for more information. |
169,976 | from __future__ import annotations
from typing import TYPE_CHECKING, List, Optional, Tuple, Union
from ._dtypes import _all_dtypes
import numpy as np
def _check_valid_dtype(dtype):
# Note: Only spelling dtypes as the dtype objects is supported.
# We use this instead of "dtype in _all_dtypes" because the dtype objects
# define equality with the sorts of things we want to disallow.
for d in (None,) + _all_dtypes:
if dtype is d:
return
raise ValueError("dtype must be one of the supported dtypes")
Optional: _SpecialForm = ...
Device = Literal["cpu"]
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `ones_like` function. Write a Python function `def ones_like( x: Array, /, *, dtype: Optional[Dtype] = None, device: Optional[Device] = None ) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.ones_like <numpy.ones_like>`. See its docstring for more information.
Here is the function:
def ones_like(
x: Array, /, *, dtype: Optional[Dtype] = None, device: Optional[Device] = None
) -> Array:
"""
Array API compatible wrapper for :py:func:`np.ones_like <numpy.ones_like>`.
See its docstring for more information.
"""
from ._array_object import Array
_check_valid_dtype(dtype)
if device not in ["cpu", None]:
raise ValueError(f"Unsupported device {device!r}")
return Array._new(np.ones_like(x._array, dtype=dtype)) | Array API compatible wrapper for :py:func:`np.ones_like <numpy.ones_like>`. See its docstring for more information. |
169,977 | from __future__ import annotations
from typing import TYPE_CHECKING, List, Optional, Tuple, Union
from ._dtypes import _all_dtypes
import numpy as np
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `tril` function. Write a Python function `def tril(x: Array, /, *, k: int = 0) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.tril <numpy.tril>`. See its docstring for more information.
Here is the function:
def tril(x: Array, /, *, k: int = 0) -> Array:
"""
Array API compatible wrapper for :py:func:`np.tril <numpy.tril>`.
See its docstring for more information.
"""
from ._array_object import Array
if x.ndim < 2:
# Note: Unlike np.tril, x must be at least 2-D
raise ValueError("x must be at least 2-dimensional for tril")
return Array._new(np.tril(x._array, k=k)) | Array API compatible wrapper for :py:func:`np.tril <numpy.tril>`. See its docstring for more information. |
169,978 | from __future__ import annotations
from typing import TYPE_CHECKING, List, Optional, Tuple, Union
from ._dtypes import _all_dtypes
import numpy as np
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `triu` function. Write a Python function `def triu(x: Array, /, *, k: int = 0) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.triu <numpy.triu>`. See its docstring for more information.
Here is the function:
def triu(x: Array, /, *, k: int = 0) -> Array:
"""
Array API compatible wrapper for :py:func:`np.triu <numpy.triu>`.
See its docstring for more information.
"""
from ._array_object import Array
if x.ndim < 2:
# Note: Unlike np.triu, x must be at least 2-D
raise ValueError("x must be at least 2-dimensional for triu")
return Array._new(np.triu(x._array, k=k)) | Array API compatible wrapper for :py:func:`np.triu <numpy.triu>`. See its docstring for more information. |
169,979 | from __future__ import annotations
from typing import TYPE_CHECKING, List, Optional, Tuple, Union
from ._dtypes import _all_dtypes
import numpy as np
def _check_valid_dtype(dtype):
# Note: Only spelling dtypes as the dtype objects is supported.
# We use this instead of "dtype in _all_dtypes" because the dtype objects
# define equality with the sorts of things we want to disallow.
for d in (None,) + _all_dtypes:
if dtype is d:
return
raise ValueError("dtype must be one of the supported dtypes")
Union: _SpecialForm = ...
Optional: _SpecialForm = ...
class Tuple(BaseTypingInstance):
def _is_homogenous(self):
# To specify a variable-length tuple of homogeneous type, Tuple[T, ...]
# is used.
return self._generics_manager.is_homogenous_tuple()
def py__simple_getitem__(self, index):
if self._is_homogenous():
return self._generics_manager.get_index_and_execute(0)
else:
if isinstance(index, int):
return self._generics_manager.get_index_and_execute(index)
debug.dbg('The getitem type on Tuple was %s' % index)
return NO_VALUES
def py__iter__(self, contextualized_node=None):
if self._is_homogenous():
yield LazyKnownValues(self._generics_manager.get_index_and_execute(0))
else:
for v in self._generics_manager.to_tuple():
yield LazyKnownValues(v.execute_annotation())
def py__getitem__(self, index_value_set, contextualized_node):
if self._is_homogenous():
return self._generics_manager.get_index_and_execute(0)
return ValueSet.from_sets(
self._generics_manager.to_tuple()
).execute_annotation()
def _get_wrapped_value(self):
tuple_, = self.inference_state.builtins_module \
.py__getattribute__('tuple').execute_annotation()
return tuple_
def name(self):
return self._wrapped_value.name
def infer_type_vars(self, value_set):
# Circular
from jedi.inference.gradual.annotation import merge_pairwise_generics, merge_type_var_dicts
value_set = value_set.filter(
lambda x: x.py__name__().lower() == 'tuple',
)
if self._is_homogenous():
# The parameter annotation is of the form `Tuple[T, ...]`,
# so we treat the incoming tuple like a iterable sequence
# rather than a positional container of elements.
return self._class_value.get_generics()[0].infer_type_vars(
value_set.merge_types_of_iterate(),
)
else:
# The parameter annotation has only explicit type parameters
# (e.g: `Tuple[T]`, `Tuple[T, U]`, `Tuple[T, U, V]`, etc.) so we
# treat the incoming values as needing to match the annotation
# exactly, just as we would for non-tuple annotations.
type_var_dict = {}
for element in value_set:
try:
method = element.get_annotated_class_object
except AttributeError:
# This might still happen, because the tuple name matching
# above is not 100% correct, so just catch the remaining
# cases here.
continue
py_class = method()
merge_type_var_dicts(
type_var_dict,
merge_pairwise_generics(self._class_value, py_class),
)
return type_var_dict
Device = Literal["cpu"]
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `zeros` function. Write a Python function `def zeros( shape: Union[int, Tuple[int, ...]], *, dtype: Optional[Dtype] = None, device: Optional[Device] = None, ) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.zeros <numpy.zeros>`. See its docstring for more information.
Here is the function:
def zeros(
shape: Union[int, Tuple[int, ...]],
*,
dtype: Optional[Dtype] = None,
device: Optional[Device] = None,
) -> Array:
"""
Array API compatible wrapper for :py:func:`np.zeros <numpy.zeros>`.
See its docstring for more information.
"""
from ._array_object import Array
_check_valid_dtype(dtype)
if device not in ["cpu", None]:
raise ValueError(f"Unsupported device {device!r}")
return Array._new(np.zeros(shape, dtype=dtype)) | Array API compatible wrapper for :py:func:`np.zeros <numpy.zeros>`. See its docstring for more information. |
169,980 | from __future__ import annotations
from typing import TYPE_CHECKING, List, Optional, Tuple, Union
from ._dtypes import _all_dtypes
import numpy as np
def _check_valid_dtype(dtype):
# Note: Only spelling dtypes as the dtype objects is supported.
# We use this instead of "dtype in _all_dtypes" because the dtype objects
# define equality with the sorts of things we want to disallow.
for d in (None,) + _all_dtypes:
if dtype is d:
return
raise ValueError("dtype must be one of the supported dtypes")
Optional: _SpecialForm = ...
Device = Literal["cpu"]
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `zeros_like` function. Write a Python function `def zeros_like( x: Array, /, *, dtype: Optional[Dtype] = None, device: Optional[Device] = None ) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.zeros_like <numpy.zeros_like>`. See its docstring for more information.
Here is the function:
def zeros_like(
x: Array, /, *, dtype: Optional[Dtype] = None, device: Optional[Device] = None
) -> Array:
"""
Array API compatible wrapper for :py:func:`np.zeros_like <numpy.zeros_like>`.
See its docstring for more information.
"""
from ._array_object import Array
_check_valid_dtype(dtype)
if device not in ["cpu", None]:
raise ValueError(f"Unsupported device {device!r}")
return Array._new(np.zeros_like(x._array, dtype=dtype)) | Array API compatible wrapper for :py:func:`np.zeros_like <numpy.zeros_like>`. See its docstring for more information. |
169,981 | from __future__ import annotations
from ._dtypes import (
_floating_dtypes,
_numeric_dtypes,
)
from ._array_object import Array
from ._creation_functions import asarray
from ._dtypes import float32, float64
from typing import TYPE_CHECKING, Optional, Tuple, Union
import numpy as np
_numeric_dtypes = (
float32,
float64,
int8,
int16,
int32,
int64,
uint8,
uint16,
uint32,
uint64,
)
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
Union: _SpecialForm = ...
Optional: _SpecialForm = ...
class Tuple(BaseTypingInstance):
def _is_homogenous(self):
# To specify a variable-length tuple of homogeneous type, Tuple[T, ...]
# is used.
return self._generics_manager.is_homogenous_tuple()
def py__simple_getitem__(self, index):
if self._is_homogenous():
return self._generics_manager.get_index_and_execute(0)
else:
if isinstance(index, int):
return self._generics_manager.get_index_and_execute(index)
debug.dbg('The getitem type on Tuple was %s' % index)
return NO_VALUES
def py__iter__(self, contextualized_node=None):
if self._is_homogenous():
yield LazyKnownValues(self._generics_manager.get_index_and_execute(0))
else:
for v in self._generics_manager.to_tuple():
yield LazyKnownValues(v.execute_annotation())
def py__getitem__(self, index_value_set, contextualized_node):
if self._is_homogenous():
return self._generics_manager.get_index_and_execute(0)
return ValueSet.from_sets(
self._generics_manager.to_tuple()
).execute_annotation()
def _get_wrapped_value(self):
tuple_, = self.inference_state.builtins_module \
.py__getattribute__('tuple').execute_annotation()
return tuple_
def name(self):
return self._wrapped_value.name
def infer_type_vars(self, value_set):
# Circular
from jedi.inference.gradual.annotation import merge_pairwise_generics, merge_type_var_dicts
value_set = value_set.filter(
lambda x: x.py__name__().lower() == 'tuple',
)
if self._is_homogenous():
# The parameter annotation is of the form `Tuple[T, ...]`,
# so we treat the incoming tuple like a iterable sequence
# rather than a positional container of elements.
return self._class_value.get_generics()[0].infer_type_vars(
value_set.merge_types_of_iterate(),
)
else:
# The parameter annotation has only explicit type parameters
# (e.g: `Tuple[T]`, `Tuple[T, U]`, `Tuple[T, U, V]`, etc.) so we
# treat the incoming values as needing to match the annotation
# exactly, just as we would for non-tuple annotations.
type_var_dict = {}
for element in value_set:
try:
method = element.get_annotated_class_object
except AttributeError:
# This might still happen, because the tuple name matching
# above is not 100% correct, so just catch the remaining
# cases here.
continue
py_class = method()
merge_type_var_dicts(
type_var_dict,
merge_pairwise_generics(self._class_value, py_class),
)
return type_var_dict
def max(
x: Array,
/,
*,
axis: Optional[Union[int, Tuple[int, ...]]] = None,
keepdims: bool = False,
) -> Array:
if x.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in max")
return Array._new(np.max(x._array, axis=axis, keepdims=keepdims)) | null |
169,982 | from __future__ import annotations
from ._dtypes import (
_floating_dtypes,
_numeric_dtypes,
)
from ._array_object import Array
from ._creation_functions import asarray
from ._dtypes import float32, float64
from typing import TYPE_CHECKING, Optional, Tuple, Union
import numpy as np
_floating_dtypes = (float32, float64)
class Array:
def _new(cls, x, /):
def __new__(cls, *args, **kwargs):
def __str__(self: Array, /) -> str:
def __repr__(self: Array, /) -> str:
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
def _promote_scalar(self, scalar):
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
def _validate_index(self, key):
def __abs__(self: Array, /) -> Array:
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
def __bool__(self: Array, /) -> bool:
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
def __float__(self: Array, /) -> float:
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
def __int__(self: Array, /) -> int:
def __index__(self: Array, /) -> int:
def __invert__(self: Array, /) -> Array:
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
def __matmul__(self: Array, other: Array, /) -> Array:
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
def __neg__(self: Array, /) -> Array:
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __pos__(self: Array, /) -> Array:
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
def __imatmul__(self: Array, other: Array, /) -> Array:
def __rmatmul__(self: Array, other: Array, /) -> Array:
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
def dtype(self) -> Dtype:
def device(self) -> Device:
def mT(self) -> Array:
def ndim(self) -> int:
def shape(self) -> Tuple[int, ...]:
def size(self) -> int:
def T(self) -> Array:
Union: _SpecialForm = ...
Optional: _SpecialForm = ...
class Tuple(BaseTypingInstance):
def _is_homogenous(self):
def py__simple_getitem__(self, index):
def py__iter__(self, contextualized_node=None):
def py__getitem__(self, index_value_set, contextualized_node):
def _get_wrapped_value(self):
def name(self):
def infer_type_vars(self, value_set):
def mean(
x: Array,
/,
*,
axis: Optional[Union[int, Tuple[int, ...]]] = None,
keepdims: bool = False,
) -> Array:
if x.dtype not in _floating_dtypes:
raise TypeError("Only floating-point dtypes are allowed in mean")
return Array._new(np.mean(x._array, axis=axis, keepdims=keepdims)) | null |
169,983 | from __future__ import annotations
from ._dtypes import (
_floating_dtypes,
_numeric_dtypes,
)
from ._array_object import Array
from ._creation_functions import asarray
from ._dtypes import float32, float64
from typing import TYPE_CHECKING, Optional, Tuple, Union
import numpy as np
_numeric_dtypes = (
float32,
float64,
int8,
int16,
int32,
int64,
uint8,
uint16,
uint32,
uint64,
)
class Array:
def _new(cls, x, /):
def __new__(cls, *args, **kwargs):
def __str__(self: Array, /) -> str:
def __repr__(self: Array, /) -> str:
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
def _promote_scalar(self, scalar):
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
def _validate_index(self, key):
def __abs__(self: Array, /) -> Array:
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
def __bool__(self: Array, /) -> bool:
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
def __float__(self: Array, /) -> float:
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
def __int__(self: Array, /) -> int:
def __index__(self: Array, /) -> int:
def __invert__(self: Array, /) -> Array:
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
def __matmul__(self: Array, other: Array, /) -> Array:
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
def __neg__(self: Array, /) -> Array:
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __pos__(self: Array, /) -> Array:
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
def __imatmul__(self: Array, other: Array, /) -> Array:
def __rmatmul__(self: Array, other: Array, /) -> Array:
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
def dtype(self) -> Dtype:
def device(self) -> Device:
def mT(self) -> Array:
def ndim(self) -> int:
def shape(self) -> Tuple[int, ...]:
def size(self) -> int:
def T(self) -> Array:
Union: _SpecialForm = ...
Optional: _SpecialForm = ...
class Tuple(BaseTypingInstance):
def _is_homogenous(self):
def py__simple_getitem__(self, index):
def py__iter__(self, contextualized_node=None):
def py__getitem__(self, index_value_set, contextualized_node):
def _get_wrapped_value(self):
def name(self):
def infer_type_vars(self, value_set):
def min(
x: Array,
/,
*,
axis: Optional[Union[int, Tuple[int, ...]]] = None,
keepdims: bool = False,
) -> Array:
if x.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in min")
return Array._new(np.min(x._array, axis=axis, keepdims=keepdims)) | null |
169,984 | from __future__ import annotations
from ._dtypes import (
_floating_dtypes,
_numeric_dtypes,
)
from ._array_object import Array
from ._creation_functions import asarray
from ._dtypes import float32, float64
from typing import TYPE_CHECKING, Optional, Tuple, Union
import numpy as np
float32 = np.dtype("float32")
float64 = np.dtype("float64")
_numeric_dtypes = (
float32,
float64,
int8,
int16,
int32,
int64,
uint8,
uint16,
uint32,
uint64,
)
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
Union: _SpecialForm = ...
Optional: _SpecialForm = ...
class Tuple(BaseTypingInstance):
def _is_homogenous(self):
# To specify a variable-length tuple of homogeneous type, Tuple[T, ...]
# is used.
return self._generics_manager.is_homogenous_tuple()
def py__simple_getitem__(self, index):
if self._is_homogenous():
return self._generics_manager.get_index_and_execute(0)
else:
if isinstance(index, int):
return self._generics_manager.get_index_and_execute(index)
debug.dbg('The getitem type on Tuple was %s' % index)
return NO_VALUES
def py__iter__(self, contextualized_node=None):
if self._is_homogenous():
yield LazyKnownValues(self._generics_manager.get_index_and_execute(0))
else:
for v in self._generics_manager.to_tuple():
yield LazyKnownValues(v.execute_annotation())
def py__getitem__(self, index_value_set, contextualized_node):
if self._is_homogenous():
return self._generics_manager.get_index_and_execute(0)
return ValueSet.from_sets(
self._generics_manager.to_tuple()
).execute_annotation()
def _get_wrapped_value(self):
tuple_, = self.inference_state.builtins_module \
.py__getattribute__('tuple').execute_annotation()
return tuple_
def name(self):
return self._wrapped_value.name
def infer_type_vars(self, value_set):
# Circular
from jedi.inference.gradual.annotation import merge_pairwise_generics, merge_type_var_dicts
value_set = value_set.filter(
lambda x: x.py__name__().lower() == 'tuple',
)
if self._is_homogenous():
# The parameter annotation is of the form `Tuple[T, ...]`,
# so we treat the incoming tuple like a iterable sequence
# rather than a positional container of elements.
return self._class_value.get_generics()[0].infer_type_vars(
value_set.merge_types_of_iterate(),
)
else:
# The parameter annotation has only explicit type parameters
# (e.g: `Tuple[T]`, `Tuple[T, U]`, `Tuple[T, U, V]`, etc.) so we
# treat the incoming values as needing to match the annotation
# exactly, just as we would for non-tuple annotations.
type_var_dict = {}
for element in value_set:
try:
method = element.get_annotated_class_object
except AttributeError:
# This might still happen, because the tuple name matching
# above is not 100% correct, so just catch the remaining
# cases here.
continue
py_class = method()
merge_type_var_dicts(
type_var_dict,
merge_pairwise_generics(self._class_value, py_class),
)
return type_var_dict
def prod(
x: Array,
/,
*,
axis: Optional[Union[int, Tuple[int, ...]]] = None,
dtype: Optional[Dtype] = None,
keepdims: bool = False,
) -> Array:
if x.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in prod")
# Note: sum() and prod() always upcast float32 to float64 for dtype=None
# We need to do so here before computing the product to avoid overflow
if dtype is None and x.dtype == float32:
dtype = float64
return Array._new(np.prod(x._array, dtype=dtype, axis=axis, keepdims=keepdims)) | null |
169,985 | from __future__ import annotations
from ._dtypes import (
_floating_dtypes,
_numeric_dtypes,
)
from ._array_object import Array
from ._creation_functions import asarray
from ._dtypes import float32, float64
from typing import TYPE_CHECKING, Optional, Tuple, Union
import numpy as np
_floating_dtypes = (float32, float64)
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
Union: _SpecialForm = ...
Optional: _SpecialForm = ...
class Tuple(BaseTypingInstance):
def _is_homogenous(self):
# To specify a variable-length tuple of homogeneous type, Tuple[T, ...]
# is used.
return self._generics_manager.is_homogenous_tuple()
def py__simple_getitem__(self, index):
if self._is_homogenous():
return self._generics_manager.get_index_and_execute(0)
else:
if isinstance(index, int):
return self._generics_manager.get_index_and_execute(index)
debug.dbg('The getitem type on Tuple was %s' % index)
return NO_VALUES
def py__iter__(self, contextualized_node=None):
if self._is_homogenous():
yield LazyKnownValues(self._generics_manager.get_index_and_execute(0))
else:
for v in self._generics_manager.to_tuple():
yield LazyKnownValues(v.execute_annotation())
def py__getitem__(self, index_value_set, contextualized_node):
if self._is_homogenous():
return self._generics_manager.get_index_and_execute(0)
return ValueSet.from_sets(
self._generics_manager.to_tuple()
).execute_annotation()
def _get_wrapped_value(self):
tuple_, = self.inference_state.builtins_module \
.py__getattribute__('tuple').execute_annotation()
return tuple_
def name(self):
return self._wrapped_value.name
def infer_type_vars(self, value_set):
# Circular
from jedi.inference.gradual.annotation import merge_pairwise_generics, merge_type_var_dicts
value_set = value_set.filter(
lambda x: x.py__name__().lower() == 'tuple',
)
if self._is_homogenous():
# The parameter annotation is of the form `Tuple[T, ...]`,
# so we treat the incoming tuple like a iterable sequence
# rather than a positional container of elements.
return self._class_value.get_generics()[0].infer_type_vars(
value_set.merge_types_of_iterate(),
)
else:
# The parameter annotation has only explicit type parameters
# (e.g: `Tuple[T]`, `Tuple[T, U]`, `Tuple[T, U, V]`, etc.) so we
# treat the incoming values as needing to match the annotation
# exactly, just as we would for non-tuple annotations.
type_var_dict = {}
for element in value_set:
try:
method = element.get_annotated_class_object
except AttributeError:
# This might still happen, because the tuple name matching
# above is not 100% correct, so just catch the remaining
# cases here.
continue
py_class = method()
merge_type_var_dicts(
type_var_dict,
merge_pairwise_generics(self._class_value, py_class),
)
return type_var_dict
def std(
x: Array,
/,
*,
axis: Optional[Union[int, Tuple[int, ...]]] = None,
correction: Union[int, float] = 0.0,
keepdims: bool = False,
) -> Array:
# Note: the keyword argument correction is different here
if x.dtype not in _floating_dtypes:
raise TypeError("Only floating-point dtypes are allowed in std")
return Array._new(np.std(x._array, axis=axis, ddof=correction, keepdims=keepdims)) | null |
169,986 | from __future__ import annotations
from ._dtypes import (
_floating_dtypes,
_numeric_dtypes,
)
from ._array_object import Array
from ._creation_functions import asarray
from ._dtypes import float32, float64
from typing import TYPE_CHECKING, Optional, Tuple, Union
import numpy as np
float32 = np.dtype("float32")
float64 = np.dtype("float64")
_numeric_dtypes = (
float32,
float64,
int8,
int16,
int32,
int64,
uint8,
uint16,
uint32,
uint64,
)
class Array:
def _new(cls, x, /):
def __new__(cls, *args, **kwargs):
def __str__(self: Array, /) -> str:
def __repr__(self: Array, /) -> str:
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
def _promote_scalar(self, scalar):
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
def _validate_index(self, key):
def __abs__(self: Array, /) -> Array:
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
def __bool__(self: Array, /) -> bool:
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
def __float__(self: Array, /) -> float:
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
def __int__(self: Array, /) -> int:
def __index__(self: Array, /) -> int:
def __invert__(self: Array, /) -> Array:
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
def __matmul__(self: Array, other: Array, /) -> Array:
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
def __neg__(self: Array, /) -> Array:
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __pos__(self: Array, /) -> Array:
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
def __imatmul__(self: Array, other: Array, /) -> Array:
def __rmatmul__(self: Array, other: Array, /) -> Array:
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
def dtype(self) -> Dtype:
def device(self) -> Device:
def mT(self) -> Array:
def ndim(self) -> int:
def shape(self) -> Tuple[int, ...]:
def size(self) -> int:
def T(self) -> Array:
Union: _SpecialForm = ...
Optional: _SpecialForm = ...
class Tuple(BaseTypingInstance):
def _is_homogenous(self):
def py__simple_getitem__(self, index):
def py__iter__(self, contextualized_node=None):
def py__getitem__(self, index_value_set, contextualized_node):
def _get_wrapped_value(self):
def name(self):
def infer_type_vars(self, value_set):
def sum(
x: Array,
/,
*,
axis: Optional[Union[int, Tuple[int, ...]]] = None,
dtype: Optional[Dtype] = None,
keepdims: bool = False,
) -> Array:
if x.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in sum")
# Note: sum() and prod() always upcast integers to (u)int64 and float32 to
# float64 for dtype=None. `np.sum` does that too for integers, but not for
# float32, so we need to special-case it here
if dtype is None and x.dtype == float32:
dtype = float64
return Array._new(np.sum(x._array, axis=axis, dtype=dtype, keepdims=keepdims)) | null |
169,987 | from __future__ import annotations
from ._dtypes import (
_floating_dtypes,
_numeric_dtypes,
)
from ._array_object import Array
from ._creation_functions import asarray
from ._dtypes import float32, float64
from typing import TYPE_CHECKING, Optional, Tuple, Union
import numpy as np
_floating_dtypes = (float32, float64)
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
Union: _SpecialForm = ...
Optional: _SpecialForm = ...
class Tuple(BaseTypingInstance):
def _is_homogenous(self):
# To specify a variable-length tuple of homogeneous type, Tuple[T, ...]
# is used.
return self._generics_manager.is_homogenous_tuple()
def py__simple_getitem__(self, index):
if self._is_homogenous():
return self._generics_manager.get_index_and_execute(0)
else:
if isinstance(index, int):
return self._generics_manager.get_index_and_execute(index)
debug.dbg('The getitem type on Tuple was %s' % index)
return NO_VALUES
def py__iter__(self, contextualized_node=None):
if self._is_homogenous():
yield LazyKnownValues(self._generics_manager.get_index_and_execute(0))
else:
for v in self._generics_manager.to_tuple():
yield LazyKnownValues(v.execute_annotation())
def py__getitem__(self, index_value_set, contextualized_node):
if self._is_homogenous():
return self._generics_manager.get_index_and_execute(0)
return ValueSet.from_sets(
self._generics_manager.to_tuple()
).execute_annotation()
def _get_wrapped_value(self):
tuple_, = self.inference_state.builtins_module \
.py__getattribute__('tuple').execute_annotation()
return tuple_
def name(self):
return self._wrapped_value.name
def infer_type_vars(self, value_set):
# Circular
from jedi.inference.gradual.annotation import merge_pairwise_generics, merge_type_var_dicts
value_set = value_set.filter(
lambda x: x.py__name__().lower() == 'tuple',
)
if self._is_homogenous():
# The parameter annotation is of the form `Tuple[T, ...]`,
# so we treat the incoming tuple like a iterable sequence
# rather than a positional container of elements.
return self._class_value.get_generics()[0].infer_type_vars(
value_set.merge_types_of_iterate(),
)
else:
# The parameter annotation has only explicit type parameters
# (e.g: `Tuple[T]`, `Tuple[T, U]`, `Tuple[T, U, V]`, etc.) so we
# treat the incoming values as needing to match the annotation
# exactly, just as we would for non-tuple annotations.
type_var_dict = {}
for element in value_set:
try:
method = element.get_annotated_class_object
except AttributeError:
# This might still happen, because the tuple name matching
# above is not 100% correct, so just catch the remaining
# cases here.
continue
py_class = method()
merge_type_var_dicts(
type_var_dict,
merge_pairwise_generics(self._class_value, py_class),
)
return type_var_dict
def var(
x: Array,
/,
*,
axis: Optional[Union[int, Tuple[int, ...]]] = None,
correction: Union[int, float] = 0.0,
keepdims: bool = False,
) -> Array:
# Note: the keyword argument correction is different here
if x.dtype not in _floating_dtypes:
raise TypeError("Only floating-point dtypes are allowed in var")
return Array._new(np.var(x._array, axis=axis, ddof=correction, keepdims=keepdims)) | null |
169,988 | from __future__ import annotations
from ._array_object import Array
from ._dtypes import _all_dtypes, _result_type
from dataclasses import dataclass
from typing import TYPE_CHECKING, List, Tuple, Union
import numpy as np
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
def astype(x: Array, dtype: Dtype, /, *, copy: bool = True) -> Array:
if not copy and dtype == x.dtype:
return x
return Array._new(x._array.astype(dtype=dtype, copy=copy)) | null |
169,989 | from __future__ import annotations
from ._array_object import Array
from ._dtypes import _all_dtypes, _result_type
from dataclasses import dataclass
from typing import TYPE_CHECKING, List, Tuple, Union
import numpy as np
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
List = _Alias()
The provided code snippet includes necessary dependencies for implementing the `broadcast_arrays` function. Write a Python function `def broadcast_arrays(*arrays: Array) -> List[Array]` to solve the following problem:
Array API compatible wrapper for :py:func:`np.broadcast_arrays <numpy.broadcast_arrays>`. See its docstring for more information.
Here is the function:
def broadcast_arrays(*arrays: Array) -> List[Array]:
"""
Array API compatible wrapper for :py:func:`np.broadcast_arrays <numpy.broadcast_arrays>`.
See its docstring for more information.
"""
from ._array_object import Array
return [
Array._new(array) for array in np.broadcast_arrays(*[a._array for a in arrays])
] | Array API compatible wrapper for :py:func:`np.broadcast_arrays <numpy.broadcast_arrays>`. See its docstring for more information. |
169,990 | from __future__ import annotations
from ._array_object import Array
from ._dtypes import _all_dtypes, _result_type
from dataclasses import dataclass
from typing import TYPE_CHECKING, List, Tuple, Union
import numpy as np
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
class Tuple(BaseTypingInstance):
def _is_homogenous(self):
# To specify a variable-length tuple of homogeneous type, Tuple[T, ...]
# is used.
return self._generics_manager.is_homogenous_tuple()
def py__simple_getitem__(self, index):
if self._is_homogenous():
return self._generics_manager.get_index_and_execute(0)
else:
if isinstance(index, int):
return self._generics_manager.get_index_and_execute(index)
debug.dbg('The getitem type on Tuple was %s' % index)
return NO_VALUES
def py__iter__(self, contextualized_node=None):
if self._is_homogenous():
yield LazyKnownValues(self._generics_manager.get_index_and_execute(0))
else:
for v in self._generics_manager.to_tuple():
yield LazyKnownValues(v.execute_annotation())
def py__getitem__(self, index_value_set, contextualized_node):
if self._is_homogenous():
return self._generics_manager.get_index_and_execute(0)
return ValueSet.from_sets(
self._generics_manager.to_tuple()
).execute_annotation()
def _get_wrapped_value(self):
tuple_, = self.inference_state.builtins_module \
.py__getattribute__('tuple').execute_annotation()
return tuple_
def name(self):
return self._wrapped_value.name
def infer_type_vars(self, value_set):
# Circular
from jedi.inference.gradual.annotation import merge_pairwise_generics, merge_type_var_dicts
value_set = value_set.filter(
lambda x: x.py__name__().lower() == 'tuple',
)
if self._is_homogenous():
# The parameter annotation is of the form `Tuple[T, ...]`,
# so we treat the incoming tuple like a iterable sequence
# rather than a positional container of elements.
return self._class_value.get_generics()[0].infer_type_vars(
value_set.merge_types_of_iterate(),
)
else:
# The parameter annotation has only explicit type parameters
# (e.g: `Tuple[T]`, `Tuple[T, U]`, `Tuple[T, U, V]`, etc.) so we
# treat the incoming values as needing to match the annotation
# exactly, just as we would for non-tuple annotations.
type_var_dict = {}
for element in value_set:
try:
method = element.get_annotated_class_object
except AttributeError:
# This might still happen, because the tuple name matching
# above is not 100% correct, so just catch the remaining
# cases here.
continue
py_class = method()
merge_type_var_dicts(
type_var_dict,
merge_pairwise_generics(self._class_value, py_class),
)
return type_var_dict
The provided code snippet includes necessary dependencies for implementing the `broadcast_to` function. Write a Python function `def broadcast_to(x: Array, /, shape: Tuple[int, ...]) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.broadcast_to <numpy.broadcast_to>`. See its docstring for more information.
Here is the function:
def broadcast_to(x: Array, /, shape: Tuple[int, ...]) -> Array:
"""
Array API compatible wrapper for :py:func:`np.broadcast_to <numpy.broadcast_to>`.
See its docstring for more information.
"""
from ._array_object import Array
return Array._new(np.broadcast_to(x._array, shape)) | Array API compatible wrapper for :py:func:`np.broadcast_to <numpy.broadcast_to>`. See its docstring for more information. |
169,991 | from __future__ import annotations
from ._array_object import Array
from ._dtypes import _all_dtypes, _result_type
from dataclasses import dataclass
from typing import TYPE_CHECKING, List, Tuple, Union
import numpy as np
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
_all_dtypes = (
int8,
int16,
int32,
int64,
uint8,
uint16,
uint32,
uint64,
float32,
float64,
bool,
)
def _result_type(type1, type2):
if (type1, type2) in _promotion_table:
return _promotion_table[type1, type2]
raise TypeError(f"{type1} and {type2} cannot be type promoted together")
Union: _SpecialForm = ...
The provided code snippet includes necessary dependencies for implementing the `can_cast` function. Write a Python function `def can_cast(from_: Union[Dtype, Array], to: Dtype, /) -> bool` to solve the following problem:
Array API compatible wrapper for :py:func:`np.can_cast <numpy.can_cast>`. See its docstring for more information.
Here is the function:
def can_cast(from_: Union[Dtype, Array], to: Dtype, /) -> bool:
"""
Array API compatible wrapper for :py:func:`np.can_cast <numpy.can_cast>`.
See its docstring for more information.
"""
if isinstance(from_, Array):
from_ = from_.dtype
elif from_ not in _all_dtypes:
raise TypeError(f"{from_=}, but should be an array_api array or dtype")
if to not in _all_dtypes:
raise TypeError(f"{to=}, but should be a dtype")
# Note: We avoid np.can_cast() as it has discrepancies with the array API,
# since NumPy allows cross-kind casting (e.g., NumPy allows bool -> int8).
# See https://github.com/numpy/numpy/issues/20870
try:
# We promote `from_` and `to` together. We then check if the promoted
# dtype is `to`, which indicates if `from_` can (up)cast to `to`.
dtype = _result_type(from_, to)
return to == dtype
except TypeError:
# _result_type() raises if the dtypes don't promote together
return False | Array API compatible wrapper for :py:func:`np.can_cast <numpy.can_cast>`. See its docstring for more information. |
169,992 | from __future__ import annotations
from ._array_object import Array
from ._dtypes import _all_dtypes, _result_type
from dataclasses import dataclass
from typing import TYPE_CHECKING, List, Tuple, Union
import numpy as np
class finfo_object:
bits: int
# Note: The types of the float data here are float, whereas in NumPy they
# are scalars of the corresponding float dtype.
eps: float
max: float
min: float
smallest_normal: float
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
Union: _SpecialForm = ...
The provided code snippet includes necessary dependencies for implementing the `finfo` function. Write a Python function `def finfo(type: Union[Dtype, Array], /) -> finfo_object` to solve the following problem:
Array API compatible wrapper for :py:func:`np.finfo <numpy.finfo>`. See its docstring for more information.
Here is the function:
def finfo(type: Union[Dtype, Array], /) -> finfo_object:
"""
Array API compatible wrapper for :py:func:`np.finfo <numpy.finfo>`.
See its docstring for more information.
"""
fi = np.finfo(type)
# Note: The types of the float data here are float, whereas in NumPy they
# are scalars of the corresponding float dtype.
return finfo_object(
fi.bits,
float(fi.eps),
float(fi.max),
float(fi.min),
float(fi.smallest_normal),
) | Array API compatible wrapper for :py:func:`np.finfo <numpy.finfo>`. See its docstring for more information. |
169,993 | from __future__ import annotations
from ._array_object import Array
from ._dtypes import _all_dtypes, _result_type
from dataclasses import dataclass
from typing import TYPE_CHECKING, List, Tuple, Union
import numpy as np
class iinfo_object:
bits: int
max: int
min: int
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
Union: _SpecialForm = ...
The provided code snippet includes necessary dependencies for implementing the `iinfo` function. Write a Python function `def iinfo(type: Union[Dtype, Array], /) -> iinfo_object` to solve the following problem:
Array API compatible wrapper for :py:func:`np.iinfo <numpy.iinfo>`. See its docstring for more information.
Here is the function:
def iinfo(type: Union[Dtype, Array], /) -> iinfo_object:
"""
Array API compatible wrapper for :py:func:`np.iinfo <numpy.iinfo>`.
See its docstring for more information.
"""
ii = np.iinfo(type)
return iinfo_object(ii.bits, ii.max, ii.min) | Array API compatible wrapper for :py:func:`np.iinfo <numpy.iinfo>`. See its docstring for more information. |
169,994 | from __future__ import annotations
from ._array_object import Array
from ._dtypes import _result_type
from typing import Optional, Tuple
import numpy as np
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
Optional: _SpecialForm = ...
The provided code snippet includes necessary dependencies for implementing the `argmax` function. Write a Python function `def argmax(x: Array, /, *, axis: Optional[int] = None, keepdims: bool = False) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.argmax <numpy.argmax>`. See its docstring for more information.
Here is the function:
def argmax(x: Array, /, *, axis: Optional[int] = None, keepdims: bool = False) -> Array:
"""
Array API compatible wrapper for :py:func:`np.argmax <numpy.argmax>`.
See its docstring for more information.
"""
return Array._new(np.asarray(np.argmax(x._array, axis=axis, keepdims=keepdims))) | Array API compatible wrapper for :py:func:`np.argmax <numpy.argmax>`. See its docstring for more information. |
169,995 | from __future__ import annotations
from ._array_object import Array
from ._dtypes import _result_type
from typing import Optional, Tuple
import numpy as np
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
Optional: _SpecialForm = ...
The provided code snippet includes necessary dependencies for implementing the `argmin` function. Write a Python function `def argmin(x: Array, /, *, axis: Optional[int] = None, keepdims: bool = False) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.argmin <numpy.argmin>`. See its docstring for more information.
Here is the function:
def argmin(x: Array, /, *, axis: Optional[int] = None, keepdims: bool = False) -> Array:
"""
Array API compatible wrapper for :py:func:`np.argmin <numpy.argmin>`.
See its docstring for more information.
"""
return Array._new(np.asarray(np.argmin(x._array, axis=axis, keepdims=keepdims))) | Array API compatible wrapper for :py:func:`np.argmin <numpy.argmin>`. See its docstring for more information. |
169,996 | from __future__ import annotations
from ._array_object import Array
from ._dtypes import _result_type
from typing import Optional, Tuple
import numpy as np
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
class Tuple(BaseTypingInstance):
def _is_homogenous(self):
# To specify a variable-length tuple of homogeneous type, Tuple[T, ...]
# is used.
return self._generics_manager.is_homogenous_tuple()
def py__simple_getitem__(self, index):
if self._is_homogenous():
return self._generics_manager.get_index_and_execute(0)
else:
if isinstance(index, int):
return self._generics_manager.get_index_and_execute(index)
debug.dbg('The getitem type on Tuple was %s' % index)
return NO_VALUES
def py__iter__(self, contextualized_node=None):
if self._is_homogenous():
yield LazyKnownValues(self._generics_manager.get_index_and_execute(0))
else:
for v in self._generics_manager.to_tuple():
yield LazyKnownValues(v.execute_annotation())
def py__getitem__(self, index_value_set, contextualized_node):
if self._is_homogenous():
return self._generics_manager.get_index_and_execute(0)
return ValueSet.from_sets(
self._generics_manager.to_tuple()
).execute_annotation()
def _get_wrapped_value(self):
tuple_, = self.inference_state.builtins_module \
.py__getattribute__('tuple').execute_annotation()
return tuple_
def name(self):
return self._wrapped_value.name
def infer_type_vars(self, value_set):
# Circular
from jedi.inference.gradual.annotation import merge_pairwise_generics, merge_type_var_dicts
value_set = value_set.filter(
lambda x: x.py__name__().lower() == 'tuple',
)
if self._is_homogenous():
# The parameter annotation is of the form `Tuple[T, ...]`,
# so we treat the incoming tuple like a iterable sequence
# rather than a positional container of elements.
return self._class_value.get_generics()[0].infer_type_vars(
value_set.merge_types_of_iterate(),
)
else:
# The parameter annotation has only explicit type parameters
# (e.g: `Tuple[T]`, `Tuple[T, U]`, `Tuple[T, U, V]`, etc.) so we
# treat the incoming values as needing to match the annotation
# exactly, just as we would for non-tuple annotations.
type_var_dict = {}
for element in value_set:
try:
method = element.get_annotated_class_object
except AttributeError:
# This might still happen, because the tuple name matching
# above is not 100% correct, so just catch the remaining
# cases here.
continue
py_class = method()
merge_type_var_dicts(
type_var_dict,
merge_pairwise_generics(self._class_value, py_class),
)
return type_var_dict
The provided code snippet includes necessary dependencies for implementing the `nonzero` function. Write a Python function `def nonzero(x: Array, /) -> Tuple[Array, ...]` to solve the following problem:
Array API compatible wrapper for :py:func:`np.nonzero <numpy.nonzero>`. See its docstring for more information.
Here is the function:
def nonzero(x: Array, /) -> Tuple[Array, ...]:
"""
Array API compatible wrapper for :py:func:`np.nonzero <numpy.nonzero>`.
See its docstring for more information.
"""
return tuple(Array._new(i) for i in np.nonzero(x._array)) | Array API compatible wrapper for :py:func:`np.nonzero <numpy.nonzero>`. See its docstring for more information. |
169,997 | from __future__ import annotations
from ._array_object import Array
from ._dtypes import _result_type
from typing import Optional, Tuple
import numpy as np
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
def _result_type(type1, type2):
if (type1, type2) in _promotion_table:
return _promotion_table[type1, type2]
raise TypeError(f"{type1} and {type2} cannot be type promoted together")
The provided code snippet includes necessary dependencies for implementing the `where` function. Write a Python function `def where(condition: Array, x1: Array, x2: Array, /) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.where <numpy.where>`. See its docstring for more information.
Here is the function:
def where(condition: Array, x1: Array, x2: Array, /) -> Array:
"""
Array API compatible wrapper for :py:func:`np.where <numpy.where>`.
See its docstring for more information.
"""
# Call result type here just to raise on disallowed type combinations
_result_type(x1.dtype, x2.dtype)
x1, x2 = Array._normalize_two_args(x1, x2)
return Array._new(np.where(condition._array, x1._array, x2._array)) | Array API compatible wrapper for :py:func:`np.where <numpy.where>`. See its docstring for more information. |
169,998 | from __future__ import annotations
from ._dtypes import _floating_dtypes, _numeric_dtypes
from ._manipulation_functions import reshape
from ._array_object import Array
from ..core.numeric import normalize_axis_tuple
from typing import TYPE_CHECKING
from typing import NamedTuple
import numpy.linalg
import numpy as np
_floating_dtypes = (float32, float64)
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `cholesky` function. Write a Python function `def cholesky(x: Array, /, *, upper: bool = False) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.linalg.cholesky <numpy.linalg.cholesky>`. See its docstring for more information.
Here is the function:
def cholesky(x: Array, /, *, upper: bool = False) -> Array:
"""
Array API compatible wrapper for :py:func:`np.linalg.cholesky <numpy.linalg.cholesky>`.
See its docstring for more information.
"""
# Note: the restriction to floating-point dtypes only is different from
# np.linalg.cholesky.
if x.dtype not in _floating_dtypes:
raise TypeError('Only floating-point dtypes are allowed in cholesky')
L = np.linalg.cholesky(x._array)
if upper:
return Array._new(L).mT
return Array._new(L) | Array API compatible wrapper for :py:func:`np.linalg.cholesky <numpy.linalg.cholesky>`. See its docstring for more information. |
169,999 | from __future__ import annotations
from ._dtypes import _floating_dtypes, _numeric_dtypes
from ._manipulation_functions import reshape
from ._array_object import Array
from ..core.numeric import normalize_axis_tuple
from typing import TYPE_CHECKING
from typing import NamedTuple
import numpy.linalg
import numpy as np
_numeric_dtypes = (
float32,
float64,
int8,
int16,
int32,
int64,
uint8,
uint16,
uint32,
uint64,
)
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `cross` function. Write a Python function `def cross(x1: Array, x2: Array, /, *, axis: int = -1) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.cross <numpy.cross>`. See its docstring for more information.
Here is the function:
def cross(x1: Array, x2: Array, /, *, axis: int = -1) -> Array:
"""
Array API compatible wrapper for :py:func:`np.cross <numpy.cross>`.
See its docstring for more information.
"""
if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
raise TypeError('Only numeric dtypes are allowed in cross')
# Note: this is different from np.cross(), which broadcasts
if x1.shape != x2.shape:
raise ValueError('x1 and x2 must have the same shape')
if x1.ndim == 0:
raise ValueError('cross() requires arrays of dimension at least 1')
# Note: this is different from np.cross(), which allows dimension 2
if x1.shape[axis] != 3:
raise ValueError('cross() dimension must equal 3')
return Array._new(np.cross(x1._array, x2._array, axis=axis)) | Array API compatible wrapper for :py:func:`np.cross <numpy.cross>`. See its docstring for more information. |
170,000 | from __future__ import annotations
from ._dtypes import _floating_dtypes, _numeric_dtypes
from ._manipulation_functions import reshape
from ._array_object import Array
from ..core.numeric import normalize_axis_tuple
from typing import TYPE_CHECKING
from typing import NamedTuple
import numpy.linalg
import numpy as np
_floating_dtypes = (float32, float64)
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `det` function. Write a Python function `def det(x: Array, /) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.linalg.det <numpy.linalg.det>`. See its docstring for more information.
Here is the function:
def det(x: Array, /) -> Array:
"""
Array API compatible wrapper for :py:func:`np.linalg.det <numpy.linalg.det>`.
See its docstring for more information.
"""
# Note: the restriction to floating-point dtypes only is different from
# np.linalg.det.
if x.dtype not in _floating_dtypes:
raise TypeError('Only floating-point dtypes are allowed in det')
return Array._new(np.linalg.det(x._array)) | Array API compatible wrapper for :py:func:`np.linalg.det <numpy.linalg.det>`. See its docstring for more information. |
170,001 | from __future__ import annotations
from ._dtypes import _floating_dtypes, _numeric_dtypes
from ._manipulation_functions import reshape
from ._array_object import Array
from ..core.numeric import normalize_axis_tuple
from typing import TYPE_CHECKING
from typing import NamedTuple
import numpy.linalg
import numpy as np
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `diagonal` function. Write a Python function `def diagonal(x: Array, /, *, offset: int = 0) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.diagonal <numpy.diagonal>`. See its docstring for more information.
Here is the function:
def diagonal(x: Array, /, *, offset: int = 0) -> Array:
"""
Array API compatible wrapper for :py:func:`np.diagonal <numpy.diagonal>`.
See its docstring for more information.
"""
# Note: diagonal always operates on the last two axes, whereas np.diagonal
# operates on the first two axes by default
return Array._new(np.diagonal(x._array, offset=offset, axis1=-2, axis2=-1)) | Array API compatible wrapper for :py:func:`np.diagonal <numpy.diagonal>`. See its docstring for more information. |
170,002 | from __future__ import annotations
from ._dtypes import _floating_dtypes, _numeric_dtypes
from ._manipulation_functions import reshape
from ._array_object import Array
from ..core.numeric import normalize_axis_tuple
from typing import TYPE_CHECKING
from typing import NamedTuple
import numpy.linalg
import numpy as np
class EighResult(NamedTuple):
eigenvalues: Array
eigenvectors: Array
_floating_dtypes = (float32, float64)
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `eigh` function. Write a Python function `def eigh(x: Array, /) -> EighResult` to solve the following problem:
Array API compatible wrapper for :py:func:`np.linalg.eigh <numpy.linalg.eigh>`. See its docstring for more information.
Here is the function:
def eigh(x: Array, /) -> EighResult:
"""
Array API compatible wrapper for :py:func:`np.linalg.eigh <numpy.linalg.eigh>`.
See its docstring for more information.
"""
# Note: the restriction to floating-point dtypes only is different from
# np.linalg.eigh.
if x.dtype not in _floating_dtypes:
raise TypeError('Only floating-point dtypes are allowed in eigh')
# Note: the return type here is a namedtuple, which is different from
# np.eigh, which only returns a tuple.
return EighResult(*map(Array._new, np.linalg.eigh(x._array))) | Array API compatible wrapper for :py:func:`np.linalg.eigh <numpy.linalg.eigh>`. See its docstring for more information. |
170,003 | from __future__ import annotations
from ._dtypes import _floating_dtypes, _numeric_dtypes
from ._manipulation_functions import reshape
from ._array_object import Array
from ..core.numeric import normalize_axis_tuple
from typing import TYPE_CHECKING
from typing import NamedTuple
import numpy.linalg
import numpy as np
_floating_dtypes = (float32, float64)
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `eigvalsh` function. Write a Python function `def eigvalsh(x: Array, /) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.linalg.eigvalsh <numpy.linalg.eigvalsh>`. See its docstring for more information.
Here is the function:
def eigvalsh(x: Array, /) -> Array:
"""
Array API compatible wrapper for :py:func:`np.linalg.eigvalsh <numpy.linalg.eigvalsh>`.
See its docstring for more information.
"""
# Note: the restriction to floating-point dtypes only is different from
# np.linalg.eigvalsh.
if x.dtype not in _floating_dtypes:
raise TypeError('Only floating-point dtypes are allowed in eigvalsh')
return Array._new(np.linalg.eigvalsh(x._array)) | Array API compatible wrapper for :py:func:`np.linalg.eigvalsh <numpy.linalg.eigvalsh>`. See its docstring for more information. |
170,004 | from __future__ import annotations
from ._dtypes import _floating_dtypes, _numeric_dtypes
from ._manipulation_functions import reshape
from ._array_object import Array
from ..core.numeric import normalize_axis_tuple
from typing import TYPE_CHECKING
from typing import NamedTuple
import numpy.linalg
import numpy as np
_floating_dtypes = (float32, float64)
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `inv` function. Write a Python function `def inv(x: Array, /) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.linalg.inv <numpy.linalg.inv>`. See its docstring for more information.
Here is the function:
def inv(x: Array, /) -> Array:
"""
Array API compatible wrapper for :py:func:`np.linalg.inv <numpy.linalg.inv>`.
See its docstring for more information.
"""
# Note: the restriction to floating-point dtypes only is different from
# np.linalg.inv.
if x.dtype not in _floating_dtypes:
raise TypeError('Only floating-point dtypes are allowed in inv')
return Array._new(np.linalg.inv(x._array)) | Array API compatible wrapper for :py:func:`np.linalg.inv <numpy.linalg.inv>`. See its docstring for more information. |
170,005 | from __future__ import annotations
from ._dtypes import _floating_dtypes, _numeric_dtypes
from ._manipulation_functions import reshape
from ._array_object import Array
from ..core.numeric import normalize_axis_tuple
from typing import TYPE_CHECKING
from typing import NamedTuple
import numpy.linalg
import numpy as np
_numeric_dtypes = (
float32,
float64,
int8,
int16,
int32,
int64,
uint8,
uint16,
uint32,
uint64,
)
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `matmul` function. Write a Python function `def matmul(x1: Array, x2: Array, /) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.matmul <numpy.matmul>`. See its docstring for more information.
Here is the function:
def matmul(x1: Array, x2: Array, /) -> Array:
"""
Array API compatible wrapper for :py:func:`np.matmul <numpy.matmul>`.
See its docstring for more information.
"""
# Note: the restriction to numeric dtypes only is different from
# np.matmul.
if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
raise TypeError('Only numeric dtypes are allowed in matmul')
return Array._new(np.matmul(x1._array, x2._array)) | Array API compatible wrapper for :py:func:`np.matmul <numpy.matmul>`. See its docstring for more information. |
170,006 | from __future__ import annotations
from ._dtypes import _floating_dtypes, _numeric_dtypes
from ._manipulation_functions import reshape
from ._array_object import Array
from ..core.numeric import normalize_axis_tuple
from typing import TYPE_CHECKING
from typing import NamedTuple
import numpy.linalg
import numpy as np
_floating_dtypes = (float32, float64)
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `matrix_norm` function. Write a Python function `def matrix_norm(x: Array, /, *, keepdims: bool = False, ord: Optional[Union[int, float, Literal['fro', 'nuc']]] = 'fro') -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.linalg.norm <numpy.linalg.norm>`. See its docstring for more information.
Here is the function:
def matrix_norm(x: Array, /, *, keepdims: bool = False, ord: Optional[Union[int, float, Literal['fro', 'nuc']]] = 'fro') -> Array:
"""
Array API compatible wrapper for :py:func:`np.linalg.norm <numpy.linalg.norm>`.
See its docstring for more information.
"""
# Note: the restriction to floating-point dtypes only is different from
# np.linalg.norm.
if x.dtype not in _floating_dtypes:
raise TypeError('Only floating-point dtypes are allowed in matrix_norm')
return Array._new(np.linalg.norm(x._array, axis=(-2, -1), keepdims=keepdims, ord=ord)) | Array API compatible wrapper for :py:func:`np.linalg.norm <numpy.linalg.norm>`. See its docstring for more information. |
170,007 | from __future__ import annotations
from ._dtypes import _floating_dtypes, _numeric_dtypes
from ._manipulation_functions import reshape
from ._array_object import Array
from ..core.numeric import normalize_axis_tuple
from typing import TYPE_CHECKING
from typing import NamedTuple
import numpy.linalg
import numpy as np
_floating_dtypes = (float32, float64)
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `matrix_power` function. Write a Python function `def matrix_power(x: Array, n: int, /) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.matrix_power <numpy.matrix_power>`. See its docstring for more information.
Here is the function:
def matrix_power(x: Array, n: int, /) -> Array:
"""
Array API compatible wrapper for :py:func:`np.matrix_power <numpy.matrix_power>`.
See its docstring for more information.
"""
# Note: the restriction to floating-point dtypes only is different from
# np.linalg.matrix_power.
if x.dtype not in _floating_dtypes:
raise TypeError('Only floating-point dtypes are allowed for the first argument of matrix_power')
# np.matrix_power already checks if n is an integer
return Array._new(np.linalg.matrix_power(x._array, n)) | Array API compatible wrapper for :py:func:`np.matrix_power <numpy.matrix_power>`. See its docstring for more information. |
170,008 | from __future__ import annotations
from ._dtypes import _floating_dtypes, _numeric_dtypes
from ._manipulation_functions import reshape
from ._array_object import Array
from ..core.numeric import normalize_axis_tuple
from typing import TYPE_CHECKING
from typing import NamedTuple
import numpy.linalg
import numpy as np
def svd(x: Array, /, *, full_matrices: bool = True) -> SVDResult:
"""
Array API compatible wrapper for :py:func:`np.linalg.svd <numpy.linalg.svd>`.
See its docstring for more information.
"""
# Note: the restriction to floating-point dtypes only is different from
# np.linalg.svd.
if x.dtype not in _floating_dtypes:
raise TypeError('Only floating-point dtypes are allowed in svd')
# Note: the return type here is a namedtuple, which is different from
# np.svd, which only returns a tuple.
return SVDResult(*map(Array._new, np.linalg.svd(x._array, full_matrices=full_matrices)))
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `matrix_rank` function. Write a Python function `def matrix_rank(x: Array, /, *, rtol: Optional[Union[float, Array]] = None) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.matrix_rank <numpy.matrix_rank>`. See its docstring for more information.
Here is the function:
def matrix_rank(x: Array, /, *, rtol: Optional[Union[float, Array]] = None) -> Array:
"""
Array API compatible wrapper for :py:func:`np.matrix_rank <numpy.matrix_rank>`.
See its docstring for more information.
"""
# Note: this is different from np.linalg.matrix_rank, which supports 1
# dimensional arrays.
if x.ndim < 2:
raise np.linalg.LinAlgError("1-dimensional array given. Array must be at least two-dimensional")
S = np.linalg.svd(x._array, compute_uv=False)
if rtol is None:
tol = S.max(axis=-1, keepdims=True) * max(x.shape[-2:]) * np.finfo(S.dtype).eps
else:
if isinstance(rtol, Array):
rtol = rtol._array
# Note: this is different from np.linalg.matrix_rank, which does not multiply
# the tolerance by the largest singular value.
tol = S.max(axis=-1, keepdims=True)*np.asarray(rtol)[..., np.newaxis]
return Array._new(np.count_nonzero(S > tol, axis=-1)) | Array API compatible wrapper for :py:func:`np.matrix_rank <numpy.matrix_rank>`. See its docstring for more information. |
170,009 | from __future__ import annotations
from ._dtypes import _floating_dtypes, _numeric_dtypes
from ._manipulation_functions import reshape
from ._array_object import Array
from ..core.numeric import normalize_axis_tuple
from typing import TYPE_CHECKING
from typing import NamedTuple
import numpy.linalg
import numpy as np
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
def matrix_transpose(x: Array, /) -> Array:
if x.ndim < 2:
raise ValueError("x must be at least 2-dimensional for matrix_transpose")
return Array._new(np.swapaxes(x._array, -1, -2)) | null |
170,010 | from __future__ import annotations
from ._dtypes import _floating_dtypes, _numeric_dtypes
from ._manipulation_functions import reshape
from ._array_object import Array
from ..core.numeric import normalize_axis_tuple
from typing import TYPE_CHECKING
from typing import NamedTuple
import numpy.linalg
import numpy as np
_numeric_dtypes = (
float32,
float64,
int8,
int16,
int32,
int64,
uint8,
uint16,
uint32,
uint64,
)
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `outer` function. Write a Python function `def outer(x1: Array, x2: Array, /) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.outer <numpy.outer>`. See its docstring for more information.
Here is the function:
def outer(x1: Array, x2: Array, /) -> Array:
"""
Array API compatible wrapper for :py:func:`np.outer <numpy.outer>`.
See its docstring for more information.
"""
# Note: the restriction to numeric dtypes only is different from
# np.outer.
if x1.dtype not in _numeric_dtypes or x2.dtype not in _numeric_dtypes:
raise TypeError('Only numeric dtypes are allowed in outer')
# Note: the restriction to only 1-dim arrays is different from np.outer
if x1.ndim != 1 or x2.ndim != 1:
raise ValueError('The input arrays to outer must be 1-dimensional')
return Array._new(np.outer(x1._array, x2._array)) | Array API compatible wrapper for :py:func:`np.outer <numpy.outer>`. See its docstring for more information. |
170,011 | from __future__ import annotations
from ._dtypes import _floating_dtypes, _numeric_dtypes
from ._manipulation_functions import reshape
from ._array_object import Array
from ..core.numeric import normalize_axis_tuple
from typing import TYPE_CHECKING
from typing import NamedTuple
import numpy.linalg
import numpy as np
_floating_dtypes = (float32, float64)
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `pinv` function. Write a Python function `def pinv(x: Array, /, *, rtol: Optional[Union[float, Array]] = None) -> Array` to solve the following problem:
Array API compatible wrapper for :py:func:`np.linalg.pinv <numpy.linalg.pinv>`. See its docstring for more information.
Here is the function:
def pinv(x: Array, /, *, rtol: Optional[Union[float, Array]] = None) -> Array:
"""
Array API compatible wrapper for :py:func:`np.linalg.pinv <numpy.linalg.pinv>`.
See its docstring for more information.
"""
# Note: the restriction to floating-point dtypes only is different from
# np.linalg.pinv.
if x.dtype not in _floating_dtypes:
raise TypeError('Only floating-point dtypes are allowed in pinv')
# Note: this is different from np.linalg.pinv, which does not multiply the
# default tolerance by max(M, N).
if rtol is None:
rtol = max(x.shape[-2:]) * np.finfo(x.dtype).eps
return Array._new(np.linalg.pinv(x._array, rcond=rtol)) | Array API compatible wrapper for :py:func:`np.linalg.pinv <numpy.linalg.pinv>`. See its docstring for more information. |
170,012 | from __future__ import annotations
from ._dtypes import _floating_dtypes, _numeric_dtypes
from ._manipulation_functions import reshape
from ._array_object import Array
from ..core.numeric import normalize_axis_tuple
from typing import TYPE_CHECKING
from typing import NamedTuple
import numpy.linalg
import numpy as np
class QRResult(NamedTuple):
Q: Array
R: Array
_floating_dtypes = (float32, float64)
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `qr` function. Write a Python function `def qr(x: Array, /, *, mode: Literal['reduced', 'complete'] = 'reduced') -> QRResult` to solve the following problem:
Array API compatible wrapper for :py:func:`np.linalg.qr <numpy.linalg.qr>`. See its docstring for more information.
Here is the function:
def qr(x: Array, /, *, mode: Literal['reduced', 'complete'] = 'reduced') -> QRResult:
"""
Array API compatible wrapper for :py:func:`np.linalg.qr <numpy.linalg.qr>`.
See its docstring for more information.
"""
# Note: the restriction to floating-point dtypes only is different from
# np.linalg.qr.
if x.dtype not in _floating_dtypes:
raise TypeError('Only floating-point dtypes are allowed in qr')
# Note: the return type here is a namedtuple, which is different from
# np.linalg.qr, which only returns a tuple.
return QRResult(*map(Array._new, np.linalg.qr(x._array, mode=mode))) | Array API compatible wrapper for :py:func:`np.linalg.qr <numpy.linalg.qr>`. See its docstring for more information. |
170,013 | from __future__ import annotations
from ._dtypes import _floating_dtypes, _numeric_dtypes
from ._manipulation_functions import reshape
from ._array_object import Array
from ..core.numeric import normalize_axis_tuple
from typing import TYPE_CHECKING
from typing import NamedTuple
import numpy.linalg
import numpy as np
class SlogdetResult(NamedTuple):
sign: Array
logabsdet: Array
_floating_dtypes = (float32, float64)
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
The provided code snippet includes necessary dependencies for implementing the `slogdet` function. Write a Python function `def slogdet(x: Array, /) -> SlogdetResult` to solve the following problem:
Array API compatible wrapper for :py:func:`np.linalg.slogdet <numpy.linalg.slogdet>`. See its docstring for more information.
Here is the function:
def slogdet(x: Array, /) -> SlogdetResult:
"""
Array API compatible wrapper for :py:func:`np.linalg.slogdet <numpy.linalg.slogdet>`.
See its docstring for more information.
"""
# Note: the restriction to floating-point dtypes only is different from
# np.linalg.slogdet.
if x.dtype not in _floating_dtypes:
raise TypeError('Only floating-point dtypes are allowed in slogdet')
# Note: the return type here is a namedtuple, which is different from
# np.linalg.slogdet, which only returns a tuple.
return SlogdetResult(*map(Array._new, np.linalg.slogdet(x._array))) | Array API compatible wrapper for :py:func:`np.linalg.slogdet <numpy.linalg.slogdet>`. See its docstring for more information. |
170,014 | from __future__ import annotations
from ._dtypes import _floating_dtypes, _numeric_dtypes
from ._manipulation_functions import reshape
from ._array_object import Array
from ..core.numeric import normalize_axis_tuple
from typing import TYPE_CHECKING
from typing import NamedTuple
import numpy.linalg
import numpy as np
def svd(x: Array, /, *, full_matrices: bool = True) -> SVDResult:
"""
Array API compatible wrapper for :py:func:`np.linalg.svd <numpy.linalg.svd>`.
See its docstring for more information.
"""
# Note: the restriction to floating-point dtypes only is different from
# np.linalg.svd.
if x.dtype not in _floating_dtypes:
raise TypeError('Only floating-point dtypes are allowed in svd')
# Note: the return type here is a namedtuple, which is different from
# np.svd, which only returns a tuple.
return SVDResult(*map(Array._new, np.linalg.svd(x._array, full_matrices=full_matrices)))
_floating_dtypes = (float32, float64)
class Array:
"""
n-d array object for the array API namespace.
See the docstring of :py:obj:`np.ndarray <numpy.ndarray>` for more
information.
This is a wrapper around numpy.ndarray that restricts the usage to only
those things that are required by the array API namespace. Note,
attributes on this object that start with a single underscore are not part
of the API specification and should only be used internally. This object
should not be constructed directly. Rather, use one of the creation
functions, such as asarray().
"""
_array: np.ndarray
# Use a custom constructor instead of __init__, as manually initializing
# this class is not supported API.
def _new(cls, x, /):
"""
This is a private method for initializing the array API Array
object.
Functions outside of the array_api submodule should not use this
method. Use one of the creation functions instead, such as
``asarray``.
"""
obj = super().__new__(cls)
# Note: The spec does not have array scalars, only 0-D arrays.
if isinstance(x, np.generic):
# Convert the array scalar to a 0-D array
x = np.asarray(x)
if x.dtype not in _all_dtypes:
raise TypeError(
f"The array_api namespace does not support the dtype '{x.dtype}'"
)
obj._array = x
return obj
# Prevent Array() from working
def __new__(cls, *args, **kwargs):
raise TypeError(
"The array_api Array object should not be instantiated directly. Use an array creation function, such as asarray(), instead."
)
# These functions are not required by the spec, but are implemented for
# the sake of usability.
def __str__(self: Array, /) -> str:
"""
Performs the operation __str__.
"""
return self._array.__str__().replace("array", "Array")
def __repr__(self: Array, /) -> str:
"""
Performs the operation __repr__.
"""
suffix = f", dtype={self.dtype.name})"
if 0 in self.shape:
prefix = "empty("
mid = str(self.shape)
else:
prefix = "Array("
mid = np.array2string(self._array, separator=', ', prefix=prefix, suffix=suffix)
return prefix + mid + suffix
# This function is not required by the spec, but we implement it here for
# convenience so that np.asarray(np.array_api.Array) will work.
def __array__(self, dtype: None | np.dtype[Any] = None) -> npt.NDArray[Any]:
"""
Warning: this method is NOT part of the array API spec. Implementers
of other libraries need not include it, and users should not assume it
will be present in other implementations.
"""
return np.asarray(self._array, dtype=dtype)
# These are various helper functions to make the array behavior match the
# spec in places where it either deviates from or is more strict than
# NumPy behavior
def _check_allowed_dtypes(self, other: bool | int | float | Array, dtype_category: str, op: str) -> Array:
"""
Helper function for operators to only allow specific input dtypes
Use like
other = self._check_allowed_dtypes(other, 'numeric', '__add__')
if other is NotImplemented:
return other
"""
if self.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
if isinstance(other, (int, float, bool)):
other = self._promote_scalar(other)
elif isinstance(other, Array):
if other.dtype not in _dtype_categories[dtype_category]:
raise TypeError(f"Only {dtype_category} dtypes are allowed in {op}")
else:
return NotImplemented
# This will raise TypeError for type combinations that are not allowed
# to promote in the spec (even if the NumPy array operator would
# promote them).
res_dtype = _result_type(self.dtype, other.dtype)
if op.startswith("__i"):
# Note: NumPy will allow in-place operators in some cases where
# the type promoted operator does not match the left-hand side
# operand. For example,
# >>> a = np.array(1, dtype=np.int8)
# >>> a += np.array(1, dtype=np.int16)
# The spec explicitly disallows this.
if res_dtype != self.dtype:
raise TypeError(
f"Cannot perform {op} with dtypes {self.dtype} and {other.dtype}"
)
return other
# Helper function to match the type promotion rules in the spec
def _promote_scalar(self, scalar):
"""
Returns a promoted version of a Python scalar appropriate for use with
operations on self.
This may raise an OverflowError in cases where the scalar is an
integer that is too large to fit in a NumPy integer dtype, or
TypeError when the scalar type is incompatible with the dtype of self.
"""
# Note: Only Python scalar types that match the array dtype are
# allowed.
if isinstance(scalar, bool):
if self.dtype not in _boolean_dtypes:
raise TypeError(
"Python bool scalars can only be promoted with bool arrays"
)
elif isinstance(scalar, int):
if self.dtype in _boolean_dtypes:
raise TypeError(
"Python int scalars cannot be promoted with bool arrays"
)
elif isinstance(scalar, float):
if self.dtype not in _floating_dtypes:
raise TypeError(
"Python float scalars can only be promoted with floating-point arrays."
)
else:
raise TypeError("'scalar' must be a Python scalar")
# Note: scalars are unconditionally cast to the same dtype as the
# array.
# Note: the spec only specifies integer-dtype/int promotion
# behavior for integers within the bounds of the integer dtype.
# Outside of those bounds we use the default NumPy behavior (either
# cast or raise OverflowError).
return Array._new(np.array(scalar, self.dtype))
def _normalize_two_args(x1, x2) -> Tuple[Array, Array]:
"""
Normalize inputs to two arg functions to fix type promotion rules
NumPy deviates from the spec type promotion rules in cases where one
argument is 0-dimensional and the other is not. For example:
>>> import numpy as np
>>> a = np.array([1.0], dtype=np.float32)
>>> b = np.array(1.0, dtype=np.float64)
>>> np.add(a, b) # The spec says this should be float64
array([2.], dtype=float32)
To fix this, we add a dimension to the 0-dimension array before passing it
through. This works because a dimension would be added anyway from
broadcasting, so the resulting shape is the same, but this prevents NumPy
from not promoting the dtype.
"""
# Another option would be to use signature=(x1.dtype, x2.dtype, None),
# but that only works for ufuncs, so we would have to call the ufuncs
# directly in the operator methods. One should also note that this
# sort of trick wouldn't work for functions like searchsorted, which
# don't do normal broadcasting, but there aren't any functions like
# that in the array API namespace.
if x1.ndim == 0 and x2.ndim != 0:
# The _array[None] workaround was chosen because it is relatively
# performant. broadcast_to(x1._array, x2.shape) is much slower. We
# could also manually type promote x2, but that is more complicated
# and about the same performance as this.
x1 = Array._new(x1._array[None])
elif x2.ndim == 0 and x1.ndim != 0:
x2 = Array._new(x2._array[None])
return (x1, x2)
# Note: A large fraction of allowed indices are disallowed here (see the
# docstring below)
def _validate_index(self, key):
"""
Validate an index according to the array API.
The array API specification only requires a subset of indices that are
supported by NumPy. This function will reject any index that is
allowed by NumPy but not required by the array API specification. We
always raise ``IndexError`` on such indices (the spec does not require
any specific behavior on them, but this makes the NumPy array API
namespace a minimal implementation of the spec). See
https://data-apis.org/array-api/latest/API_specification/indexing.html
for the full list of required indexing behavior
This function raises IndexError if the index ``key`` is invalid. It
only raises ``IndexError`` on indices that are not already rejected by
NumPy, as NumPy will already raise the appropriate error on such
indices. ``shape`` may be None, in which case, only cases that are
independent of the array shape are checked.
The following cases are allowed by NumPy, but not specified by the array
API specification:
- Indices to not include an implicit ellipsis at the end. That is,
every axis of an array must be explicitly indexed or an ellipsis
included. This behaviour is sometimes referred to as flat indexing.
- The start and stop of a slice may not be out of bounds. In
particular, for a slice ``i:j:k`` on an axis of size ``n``, only the
following are allowed:
- ``i`` or ``j`` omitted (``None``).
- ``-n <= i <= max(0, n - 1)``.
- For ``k > 0`` or ``k`` omitted (``None``), ``-n <= j <= n``.
- For ``k < 0``, ``-n - 1 <= j <= max(0, n - 1)``.
- Boolean array indices are not allowed as part of a larger tuple
index.
- Integer array indices are not allowed (with the exception of 0-D
arrays, which are treated the same as scalars).
Additionally, it should be noted that indices that would return a
scalar in NumPy will return a 0-D array. Array scalars are not allowed
in the specification, only 0-D arrays. This is done in the
``Array._new`` constructor, not this function.
"""
_key = key if isinstance(key, tuple) else (key,)
for i in _key:
if isinstance(i, bool) or not (
isinstance(i, SupportsIndex) # i.e. ints
or isinstance(i, slice)
or i == Ellipsis
or i is None
or isinstance(i, Array)
or isinstance(i, np.ndarray)
):
raise IndexError(
f"Single-axes index {i} has {type(i)=}, but only "
"integers, slices (:), ellipsis (...), newaxis (None), "
"zero-dimensional integer arrays and boolean arrays "
"are specified in the Array API."
)
nonexpanding_key = []
single_axes = []
n_ellipsis = 0
key_has_mask = False
for i in _key:
if i is not None:
nonexpanding_key.append(i)
if isinstance(i, Array) or isinstance(i, np.ndarray):
if i.dtype in _boolean_dtypes:
key_has_mask = True
single_axes.append(i)
else:
# i must not be an array here, to avoid elementwise equals
if i == Ellipsis:
n_ellipsis += 1
else:
single_axes.append(i)
n_single_axes = len(single_axes)
if n_ellipsis > 1:
return # handled by ndarray
elif n_ellipsis == 0:
# Note boolean masks must be the sole index, which we check for
# later on.
if not key_has_mask and n_single_axes < self.ndim:
raise IndexError(
f"{self.ndim=}, but the multi-axes index only specifies "
f"{n_single_axes} dimensions. If this was intentional, "
"add a trailing ellipsis (...) which expands into as many "
"slices (:) as necessary - this is what np.ndarray arrays "
"implicitly do, but such flat indexing behaviour is not "
"specified in the Array API."
)
if n_ellipsis == 0:
indexed_shape = self.shape
else:
ellipsis_start = None
for pos, i in enumerate(nonexpanding_key):
if not (isinstance(i, Array) or isinstance(i, np.ndarray)):
if i == Ellipsis:
ellipsis_start = pos
break
assert ellipsis_start is not None # sanity check
ellipsis_end = self.ndim - (n_single_axes - ellipsis_start)
indexed_shape = (
self.shape[:ellipsis_start] + self.shape[ellipsis_end:]
)
for i, side in zip(single_axes, indexed_shape):
if isinstance(i, slice):
if side == 0:
f_range = "0 (or None)"
else:
f_range = f"between -{side} and {side - 1} (or None)"
if i.start is not None:
try:
start = operator.index(i.start)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= start <= side):
raise IndexError(
f"Slice {i} contains {start=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds starts are not specified in "
"the Array API)"
)
if i.stop is not None:
try:
stop = operator.index(i.stop)
except TypeError:
pass # handled by ndarray
else:
if not (-side <= stop <= side):
raise IndexError(
f"Slice {i} contains {stop=}, but should be "
f"{f_range} for an axis of size {side} "
"(out-of-bounds stops are not specified in "
"the Array API)"
)
elif isinstance(i, Array):
if i.dtype in _boolean_dtypes and len(_key) != 1:
assert isinstance(key, tuple) # sanity check
raise IndexError(
f"Single-axes index {i} is a boolean array and "
f"{len(key)=}, but masking is only specified in the "
"Array API when the array is the sole index."
)
elif i.dtype in _integer_dtypes and i.ndim != 0:
raise IndexError(
f"Single-axes index {i} is a non-zero-dimensional "
"integer array, but advanced integer indexing is not "
"specified in the Array API."
)
elif isinstance(i, tuple):
raise IndexError(
f"Single-axes index {i} is a tuple, but nested tuple "
"indices are not specified in the Array API."
)
# Everything below this line is required by the spec.
def __abs__(self: Array, /) -> Array:
"""
Performs the operation __abs__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __abs__")
res = self._array.__abs__()
return self.__class__._new(res)
def __add__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __add__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__add__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__add__(other._array)
return self.__class__._new(res)
def __and__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __and__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__and__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__and__(other._array)
return self.__class__._new(res)
def __array_namespace__(
self: Array, /, *, api_version: Optional[str] = None
) -> types.ModuleType:
if api_version is not None and not api_version.startswith("2021."):
raise ValueError(f"Unrecognized array API version: {api_version!r}")
return array_api
def __bool__(self: Array, /) -> bool:
"""
Performs the operation __bool__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("bool is only allowed on arrays with 0 dimensions")
if self.dtype not in _boolean_dtypes:
raise ValueError("bool is only allowed on boolean arrays")
res = self._array.__bool__()
return res
def __dlpack__(self: Array, /, *, stream: None = None) -> PyCapsule:
"""
Performs the operation __dlpack__.
"""
return self._array.__dlpack__(stream=stream)
def __dlpack_device__(self: Array, /) -> Tuple[IntEnum, int]:
"""
Performs the operation __dlpack_device__.
"""
# Note: device support is required for this
return self._array.__dlpack_device__()
def __eq__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __eq__.
"""
# Even though "all" dtypes are allowed, we still require them to be
# promotable with each other.
other = self._check_allowed_dtypes(other, "all", "__eq__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__eq__(other._array)
return self.__class__._new(res)
def __float__(self: Array, /) -> float:
"""
Performs the operation __float__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("float is only allowed on arrays with 0 dimensions")
if self.dtype not in _floating_dtypes:
raise ValueError("float is only allowed on floating-point arrays")
res = self._array.__float__()
return res
def __floordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __floordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__floordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__floordiv__(other._array)
return self.__class__._new(res)
def __ge__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ge__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ge__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ge__(other._array)
return self.__class__._new(res)
def __getitem__(
self: Array,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
/,
) -> Array:
"""
Performs the operation __getitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
res = self._array.__getitem__(key)
return self._new(res)
def __gt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __gt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__gt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__gt__(other._array)
return self.__class__._new(res)
def __int__(self: Array, /) -> int:
"""
Performs the operation __int__.
"""
# Note: This is an error here.
if self._array.ndim != 0:
raise TypeError("int is only allowed on arrays with 0 dimensions")
if self.dtype not in _integer_dtypes:
raise ValueError("int is only allowed on integer arrays")
res = self._array.__int__()
return res
def __index__(self: Array, /) -> int:
"""
Performs the operation __index__.
"""
res = self._array.__index__()
return res
def __invert__(self: Array, /) -> Array:
"""
Performs the operation __invert__.
"""
if self.dtype not in _integer_or_boolean_dtypes:
raise TypeError("Only integer or boolean dtypes are allowed in __invert__")
res = self._array.__invert__()
return self.__class__._new(res)
def __le__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __le__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__le__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__le__(other._array)
return self.__class__._new(res)
def __lshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __lshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__lshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lshift__(other._array)
return self.__class__._new(res)
def __lt__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __lt__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__lt__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__lt__(other._array)
return self.__class__._new(res)
def __matmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __matmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__matmul__")
if other is NotImplemented:
return other
res = self._array.__matmul__(other._array)
return self.__class__._new(res)
def __mod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mod__(other._array)
return self.__class__._new(res)
def __mul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __mul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__mul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__mul__(other._array)
return self.__class__._new(res)
def __ne__(self: Array, other: Union[int, float, bool, Array], /) -> Array:
"""
Performs the operation __ne__.
"""
other = self._check_allowed_dtypes(other, "all", "__ne__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ne__(other._array)
return self.__class__._new(res)
def __neg__(self: Array, /) -> Array:
"""
Performs the operation __neg__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __neg__")
res = self._array.__neg__()
return self.__class__._new(res)
def __or__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __or__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__or__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__or__(other._array)
return self.__class__._new(res)
def __pos__(self: Array, /) -> Array:
"""
Performs the operation __pos__.
"""
if self.dtype not in _numeric_dtypes:
raise TypeError("Only numeric dtypes are allowed in __pos__")
res = self._array.__pos__()
return self.__class__._new(res)
def __pow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __pow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__pow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow type promotion rules for 0-d
# arrays, so we use pow() here instead.
return pow(self, other)
def __rshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rshift__(other._array)
return self.__class__._new(res)
def __setitem__(
self,
key: Union[
int, slice, ellipsis, Tuple[Union[int, slice, ellipsis], ...], Array
],
value: Union[int, float, bool, Array],
/,
) -> None:
"""
Performs the operation __setitem__.
"""
# Note: Only indices required by the spec are allowed. See the
# docstring of _validate_index
self._validate_index(key)
if isinstance(key, Array):
# Indexing self._array with array_api arrays can be erroneous
key = key._array
self._array.__setitem__(key, asarray(value)._array)
def __sub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __sub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__sub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__sub__(other._array)
return self.__class__._new(res)
# PEP 484 requires int to be a subtype of float, but __truediv__ should
# not accept int.
def __truediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __truediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__truediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__truediv__(other._array)
return self.__class__._new(res)
def __xor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __xor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__xor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__xor__(other._array)
return self.__class__._new(res)
def __iadd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __iadd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__iadd__")
if other is NotImplemented:
return other
self._array.__iadd__(other._array)
return self
def __radd__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __radd__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__radd__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__radd__(other._array)
return self.__class__._new(res)
def __iand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __iand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__iand__")
if other is NotImplemented:
return other
self._array.__iand__(other._array)
return self
def __rand__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rand__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rand__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rand__(other._array)
return self.__class__._new(res)
def __ifloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ifloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ifloordiv__")
if other is NotImplemented:
return other
self._array.__ifloordiv__(other._array)
return self
def __rfloordiv__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rfloordiv__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rfloordiv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rfloordiv__(other._array)
return self.__class__._new(res)
def __ilshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __ilshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__ilshift__")
if other is NotImplemented:
return other
self._array.__ilshift__(other._array)
return self
def __rlshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rlshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rlshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rlshift__(other._array)
return self.__class__._new(res)
def __imatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __imatmul__.
"""
# Note: NumPy does not implement __imatmul__.
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__imatmul__")
if other is NotImplemented:
return other
# __imatmul__ can only be allowed when it would not change the shape
# of self.
other_shape = other.shape
if self.shape == () or other_shape == ():
raise ValueError("@= requires at least one dimension")
if len(other_shape) == 1 or other_shape[-1] != other_shape[-2]:
raise ValueError("@= cannot change the shape of the input array")
self._array[:] = self._array.__matmul__(other._array)
return self
def __rmatmul__(self: Array, other: Array, /) -> Array:
"""
Performs the operation __rmatmul__.
"""
# matmul is not defined for scalars, but without this, we may get
# the wrong error message from asarray.
other = self._check_allowed_dtypes(other, "numeric", "__rmatmul__")
if other is NotImplemented:
return other
res = self._array.__rmatmul__(other._array)
return self.__class__._new(res)
def __imod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imod__")
if other is NotImplemented:
return other
self._array.__imod__(other._array)
return self
def __rmod__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmod__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmod__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmod__(other._array)
return self.__class__._new(res)
def __imul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __imul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__imul__")
if other is NotImplemented:
return other
self._array.__imul__(other._array)
return self
def __rmul__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rmul__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rmul__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rmul__(other._array)
return self.__class__._new(res)
def __ior__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ior__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ior__")
if other is NotImplemented:
return other
self._array.__ior__(other._array)
return self
def __ror__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ror__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ror__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__ror__(other._array)
return self.__class__._new(res)
def __ipow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __ipow__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__ipow__")
if other is NotImplemented:
return other
self._array.__ipow__(other._array)
return self
def __rpow__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rpow__.
"""
from ._elementwise_functions import pow
other = self._check_allowed_dtypes(other, "numeric", "__rpow__")
if other is NotImplemented:
return other
# Note: NumPy's __pow__ does not follow the spec type promotion rules
# for 0-d arrays, so we use pow() here instead.
return pow(other, self)
def __irshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __irshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__irshift__")
if other is NotImplemented:
return other
self._array.__irshift__(other._array)
return self
def __rrshift__(self: Array, other: Union[int, Array], /) -> Array:
"""
Performs the operation __rrshift__.
"""
other = self._check_allowed_dtypes(other, "integer", "__rrshift__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rrshift__(other._array)
return self.__class__._new(res)
def __isub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __isub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__isub__")
if other is NotImplemented:
return other
self._array.__isub__(other._array)
return self
def __rsub__(self: Array, other: Union[int, float, Array], /) -> Array:
"""
Performs the operation __rsub__.
"""
other = self._check_allowed_dtypes(other, "numeric", "__rsub__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rsub__(other._array)
return self.__class__._new(res)
def __itruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __itruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__itruediv__")
if other is NotImplemented:
return other
self._array.__itruediv__(other._array)
return self
def __rtruediv__(self: Array, other: Union[float, Array], /) -> Array:
"""
Performs the operation __rtruediv__.
"""
other = self._check_allowed_dtypes(other, "floating-point", "__rtruediv__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rtruediv__(other._array)
return self.__class__._new(res)
def __ixor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __ixor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__ixor__")
if other is NotImplemented:
return other
self._array.__ixor__(other._array)
return self
def __rxor__(self: Array, other: Union[int, bool, Array], /) -> Array:
"""
Performs the operation __rxor__.
"""
other = self._check_allowed_dtypes(other, "integer or boolean", "__rxor__")
if other is NotImplemented:
return other
self, other = self._normalize_two_args(self, other)
res = self._array.__rxor__(other._array)
return self.__class__._new(res)
def to_device(self: Array, device: Device, /, stream: None = None) -> Array:
if stream is not None:
raise ValueError("The stream argument to to_device() is not supported")
if device == 'cpu':
return self
raise ValueError(f"Unsupported device {device!r}")
def dtype(self) -> Dtype:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.dtype <numpy.ndarray.dtype>`.
See its docstring for more information.
"""
return self._array.dtype
def device(self) -> Device:
return "cpu"
# Note: mT is new in array API spec (see matrix_transpose)
def mT(self) -> Array:
from .linalg import matrix_transpose
return matrix_transpose(self)
def ndim(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.ndim <numpy.ndarray.ndim>`.
See its docstring for more information.
"""
return self._array.ndim
def shape(self) -> Tuple[int, ...]:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.shape <numpy.ndarray.shape>`.
See its docstring for more information.
"""
return self._array.shape
def size(self) -> int:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.size <numpy.ndarray.size>`.
See its docstring for more information.
"""
return self._array.size
def T(self) -> Array:
"""
Array API compatible wrapper for :py:meth:`np.ndarray.T <numpy.ndarray.T>`.
See its docstring for more information.
"""
# Note: T only works on 2-dimensional arrays. See the corresponding
# note in the specification:
# https://data-apis.org/array-api/latest/API_specification/array_object.html#t
if self.ndim != 2:
raise ValueError("x.T requires x to have 2 dimensions. Use x.mT to transpose stacks of matrices and permute_dims() to permute dimensions.")
return self.__class__._new(self._array.T)
def svdvals(x: Array, /) -> Union[Array, Tuple[Array, ...]]:
if x.dtype not in _floating_dtypes:
raise TypeError('Only floating-point dtypes are allowed in svdvals')
return Array._new(np.linalg.svd(x._array, compute_uv=False)) | null |
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