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@@ -351,3 +351,5 @@ llava_next/lib/python3.10/site-packages/scipy/stats/tests/__pycache__/test_stats
 llava_next/lib/python3.10/site-packages/scipy/stats/__pycache__/_morestats.cpython-310.pyc filter=lfs diff=lfs merge=lfs -text
 llava_next/lib/python3.10/site-packages/scipy/cluster/__pycache__/hierarchy.cpython-310.pyc filter=lfs diff=lfs merge=lfs -text
 llava_next/lib/python3.10/site-packages/scipy/optimize/_moduleTNC.cpython-310-x86_64-linux-gnu.so filter=lfs diff=lfs merge=lfs -text
+parrot/lib/python3.10/site-packages/gradio_client/__pycache__/media_data.cpython-310.pyc filter=lfs diff=lfs merge=lfs -text
+parrot/lib/python3.10/site-packages/torchvision.libs/libjpeg.ceea7512.so.62 filter=lfs diff=lfs merge=lfs -text

llava_next/lib/python3.10/site-packages/scipy/optimize/_differentiate.py

@@ -0,0 +1,856 @@
+# mypy: disable-error-code="attr-defined"
+import numpy as np
+import scipy._lib._elementwise_iterative_method as eim
+from scipy._lib._util import _RichResult
+
+_EERRORINCREASE = -1  # used in _differentiate
+
+def _differentiate_iv(func, x, args, atol, rtol, maxiter, order, initial_step,
+                      step_factor, step_direction, preserve_shape, callback):
+    # Input validation for `_differentiate`
+
+    if not callable(func):
+        raise ValueError('`func` must be callable.')
+
+    # x has more complex IV that is taken care of during initialization
+    x = np.asarray(x)
+    dtype = x.dtype if np.issubdtype(x.dtype, np.inexact) else np.float64
+
+    if not np.iterable(args):
+        args = (args,)
+
+    if atol is None:
+        atol = np.finfo(dtype).tiny
+
+    if rtol is None:
+        rtol = np.sqrt(np.finfo(dtype).eps)
+
+    message = 'Tolerances and step parameters must be non-negative scalars.'
+    tols = np.asarray([atol, rtol, initial_step, step_factor])
+    if (not np.issubdtype(tols.dtype, np.number)
+            or np.any(tols < 0)
+            or tols.shape != (4,)):
+        raise ValueError(message)
+    initial_step, step_factor = tols[2:].astype(dtype)
+
+    maxiter_int = int(maxiter)
+    if maxiter != maxiter_int or maxiter <= 0:
+        raise ValueError('`maxiter` must be a positive integer.')
+
+    order_int = int(order)
+    if order_int != order or order <= 0:
+        raise ValueError('`order` must be a positive integer.')
+
+    step_direction = np.sign(step_direction).astype(dtype)
+    x, step_direction = np.broadcast_arrays(x, step_direction)
+    x, step_direction = x[()], step_direction[()]
+
+    message = '`preserve_shape` must be True or False.'
+    if preserve_shape not in {True, False}:
+        raise ValueError(message)
+
+    if callback is not None and not callable(callback):
+        raise ValueError('`callback` must be callable.')
+
+    return (func, x, args, atol, rtol, maxiter_int, order_int, initial_step,
+            step_factor, step_direction, preserve_shape, callback)
+
+
+def _differentiate(func, x, *, args=(), atol=None, rtol=None, maxiter=10,
+                   order=8, initial_step=0.5, step_factor=2.0,
+                   step_direction=0, preserve_shape=False, callback=None):
+    """Evaluate the derivative of an elementwise scalar function numerically.
+
+    Parameters
+    ----------
+    func : callable
+        The function whose derivative is desired. The signature must be::
+
+            func(x: ndarray, *fargs) -> ndarray
+
+         where each element of ``x`` is a finite real number and ``fargs`` is a tuple,
+         which may contain an arbitrary number of arrays that are broadcastable
+         with `x`. ``func`` must be an elementwise function: each element
+         ``func(x)[i]`` must equal ``func(x[i])`` for all indices ``i``.
+    x : array_like
+        Abscissae at which to evaluate the derivative.
+    args : tuple, optional
+        Additional positional arguments to be passed to `func`. Must be arrays
+        broadcastable with `x`. If the callable to be differentiated requires
+        arguments that are not broadcastable with `x`, wrap that callable with
+        `func`. See Examples.
+    atol, rtol : float, optional
+        Absolute and relative tolerances for the stopping condition: iteration
+        will stop when ``res.error < atol + rtol * abs(res.df)``. The default
+        `atol` is the smallest normal number of the appropriate dtype, and
+        the default `rtol` is the square root of the precision of the
+        appropriate dtype.
+    order : int, default: 8
+        The (positive integer) order of the finite difference formula to be
+        used. Odd integers will be rounded up to the next even integer.
+    initial_step : float, default: 0.5
+        The (absolute) initial step size for the finite difference derivative
+        approximation.
+    step_factor : float, default: 2.0
+        The factor by which the step size is *reduced* in each iteration; i.e.
+        the step size in iteration 1 is ``initial_step/step_factor``. If
+        ``step_factor < 1``, subsequent steps will be greater than the initial
+        step; this may be useful if steps smaller than some threshold are
+        undesirable (e.g. due to subtractive cancellation error).
+    maxiter : int, default: 10
+        The maximum number of iterations of the algorithm to perform. See
+        notes.
+    step_direction : array_like
+        An array representing the direction of the finite difference steps (for
+        use when `x` lies near to the boundary of the domain of the function.)
+        Must be broadcastable with `x` and all `args`.
+        Where 0 (default), central differences are used; where negative (e.g.
+        -1), steps are non-positive; and where positive (e.g. 1), all steps are
+        non-negative.
+    preserve_shape : bool, default: False
+        In the following, "arguments of `func`" refers to the array ``x`` and
+        any arrays within ``fargs``. Let ``shape`` be the broadcasted shape
+        of `x` and all elements of `args` (which is conceptually
+        distinct from ``fargs`` passed into `f`).
+
+        - When ``preserve_shape=False`` (default), `f` must accept arguments
+          of *any* broadcastable shapes.
+
+        - When ``preserve_shape=True``, `f` must accept arguments of shape
+          ``shape`` *or* ``shape + (n,)``, where ``(n,)`` is the number of
+          abscissae at which the function is being evaluated.
+
+        In either case, for each scalar element ``xi`` within `x`, the array
+        returned by `f` must include the scalar ``f(xi)`` at the same index.
+        Consequently, the shape of the output is always the shape of the input
+        ``x``.
+
+        See Examples.
+    callback : callable, optional
+        An optional user-supplied function to be called before the first
+        iteration and after each iteration.
+        Called as ``callback(res)``, where ``res`` is a ``_RichResult``
+        similar to that returned by `_differentiate` (but containing the
+        current iterate's values of all variables). If `callback` raises a
+        ``StopIteration``, the algorithm will terminate immediately and
+        `_differentiate` will return a result.
+
+    Returns
+    -------
+    res : _RichResult
+        An instance of `scipy._lib._util._RichResult` with the following
+        attributes. (The descriptions are written as though the values will be
+        scalars; however, if `func` returns an array, the outputs will be
+        arrays of the same shape.)
+
+        success : bool
+            ``True`` when the algorithm terminated successfully (status ``0``).
+        status : int
+            An integer representing the exit status of the algorithm.
+            ``0`` : The algorithm converged to the specified tolerances.
+            ``-1`` : The error estimate increased, so iteration was terminated.
+            ``-2`` : The maximum number of iterations was reached.
+            ``-3`` : A non-finite value was encountered.
+            ``-4`` : Iteration was terminated by `callback`.
+            ``1`` : The algorithm is proceeding normally (in `callback` only).
+        df : float
+            The derivative of `func` at `x`, if the algorithm terminated
+            successfully.
+        error : float
+            An estimate of the error: the magnitude of the difference between
+            the current estimate of the derivative and the estimate in the
+            previous iteration.
+        nit : int
+            The number of iterations performed.
+        nfev : int
+            The number of points at which `func` was evaluated.
+        x : float
+            The value at which the derivative of `func` was evaluated
+            (after broadcasting with `args` and `step_direction`).
+
+    Notes
+    -----
+    The implementation was inspired by jacobi [1]_, numdifftools [2]_, and
+    DERIVEST [3]_, but the implementation follows the theory of Taylor series
+    more straightforwardly (and arguably naively so).
+    In the first iteration, the derivative is estimated using a finite
+    difference formula of order `order` with maximum step size `initial_step`.
+    Each subsequent iteration, the maximum step size is reduced by
+    `step_factor`, and the derivative is estimated again until a termination
+    condition is reached. The error estimate is the magnitude of the difference
+    between the current derivative approximation and that of the previous
+    iteration.
+
+    The stencils of the finite difference formulae are designed such that
+    abscissae are "nested": after `func` is evaluated at ``order + 1``
+    points in the first iteration, `func` is evaluated at only two new points
+    in each subsequent iteration; ``order - 1`` previously evaluated function
+    values required by the finite difference formula are reused, and two
+    function values (evaluations at the points furthest from `x`) are unused.
+
+    Step sizes are absolute. When the step size is small relative to the
+    magnitude of `x`, precision is lost; for example, if `x` is ``1e20``, the
+    default initial step size of ``0.5`` cannot be resolved. Accordingly,
+    consider using larger initial step sizes for large magnitudes of `x`.
+
+    The default tolerances are challenging to satisfy at points where the
+    true derivative is exactly zero. If the derivative may be exactly zero,
+    consider specifying an absolute tolerance (e.g. ``atol=1e-16``) to
+    improve convergence.
+
+    References
+    ----------
+    [1]_ Hans Dembinski (@HDembinski). jacobi.
+         https://github.com/HDembinski/jacobi
+    [2]_ Per A. Brodtkorb and John D'Errico. numdifftools.
+         https://numdifftools.readthedocs.io/en/latest/
+    [3]_ John D'Errico. DERIVEST: Adaptive Robust Numerical Differentiation.
+         https://www.mathworks.com/matlabcentral/fileexchange/13490-adaptive-robust-numerical-differentiation
+    [4]_ Numerical Differentition. Wikipedia.
+         https://en.wikipedia.org/wiki/Numerical_differentiation
+
+    Examples
+    --------
+    Evaluate the derivative of ``np.exp`` at several points ``x``.
+
+    >>> import numpy as np
+    >>> from scipy.optimize._differentiate import _differentiate
+    >>> f = np.exp
+    >>> df = np.exp  # true derivative
+    >>> x = np.linspace(1, 2, 5)
+    >>> res = _differentiate(f, x)
+    >>> res.df  # approximation of the derivative
+    array([2.71828183, 3.49034296, 4.48168907, 5.75460268, 7.3890561 ])
+    >>> res.error  # estimate of the error
+    array(
+        [7.12940817e-12, 9.16688947e-12, 1.17594823e-11, 1.50972568e-11, 1.93942640e-11]
+    )
+    >>> abs(res.df - df(x))  # true error
+    array(
+        [3.06421555e-14, 3.01980663e-14, 5.06261699e-14, 6.30606678e-14, 8.34887715e-14]
+    )
+
+    Show the convergence of the approximation as the step size is reduced.
+    Each iteration, the step size is reduced by `step_factor`, so for
+    sufficiently small initial step, each iteration reduces the error by a
+    factor of ``1/step_factor**order`` until finite precision arithmetic
+    inhibits further improvement.
+
+    >>> iter = list(range(1, 12))  # maximum iterations
+    >>> hfac = 2  # step size reduction per iteration
+    >>> hdir = [-1, 0, 1]  # compare left-, central-, and right- steps
+    >>> order = 4  # order of differentiation formula
+    >>> x = 1
+    >>> ref = df(x)
+    >>> errors = []  # true error
+    >>> for i in iter:
+    ...     res = _differentiate(f, x, maxiter=i, step_factor=hfac,
+    ...                          step_direction=hdir, order=order,
+    ...                          atol=0, rtol=0)  # prevent early termination
+    ...     errors.append(abs(res.df - ref))
+    >>> errors = np.array(errors)
+    >>> plt.semilogy(iter, errors[:, 0], label='left differences')
+    >>> plt.semilogy(iter, errors[:, 1], label='central differences')
+    >>> plt.semilogy(iter, errors[:, 2], label='right differences')
+    >>> plt.xlabel('iteration')
+    >>> plt.ylabel('error')
+    >>> plt.legend()
+    >>> plt.show()
+    >>> (errors[1, 1] / errors[0, 1], 1 / hfac**order)
+    (0.06215223140159822, 0.0625)
+
+    The implementation is vectorized over `x`, `step_direction`, and `args`.
+    The function is evaluated once before the first iteration to perform input
+    validation and standardization, and once per iteration thereafter.
+
+    >>> def f(x, p):
+    ...     print('here')
+    ...     f.nit += 1
+    ...     return x**p
+    >>> f.nit = 0
+    >>> def df(x, p):
+    ...     return p*x**(p-1)
+    >>> x = np.arange(1, 5)
+    >>> p = np.arange(1, 6).reshape((-1, 1))
+    >>> hdir = np.arange(-1, 2).reshape((-1, 1, 1))
+    >>> res = _differentiate(f, x, args=(p,), step_direction=hdir, maxiter=1)
+    >>> np.allclose(res.df, df(x, p))
+    True
+    >>> res.df.shape
+    (3, 5, 4)
+    >>> f.nit
+    2
+
+    By default, `preserve_shape` is False, and therefore the callable
+    `f` may be called with arrays of any broadcastable shapes.
+    For example:
+
+    >>> shapes = []
+    >>> def f(x, c):
+    ...    shape = np.broadcast_shapes(x.shape, c.shape)
+    ...    shapes.append(shape)
+    ...    return np.sin(c*x)
+    >>>
+    >>> c = [1, 5, 10, 20]
+    >>> res = _differentiate(f, 0, args=(c,))
+    >>> shapes
+    [(4,), (4, 8), (4, 2), (3, 2), (2, 2), (1, 2)]
+
+    To understand where these shapes are coming from - and to better
+    understand how `_differentiate` computes accurate results - note that
+    higher values of ``c`` correspond with higher frequency sinusoids.
+    The higher frequency sinusoids make the function's derivative change
+    faster, so more function evaluations are required to achieve the target
+    accuracy:
+
+    >>> res.nfev
+    array([11, 13, 15, 17])
+
+    The initial ``shape``, ``(4,)``, corresponds with evaluating the
+    function at a single abscissa and all four frequencies; this is used
+    for input validation and to determine the size and dtype of the arrays
+    that store results. The next shape corresponds with evaluating the
+    function at an initial grid of abscissae and all four frequencies.
+    Successive calls to the function evaluate the function at two more
+    abscissae, increasing the effective order of the approximation by two.
+    However, in later function evaluations, the function is evaluated at
+    fewer frequencies because the corresponding derivative has already
+    converged to the required tolerance. This saves function evaluations to
+    improve performance, but it requires the function to accept arguments of
+    any shape.
+
+    "Vector-valued" functions are unlikely to satisfy this requirement.
+    For example, consider
+
+    >>> def f(x):
+    ...    return [x, np.sin(3*x), x+np.sin(10*x), np.sin(20*x)*(x-1)**2]
+
+    This integrand is not compatible with `_differentiate` as written; for instance,
+    the shape of the output will not be the same as the shape of ``x``. Such a
+    function *could* be converted to a compatible form with the introduction of
+    additional parameters, but this would be inconvenient. In such cases,
+    a simpler solution would be to use `preserve_shape`.
+
+    >>> shapes = []
+    >>> def f(x):
+    ...     shapes.append(x.shape)
+    ...     x0, x1, x2, x3 = x
+    ...     return [x0, np.sin(3*x1), x2+np.sin(10*x2), np.sin(20*x3)*(x3-1)**2]
+    >>>
+    >>> x = np.zeros(4)
+    >>> res = _differentiate(f, x, preserve_shape=True)
+    >>> shapes
+    [(4,), (4, 8), (4, 2), (4, 2), (4, 2), (4, 2)]
+
+    Here, the shape of ``x`` is ``(4,)``. With ``preserve_shape=True``, the
+    function may be called with argument ``x`` of shape ``(4,)`` or ``(4, n)``,
+    and this is what we observe.
+
+    """
+    # TODO (followup):
+    #  - investigate behavior at saddle points
+    #  - array initial_step / step_factor?
+    #  - multivariate functions?
+
+    res = _differentiate_iv(func, x, args, atol, rtol, maxiter, order, initial_step,
+                            step_factor, step_direction, preserve_shape, callback)
+    (func, x, args, atol, rtol, maxiter, order,
+     h0, fac, hdir, preserve_shape, callback) = res
+
+    # Initialization
+    # Since f(x) (no step) is not needed for central differences, it may be
+    # possible to eliminate this function evaluation. However, it's useful for
+    # input validation and standardization, and everything else is designed to
+    # reduce function calls, so let's keep it simple.
+    temp = eim._initialize(func, (x,), args, preserve_shape=preserve_shape)
+    func, xs, fs, args, shape, dtype, xp = temp
+    x, f = xs[0], fs[0]
+    df = np.full_like(f, np.nan)
+    # Ideally we'd broadcast the shape of `hdir` in `_elementwise_algo_init`, but
+    # it's simpler to do it here than to generalize `_elementwise_algo_init` further.
+    # `hdir` and `x` are already broadcasted in `_differentiate_iv`, so we know
+    # that `hdir` can be broadcasted to the final shape.
+    hdir = np.broadcast_to(hdir, shape).flatten()
+
+    status = np.full_like(x, eim._EINPROGRESS, dtype=int)  # in progress
+    nit, nfev = 0, 1  # one function evaluations performed above
+    # Boolean indices of left, central, right, and (all) one-sided steps
+    il = hdir < 0
+    ic = hdir == 0
+    ir = hdir > 0
+    io = il | ir
+
+    # Most of these attributes are reasonably obvious, but:
+    # - `fs` holds all the function values of all active `x`. The zeroth
+    #   axis corresponds with active points `x`, the first axis corresponds
+    #   with the different steps (in the order described in
+    #   `_differentiate_weights`).
+    # - `terms` (which could probably use a better name) is half the `order`,
+    #   which is always even.
+    work = _RichResult(x=x, df=df, fs=f[:, np.newaxis], error=np.nan, h=h0,
+                       df_last=np.nan, error_last=np.nan, h0=h0, fac=fac,
+                       atol=atol, rtol=rtol, nit=nit, nfev=nfev,
+                       status=status, dtype=dtype, terms=(order+1)//2,
+                       hdir=hdir, il=il, ic=ic, ir=ir, io=io)
+    # This is the correspondence between terms in the `work` object and the
+    # final result. In this case, the mapping is trivial. Note that `success`
+    # is prepended automatically.
+    res_work_pairs = [('status', 'status'), ('df', 'df'), ('error', 'error'),
+                      ('nit', 'nit'), ('nfev', 'nfev'), ('x', 'x')]
+
+    def pre_func_eval(work):
+        """Determine the abscissae at which the function needs to be evaluated.
+
+        See `_differentiate_weights` for a description of the stencil (pattern
+        of the abscissae).
+
+        In the first iteration, there is only one stored function value in
+        `work.fs`, `f(x)`, so we need to evaluate at `order` new points. In
+        subsequent iterations, we evaluate at two new points. Note that
+        `work.x` is always flattened into a 1D array after broadcasting with
+        all `args`, so we add a new axis at the end and evaluate all point
+        in one call to the function.
+
+        For improvement:
+        - Consider measuring the step size actually taken, since `(x + h) - x`
+          is not identically equal to `h` with floating point arithmetic.
+        - Adjust the step size automatically if `x` is too big to resolve the
+          step.
+        - We could probably save some work if there are no central difference
+          steps or no one-sided steps.
+        """
+        n = work.terms  # half the order
+        h = work.h  # step size
+        c = work.fac  # step reduction factor
+        d = c**0.5  # square root of step reduction factor (one-sided stencil)
+        # Note - no need to be careful about dtypes until we allocate `x_eval`
+
+        if work.nit == 0:
+            hc = h / c**np.arange(n)
+            hc = np.concatenate((-hc[::-1], hc))
+        else:
+            hc = np.asarray([-h, h]) / c**(n-1)
+
+        if work.nit == 0:
+            hr = h / d**np.arange(2*n)
+        else:
+            hr = np.asarray([h, h/d]) / c**(n-1)
+
+        n_new = 2*n if work.nit == 0 else 2  # number of new abscissae
+        x_eval = np.zeros((len(work.hdir), n_new), dtype=work.dtype)
+        il, ic, ir = work.il, work.ic, work.ir
+        x_eval[ir] = work.x[ir, np.newaxis] + hr
+        x_eval[ic] = work.x[ic, np.newaxis] + hc
+        x_eval[il] = work.x[il, np.newaxis] - hr
+        return x_eval
+
+    def post_func_eval(x, f, work):
+        """ Estimate the derivative and error from the function evaluations
+
+        As in `pre_func_eval`: in the first iteration, there is only one stored
+        function value in `work.fs`, `f(x)`, so we need to add the `order` new
+        points. In subsequent iterations, we add two new points. The tricky
+        part is getting the order to match that of the weights, which is
+        described in `_differentiate_weights`.
+
+        For improvement:
+        - Change the order of the weights (and steps in `pre_func_eval`) to
+          simplify `work_fc` concatenation and eliminate `fc` concatenation.
+        - It would be simple to do one-step Richardson extrapolation with `df`
+          and `df_last` to increase the order of the estimate and/or improve
+          the error estimate.
+        - Process the function evaluations in a more numerically favorable
+          way. For instance, combining the pairs of central difference evals
+          into a second-order approximation and using Richardson extrapolation
+          to produce a higher order approximation seemed to retain accuracy up
+          to very high order.
+        - Alternatively, we could use `polyfit` like Jacobi. An advantage of
+          fitting polynomial to more points than necessary is improved noise
+          tolerance.
+        """
+        n = work.terms
+        n_new = n if work.nit == 0 else 1
+        il, ic, io = work.il, work.ic, work.io
+
+        # Central difference
+        # `work_fc` is *all* the points at which the function has been evaluated
+        # `fc` is the points we're using *this iteration* to produce the estimate
+        work_fc = (f[ic, :n_new], work.fs[ic, :], f[ic, -n_new:])
+        work_fc = np.concatenate(work_fc, axis=-1)
+        if work.nit == 0:
+            fc = work_fc
+        else:
+            fc = (work_fc[:, :n], work_fc[:, n:n+1], work_fc[:, -n:])
+            fc = np.concatenate(fc, axis=-1)
+
+        # One-sided difference
+        work_fo = np.concatenate((work.fs[io, :], f[io, :]), axis=-1)
+        if work.nit == 0:
+            fo = work_fo
+        else:
+            fo = np.concatenate((work_fo[:, 0:1], work_fo[:, -2*n:]), axis=-1)
+
+        work.fs = np.zeros((len(ic), work.fs.shape[-1] + 2*n_new))
+        work.fs[ic] = work_fc
+        work.fs[io] = work_fo
+
+        wc, wo = _differentiate_weights(work, n)
+        work.df_last = work.df.copy()
+        work.df[ic] = fc @ wc / work.h
+        work.df[io] = fo @ wo / work.h
+        work.df[il] *= -1
+
+        work.h /= work.fac
+        work.error_last = work.error
+        # Simple error estimate - the difference in derivative estimates between
+        # this iteration and the last. This is typically conservative because if
+        # convergence has begin, the true error is much closer to the difference
+        # between the current estimate and the *next* error estimate. However,
+        # we could use Richarson extrapolation to produce an error estimate that
+        # is one order higher, and take the difference between that and
+        # `work.df` (which would just be constant factor that depends on `fac`.)
+        work.error = abs(work.df - work.df_last)
+
+    def check_termination(work):
+        """Terminate due to convergence, non-finite values, or error increase"""
+        stop = np.zeros_like(work.df).astype(bool)
+
+        i = work.error < work.atol + work.rtol*abs(work.df)
+        work.status[i] = eim._ECONVERGED
+        stop[i] = True
+
+        if work.nit > 0:
+            i = ~((np.isfinite(work.x) & np.isfinite(work.df)) | stop)
+            work.df[i], work.status[i] = np.nan, eim._EVALUEERR
+            stop[i] = True
+
+        # With infinite precision, there is a step size below which
+        # all smaller step sizes will reduce the error. But in floating point
+        # arithmetic, catastrophic cancellation will begin to cause the error
+        # to increase again. This heuristic tries to avoid step sizes that are
+        # too small. There may be more theoretically sound approaches for
+        # detecting a step size that minimizes the total error, but this
+        # heuristic seems simple and effective.
+        i = (work.error > work.error_last*10) & ~stop
+        work.status[i] = _EERRORINCREASE
+        stop[i] = True
+
+        return stop
+
+    def post_termination_check(work):
+        return
+
+    def customize_result(res, shape):
+        return shape
+
+    return eim._loop(work, callback, shape, maxiter, func, args, dtype,
+                     pre_func_eval, post_func_eval, check_termination,
+                     post_termination_check, customize_result, res_work_pairs,
+                     xp, preserve_shape)
+
+
+def _differentiate_weights(work, n):
+    # This produces the weights of the finite difference formula for a given
+    # stencil. In experiments, use of a second-order central difference formula
+    # with Richardson extrapolation was more accurate numerically, but it was
+    # more complicated, and it would have become even more complicated when
+    # adding support for one-sided differences. However, now that all the
+    # function evaluation values are stored, they can be processed in whatever
+    # way is desired to produce the derivative estimate. We leave alternative
+    # approaches to future work. To be more self-contained, here is the theory
+    # for deriving the weights below.
+    #
+    # Recall that the Taylor expansion of a univariate, scalar-values function
+    # about a point `x` may be expressed as:
+    #      f(x + h)  =     f(x) + f'(x)*h + f''(x)/2!*h**2  + O(h**3)
+    # Suppose we evaluate f(x), f(x+h), and f(x-h).  We have:
+    #      f(x)      =     f(x)
+    #      f(x + h)  =     f(x) + f'(x)*h + f''(x)/2!*h**2  + O(h**3)
+    #      f(x - h)  =     f(x) - f'(x)*h + f''(x)/2!*h**2  + O(h**3)
+    # We can solve for weights `wi` such that:
+    #   w1*f(x)      = w1*(f(x))
+    # + w2*f(x + h)  = w2*(f(x) + f'(x)*h + f''(x)/2!*h**2) + O(h**3)
+    # + w3*f(x - h)  = w3*(f(x) - f'(x)*h + f''(x)/2!*h**2) + O(h**3)
+    #                =     0    + f'(x)*h + 0               + O(h**3)
+    # Then
+    #     f'(x) ~ (w1*f(x) + w2*f(x+h) + w3*f(x-h))/h
+    # is a finite difference derivative approximation with error O(h**2),
+    # and so it is said to be a "second-order" approximation. Under certain
+    # conditions (e.g. well-behaved function, `h` sufficiently small), the
+    # error in the approximation will decrease with h**2; that is, if `h` is
+    # reduced by a factor of 2, the error is reduced by a factor of 4.
+    #
+    # By default, we use eighth-order formulae. Our central-difference formula
+    # uses abscissae:
+    #   x-h/c**3, x-h/c**2, x-h/c, x-h, x, x+h, x+h/c, x+h/c**2, x+h/c**3
+    # where `c` is the step factor. (Typically, the step factor is greater than
+    # one, so the outermost points - as written above - are actually closest to
+    # `x`.) This "stencil" is chosen so that each iteration, the step can be
+    # reduced by the factor `c`, and most of the function evaluations can be
+    # reused with the new step size. For example, in the next iteration, we
+    # will have:
+    #   x-h/c**4, x-h/c**3, x-h/c**2, x-h/c, x, x+h/c, x+h/c**2, x+h/c**3, x+h/c**4
+    # We do not reuse `x-h` and `x+h` for the new derivative estimate.
+    # While this would increase the order of the formula and thus the
+    # theoretical convergence rate, it is also less stable numerically.
+    # (As noted above, there are other ways of processing the values that are
+    # more stable. Thus, even now we store `f(x-h)` and `f(x+h)` in `work.fs`
+    # to simplify future development of this sort of improvement.)
+    #
+    # The (right) one-sided formula is produced similarly using abscissae
+    #   x, x+h, x+h/d, x+h/d**2, ..., x+h/d**6, x+h/d**7, x+h/d**7
+    # where `d` is the square root of `c`. (The left one-sided formula simply
+    # uses -h.) When the step size is reduced by factor `c = d**2`, we have
+    # abscissae:
+    #   x, x+h/d**2, x+h/d**3..., x+h/d**8, x+h/d**9, x+h/d**9
+    # `d` is chosen as the square root of `c` so that the rate of the step-size
+    # reduction is the same per iteration as in the central difference case.
+    # Note that because the central difference formulas are inherently of even
+    # order, for simplicity, we use only even-order formulas for one-sided
+    # differences, too.
+
+    # It's possible for the user to specify `fac` in, say, double precision but
+    # `x` and `args` in single precision. `fac` gets converted to single
+    # precision, but we should always use double precision for the intermediate
+    # calculations here to avoid additional error in the weights.
+    fac = work.fac.astype(np.float64)
+
+    # Note that if the user switches back to floating point precision with
+    # `x` and `args`, then `fac` will not necessarily equal the (lower
+    # precision) cached `_differentiate_weights.fac`, and the weights will
+    # need to be recalculated. This could be fixed, but it's late, and of
+    # low consequence.
+    if fac != _differentiate_weights.fac:
+        _differentiate_weights.central = []
+        _differentiate_weights.right = []
+        _differentiate_weights.fac = fac
+
+    if len(_differentiate_weights.central) != 2*n + 1:
+        # Central difference weights. Consider refactoring this; it could
+        # probably be more compact.
+        i = np.arange(-n, n + 1)
+        p = np.abs(i) - 1.  # center point has power `p` -1, but sign `s` is 0
+        s = np.sign(i)
+
+        h = s / fac ** p
+        A = np.vander(h, increasing=True).T
+        b = np.zeros(2*n + 1)
+        b[1] = 1
+        weights = np.linalg.solve(A, b)
+
+        # Enforce identities to improve accuracy
+        weights[n] = 0
+        for i in range(n):
+            weights[-i-1] = -weights[i]
+
+        # Cache the weights. We only need to calculate them once unless
+        # the step factor changes.
+        _differentiate_weights.central = weights
+
+        # One-sided difference weights. The left one-sided weights (with
+        # negative steps) are simply the negative of the right one-sided
+        # weights, so no need to compute them separately.
+        i = np.arange(2*n + 1)
+        p = i - 1.
+        s = np.sign(i)
+
+        h = s / np.sqrt(fac) ** p
+        A = np.vander(h, increasing=True).T
+        b = np.zeros(2 * n + 1)
+        b[1] = 1
+        weights = np.linalg.solve(A, b)
+
+        _differentiate_weights.right = weights
+
+    return (_differentiate_weights.central.astype(work.dtype, copy=False),
+            _differentiate_weights.right.astype(work.dtype, copy=False))
+_differentiate_weights.central = []
+_differentiate_weights.right = []
+_differentiate_weights.fac = None
+
+
+def _jacobian(func, x, *, atol=None, rtol=None, maxiter=10,
+              order=8, initial_step=0.5, step_factor=2.0):
+    r"""Evaluate the Jacobian of a function numerically.
+
+    Parameters
+    ----------
+    func : callable
+        The function whose Jacobian is desired. The signature must be::
+
+            func(x: ndarray) -> ndarray
+
+         where each element of ``x`` is a finite real. If the function to be
+         differentiated accepts additional, arguments wrap it (e.g. using
+         `functools.partial` or ``lambda``) and pass the wrapped callable
+         into `_jacobian`. See Notes regarding vectorization and the dimensionality
+         of the input and output.
+    x : array_like
+        Points at which to evaluate the Jacobian. Must have at least one dimension.
+        See Notes regarding the dimensionality and vectorization.
+    atol, rtol : float, optional
+        Absolute and relative tolerances for the stopping condition: iteration
+        will stop for each element of the Jacobian when
+        ``res.error < atol + rtol * abs(res.df)``. The default `atol` is the
+        smallest normal number of the appropriate dtype, and the default `rtol`
+        is the square root of the precision of the appropriate dtype.
+    order : int, default: 8
+        The (positive integer) order of the finite difference formula to be
+        used. Odd integers will be rounded up to the next even integer.
+    initial_step : float, default: 0.5
+        The (absolute) initial step size for the finite difference derivative
+        approximation.
+    step_factor : float, default: 2.0
+        The factor by which the step size is *reduced* in each iteration; i.e.
+        the step size in iteration 1 is ``initial_step/step_factor``. If
+        ``step_factor < 1``, subsequent steps will be greater than the initial
+        step; this may be useful if steps smaller than some threshold are
+        undesirable (e.g. due to subtractive cancellation error).
+    maxiter : int, default: 10
+        The maximum number of iterations of the algorithm to perform.
+
+    Returns
+    -------
+    res : _RichResult
+        An instance of `scipy._lib._util._RichResult` with the following
+        attributes.
+
+        success : bool array
+            ``True`` when the algorithm terminated successfully (status ``0``).
+        status : int array
+            An integer representing the exit status of the algorithm.
+            ``0`` : The algorithm converged to the specified tolerances.
+            ``-1`` : The error estimate increased, so iteration was terminated.
+            ``-2`` : The maximum number of iterations was reached.
+            ``-3`` : A non-finite value was encountered.
+            ``-4`` : Iteration was terminated by `callback`.
+            ``1`` : The algorithm is proceeding normally (in `callback` only).
+        df : float array
+            The Jacobian of `func` at `x`, if the algorithm terminated
+            successfully.
+        error : float array
+            An estimate of the error: the magnitude of the difference between
+            the current estimate of the derivative and the estimate in the
+            previous iteration.
+        nit : int array
+            The number of iterations performed.
+        nfev : int array
+            The number of points at which `func` was evaluated.
+        x : float array
+            The value at which the derivative of `func` was evaluated.
+
+    See Also
+    --------
+    _differentiate
+
+    Notes
+    -----
+    Suppose we wish to evaluate the Jacobian of a function
+    :math:`f: \mathbf{R^m} \rightarrow \mathbf{R^n}`, and assign to variables
+    ``m`` and ``n`` the positive integer values of :math:`m` and :math:`n`,
+    respectively. If we wish to evaluate the Jacobian at a single point,
+    then:
+
+    - argument `x` must be an array of shape ``(m,)``
+    - argument `func` must be vectorized to accept an array of shape ``(m, p)``.
+      The first axis represents the :math:`m` inputs of :math:`f`; the second
+      is for evaluating the function at multiple points in a single call.
+    - argument `func` must return an array of shape ``(n, p)``. The first
+      axis represents the :math:`n` outputs of :math:`f`; the second
+      is for the result of evaluating the function at multiple points.
+    - attribute ``df`` of the result object will be an array of shape ``(n, m)``,
+      the Jacobian.
+
+    This function is also vectorized in the sense that the Jacobian can be
+    evaluated at ``k`` points in a single call. In this case, `x` would be an
+    array of shape ``(m, k)``, `func` would accept an array of shape
+    ``(m, k, p)`` and return an array of shape ``(n, k, p)``, and the ``df``
+    attribute of the result would have shape ``(n, m, k)``.
+
+    References
+    ----------
+    .. [1] Jacobian matrix and determinant, *Wikipedia*,
+           https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant
+
+    Examples
+    --------
+    The Rosenbrock function maps from :math:`\mathbf{R}^m \righarrow \mathbf{R}`;
+    the SciPy implementation `scipy.optimize.rosen` is vectorized to accept an
+    array of shape ``(m, p)`` and return an array of shape ``m``. Suppose we wish
+    to evaluate the Jacobian (AKA the gradient because the function returns a scalar)
+    at ``[0.5, 0.5, 0.5]``.
+
+    >>> import numpy as np
+    >>> from scipy.optimize._differentiate import _jacobian as jacobian
+    >>> from scipy.optimize import rosen, rosen_der
+    >>> m = 3
+    >>> x = np.full(m, 0.5)
+    >>> res = jacobian(rosen, x)
+    >>> ref = rosen_der(x)  # reference value of the gradient
+    >>> res.df, ref
+    (array([-51.,  -1.,  50.]), array([-51.,  -1.,  50.]))
+
+    As an example of a function with multiple outputs, consider Example 4
+    from [1]_.
+
+    >>> def f(x):
+    ...     x1, x2, x3 = x    ...
+    ...     return [x1, 5*x3, 4*x2**2 - 2*x3, x3*np.sin(x1)]
+
+    The true Jacobian is given by:
+
+    >>> def df(x):
+    ...         x1, x2, x3 = x
+    ...         one = np.ones_like(x1)
+    ...         return [[one, 0*one, 0*one],
+    ...                 [0*one, 0*one, 5*one],
+    ...                 [0*one, 8*x2, -2*one],
+    ...                 [x3*np.cos(x1), 0*one, np.sin(x1)]]
+
+    Evaluate the Jacobian at an arbitrary point.
+
+    >>> rng = np.random.default_rng(389252938452)
+    >>> x = rng.random(size=3)
+    >>> res = jacobian(f, x)
+    >>> ref = df(x)
+    >>> res.df.shape == (4, 3)
+    True
+    >>> np.allclose(res.df, ref)
+    True
+
+    Evaluate the Jacobian at 10 arbitrary points in a single call.
+
+    >>> x = rng.random(size=(3, 10))
+    >>> res = jacobian(f, x)
+    >>> ref = df(x)
+    >>> res.df.shape == (4, 3, 10)
+    True
+    >>> np.allclose(res.df, ref)
+    True
+
+    """
+    x = np.asarray(x)
+    int_dtype = np.issubdtype(x.dtype, np.integer)
+    x0 = np.asarray(x, dtype=float) if int_dtype else x
+
+    if x0.ndim < 1:
+        message = "Argument `x` must be at least 1-D."
+        raise ValueError(message)
+
+    m = x0.shape[0]
+    i = np.arange(m)
+
+    def wrapped(x):
+        p = () if x.ndim == x0.ndim else (x.shape[-1],)  # number of abscissae
+        new_dims = (1,) if x.ndim == x0.ndim else (1, -1)
+        new_shape = (m, m) + x0.shape[1:] + p
+        xph = np.expand_dims(x0, new_dims)
+        xph = np.broadcast_to(xph, new_shape).copy()
+        xph[i, i] = x
+        return func(xph)
+
+    res = _differentiate(wrapped, x, atol=atol, rtol=rtol,
+                         maxiter=maxiter, order=order, initial_step=initial_step,
+                         step_factor=step_factor, preserve_shape=True)
+    del res.x  # the user knows `x`, and the way it gets broadcasted is meaningless here
+    return res

llava_next/lib/python3.10/site-packages/scipy/optimize/_hessian_update_strategy.py

@@ -0,0 +1,475 @@
+"""Hessian update strategies for quasi-Newton optimization methods."""
+import numpy as np
+from numpy.linalg import norm
+from scipy.linalg import get_blas_funcs, issymmetric
+from warnings import warn
+
+
+__all__ = ['HessianUpdateStrategy', 'BFGS', 'SR1']
+
+
+class HessianUpdateStrategy:
+    """Interface for implementing Hessian update strategies.
+
+    Many optimization methods make use of Hessian (or inverse Hessian)
+    approximations, such as the quasi-Newton methods BFGS, SR1, L-BFGS.
+    Some of these  approximations, however, do not actually need to store
+    the entire matrix or can compute the internal matrix product with a
+    given vector in a very efficiently manner. This class serves as an
+    abstract interface between the optimization algorithm and the
+    quasi-Newton update strategies, giving freedom of implementation
+    to store and update the internal matrix as efficiently as possible.
+    Different choices of initialization and update procedure will result
+    in different quasi-Newton strategies.
+
+    Four methods should be implemented in derived classes: ``initialize``,
+    ``update``, ``dot`` and ``get_matrix``.
+
+    Notes
+    -----
+    Any instance of a class that implements this interface,
+    can be accepted by the method ``minimize`` and used by
+    the compatible solvers to approximate the Hessian (or
+    inverse Hessian) used by the optimization algorithms.
+    """
+
+    def initialize(self, n, approx_type):
+        """Initialize internal matrix.
+
+        Allocate internal memory for storing and updating
+        the Hessian or its inverse.
+
+        Parameters
+        ----------
+        n : int
+            Problem dimension.
+        approx_type : {'hess', 'inv_hess'}
+            Selects either the Hessian or the inverse Hessian.
+            When set to 'hess' the Hessian will be stored and updated.
+            When set to 'inv_hess' its inverse will be used instead.
+        """
+        raise NotImplementedError("The method ``initialize(n, approx_type)``"
+                                  " is not implemented.")
+
+    def update(self, delta_x, delta_grad):
+        """Update internal matrix.
+
+        Update Hessian matrix or its inverse (depending on how 'approx_type'
+        is defined) using information about the last evaluated points.
+
+        Parameters
+        ----------
+        delta_x : ndarray
+            The difference between two points the gradient
+            function have been evaluated at: ``delta_x = x2 - x1``.
+        delta_grad : ndarray
+            The difference between the gradients:
+            ``delta_grad = grad(x2) - grad(x1)``.
+        """
+        raise NotImplementedError("The method ``update(delta_x, delta_grad)``"
+                                  " is not implemented.")
+
+    def dot(self, p):
+        """Compute the product of the internal matrix with the given vector.
+
+        Parameters
+        ----------
+        p : array_like
+            1-D array representing a vector.
+
+        Returns
+        -------
+        Hp : array
+            1-D represents the result of multiplying the approximation matrix
+            by vector p.
+        """
+        raise NotImplementedError("The method ``dot(p)``"
+                                  " is not implemented.")
+
+    def get_matrix(self):
+        """Return current internal matrix.
+
+        Returns
+        -------
+        H : ndarray, shape (n, n)
+            Dense matrix containing either the Hessian
+            or its inverse (depending on how 'approx_type'
+            is defined).
+        """
+        raise NotImplementedError("The method ``get_matrix(p)``"
+                                  " is not implemented.")
+
+
+class FullHessianUpdateStrategy(HessianUpdateStrategy):
+    """Hessian update strategy with full dimensional internal representation.
+    """
+    _syr = get_blas_funcs('syr', dtype='d')  # Symmetric rank 1 update
+    _syr2 = get_blas_funcs('syr2', dtype='d')  # Symmetric rank 2 update
+    # Symmetric matrix-vector product
+    _symv = get_blas_funcs('symv', dtype='d')
+
+    def __init__(self, init_scale='auto'):
+        self.init_scale = init_scale
+        # Until initialize is called we can't really use the class,
+        # so it makes sense to set everything to None.
+        self.first_iteration = None
+        self.approx_type = None
+        self.B = None
+        self.H = None
+
+    def initialize(self, n, approx_type):
+        """Initialize internal matrix.
+
+        Allocate internal memory for storing and updating
+        the Hessian or its inverse.
+
+        Parameters
+        ----------
+        n : int
+            Problem dimension.
+        approx_type : {'hess', 'inv_hess'}
+            Selects either the Hessian or the inverse Hessian.
+            When set to 'hess' the Hessian will be stored and updated.
+            When set to 'inv_hess' its inverse will be used instead.
+        """
+        self.first_iteration = True
+        self.n = n
+        self.approx_type = approx_type
+        if approx_type not in ('hess', 'inv_hess'):
+            raise ValueError("`approx_type` must be 'hess' or 'inv_hess'.")
+        # Create matrix
+        if self.approx_type == 'hess':
+            self.B = np.eye(n, dtype=float)
+        else:
+            self.H = np.eye(n, dtype=float)
+
+    def _auto_scale(self, delta_x, delta_grad):
+        # Heuristic to scale matrix at first iteration.
+        # Described in Nocedal and Wright "Numerical Optimization"
+        # p.143 formula (6.20).
+        s_norm2 = np.dot(delta_x, delta_x)
+        y_norm2 = np.dot(delta_grad, delta_grad)
+        ys = np.abs(np.dot(delta_grad, delta_x))
+        if ys == 0.0 or y_norm2 == 0 or s_norm2 == 0:
+            return 1
+        if self.approx_type == 'hess':
+            return y_norm2 / ys
+        else:
+            return ys / y_norm2
+
+    def _update_implementation(self, delta_x, delta_grad):
+        raise NotImplementedError("The method ``_update_implementation``"
+                                  " is not implemented.")
+
+    def update(self, delta_x, delta_grad):
+        """Update internal matrix.
+
+        Update Hessian matrix or its inverse (depending on how 'approx_type'
+        is defined) using information about the last evaluated points.
+
+        Parameters
+        ----------
+        delta_x : ndarray
+            The difference between two points the gradient
+            function have been evaluated at: ``delta_x = x2 - x1``.
+        delta_grad : ndarray
+            The difference between the gradients:
+            ``delta_grad = grad(x2) - grad(x1)``.
+        """
+        if np.all(delta_x == 0.0):
+            return
+        if np.all(delta_grad == 0.0):
+            warn('delta_grad == 0.0. Check if the approximated '
+                 'function is linear. If the function is linear '
+                 'better results can be obtained by defining the '
+                 'Hessian as zero instead of using quasi-Newton '
+                 'approximations.',
+                 UserWarning, stacklevel=2)
+            return
+        if self.first_iteration:
+            # Get user specific scale
+            if isinstance(self.init_scale, str) and self.init_scale == "auto":
+                scale = self._auto_scale(delta_x, delta_grad)
+            else:
+                scale = self.init_scale
+
+            # Check for complex: numpy will silently cast a complex array to
+            # a real one but not so for scalar as it raises a TypeError.
+            # Checking here brings a consistent behavior.
+            replace = False
+            if np.size(scale) == 1:
+                # to account for the legacy behavior having the exact same cast
+                scale = float(scale)
+            elif np.iscomplexobj(scale):
+                raise TypeError("init_scale contains complex elements, "
+                                "must be real.")
+            else:  # test explicitly for allowed shapes and values
+                replace = True
+                if self.approx_type == 'hess':
+                    shape = np.shape(self.B)
+                    dtype = self.B.dtype
+                else:
+                    shape = np.shape(self.H)
+                    dtype = self.H.dtype
+                # copy, will replace the original
+                scale = np.array(scale, dtype=dtype, copy=True)
+
+                # it has to match the shape of the matrix for the multiplication,
+                # no implicit broadcasting is allowed
+                if shape != (init_shape := np.shape(scale)):
+                    raise ValueError("If init_scale is an array, it must have the "
+                                     f"dimensions of the hess/inv_hess: {shape}."
+                                     f" Got {init_shape}.")
+                if not issymmetric(scale):
+                    raise ValueError("If init_scale is an array, it must be"
+                                     " symmetric (passing scipy.linalg.issymmetric)"
+                                     " to be an approximation of a hess/inv_hess.")
+
+            # Scale initial matrix with ``scale * np.eye(n)`` or replace
+            # This is not ideal, we could assign the scale directly in
+            # initialize, but we would need to
+            if self.approx_type == 'hess':
+                if replace:
+                    self.B = scale
+                else:
+                    self.B *= scale
+            else:
+                if replace:
+                    self.H = scale
+                else:
+                    self.H *= scale
+            self.first_iteration = False
+        self._update_implementation(delta_x, delta_grad)
+
+    def dot(self, p):
+        """Compute the product of the internal matrix with the given vector.
+
+        Parameters
+        ----------
+        p : array_like
+            1-D array representing a vector.
+
+        Returns
+        -------
+        Hp : array
+            1-D represents the result of multiplying the approximation matrix
+            by vector p.
+        """
+        if self.approx_type == 'hess':
+            return self._symv(1, self.B, p)
+        else:
+            return self._symv(1, self.H, p)
+
+    def get_matrix(self):
+        """Return the current internal matrix.
+
+        Returns
+        -------
+        M : ndarray, shape (n, n)
+            Dense matrix containing either the Hessian or its inverse
+            (depending on how `approx_type` was defined).
+        """
+        if self.approx_type == 'hess':
+            M = np.copy(self.B)
+        else:
+            M = np.copy(self.H)
+        li = np.tril_indices_from(M, k=-1)
+        M[li] = M.T[li]
+        return M
+
+
+class BFGS(FullHessianUpdateStrategy):
+    """Broyden-Fletcher-Goldfarb-Shanno (BFGS) Hessian update strategy.
+
+    Parameters
+    ----------
+    exception_strategy : {'skip_update', 'damp_update'}, optional
+        Define how to proceed when the curvature condition is violated.
+        Set it to 'skip_update' to just skip the update. Or, alternatively,
+        set it to 'damp_update' to interpolate between the actual BFGS
+        result and the unmodified matrix. Both exceptions strategies
+        are explained  in [1]_, p.536-537.
+    min_curvature : float
+        This number, scaled by a normalization factor, defines the
+        minimum curvature ``dot(delta_grad, delta_x)`` allowed to go
+        unaffected by the exception strategy. By default is equal to
+        1e-8 when ``exception_strategy = 'skip_update'`` and equal
+        to 0.2 when ``exception_strategy = 'damp_update'``.
+    init_scale : {float, np.array, 'auto'}
+        This parameter can be used to initialize the Hessian or its
+        inverse. When a float is given, the relevant array is initialized
+        to ``np.eye(n) * init_scale``, where ``n`` is the problem dimension.
+        Alternatively, if a precisely ``(n, n)`` shaped, symmetric array is given,
+        this array will be used. Otherwise an error is generated.
+        Set it to 'auto' in order to use an automatic heuristic for choosing
+        the initial scale. The heuristic is described in [1]_, p.143.
+        The default is 'auto'.
+
+    Notes
+    -----
+    The update is based on the description in [1]_, p.140.
+
+    References
+    ----------
+    .. [1] Nocedal, Jorge, and Stephen J. Wright. "Numerical optimization"
+           Second Edition (2006).
+    """
+
+    def __init__(self, exception_strategy='skip_update', min_curvature=None,
+                 init_scale='auto'):
+        if exception_strategy == 'skip_update':
+            if min_curvature is not None:
+                self.min_curvature = min_curvature
+            else:
+                self.min_curvature = 1e-8
+        elif exception_strategy == 'damp_update':
+            if min_curvature is not None:
+                self.min_curvature = min_curvature
+            else:
+                self.min_curvature = 0.2
+        else:
+            raise ValueError("`exception_strategy` must be 'skip_update' "
+                             "or 'damp_update'.")
+
+        super().__init__(init_scale)
+        self.exception_strategy = exception_strategy
+
+    def _update_inverse_hessian(self, ys, Hy, yHy, s):
+        """Update the inverse Hessian matrix.
+
+        BFGS update using the formula:
+
+            ``H <- H + ((H*y).T*y + s.T*y)/(s.T*y)^2 * (s*s.T)
+                     - 1/(s.T*y) * ((H*y)*s.T + s*(H*y).T)``
+
+        where ``s = delta_x`` and ``y = delta_grad``. This formula is
+        equivalent to (6.17) in [1]_ written in a more efficient way
+        for implementation.
+
+        References
+        ----------
+        .. [1] Nocedal, Jorge, and Stephen J. Wright. "Numerical optimization"
+               Second Edition (2006).
+        """
+        self.H = self._syr2(-1.0 / ys, s, Hy, a=self.H)
+        self.H = self._syr((ys + yHy) / ys ** 2, s, a=self.H)
+
+    def _update_hessian(self, ys, Bs, sBs, y):
+        """Update the Hessian matrix.
+
+        BFGS update using the formula:
+
+            ``B <- B - (B*s)*(B*s).T/s.T*(B*s) + y*y^T/s.T*y``
+
+        where ``s`` is short for ``delta_x`` and ``y`` is short
+        for ``delta_grad``. Formula (6.19) in [1]_.
+
+        References
+        ----------
+        .. [1] Nocedal, Jorge, and Stephen J. Wright. "Numerical optimization"
+               Second Edition (2006).
+        """
+        self.B = self._syr(1.0 / ys, y, a=self.B)
+        self.B = self._syr(-1.0 / sBs, Bs, a=self.B)
+
+    def _update_implementation(self, delta_x, delta_grad):
+        # Auxiliary variables w and z
+        if self.approx_type == 'hess':
+            w = delta_x
+            z = delta_grad
+        else:
+            w = delta_grad
+            z = delta_x
+        # Do some common operations
+        wz = np.dot(w, z)
+        Mw = self.dot(w)
+        wMw = Mw.dot(w)
+        # Guarantee that wMw > 0 by reinitializing matrix.
+        # While this is always true in exact arithmetic,
+        # indefinite matrix may appear due to roundoff errors.
+        if wMw <= 0.0:
+            scale = self._auto_scale(delta_x, delta_grad)
+            # Reinitialize matrix
+            if self.approx_type == 'hess':
+                self.B = scale * np.eye(self.n, dtype=float)
+            else:
+                self.H = scale * np.eye(self.n, dtype=float)
+            # Do common operations for new matrix
+            Mw = self.dot(w)
+            wMw = Mw.dot(w)
+        # Check if curvature condition is violated
+        if wz <= self.min_curvature * wMw:
+            # If the option 'skip_update' is set
+            # we just skip the update when the condition
+            # is violated.
+            if self.exception_strategy == 'skip_update':
+                return
+            # If the option 'damp_update' is set we
+            # interpolate between the actual BFGS
+            # result and the unmodified matrix.
+            elif self.exception_strategy == 'damp_update':
+                update_factor = (1-self.min_curvature) / (1 - wz/wMw)
+                z = update_factor*z + (1-update_factor)*Mw
+                wz = np.dot(w, z)
+        # Update matrix
+        if self.approx_type == 'hess':
+            self._update_hessian(wz, Mw, wMw, z)
+        else:
+            self._update_inverse_hessian(wz, Mw, wMw, z)
+
+
+class SR1(FullHessianUpdateStrategy):
+    """Symmetric-rank-1 Hessian update strategy.
+
+    Parameters
+    ----------
+    min_denominator : float
+        This number, scaled by a normalization factor,
+        defines the minimum denominator magnitude allowed
+        in the update. When the condition is violated we skip
+        the update. By default uses ``1e-8``.
+    init_scale : {float, np.array, 'auto'}, optional
+        This parameter can be used to initialize the Hessian or its
+        inverse. When a float is given, the relevant array is initialized
+        to ``np.eye(n) * init_scale``, where ``n`` is the problem dimension.
+        Alternatively, if a precisely ``(n, n)`` shaped, symmetric array is given,
+        this array will be used. Otherwise an error is generated.
+        Set it to 'auto' in order to use an automatic heuristic for choosing
+        the initial scale. The heuristic is described in [1]_, p.143.
+        The default is 'auto'.
+
+    Notes
+    -----
+    The update is based on the description in [1]_, p.144-146.
+
+    References
+    ----------
+    .. [1] Nocedal, Jorge, and Stephen J. Wright. "Numerical optimization"
+           Second Edition (2006).
+    """
+
+    def __init__(self, min_denominator=1e-8, init_scale='auto'):
+        self.min_denominator = min_denominator
+        super().__init__(init_scale)
+
+    def _update_implementation(self, delta_x, delta_grad):
+        # Auxiliary variables w and z
+        if self.approx_type == 'hess':
+            w = delta_x
+            z = delta_grad
+        else:
+            w = delta_grad
+            z = delta_x
+        # Do some common operations
+        Mw = self.dot(w)
+        z_minus_Mw = z - Mw
+        denominator = np.dot(w, z_minus_Mw)
+        # If the denominator is too small
+        # we just skip the update.
+        if np.abs(denominator) <= self.min_denominator*norm(w)*norm(z_minus_Mw):
+            return
+        # Update matrix
+        if self.approx_type == 'hess':
+            self.B = self._syr(1/denominator, z_minus_Mw, a=self.B)
+        else:
+            self.H = self._syr(1/denominator, z_minus_Mw, a=self.H)

llava_next/lib/python3.10/site-packages/scipy/optimize/_linprog_ip.py

@@ -0,0 +1,1126 @@
+"""Interior-point method for linear programming
+
+The *interior-point* method uses the primal-dual path following algorithm
+outlined in [1]_. This algorithm supports sparse constraint matrices and
+is typically faster than the simplex methods, especially for large, sparse
+problems. Note, however, that the solution returned may be slightly less
+accurate than those of the simplex methods and will not, in general,
+correspond with a vertex of the polytope defined by the constraints.
+
+    .. versionadded:: 1.0.0
+
+References
+----------
+.. [1] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
+       optimizer for linear programming: an implementation of the
+       homogeneous algorithm." High performance optimization. Springer US,
+       2000. 197-232.
+"""
+# Author: Matt Haberland
+
+import numpy as np
+import scipy as sp
+import scipy.sparse as sps
+from warnings import warn
+from scipy.linalg import LinAlgError
+from ._optimize import OptimizeWarning, OptimizeResult, _check_unknown_options
+from ._linprog_util import _postsolve
+has_umfpack = True
+has_cholmod = True
+try:
+    import sksparse  # noqa: F401
+    from sksparse.cholmod import cholesky as cholmod  # noqa: F401
+    from sksparse.cholmod import analyze as cholmod_analyze
+except ImportError:
+    has_cholmod = False
+try:
+    import scikits.umfpack  # test whether to use factorized  # noqa: F401
+except ImportError:
+    has_umfpack = False
+
+
+def _get_solver(M, sparse=False, lstsq=False, sym_pos=True,
+                cholesky=True, permc_spec='MMD_AT_PLUS_A'):
+    """
+    Given solver options, return a handle to the appropriate linear system
+    solver.
+
+    Parameters
+    ----------
+    M : 2-D array
+        As defined in [4] Equation 8.31
+    sparse : bool (default = False)
+        True if the system to be solved is sparse. This is typically set
+        True when the original ``A_ub`` and ``A_eq`` arrays are sparse.
+    lstsq : bool (default = False)
+        True if the system is ill-conditioned and/or (nearly) singular and
+        thus a more robust least-squares solver is desired. This is sometimes
+        needed as the solution is approached.
+    sym_pos : bool (default = True)
+        True if the system matrix is symmetric positive definite
+        Sometimes this needs to be set false as the solution is approached,
+        even when the system should be symmetric positive definite, due to
+        numerical difficulties.
+    cholesky : bool (default = True)
+        True if the system is to be solved by Cholesky, rather than LU,
+        decomposition. This is typically faster unless the problem is very
+        small or prone to numerical difficulties.
+    permc_spec : str (default = 'MMD_AT_PLUS_A')
+        Sparsity preservation strategy used by SuperLU. Acceptable values are:
+
+        - ``NATURAL``: natural ordering.
+        - ``MMD_ATA``: minimum degree ordering on the structure of A^T A.
+        - ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A.
+        - ``COLAMD``: approximate minimum degree column ordering.
+
+        See SuperLU documentation.
+
+    Returns
+    -------
+    solve : function
+        Handle to the appropriate solver function
+
+    """
+    try:
+        if sparse:
+            if lstsq:
+                def solve(r, sym_pos=False):
+                    return sps.linalg.lsqr(M, r)[0]
+            elif cholesky:
+                try:
+                    # Will raise an exception in the first call,
+                    # or when the matrix changes due to a new problem
+                    _get_solver.cholmod_factor.cholesky_inplace(M)
+                except Exception:
+                    _get_solver.cholmod_factor = cholmod_analyze(M)
+                    _get_solver.cholmod_factor.cholesky_inplace(M)
+                solve = _get_solver.cholmod_factor
+            else:
+                if has_umfpack and sym_pos:
+                    solve = sps.linalg.factorized(M)
+                else:  # factorized doesn't pass permc_spec
+                    solve = sps.linalg.splu(M, permc_spec=permc_spec).solve
+
+        else:
+            if lstsq:  # sometimes necessary as solution is approached
+                def solve(r):
+                    return sp.linalg.lstsq(M, r)[0]
+            elif cholesky:
+                L = sp.linalg.cho_factor(M)
+
+                def solve(r):
+                    return sp.linalg.cho_solve(L, r)
+            else:
+                # this seems to cache the matrix factorization, so solving
+                # with multiple right hand sides is much faster
+                def solve(r, sym_pos=sym_pos):
+                    if sym_pos:
+                        return sp.linalg.solve(M, r, assume_a="pos")
+                    else:
+                        return sp.linalg.solve(M, r)
+    # There are many things that can go wrong here, and it's hard to say
+    # what all of them are. It doesn't really matter: if the matrix can't be
+    # factorized, return None. get_solver will be called again with different
+    # inputs, and a new routine will try to factorize the matrix.
+    except KeyboardInterrupt:
+        raise
+    except Exception:
+        return None
+    return solve
+
+
+def _get_delta(A, b, c, x, y, z, tau, kappa, gamma, eta, sparse=False,
+               lstsq=False, sym_pos=True, cholesky=True, pc=True, ip=False,
+               permc_spec='MMD_AT_PLUS_A'):
+    """
+    Given standard form problem defined by ``A``, ``b``, and ``c``;
+    current variable estimates ``x``, ``y``, ``z``, ``tau``, and ``kappa``;
+    algorithmic parameters ``gamma and ``eta;
+    and options ``sparse``, ``lstsq``, ``sym_pos``, ``cholesky``, ``pc``
+    (predictor-corrector), and ``ip`` (initial point improvement),
+    get the search direction for increments to the variable estimates.
+
+    Parameters
+    ----------
+    As defined in [4], except:
+    sparse : bool
+        True if the system to be solved is sparse. This is typically set
+        True when the original ``A_ub`` and ``A_eq`` arrays are sparse.
+    lstsq : bool
+        True if the system is ill-conditioned and/or (nearly) singular and
+        thus a more robust least-squares solver is desired. This is sometimes
+        needed as the solution is approached.
+    sym_pos : bool
+        True if the system matrix is symmetric positive definite
+        Sometimes this needs to be set false as the solution is approached,
+        even when the system should be symmetric positive definite, due to
+        numerical difficulties.
+    cholesky : bool
+        True if the system is to be solved by Cholesky, rather than LU,
+        decomposition. This is typically faster unless the problem is very
+        small or prone to numerical difficulties.
+    pc : bool
+        True if the predictor-corrector method of Mehrota is to be used. This
+        is almost always (if not always) beneficial. Even though it requires
+        the solution of an additional linear system, the factorization
+        is typically (implicitly) reused so solution is efficient, and the
+        number of algorithm iterations is typically reduced.
+    ip : bool
+        True if the improved initial point suggestion due to [4] section 4.3
+        is desired. It's unclear whether this is beneficial.
+    permc_spec : str (default = 'MMD_AT_PLUS_A')
+        (Has effect only with ``sparse = True``, ``lstsq = False``, ``sym_pos =
+        True``.) A matrix is factorized in each iteration of the algorithm.
+        This option specifies how to permute the columns of the matrix for
+        sparsity preservation. Acceptable values are:
+
+        - ``NATURAL``: natural ordering.
+        - ``MMD_ATA``: minimum degree ordering on the structure of A^T A.
+        - ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A.
+        - ``COLAMD``: approximate minimum degree column ordering.
+
+        This option can impact the convergence of the
+        interior point algorithm; test different values to determine which
+        performs best for your problem. For more information, refer to
+        ``scipy.sparse.linalg.splu``.
+
+    Returns
+    -------
+    Search directions as defined in [4]
+
+    References
+    ----------
+    .. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
+           optimizer for linear programming: an implementation of the
+           homogeneous algorithm." High performance optimization. Springer US,
+           2000. 197-232.
+
+    """
+    if A.shape[0] == 0:
+        # If there are no constraints, some solvers fail (understandably)
+        # rather than returning empty solution. This gets the job done.
+        sparse, lstsq, sym_pos, cholesky = False, False, True, False
+    n_x = len(x)
+
+    # [4] Equation 8.8
+    r_P = b * tau - A.dot(x)
+    r_D = c * tau - A.T.dot(y) - z
+    r_G = c.dot(x) - b.transpose().dot(y) + kappa
+    mu = (x.dot(z) + tau * kappa) / (n_x + 1)
+
+    #  Assemble M from [4] Equation 8.31
+    Dinv = x / z
+
+    if sparse:
+        M = A.dot(sps.diags(Dinv, 0, format="csc").dot(A.T))
+    else:
+        M = A.dot(Dinv.reshape(-1, 1) * A.T)
+    solve = _get_solver(M, sparse, lstsq, sym_pos, cholesky, permc_spec)
+
+    # pc: "predictor-corrector" [4] Section 4.1
+    # In development this option could be turned off
+    # but it always seems to improve performance substantially
+    n_corrections = 1 if pc else 0
+
+    i = 0
+    alpha, d_x, d_z, d_tau, d_kappa = 0, 0, 0, 0, 0
+    while i <= n_corrections:
+        # Reference [4] Eq. 8.6
+        rhatp = eta(gamma) * r_P
+        rhatd = eta(gamma) * r_D
+        rhatg = eta(gamma) * r_G
+
+        # Reference [4] Eq. 8.7
+        rhatxs = gamma * mu - x * z
+        rhattk = gamma * mu - tau * kappa
+
+        if i == 1:
+            if ip:  # if the correction is to get "initial point"
+                # Reference [4] Eq. 8.23
+                rhatxs = ((1 - alpha) * gamma * mu -
+                          x * z - alpha**2 * d_x * d_z)
+                rhattk = ((1 - alpha) * gamma * mu -
+                    tau * kappa -
+                    alpha**2 * d_tau * d_kappa)
+            else:  # if the correction is for "predictor-corrector"
+                # Reference [4] Eq. 8.13
+                rhatxs -= d_x * d_z
+                rhattk -= d_tau * d_kappa
+
+        # sometimes numerical difficulties arise as the solution is approached
+        # this loop tries to solve the equations using a sequence of functions
+        # for solve. For dense systems, the order is:
+        # 1. scipy.linalg.cho_factor/scipy.linalg.cho_solve,
+        # 2. scipy.linalg.solve w/ sym_pos = True,
+        # 3. scipy.linalg.solve w/ sym_pos = False, and if all else fails
+        # 4. scipy.linalg.lstsq
+        # For sparse systems, the order is:
+        # 1. sksparse.cholmod.cholesky (if available)
+        # 2. scipy.sparse.linalg.factorized (if umfpack available)
+        # 3. scipy.sparse.linalg.splu
+        # 4. scipy.sparse.linalg.lsqr
+        solved = False
+        while not solved:
+            try:
+                # [4] Equation 8.28
+                p, q = _sym_solve(Dinv, A, c, b, solve)
+                # [4] Equation 8.29
+                u, v = _sym_solve(Dinv, A, rhatd -
+                                  (1 / x) * rhatxs, rhatp, solve)
+                if np.any(np.isnan(p)) or np.any(np.isnan(q)):
+                    raise LinAlgError
+                solved = True
+            except (LinAlgError, ValueError, TypeError) as e:
+                # Usually this doesn't happen. If it does, it happens when
+                # there are redundant constraints or when approaching the
+                # solution. If so, change solver.
+                if cholesky:
+                    cholesky = False
+                    warn(
+                        "Solving system with option 'cholesky':True "
+                        "failed. It is normal for this to happen "
+                        "occasionally, especially as the solution is "
+                        "approached. However, if you see this frequently, "
+                        "consider setting option 'cholesky' to False.",
+                        OptimizeWarning, stacklevel=5)
+                elif sym_pos:
+                    sym_pos = False
+                    warn(
+                        "Solving system with option 'sym_pos':True "
+                        "failed. It is normal for this to happen "
+                        "occasionally, especially as the solution is "
+                        "approached. However, if you see this frequently, "
+                        "consider setting option 'sym_pos' to False.",
+                        OptimizeWarning, stacklevel=5)
+                elif not lstsq:
+                    lstsq = True
+                    warn(
+                        "Solving system with option 'sym_pos':False "
+                        "failed. This may happen occasionally, "
+                        "especially as the solution is "
+                        "approached. However, if you see this frequently, "
+                        "your problem may be numerically challenging. "
+                        "If you cannot improve the formulation, consider "
+                        "setting 'lstsq' to True. Consider also setting "
+                        "`presolve` to True, if it is not already.",
+                        OptimizeWarning, stacklevel=5)
+                else:
+                    raise e
+                solve = _get_solver(M, sparse, lstsq, sym_pos,
+                                    cholesky, permc_spec)
+        # [4] Results after 8.29
+        d_tau = ((rhatg + 1 / tau * rhattk - (-c.dot(u) + b.dot(v))) /
+                 (1 / tau * kappa + (-c.dot(p) + b.dot(q))))
+        d_x = u + p * d_tau
+        d_y = v + q * d_tau
+
+        # [4] Relations between  after 8.25 and 8.26
+        d_z = (1 / x) * (rhatxs - z * d_x)
+        d_kappa = 1 / tau * (rhattk - kappa * d_tau)
+
+        # [4] 8.12 and "Let alpha be the maximal possible step..." before 8.23
+        alpha = _get_step(x, d_x, z, d_z, tau, d_tau, kappa, d_kappa, 1)
+        if ip:  # initial point - see [4] 4.4
+            gamma = 10
+        else:  # predictor-corrector, [4] definition after 8.12
+            beta1 = 0.1  # [4] pg. 220 (Table 8.1)
+            gamma = (1 - alpha)**2 * min(beta1, (1 - alpha))
+        i += 1
+
+    return d_x, d_y, d_z, d_tau, d_kappa
+
+
+def _sym_solve(Dinv, A, r1, r2, solve):
+    """
+    An implementation of [4] equation 8.31 and 8.32
+
+    References
+    ----------
+    .. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
+           optimizer for linear programming: an implementation of the
+           homogeneous algorithm." High performance optimization. Springer US,
+           2000. 197-232.
+
+    """
+    # [4] 8.31
+    r = r2 + A.dot(Dinv * r1)
+    v = solve(r)
+    # [4] 8.32
+    u = Dinv * (A.T.dot(v) - r1)
+    return u, v
+
+
+def _get_step(x, d_x, z, d_z, tau, d_tau, kappa, d_kappa, alpha0):
+    """
+    An implementation of [4] equation 8.21
+
+    References
+    ----------
+    .. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
+           optimizer for linear programming: an implementation of the
+           homogeneous algorithm." High performance optimization. Springer US,
+           2000. 197-232.
+
+    """
+    # [4] 4.3 Equation 8.21, ignoring 8.20 requirement
+    # same step is taken in primal and dual spaces
+    # alpha0 is basically beta3 from [4] Table 8.1, but instead of beta3
+    # the value 1 is used in Mehrota corrector and initial point correction
+    i_x = d_x < 0
+    i_z = d_z < 0
+    alpha_x = alpha0 * np.min(x[i_x] / -d_x[i_x]) if np.any(i_x) else 1
+    alpha_tau = alpha0 * tau / -d_tau if d_tau < 0 else 1
+    alpha_z = alpha0 * np.min(z[i_z] / -d_z[i_z]) if np.any(i_z) else 1
+    alpha_kappa = alpha0 * kappa / -d_kappa if d_kappa < 0 else 1
+    alpha = np.min([1, alpha_x, alpha_tau, alpha_z, alpha_kappa])
+    return alpha
+
+
+def _get_message(status):
+    """
+    Given problem status code, return a more detailed message.
+
+    Parameters
+    ----------
+    status : int
+        An integer representing the exit status of the optimization::
+
+         0 : Optimization terminated successfully
+         1 : Iteration limit reached
+         2 : Problem appears to be infeasible
+         3 : Problem appears to be unbounded
+         4 : Serious numerical difficulties encountered
+
+    Returns
+    -------
+    message : str
+        A string descriptor of the exit status of the optimization.
+
+    """
+    messages = (
+        ["Optimization terminated successfully.",
+         "The iteration limit was reached before the algorithm converged.",
+         "The algorithm terminated successfully and determined that the "
+         "problem is infeasible.",
+         "The algorithm terminated successfully and determined that the "
+         "problem is unbounded.",
+         "Numerical difficulties were encountered before the problem "
+         "converged. Please check your problem formulation for errors, "
+         "independence of linear equality constraints, and reasonable "
+         "scaling and matrix condition numbers. If you continue to "
+         "encounter this error, please submit a bug report."
+         ])
+    return messages[status]
+
+
+def _do_step(x, y, z, tau, kappa, d_x, d_y, d_z, d_tau, d_kappa, alpha):
+    """
+    An implementation of [4] Equation 8.9
+
+    References
+    ----------
+    .. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
+           optimizer for linear programming: an implementation of the
+           homogeneous algorithm." High performance optimization. Springer US,
+           2000. 197-232.
+
+    """
+    x = x + alpha * d_x
+    tau = tau + alpha * d_tau
+    z = z + alpha * d_z
+    kappa = kappa + alpha * d_kappa
+    y = y + alpha * d_y
+    return x, y, z, tau, kappa
+
+
+def _get_blind_start(shape):
+    """
+    Return the starting point from [4] 4.4
+
+    References
+    ----------
+    .. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
+           optimizer for linear programming: an implementation of the
+           homogeneous algorithm." High performance optimization. Springer US,
+           2000. 197-232.
+
+    """
+    m, n = shape
+    x0 = np.ones(n)
+    y0 = np.zeros(m)
+    z0 = np.ones(n)
+    tau0 = 1
+    kappa0 = 1
+    return x0, y0, z0, tau0, kappa0
+
+
+def _indicators(A, b, c, c0, x, y, z, tau, kappa):
+    """
+    Implementation of several equations from [4] used as indicators of
+    the status of optimization.
+
+    References
+    ----------
+    .. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
+           optimizer for linear programming: an implementation of the
+           homogeneous algorithm." High performance optimization. Springer US,
+           2000. 197-232.
+
+    """
+
+    # residuals for termination are relative to initial values
+    x0, y0, z0, tau0, kappa0 = _get_blind_start(A.shape)
+
+    # See [4], Section 4 - The Homogeneous Algorithm, Equation 8.8
+    def r_p(x, tau):
+        return b * tau - A.dot(x)
+
+    def r_d(y, z, tau):
+        return c * tau - A.T.dot(y) - z
+
+    def r_g(x, y, kappa):
+        return kappa + c.dot(x) - b.dot(y)
+
+    # np.dot unpacks if they are arrays of size one
+    def mu(x, tau, z, kappa):
+        return (x.dot(z) + np.dot(tau, kappa)) / (len(x) + 1)
+
+    obj = c.dot(x / tau) + c0
+
+    def norm(a):
+        return np.linalg.norm(a)
+
+    # See [4], Section 4.5 - The Stopping Criteria
+    r_p0 = r_p(x0, tau0)
+    r_d0 = r_d(y0, z0, tau0)
+    r_g0 = r_g(x0, y0, kappa0)
+    mu_0 = mu(x0, tau0, z0, kappa0)
+    rho_A = norm(c.T.dot(x) - b.T.dot(y)) / (tau + norm(b.T.dot(y)))
+    rho_p = norm(r_p(x, tau)) / max(1, norm(r_p0))
+    rho_d = norm(r_d(y, z, tau)) / max(1, norm(r_d0))
+    rho_g = norm(r_g(x, y, kappa)) / max(1, norm(r_g0))
+    rho_mu = mu(x, tau, z, kappa) / mu_0
+    return rho_p, rho_d, rho_A, rho_g, rho_mu, obj
+
+
+def _display_iter(rho_p, rho_d, rho_g, alpha, rho_mu, obj, header=False):
+    """
+    Print indicators of optimization status to the console.
+
+    Parameters
+    ----------
+    rho_p : float
+        The (normalized) primal feasibility, see [4] 4.5
+    rho_d : float
+        The (normalized) dual feasibility, see [4] 4.5
+    rho_g : float
+        The (normalized) duality gap, see [4] 4.5
+    alpha : float
+        The step size, see [4] 4.3
+    rho_mu : float
+        The (normalized) path parameter, see [4] 4.5
+    obj : float
+        The objective function value of the current iterate
+    header : bool
+        True if a header is to be printed
+
+    References
+    ----------
+    .. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
+           optimizer for linear programming: an implementation of the
+           homogeneous algorithm." High performance optimization. Springer US,
+           2000. 197-232.
+
+    """
+    if header:
+        print("Primal Feasibility ",
+              "Dual Feasibility   ",
+              "Duality Gap        ",
+              "Step            ",
+              "Path Parameter     ",
+              "Objective          ")
+
+    # no clue why this works
+    fmt = '{0:<20.13}{1:<20.13}{2:<20.13}{3:<17.13}{4:<20.13}{5:<20.13}'
+    print(fmt.format(
+        float(rho_p),
+        float(rho_d),
+        float(rho_g),
+        alpha if isinstance(alpha, str) else float(alpha),
+        float(rho_mu),
+        float(obj)))
+
+
+def _ip_hsd(A, b, c, c0, alpha0, beta, maxiter, disp, tol, sparse, lstsq,
+            sym_pos, cholesky, pc, ip, permc_spec, callback, postsolve_args):
+    r"""
+    Solve a linear programming problem in standard form:
+
+    Minimize::
+
+        c @ x
+
+    Subject to::
+
+        A @ x == b
+            x >= 0
+
+    using the interior point method of [4].
+
+    Parameters
+    ----------
+    A : 2-D array
+        2-D array such that ``A @ x``, gives the values of the equality
+        constraints at ``x``.
+    b : 1-D array
+        1-D array of values representing the RHS of each equality constraint
+        (row) in ``A`` (for standard form problem).
+    c : 1-D array
+        Coefficients of the linear objective function to be minimized (for
+        standard form problem).
+    c0 : float
+        Constant term in objective function due to fixed (and eliminated)
+        variables. (Purely for display.)
+    alpha0 : float
+        The maximal step size for Mehrota's predictor-corrector search
+        direction; see :math:`\beta_3`of [4] Table 8.1
+    beta : float
+        The desired reduction of the path parameter :math:`\mu` (see  [6]_)
+    maxiter : int
+        The maximum number of iterations of the algorithm.
+    disp : bool
+        Set to ``True`` if indicators of optimization status are to be printed
+        to the console each iteration.
+    tol : float
+        Termination tolerance; see [4]_ Section 4.5.
+    sparse : bool
+        Set to ``True`` if the problem is to be treated as sparse. However,
+        the inputs ``A_eq`` and ``A_ub`` should nonetheless be provided as
+        (dense) arrays rather than sparse matrices.
+    lstsq : bool
+        Set to ``True`` if the problem is expected to be very poorly
+        conditioned. This should always be left as ``False`` unless severe
+        numerical difficulties are frequently encountered, and a better option
+        would be to improve the formulation of the problem.
+    sym_pos : bool
+        Leave ``True`` if the problem is expected to yield a well conditioned
+        symmetric positive definite normal equation matrix (almost always).
+    cholesky : bool
+        Set to ``True`` if the normal equations are to be solved by explicit
+        Cholesky decomposition followed by explicit forward/backward
+        substitution. This is typically faster for moderate, dense problems
+        that are numerically well-behaved.
+    pc : bool
+        Leave ``True`` if the predictor-corrector method of Mehrota is to be
+        used. This is almost always (if not always) beneficial.
+    ip : bool
+        Set to ``True`` if the improved initial point suggestion due to [4]_
+        Section 4.3 is desired. It's unclear whether this is beneficial.
+    permc_spec : str (default = 'MMD_AT_PLUS_A')
+        (Has effect only with ``sparse = True``, ``lstsq = False``, ``sym_pos =
+        True``.) A matrix is factorized in each iteration of the algorithm.
+        This option specifies how to permute the columns of the matrix for
+        sparsity preservation. Acceptable values are:
+
+        - ``NATURAL``: natural ordering.
+        - ``MMD_ATA``: minimum degree ordering on the structure of A^T A.
+        - ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A.
+        - ``COLAMD``: approximate minimum degree column ordering.
+
+        This option can impact the convergence of the
+        interior point algorithm; test different values to determine which
+        performs best for your problem. For more information, refer to
+        ``scipy.sparse.linalg.splu``.
+    callback : callable, optional
+        If a callback function is provided, it will be called within each
+        iteration of the algorithm. The callback function must accept a single
+        `scipy.optimize.OptimizeResult` consisting of the following fields:
+
+            x : 1-D array
+                Current solution vector
+            fun : float
+                Current value of the objective function
+            success : bool
+                True only when an algorithm has completed successfully,
+                so this is always False as the callback function is called
+                only while the algorithm is still iterating.
+            slack : 1-D array
+                The values of the slack variables. Each slack variable
+                corresponds to an inequality constraint. If the slack is zero,
+                the corresponding constraint is active.
+            con : 1-D array
+                The (nominally zero) residuals of the equality constraints,
+                that is, ``b - A_eq @ x``
+            phase : int
+                The phase of the algorithm being executed. This is always
+                1 for the interior-point method because it has only one phase.
+            status : int
+                For revised simplex, this is always 0 because if a different
+                status is detected, the algorithm terminates.
+            nit : int
+                The number of iterations performed.
+            message : str
+                A string descriptor of the exit status of the optimization.
+    postsolve_args : tuple
+        Data needed by _postsolve to convert the solution to the standard-form
+        problem into the solution to the original problem.
+
+    Returns
+    -------
+    x_hat : float
+        Solution vector (for standard form problem).
+    status : int
+        An integer representing the exit status of the optimization::
+
+         0 : Optimization terminated successfully
+         1 : Iteration limit reached
+         2 : Problem appears to be infeasible
+         3 : Problem appears to be unbounded
+         4 : Serious numerical difficulties encountered
+
+    message : str
+        A string descriptor of the exit status of the optimization.
+    iteration : int
+        The number of iterations taken to solve the problem
+
+    References
+    ----------
+    .. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
+           optimizer for linear programming: an implementation of the
+           homogeneous algorithm." High performance optimization. Springer US,
+           2000. 197-232.
+    .. [6] Freund, Robert M. "Primal-Dual Interior-Point Methods for Linear
+           Programming based on Newton's Method." Unpublished Course Notes,
+           March 2004. Available 2/25/2017 at:
+           https://ocw.mit.edu/courses/sloan-school-of-management/15-084j-nonlinear-programming-spring-2004/lecture-notes/lec14_int_pt_mthd.pdf
+
+    """
+
+    iteration = 0
+
+    # default initial point
+    x, y, z, tau, kappa = _get_blind_start(A.shape)
+
+    # first iteration is special improvement of initial point
+    ip = ip if pc else False
+
+    # [4] 4.5
+    rho_p, rho_d, rho_A, rho_g, rho_mu, obj = _indicators(
+        A, b, c, c0, x, y, z, tau, kappa)
+    go = rho_p > tol or rho_d > tol or rho_A > tol  # we might get lucky : )
+
+    if disp:
+        _display_iter(rho_p, rho_d, rho_g, "-", rho_mu, obj, header=True)
+    if callback is not None:
+        x_o, fun, slack, con = _postsolve(x/tau, postsolve_args)
+        res = OptimizeResult({'x': x_o, 'fun': fun, 'slack': slack,
+                              'con': con, 'nit': iteration, 'phase': 1,
+                              'complete': False, 'status': 0,
+                              'message': "", 'success': False})
+        callback(res)
+
+    status = 0
+    message = "Optimization terminated successfully."
+
+    if sparse:
+        A = sps.csc_matrix(A)
+
+    while go:
+
+        iteration += 1
+
+        if ip:  # initial point
+            # [4] Section 4.4
+            gamma = 1
+
+            def eta(g):
+                return 1
+        else:
+            # gamma = 0 in predictor step according to [4] 4.1
+            # if predictor/corrector is off, use mean of complementarity [6]
+            # 5.1 / [4] Below Figure 10-4
+            gamma = 0 if pc else beta * np.mean(z * x)
+            # [4] Section 4.1
+
+            def eta(g=gamma):
+                return 1 - g
+
+        try:
+            # Solve [4] 8.6 and 8.7/8.13/8.23
+            d_x, d_y, d_z, d_tau, d_kappa = _get_delta(
+                A, b, c, x, y, z, tau, kappa, gamma, eta,
+                sparse, lstsq, sym_pos, cholesky, pc, ip, permc_spec)
+
+            if ip:  # initial point
+                # [4] 4.4
+                # Formula after 8.23 takes a full step regardless if this will
+                # take it negative
+                alpha = 1.0
+                x, y, z, tau, kappa = _do_step(
+                    x, y, z, tau, kappa, d_x, d_y,
+                    d_z, d_tau, d_kappa, alpha)
+                x[x < 1] = 1
+                z[z < 1] = 1
+                tau = max(1, tau)
+                kappa = max(1, kappa)
+                ip = False  # done with initial point
+            else:
+                # [4] Section 4.3
+                alpha = _get_step(x, d_x, z, d_z, tau,
+                                  d_tau, kappa, d_kappa, alpha0)
+                # [4] Equation 8.9
+                x, y, z, tau, kappa = _do_step(
+                    x, y, z, tau, kappa, d_x, d_y, d_z, d_tau, d_kappa, alpha)
+
+        except (LinAlgError, FloatingPointError,
+                ValueError, ZeroDivisionError):
+            # this can happen when sparse solver is used and presolve
+            # is turned off. Also observed ValueError in AppVeyor Python 3.6
+            # Win32 build (PR #8676). I've never seen it otherwise.
+            status = 4
+            message = _get_message(status)
+            break
+
+        # [4] 4.5
+        rho_p, rho_d, rho_A, rho_g, rho_mu, obj = _indicators(
+            A, b, c, c0, x, y, z, tau, kappa)
+        go = rho_p > tol or rho_d > tol or rho_A > tol
+
+        if disp:
+            _display_iter(rho_p, rho_d, rho_g, alpha, rho_mu, obj)
+        if callback is not None:
+            x_o, fun, slack, con = _postsolve(x/tau, postsolve_args)
+            res = OptimizeResult({'x': x_o, 'fun': fun, 'slack': slack,
+                                  'con': con, 'nit': iteration, 'phase': 1,
+                                  'complete': False, 'status': 0,
+                                  'message': "", 'success': False})
+            callback(res)
+
+        # [4] 4.5
+        inf1 = (rho_p < tol and rho_d < tol and rho_g < tol and tau < tol *
+                max(1, kappa))
+        inf2 = rho_mu < tol and tau < tol * min(1, kappa)
+        if inf1 or inf2:
+            # [4] Lemma 8.4 / Theorem 8.3
+            if b.transpose().dot(y) > tol:
+                status = 2
+            else:  # elif c.T.dot(x) < tol: ? Probably not necessary.
+                status = 3
+            message = _get_message(status)
+            break
+        elif iteration >= maxiter:
+            status = 1
+            message = _get_message(status)
+            break
+
+    x_hat = x / tau
+    # [4] Statement after Theorem 8.2
+    return x_hat, status, message, iteration
+
+
+def _linprog_ip(c, c0, A, b, callback, postsolve_args, maxiter=1000, tol=1e-8,
+                disp=False, alpha0=.99995, beta=0.1, sparse=False, lstsq=False,
+                sym_pos=True, cholesky=None, pc=True, ip=False,
+                permc_spec='MMD_AT_PLUS_A', **unknown_options):
+    r"""
+    Minimize a linear objective function subject to linear
+    equality and non-negativity constraints using the interior point method
+    of [4]_. Linear programming is intended to solve problems
+    of the following form:
+
+    Minimize::
+
+        c @ x
+
+    Subject to::
+
+        A @ x == b
+            x >= 0
+
+    User-facing documentation is in _linprog_doc.py.
+
+    Parameters
+    ----------
+    c : 1-D array
+        Coefficients of the linear objective function to be minimized.
+    c0 : float
+        Constant term in objective function due to fixed (and eliminated)
+        variables. (Purely for display.)
+    A : 2-D array
+        2-D array such that ``A @ x``, gives the values of the equality
+        constraints at ``x``.
+    b : 1-D array
+        1-D array of values representing the right hand side of each equality
+        constraint (row) in ``A``.
+    callback : callable, optional
+        Callback function to be executed once per iteration.
+    postsolve_args : tuple
+        Data needed by _postsolve to convert the solution to the standard-form
+        problem into the solution to the original problem.
+
+    Options
+    -------
+    maxiter : int (default = 1000)
+        The maximum number of iterations of the algorithm.
+    tol : float (default = 1e-8)
+        Termination tolerance to be used for all termination criteria;
+        see [4]_ Section 4.5.
+    disp : bool (default = False)
+        Set to ``True`` if indicators of optimization status are to be printed
+        to the console each iteration.
+    alpha0 : float (default = 0.99995)
+        The maximal step size for Mehrota's predictor-corrector search
+        direction; see :math:`\beta_{3}` of [4]_ Table 8.1.
+    beta : float (default = 0.1)
+        The desired reduction of the path parameter :math:`\mu` (see [6]_)
+        when Mehrota's predictor-corrector is not in use (uncommon).
+    sparse : bool (default = False)
+        Set to ``True`` if the problem is to be treated as sparse after
+        presolve. If either ``A_eq`` or ``A_ub`` is a sparse matrix,
+        this option will automatically be set ``True``, and the problem
+        will be treated as sparse even during presolve. If your constraint
+        matrices contain mostly zeros and the problem is not very small (less
+        than about 100 constraints or variables), consider setting ``True``
+        or providing ``A_eq`` and ``A_ub`` as sparse matrices.
+    lstsq : bool (default = False)
+        Set to ``True`` if the problem is expected to be very poorly
+        conditioned. This should always be left ``False`` unless severe
+        numerical difficulties are encountered. Leave this at the default
+        unless you receive a warning message suggesting otherwise.
+    sym_pos : bool (default = True)
+        Leave ``True`` if the problem is expected to yield a well conditioned
+        symmetric positive definite normal equation matrix
+        (almost always). Leave this at the default unless you receive
+        a warning message suggesting otherwise.
+    cholesky : bool (default = True)
+        Set to ``True`` if the normal equations are to be solved by explicit
+        Cholesky decomposition followed by explicit forward/backward
+        substitution. This is typically faster for problems
+        that are numerically well-behaved.
+    pc : bool (default = True)
+        Leave ``True`` if the predictor-corrector method of Mehrota is to be
+        used. This is almost always (if not always) beneficial.
+    ip : bool (default = False)
+        Set to ``True`` if the improved initial point suggestion due to [4]_
+        Section 4.3 is desired. Whether this is beneficial or not
+        depends on the problem.
+    permc_spec : str (default = 'MMD_AT_PLUS_A')
+        (Has effect only with ``sparse = True``, ``lstsq = False``, ``sym_pos =
+        True``, and no SuiteSparse.)
+        A matrix is factorized in each iteration of the algorithm.
+        This option specifies how to permute the columns of the matrix for
+        sparsity preservation. Acceptable values are:
+
+        - ``NATURAL``: natural ordering.
+        - ``MMD_ATA``: minimum degree ordering on the structure of A^T A.
+        - ``MMD_AT_PLUS_A``: minimum degree ordering on the structure of A^T+A.
+        - ``COLAMD``: approximate minimum degree column ordering.
+
+        This option can impact the convergence of the
+        interior point algorithm; test different values to determine which
+        performs best for your problem. For more information, refer to
+        ``scipy.sparse.linalg.splu``.
+    unknown_options : dict
+        Optional arguments not used by this particular solver. If
+        `unknown_options` is non-empty a warning is issued listing all
+        unused options.
+
+    Returns
+    -------
+    x : 1-D array
+        Solution vector.
+    status : int
+        An integer representing the exit status of the optimization::
+
+         0 : Optimization terminated successfully
+         1 : Iteration limit reached
+         2 : Problem appears to be infeasible
+         3 : Problem appears to be unbounded
+         4 : Serious numerical difficulties encountered
+
+    message : str
+        A string descriptor of the exit status of the optimization.
+    iteration : int
+        The number of iterations taken to solve the problem.
+
+    Notes
+    -----
+    This method implements the algorithm outlined in [4]_ with ideas from [8]_
+    and a structure inspired by the simpler methods of [6]_.
+
+    The primal-dual path following method begins with initial 'guesses' of
+    the primal and dual variables of the standard form problem and iteratively
+    attempts to solve the (nonlinear) Karush-Kuhn-Tucker conditions for the
+    problem with a gradually reduced logarithmic barrier term added to the
+    objective. This particular implementation uses a homogeneous self-dual
+    formulation, which provides certificates of infeasibility or unboundedness
+    where applicable.
+
+    The default initial point for the primal and dual variables is that
+    defined in [4]_ Section 4.4 Equation 8.22. Optionally (by setting initial
+    point option ``ip=True``), an alternate (potentially improved) starting
+    point can be calculated according to the additional recommendations of
+    [4]_ Section 4.4.
+
+    A search direction is calculated using the predictor-corrector method
+    (single correction) proposed by Mehrota and detailed in [4]_ Section 4.1.
+    (A potential improvement would be to implement the method of multiple
+    corrections described in [4]_ Section 4.2.) In practice, this is
+    accomplished by solving the normal equations, [4]_ Section 5.1 Equations
+    8.31 and 8.32, derived from the Newton equations [4]_ Section 5 Equations
+    8.25 (compare to [4]_ Section 4 Equations 8.6-8.8). The advantage of
+    solving the normal equations rather than 8.25 directly is that the
+    matrices involved are symmetric positive definite, so Cholesky
+    decomposition can be used rather than the more expensive LU factorization.
+
+    With default options, the solver used to perform the factorization depends
+    on third-party software availability and the conditioning of the problem.
+
+    For dense problems, solvers are tried in the following order:
+
+    1. ``scipy.linalg.cho_factor``
+
+    2. ``scipy.linalg.solve`` with option ``sym_pos=True``
+
+    3. ``scipy.linalg.solve`` with option ``sym_pos=False``
+
+    4. ``scipy.linalg.lstsq``
+
+    For sparse problems:
+
+    1. ``sksparse.cholmod.cholesky`` (if scikit-sparse and SuiteSparse are installed)
+
+    2. ``scipy.sparse.linalg.factorized``
+        (if scikit-umfpack and SuiteSparse are installed)
+
+    3. ``scipy.sparse.linalg.splu`` (which uses SuperLU distributed with SciPy)
+
+    4. ``scipy.sparse.linalg.lsqr``
+
+    If the solver fails for any reason, successively more robust (but slower)
+    solvers are attempted in the order indicated. Attempting, failing, and
+    re-starting factorization can be time consuming, so if the problem is
+    numerically challenging, options can be set to  bypass solvers that are
+    failing. Setting ``cholesky=False`` skips to solver 2,
+    ``sym_pos=False`` skips to solver 3, and ``lstsq=True`` skips
+    to solver 4 for both sparse and dense problems.
+
+    Potential improvements for combatting issues associated with dense
+    columns in otherwise sparse problems are outlined in [4]_ Section 5.3 and
+    [10]_ Section 4.1-4.2; the latter also discusses the alleviation of
+    accuracy issues associated with the substitution approach to free
+    variables.
+
+    After calculating the search direction, the maximum possible step size
+    that does not activate the non-negativity constraints is calculated, and
+    the smaller of this step size and unity is applied (as in [4]_ Section
+    4.1.) [4]_ Section 4.3 suggests improvements for choosing the step size.
+
+    The new point is tested according to the termination conditions of [4]_
+    Section 4.5. The same tolerance, which can be set using the ``tol`` option,
+    is used for all checks. (A potential improvement would be to expose
+    the different tolerances to be set independently.) If optimality,
+    unboundedness, or infeasibility is detected, the solve procedure
+    terminates; otherwise it repeats.
+
+    The expected problem formulation differs between the top level ``linprog``
+    module and the method specific solvers. The method specific solvers expect a
+    problem in standard form:
+
+    Minimize::
+
+        c @ x
+
+    Subject to::
+
+        A @ x == b
+            x >= 0
+
+    Whereas the top level ``linprog`` module expects a problem of form:
+
+    Minimize::
+
+        c @ x
+
+    Subject to::
+
+        A_ub @ x <= b_ub
+        A_eq @ x == b_eq
+         lb <= x <= ub
+
+    where ``lb = 0`` and ``ub = None`` unless set in ``bounds``.
+
+    The original problem contains equality, upper-bound and variable constraints
+    whereas the method specific solver requires equality constraints and
+    variable non-negativity.
+
+    ``linprog`` module converts the original problem to standard form by
+    converting the simple bounds to upper bound constraints, introducing
+    non-negative slack variables for inequality constraints, and expressing
+    unbounded variables as the difference between two non-negative variables.
+
+
+    References
+    ----------
+    .. [4] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
+           optimizer for linear programming: an implementation of the
+           homogeneous algorithm." High performance optimization. Springer US,
+           2000. 197-232.
+    .. [6] Freund, Robert M. "Primal-Dual Interior-Point Methods for Linear
+           Programming based on Newton's Method." Unpublished Course Notes,
+           March 2004. Available 2/25/2017 at
+           https://ocw.mit.edu/courses/sloan-school-of-management/15-084j-nonlinear-programming-spring-2004/lecture-notes/lec14_int_pt_mthd.pdf
+    .. [8] Andersen, Erling D., and Knud D. Andersen. "Presolving in linear
+           programming." Mathematical Programming 71.2 (1995): 221-245.
+    .. [9] Bertsimas, Dimitris, and J. Tsitsiklis. "Introduction to linear
+           programming." Athena Scientific 1 (1997): 997.
+    .. [10] Andersen, Erling D., et al. Implementation of interior point methods
+            for large scale linear programming. HEC/Universite de Geneve, 1996.
+
+    """
+
+    _check_unknown_options(unknown_options)
+
+    # These should be warnings, not errors
+    if (cholesky or cholesky is None) and sparse and not has_cholmod:
+        if cholesky:
+            warn("Sparse cholesky is only available with scikit-sparse. "
+                 "Setting `cholesky = False`",
+                 OptimizeWarning, stacklevel=3)
+        cholesky = False
+
+    if sparse and lstsq:
+        warn("Option combination 'sparse':True and 'lstsq':True "
+             "is not recommended.",
+             OptimizeWarning, stacklevel=3)
+
+    if lstsq and cholesky:
+        warn("Invalid option combination 'lstsq':True "
+             "and 'cholesky':True; option 'cholesky' has no effect when "
+             "'lstsq' is set True.",
+             OptimizeWarning, stacklevel=3)
+
+    valid_permc_spec = ('NATURAL', 'MMD_ATA', 'MMD_AT_PLUS_A', 'COLAMD')
+    if permc_spec.upper() not in valid_permc_spec:
+        warn("Invalid permc_spec option: '" + str(permc_spec) + "'. "
+             "Acceptable values are 'NATURAL', 'MMD_ATA', 'MMD_AT_PLUS_A', "
+             "and 'COLAMD'. Reverting to default.",
+             OptimizeWarning, stacklevel=3)
+        permc_spec = 'MMD_AT_PLUS_A'
+
+    # This can be an error
+    if not sym_pos and cholesky:
+        raise ValueError(
+            "Invalid option combination 'sym_pos':False "
+            "and 'cholesky':True: Cholesky decomposition is only possible "
+            "for symmetric positive definite matrices.")
+
+    cholesky = cholesky or (cholesky is None and sym_pos and not lstsq)
+
+    x, status, message, iteration = _ip_hsd(A, b, c, c0, alpha0, beta,
+                                            maxiter, disp, tol, sparse,
+                                            lstsq, sym_pos, cholesky,
+                                            pc, ip, permc_spec, callback,
+                                            postsolve_args)
+
+    return x, status, message, iteration

llava_next/lib/python3.10/site-packages/scipy/optimize/_linprog_simplex.py

@@ -0,0 +1,661 @@
+"""Simplex method for  linear programming
+
+The *simplex* method uses a traditional, full-tableau implementation of
+Dantzig's simplex algorithm [1]_, [2]_ (*not* the Nelder-Mead simplex).
+This algorithm is included for backwards compatibility and educational
+purposes.
+
+    .. versionadded:: 0.15.0
+
+Warnings
+--------
+
+The simplex method may encounter numerical difficulties when pivot
+values are close to the specified tolerance. If encountered try
+remove any redundant constraints, change the pivot strategy to Bland's
+rule or increase the tolerance value.
+
+Alternatively, more robust methods maybe be used. See
+:ref:`'interior-point' <optimize.linprog-interior-point>` and
+:ref:`'revised simplex' <optimize.linprog-revised_simplex>`.
+
+References
+----------
+.. [1] Dantzig, George B., Linear programming and extensions. Rand
+       Corporation Research Study Princeton Univ. Press, Princeton, NJ,
+       1963
+.. [2] Hillier, S.H. and Lieberman, G.J. (1995), "Introduction to
+       Mathematical Programming", McGraw-Hill, Chapter 4.
+"""
+
+import numpy as np
+from warnings import warn
+from ._optimize import OptimizeResult, OptimizeWarning, _check_unknown_options
+from ._linprog_util import _postsolve
+
+
+def _pivot_col(T, tol=1e-9, bland=False):
+    """
+    Given a linear programming simplex tableau, determine the column
+    of the variable to enter the basis.
+
+    Parameters
+    ----------
+    T : 2-D array
+        A 2-D array representing the simplex tableau, T, corresponding to the
+        linear programming problem. It should have the form:
+
+        [[A[0, 0], A[0, 1], ..., A[0, n_total], b[0]],
+         [A[1, 0], A[1, 1], ..., A[1, n_total], b[1]],
+         .
+         .
+         .
+         [A[m, 0], A[m, 1], ..., A[m, n_total], b[m]],
+         [c[0],   c[1], ...,   c[n_total],    0]]
+
+        for a Phase 2 problem, or the form:
+
+        [[A[0, 0], A[0, 1], ..., A[0, n_total], b[0]],
+         [A[1, 0], A[1, 1], ..., A[1, n_total], b[1]],
+         .
+         .
+         .
+         [A[m, 0], A[m, 1], ..., A[m, n_total], b[m]],
+         [c[0],   c[1], ...,   c[n_total],   0],
+         [c'[0],  c'[1], ...,  c'[n_total],  0]]
+
+         for a Phase 1 problem (a problem in which a basic feasible solution is
+         sought prior to maximizing the actual objective. ``T`` is modified in
+         place by ``_solve_simplex``.
+    tol : float
+        Elements in the objective row larger than -tol will not be considered
+        for pivoting. Nominally this value is zero, but numerical issues
+        cause a tolerance about zero to be necessary.
+    bland : bool
+        If True, use Bland's rule for selection of the column (select the
+        first column with a negative coefficient in the objective row,
+        regardless of magnitude).
+
+    Returns
+    -------
+    status: bool
+        True if a suitable pivot column was found, otherwise False.
+        A return of False indicates that the linear programming simplex
+        algorithm is complete.
+    col: int
+        The index of the column of the pivot element.
+        If status is False, col will be returned as nan.
+    """
+    ma = np.ma.masked_where(T[-1, :-1] >= -tol, T[-1, :-1], copy=False)
+    if ma.count() == 0:
+        return False, np.nan
+    if bland:
+        # ma.mask is sometimes 0d
+        return True, np.nonzero(np.logical_not(np.atleast_1d(ma.mask)))[0][0]
+    return True, np.ma.nonzero(ma == ma.min())[0][0]
+
+
+def _pivot_row(T, basis, pivcol, phase, tol=1e-9, bland=False):
+    """
+    Given a linear programming simplex tableau, determine the row for the
+    pivot operation.
+
+    Parameters
+    ----------
+    T : 2-D array
+        A 2-D array representing the simplex tableau, T, corresponding to the
+        linear programming problem. It should have the form:
+
+        [[A[0, 0], A[0, 1], ..., A[0, n_total], b[0]],
+         [A[1, 0], A[1, 1], ..., A[1, n_total], b[1]],
+         .
+         .
+         .
+         [A[m, 0], A[m, 1], ..., A[m, n_total], b[m]],
+         [c[0],   c[1], ...,   c[n_total],    0]]
+
+        for a Phase 2 problem, or the form:
+
+        [[A[0, 0], A[0, 1], ..., A[0, n_total], b[0]],
+         [A[1, 0], A[1, 1], ..., A[1, n_total], b[1]],
+         .
+         .
+         .
+         [A[m, 0], A[m, 1], ..., A[m, n_total], b[m]],
+         [c[0],   c[1], ...,   c[n_total],   0],
+         [c'[0],  c'[1], ...,  c'[n_total],  0]]
+
+         for a Phase 1 problem (a Problem in which a basic feasible solution is
+         sought prior to maximizing the actual objective. ``T`` is modified in
+         place by ``_solve_simplex``.
+    basis : array
+        A list of the current basic variables.
+    pivcol : int
+        The index of the pivot column.
+    phase : int
+        The phase of the simplex algorithm (1 or 2).
+    tol : float
+        Elements in the pivot column smaller than tol will not be considered
+        for pivoting. Nominally this value is zero, but numerical issues
+        cause a tolerance about zero to be necessary.
+    bland : bool
+        If True, use Bland's rule for selection of the row (if more than one
+        row can be used, choose the one with the lowest variable index).
+
+    Returns
+    -------
+    status: bool
+        True if a suitable pivot row was found, otherwise False. A return
+        of False indicates that the linear programming problem is unbounded.
+    row: int
+        The index of the row of the pivot element. If status is False, row
+        will be returned as nan.
+    """
+    if phase == 1:
+        k = 2
+    else:
+        k = 1
+    ma = np.ma.masked_where(T[:-k, pivcol] <= tol, T[:-k, pivcol], copy=False)
+    if ma.count() == 0:
+        return False, np.nan
+    mb = np.ma.masked_where(T[:-k, pivcol] <= tol, T[:-k, -1], copy=False)
+    q = mb / ma
+    min_rows = np.ma.nonzero(q == q.min())[0]
+    if bland:
+        return True, min_rows[np.argmin(np.take(basis, min_rows))]
+    return True, min_rows[0]
+
+
+def _apply_pivot(T, basis, pivrow, pivcol, tol=1e-9):
+    """
+    Pivot the simplex tableau inplace on the element given by (pivrow, pivol).
+    The entering variable corresponds to the column given by pivcol forcing
+    the variable basis[pivrow] to leave the basis.
+
+    Parameters
+    ----------
+    T : 2-D array
+        A 2-D array representing the simplex tableau, T, corresponding to the
+        linear programming problem. It should have the form:
+
+        [[A[0, 0], A[0, 1], ..., A[0, n_total], b[0]],
+         [A[1, 0], A[1, 1], ..., A[1, n_total], b[1]],
+         .
+         .
+         .
+         [A[m, 0], A[m, 1], ..., A[m, n_total], b[m]],
+         [c[0],   c[1], ...,   c[n_total],    0]]
+
+        for a Phase 2 problem, or the form:
+
+        [[A[0, 0], A[0, 1], ..., A[0, n_total], b[0]],
+         [A[1, 0], A[1, 1], ..., A[1, n_total], b[1]],
+         .
+         .
+         .
+         [A[m, 0], A[m, 1], ..., A[m, n_total], b[m]],
+         [c[0],   c[1], ...,   c[n_total],   0],
+         [c'[0],  c'[1], ...,  c'[n_total],  0]]
+
+         for a Phase 1 problem (a problem in which a basic feasible solution is
+         sought prior to maximizing the actual objective. ``T`` is modified in
+         place by ``_solve_simplex``.
+    basis : 1-D array
+        An array of the indices of the basic variables, such that basis[i]
+        contains the column corresponding to the basic variable for row i.
+        Basis is modified in place by _apply_pivot.
+    pivrow : int
+        Row index of the pivot.
+    pivcol : int
+        Column index of the pivot.
+    """
+    basis[pivrow] = pivcol
+    pivval = T[pivrow, pivcol]
+    T[pivrow] = T[pivrow] / pivval
+    for irow in range(T.shape[0]):
+        if irow != pivrow:
+            T[irow] = T[irow] - T[pivrow] * T[irow, pivcol]
+
+    # The selected pivot should never lead to a pivot value less than the tol.
+    if np.isclose(pivval, tol, atol=0, rtol=1e4):
+        message = (
+            f"The pivot operation produces a pivot value of:{pivval: .1e}, "
+            "which is only slightly greater than the specified "
+            f"tolerance{tol: .1e}. This may lead to issues regarding the "
+            "numerical stability of the simplex method. "
+            "Removing redundant constraints, changing the pivot strategy "
+            "via Bland's rule or increasing the tolerance may "
+            "help reduce the issue.")
+        warn(message, OptimizeWarning, stacklevel=5)
+
+
+def _solve_simplex(T, n, basis, callback, postsolve_args,
+                   maxiter=1000, tol=1e-9, phase=2, bland=False, nit0=0,
+                   ):
+    """
+    Solve a linear programming problem in "standard form" using the Simplex
+    Method. Linear Programming is intended to solve the following problem form:
+
+    Minimize::
+
+        c @ x
+
+    Subject to::
+
+        A @ x == b
+            x >= 0
+
+    Parameters
+    ----------
+    T : 2-D array
+        A 2-D array representing the simplex tableau, T, corresponding to the
+        linear programming problem. It should have the form:
+
+        [[A[0, 0], A[0, 1], ..., A[0, n_total], b[0]],
+         [A[1, 0], A[1, 1], ..., A[1, n_total], b[1]],
+         .
+         .
+         .
+         [A[m, 0], A[m, 1], ..., A[m, n_total], b[m]],
+         [c[0],   c[1], ...,   c[n_total],    0]]
+
+        for a Phase 2 problem, or the form:
+
+        [[A[0, 0], A[0, 1], ..., A[0, n_total], b[0]],
+         [A[1, 0], A[1, 1], ..., A[1, n_total], b[1]],
+         .
+         .
+         .
+         [A[m, 0], A[m, 1], ..., A[m, n_total], b[m]],
+         [c[0],   c[1], ...,   c[n_total],   0],
+         [c'[0],  c'[1], ...,  c'[n_total],  0]]
+
+         for a Phase 1 problem (a problem in which a basic feasible solution is
+         sought prior to maximizing the actual objective. ``T`` is modified in
+         place by ``_solve_simplex``.
+    n : int
+        The number of true variables in the problem.
+    basis : 1-D array
+        An array of the indices of the basic variables, such that basis[i]
+        contains the column corresponding to the basic variable for row i.
+        Basis is modified in place by _solve_simplex
+    callback : callable, optional
+        If a callback function is provided, it will be called within each
+        iteration of the algorithm. The callback must accept a
+        `scipy.optimize.OptimizeResult` consisting of the following fields:
+
+            x : 1-D array
+                Current solution vector
+            fun : float
+                Current value of the objective function
+            success : bool
+                True only when a phase has completed successfully. This
+                will be False for most iterations.
+            slack : 1-D array
+                The values of the slack variables. Each slack variable
+                corresponds to an inequality constraint. If the slack is zero,
+                the corresponding constraint is active.
+            con : 1-D array
+                The (nominally zero) residuals of the equality constraints,
+                that is, ``b - A_eq @ x``
+            phase : int
+                The phase of the optimization being executed. In phase 1 a basic
+                feasible solution is sought and the T has an additional row
+                representing an alternate objective function.
+            status : int
+                An integer representing the exit status of the optimization::
+
+                     0 : Optimization terminated successfully
+                     1 : Iteration limit reached
+                     2 : Problem appears to be infeasible
+                     3 : Problem appears to be unbounded
+                     4 : Serious numerical difficulties encountered
+
+            nit : int
+                The number of iterations performed.
+            message : str
+                A string descriptor of the exit status of the optimization.
+    postsolve_args : tuple
+        Data needed by _postsolve to convert the solution to the standard-form
+        problem into the solution to the original problem.
+    maxiter : int
+        The maximum number of iterations to perform before aborting the
+        optimization.
+    tol : float
+        The tolerance which determines when a solution is "close enough" to
+        zero in Phase 1 to be considered a basic feasible solution or close
+        enough to positive to serve as an optimal solution.
+    phase : int
+        The phase of the optimization being executed. In phase 1 a basic
+        feasible solution is sought and the T has an additional row
+        representing an alternate objective function.
+    bland : bool
+        If True, choose pivots using Bland's rule [3]_. In problems which
+        fail to converge due to cycling, using Bland's rule can provide
+        convergence at the expense of a less optimal path about the simplex.
+    nit0 : int
+        The initial iteration number used to keep an accurate iteration total
+        in a two-phase problem.
+
+    Returns
+    -------
+    nit : int
+        The number of iterations. Used to keep an accurate iteration total
+        in the two-phase problem.
+    status : int
+        An integer representing the exit status of the optimization::
+
+         0 : Optimization terminated successfully
+         1 : Iteration limit reached
+         2 : Problem appears to be infeasible
+         3 : Problem appears to be unbounded
+         4 : Serious numerical difficulties encountered
+
+    """
+    nit = nit0
+    status = 0
+    message = ''
+    complete = False
+
+    if phase == 1:
+        m = T.shape[1]-2
+    elif phase == 2:
+        m = T.shape[1]-1
+    else:
+        raise ValueError("Argument 'phase' to _solve_simplex must be 1 or 2")
+
+    if phase == 2:
+        # Check if any artificial variables are still in the basis.
+        # If yes, check if any coefficients from this row and a column
+        # corresponding to one of the non-artificial variable is non-zero.
+        # If found, pivot at this term. If not, start phase 2.
+        # Do this for all artificial variables in the basis.
+        # Ref: "An Introduction to Linear Programming and Game Theory"
+        # by Paul R. Thie, Gerard E. Keough, 3rd Ed,
+        # Chapter 3.7 Redundant Systems (pag 102)
+        for pivrow in [row for row in range(basis.size)
+                       if basis[row] > T.shape[1] - 2]:
+            non_zero_row = [col for col in range(T.shape[1] - 1)
+                            if abs(T[pivrow, col]) > tol]
+            if len(non_zero_row) > 0:
+                pivcol = non_zero_row[0]
+                _apply_pivot(T, basis, pivrow, pivcol, tol)
+                nit += 1
+
+    if len(basis[:m]) == 0:
+        solution = np.empty(T.shape[1] - 1, dtype=np.float64)
+    else:
+        solution = np.empty(max(T.shape[1] - 1, max(basis[:m]) + 1),
+                            dtype=np.float64)
+
+    while not complete:
+        # Find the pivot column
+        pivcol_found, pivcol = _pivot_col(T, tol, bland)
+        if not pivcol_found:
+            pivcol = np.nan
+            pivrow = np.nan
+            status = 0
+            complete = True
+        else:
+            # Find the pivot row
+            pivrow_found, pivrow = _pivot_row(T, basis, pivcol, phase, tol, bland)
+            if not pivrow_found:
+                status = 3
+                complete = True
+
+        if callback is not None:
+            solution[:] = 0
+            solution[basis[:n]] = T[:n, -1]
+            x = solution[:m]
+            x, fun, slack, con = _postsolve(
+                x, postsolve_args
+            )
+            res = OptimizeResult({
+                'x': x,
+                'fun': fun,
+                'slack': slack,
+                'con': con,
+                'status': status,
+                'message': message,
+                'nit': nit,
+                'success': status == 0 and complete,
+                'phase': phase,
+                'complete': complete,
+                })
+            callback(res)
+
+        if not complete:
+            if nit >= maxiter:
+                # Iteration limit exceeded
+                status = 1
+                complete = True
+            else:
+                _apply_pivot(T, basis, pivrow, pivcol, tol)
+                nit += 1
+    return nit, status
+
+
+def _linprog_simplex(c, c0, A, b, callback, postsolve_args,
+                     maxiter=1000, tol=1e-9, disp=False, bland=False,
+                     **unknown_options):
+    """
+    Minimize a linear objective function subject to linear equality and
+    non-negativity constraints using the two phase simplex method.
+    Linear programming is intended to solve problems of the following form:
+
+    Minimize::
+
+        c @ x
+
+    Subject to::
+
+        A @ x == b
+            x >= 0
+
+    User-facing documentation is in _linprog_doc.py.
+
+    Parameters
+    ----------
+    c : 1-D array
+        Coefficients of the linear objective function to be minimized.
+    c0 : float
+        Constant term in objective function due to fixed (and eliminated)
+        variables. (Purely for display.)
+    A : 2-D array
+        2-D array such that ``A @ x``, gives the values of the equality
+        constraints at ``x``.
+    b : 1-D array
+        1-D array of values representing the right hand side of each equality
+        constraint (row) in ``A``.
+    callback : callable, optional
+        If a callback function is provided, it will be called within each
+        iteration of the algorithm. The callback function must accept a single
+        `scipy.optimize.OptimizeResult` consisting of the following fields:
+
+            x : 1-D array
+                Current solution vector
+            fun : float
+                Current value of the objective function
+            success : bool
+                True when an algorithm has completed successfully.
+            slack : 1-D array
+                The values of the slack variables. Each slack variable
+                corresponds to an inequality constraint. If the slack is zero,
+                the corresponding constraint is active.
+            con : 1-D array
+                The (nominally zero) residuals of the equality constraints,
+                that is, ``b - A_eq @ x``
+            phase : int
+                The phase of the algorithm being executed.
+            status : int
+                An integer representing the status of the optimization::
+
+                     0 : Algorithm proceeding nominally
+                     1 : Iteration limit reached
+                     2 : Problem appears to be infeasible
+                     3 : Problem appears to be unbounded
+                     4 : Serious numerical difficulties encountered
+            nit : int
+                The number of iterations performed.
+            message : str
+                A string descriptor of the exit status of the optimization.
+    postsolve_args : tuple
+        Data needed by _postsolve to convert the solution to the standard-form
+        problem into the solution to the original problem.
+
+    Options
+    -------
+    maxiter : int
+       The maximum number of iterations to perform.
+    disp : bool
+        If True, print exit status message to sys.stdout
+    tol : float
+        The tolerance which determines when a solution is "close enough" to
+        zero in Phase 1 to be considered a basic feasible solution or close
+        enough to positive to serve as an optimal solution.
+    bland : bool
+        If True, use Bland's anti-cycling rule [3]_ to choose pivots to
+        prevent cycling. If False, choose pivots which should lead to a
+        converged solution more quickly. The latter method is subject to
+        cycling (non-convergence) in rare instances.
+    unknown_options : dict
+        Optional arguments not used by this particular solver. If
+        `unknown_options` is non-empty a warning is issued listing all
+        unused options.
+
+    Returns
+    -------
+    x : 1-D array
+        Solution vector.
+    status : int
+        An integer representing the exit status of the optimization::
+
+         0 : Optimization terminated successfully
+         1 : Iteration limit reached
+         2 : Problem appears to be infeasible
+         3 : Problem appears to be unbounded
+         4 : Serious numerical difficulties encountered
+
+    message : str
+        A string descriptor of the exit status of the optimization.
+    iteration : int
+        The number of iterations taken to solve the problem.
+
+    References
+    ----------
+    .. [1] Dantzig, George B., Linear programming and extensions. Rand
+           Corporation Research Study Princeton Univ. Press, Princeton, NJ,
+           1963
+    .. [2] Hillier, S.H. and Lieberman, G.J. (1995), "Introduction to
+           Mathematical Programming", McGraw-Hill, Chapter 4.
+    .. [3] Bland, Robert G. New finite pivoting rules for the simplex method.
+           Mathematics of Operations Research (2), 1977: pp. 103-107.
+
+
+    Notes
+    -----
+    The expected problem formulation differs between the top level ``linprog``
+    module and the method specific solvers. The method specific solvers expect a
+    problem in standard form:
+
+    Minimize::
+
+        c @ x
+
+    Subject to::
+
+        A @ x == b
+            x >= 0
+
+    Whereas the top level ``linprog`` module expects a problem of form:
+
+    Minimize::
+
+        c @ x
+
+    Subject to::
+
+        A_ub @ x <= b_ub
+        A_eq @ x == b_eq
+         lb <= x <= ub
+
+    where ``lb = 0`` and ``ub = None`` unless set in ``bounds``.
+
+    The original problem contains equality, upper-bound and variable constraints
+    whereas the method specific solver requires equality constraints and
+    variable non-negativity.
+
+    ``linprog`` module converts the original problem to standard form by
+    converting the simple bounds to upper bound constraints, introducing
+    non-negative slack variables for inequality constraints, and expressing
+    unbounded variables as the difference between two non-negative variables.
+    """
+    _check_unknown_options(unknown_options)
+
+    status = 0
+    messages = {0: "Optimization terminated successfully.",
+                1: "Iteration limit reached.",
+                2: "Optimization failed. Unable to find a feasible"
+                   " starting point.",
+                3: "Optimization failed. The problem appears to be unbounded.",
+                4: "Optimization failed. Singular matrix encountered."}
+
+    n, m = A.shape
+
+    # All constraints must have b >= 0.
+    is_negative_constraint = np.less(b, 0)
+    A[is_negative_constraint] *= -1
+    b[is_negative_constraint] *= -1
+
+    # As all constraints are equality constraints the artificial variables
+    # will also be basic variables.
+    av = np.arange(n) + m
+    basis = av.copy()
+
+    # Format the phase one tableau by adding artificial variables and stacking
+    # the constraints, the objective row and pseudo-objective row.
+    row_constraints = np.hstack((A, np.eye(n), b[:, np.newaxis]))
+    row_objective = np.hstack((c, np.zeros(n), c0))
+    row_pseudo_objective = -row_constraints.sum(axis=0)
+    row_pseudo_objective[av] = 0
+    T = np.vstack((row_constraints, row_objective, row_pseudo_objective))
+
+    nit1, status = _solve_simplex(T, n, basis, callback=callback,
+                                  postsolve_args=postsolve_args,
+                                  maxiter=maxiter, tol=tol, phase=1,
+                                  bland=bland
+                                  )
+    # if pseudo objective is zero, remove the last row from the tableau and
+    # proceed to phase 2
+    nit2 = nit1
+    if abs(T[-1, -1]) < tol:
+        # Remove the pseudo-objective row from the tableau
+        T = T[:-1, :]
+        # Remove the artificial variable columns from the tableau
+        T = np.delete(T, av, 1)
+    else:
+        # Failure to find a feasible starting point
+        status = 2
+        messages[status] = (
+            "Phase 1 of the simplex method failed to find a feasible "
+            "solution. The pseudo-objective function evaluates to {0:.1e} "
+            "which exceeds the required tolerance of {1} for a solution to be "
+            "considered 'close enough' to zero to be a basic solution. "
+            "Consider increasing the tolerance to be greater than {0:.1e}. "
+            "If this tolerance is unacceptably  large the problem may be "
+            "infeasible.".format(abs(T[-1, -1]), tol)
+        )
+
+    if status == 0:
+        # Phase 2
+        nit2, status = _solve_simplex(T, n, basis, callback=callback,
+                                      postsolve_args=postsolve_args,
+                                      maxiter=maxiter, tol=tol, phase=2,
+                                      bland=bland, nit0=nit1
+                                      )
+
+    solution = np.zeros(n + m)
+    solution[basis[:n]] = T[:n, -1]
+    x = solution[:m]
+
+    return x, status, messages[status], int(nit2)

llava_next/lib/python3.10/site-packages/scipy/optimize/_minimize.py

@@ -0,0 +1,1116 @@
+"""
+Unified interfaces to minimization algorithms.
+
+Functions
+---------
+- minimize : minimization of a function of several variables.
+- minimize_scalar : minimization of a function of one variable.
+"""
+
+__all__ = ['minimize', 'minimize_scalar']
+
+
+from warnings import warn
+
+import numpy as np
+
+# unconstrained minimization
+from ._optimize import (_minimize_neldermead, _minimize_powell, _minimize_cg,
+                        _minimize_bfgs, _minimize_newtoncg,
+                        _minimize_scalar_brent, _minimize_scalar_bounded,
+                        _minimize_scalar_golden, MemoizeJac, OptimizeResult,
+                        _wrap_callback, _recover_from_bracket_error)
+from ._trustregion_dogleg import _minimize_dogleg
+from ._trustregion_ncg import _minimize_trust_ncg
+from ._trustregion_krylov import _minimize_trust_krylov
+from ._trustregion_exact import _minimize_trustregion_exact
+from ._trustregion_constr import _minimize_trustregion_constr
+
+# constrained minimization
+from ._lbfgsb_py import _minimize_lbfgsb
+from ._tnc import _minimize_tnc
+from ._cobyla_py import _minimize_cobyla
+from ._cobyqa_py import _minimize_cobyqa
+from ._slsqp_py import _minimize_slsqp
+from ._constraints import (old_bound_to_new, new_bounds_to_old,
+                           old_constraint_to_new, new_constraint_to_old,
+                           NonlinearConstraint, LinearConstraint, Bounds,
+                           PreparedConstraint)
+from ._differentiable_functions import FD_METHODS
+
+MINIMIZE_METHODS = ['nelder-mead', 'powell', 'cg', 'bfgs', 'newton-cg',
+                    'l-bfgs-b', 'tnc', 'cobyla', 'cobyqa', 'slsqp',
+                    'trust-constr', 'dogleg', 'trust-ncg', 'trust-exact',
+                    'trust-krylov']
+
+# These methods support the new callback interface (passed an OptimizeResult)
+MINIMIZE_METHODS_NEW_CB = ['nelder-mead', 'powell', 'cg', 'bfgs', 'newton-cg',
+                           'l-bfgs-b', 'trust-constr', 'dogleg', 'trust-ncg',
+                           'trust-exact', 'trust-krylov', 'cobyqa']
+
+MINIMIZE_SCALAR_METHODS = ['brent', 'bounded', 'golden']
+
+def minimize(fun, x0, args=(), method=None, jac=None, hess=None,
+             hessp=None, bounds=None, constraints=(), tol=None,
+             callback=None, options=None):
+    """Minimization of scalar function of one or more variables.
+
+    Parameters
+    ----------
+    fun : callable
+        The objective function to be minimized.
+
+            ``fun(x, *args) -> float``
+
+        where ``x`` is a 1-D array with shape (n,) and ``args``
+        is a tuple of the fixed parameters needed to completely
+        specify the function.
+    x0 : ndarray, shape (n,)
+        Initial guess. Array of real elements of size (n,),
+        where ``n`` is the number of independent variables.
+    args : tuple, optional
+        Extra arguments passed to the objective function and its
+        derivatives (`fun`, `jac` and `hess` functions).
+    method : str or callable, optional
+        Type of solver.  Should be one of
+
+            - 'Nelder-Mead' :ref:`(see here) <optimize.minimize-neldermead>`
+            - 'Powell'      :ref:`(see here) <optimize.minimize-powell>`
+            - 'CG'          :ref:`(see here) <optimize.minimize-cg>`
+            - 'BFGS'        :ref:`(see here) <optimize.minimize-bfgs>`
+            - 'Newton-CG'   :ref:`(see here) <optimize.minimize-newtoncg>`
+            - 'L-BFGS-B'    :ref:`(see here) <optimize.minimize-lbfgsb>`
+            - 'TNC'         :ref:`(see here) <optimize.minimize-tnc>`
+            - 'COBYLA'      :ref:`(see here) <optimize.minimize-cobyla>`
+            - 'COBYQA'      :ref:`(see here) <optimize.minimize-cobyqa>`
+            - 'SLSQP'       :ref:`(see here) <optimize.minimize-slsqp>`
+            - 'trust-constr':ref:`(see here) <optimize.minimize-trustconstr>`
+            - 'dogleg'      :ref:`(see here) <optimize.minimize-dogleg>`
+            - 'trust-ncg'   :ref:`(see here) <optimize.minimize-trustncg>`
+            - 'trust-exact' :ref:`(see here) <optimize.minimize-trustexact>`
+            - 'trust-krylov' :ref:`(see here) <optimize.minimize-trustkrylov>`
+            - custom - a callable object, see below for description.
+
+        If not given, chosen to be one of ``BFGS``, ``L-BFGS-B``, ``SLSQP``,
+        depending on whether or not the problem has constraints or bounds.
+    jac : {callable,  '2-point', '3-point', 'cs', bool}, optional
+        Method for computing the gradient vector. Only for CG, BFGS,
+        Newton-CG, L-BFGS-B, TNC, SLSQP, dogleg, trust-ncg, trust-krylov,
+        trust-exact and trust-constr.
+        If it is a callable, it should be a function that returns the gradient
+        vector:
+
+            ``jac(x, *args) -> array_like, shape (n,)``
+
+        where ``x`` is an array with shape (n,) and ``args`` is a tuple with
+        the fixed parameters. If `jac` is a Boolean and is True, `fun` is
+        assumed to return a tuple ``(f, g)`` containing the objective
+        function and the gradient.
+        Methods 'Newton-CG', 'trust-ncg', 'dogleg', 'trust-exact', and
+        'trust-krylov' require that either a callable be supplied, or that
+        `fun` return the objective and gradient.
+        If None or False, the gradient will be estimated using 2-point finite
+        difference estimation with an absolute step size.
+        Alternatively, the keywords  {'2-point', '3-point', 'cs'} can be used
+        to select a finite difference scheme for numerical estimation of the
+        gradient with a relative step size. These finite difference schemes
+        obey any specified `bounds`.
+    hess : {callable, '2-point', '3-point', 'cs', HessianUpdateStrategy}, optional
+        Method for computing the Hessian matrix. Only for Newton-CG, dogleg,
+        trust-ncg, trust-krylov, trust-exact and trust-constr.
+        If it is callable, it should return the Hessian matrix:
+
+            ``hess(x, *args) -> {LinearOperator, spmatrix, array}, (n, n)``
+
+        where ``x`` is a (n,) ndarray and ``args`` is a tuple with the fixed
+        parameters.
+        The keywords {'2-point', '3-point', 'cs'} can also be used to select
+        a finite difference scheme for numerical estimation of the hessian.
+        Alternatively, objects implementing the `HessianUpdateStrategy`
+        interface can be used to approximate the Hessian. Available
+        quasi-Newton methods implementing this interface are:
+
+            - `BFGS`;
+            - `SR1`.
+
+        Not all of the options are available for each of the methods; for
+        availability refer to the notes.
+    hessp : callable, optional
+        Hessian of objective function times an arbitrary vector p. Only for
+        Newton-CG, trust-ncg, trust-krylov, trust-constr.
+        Only one of `hessp` or `hess` needs to be given. If `hess` is
+        provided, then `hessp` will be ignored. `hessp` must compute the
+        Hessian times an arbitrary vector:
+
+            ``hessp(x, p, *args) ->  ndarray shape (n,)``
+
+        where ``x`` is a (n,) ndarray, ``p`` is an arbitrary vector with
+        dimension (n,) and ``args`` is a tuple with the fixed
+        parameters.
+    bounds : sequence or `Bounds`, optional
+        Bounds on variables for Nelder-Mead, L-BFGS-B, TNC, SLSQP, Powell,
+        trust-constr, COBYLA, and COBYQA methods. There are two ways to specify
+        the bounds:
+
+            1. Instance of `Bounds` class.
+            2. Sequence of ``(min, max)`` pairs for each element in `x`. None
+               is used to specify no bound.
+
+    constraints : {Constraint, dict} or List of {Constraint, dict}, optional
+        Constraints definition. Only for COBYLA, COBYQA, SLSQP and trust-constr.
+
+        Constraints for 'trust-constr' and 'cobyqa' are defined as a single object
+        or a list of objects specifying constraints to the optimization problem.
+        Available constraints are:
+
+            - `LinearConstraint`
+            - `NonlinearConstraint`
+
+        Constraints for COBYLA, SLSQP are defined as a list of dictionaries.
+        Each dictionary with fields:
+
+            type : str
+                Constraint type: 'eq' for equality, 'ineq' for inequality.
+            fun : callable
+                The function defining the constraint.
+            jac : callable, optional
+                The Jacobian of `fun` (only for SLSQP).
+            args : sequence, optional
+                Extra arguments to be passed to the function and Jacobian.
+
+        Equality constraint means that the constraint function result is to
+        be zero whereas inequality means that it is to be non-negative.
+        Note that COBYLA only supports inequality constraints.
+
+    tol : float, optional
+        Tolerance for termination. When `tol` is specified, the selected
+        minimization algorithm sets some relevant solver-specific tolerance(s)
+        equal to `tol`. For detailed control, use solver-specific
+        options.
+    options : dict, optional
+        A dictionary of solver options. All methods except `TNC` accept the
+        following generic options:
+
+            maxiter : int
+                Maximum number of iterations to perform. Depending on the
+                method each iteration may use several function evaluations.
+
+                For `TNC` use `maxfun` instead of `maxiter`.
+            disp : bool
+                Set to True to print convergence messages.
+
+        For method-specific options, see :func:`show_options()`.
+    callback : callable, optional
+        A callable called after each iteration.
+
+        All methods except TNC, SLSQP, and COBYLA support a callable with
+        the signature:
+
+            ``callback(intermediate_result: OptimizeResult)``
+
+        where ``intermediate_result`` is a keyword parameter containing an
+        `OptimizeResult` with attributes ``x`` and ``fun``, the present values
+        of the parameter vector and objective function. Note that the name
+        of the parameter must be ``intermediate_result`` for the callback
+        to be passed an `OptimizeResult`. These methods will also terminate if
+        the callback raises ``StopIteration``.
+
+        All methods except trust-constr (also) support a signature like:
+
+            ``callback(xk)``
+
+        where ``xk`` is the current parameter vector.
+
+        Introspection is used to determine which of the signatures above to
+        invoke.
+
+    Returns
+    -------
+    res : OptimizeResult
+        The optimization result represented as a ``OptimizeResult`` object.
+        Important attributes are: ``x`` the solution array, ``success`` a
+        Boolean flag indicating if the optimizer exited successfully and
+        ``message`` which describes the cause of the termination. See
+        `OptimizeResult` for a description of other attributes.
+
+    See also
+    --------
+    minimize_scalar : Interface to minimization algorithms for scalar
+        univariate functions
+    show_options : Additional options accepted by the solvers
+
+    Notes
+    -----
+    This section describes the available solvers that can be selected by the
+    'method' parameter. The default method is *BFGS*.
+
+    **Unconstrained minimization**
+
+    Method :ref:`CG <optimize.minimize-cg>` uses a nonlinear conjugate
+    gradient algorithm by Polak and Ribiere, a variant of the
+    Fletcher-Reeves method described in [5]_ pp.120-122. Only the
+    first derivatives are used.
+
+    Method :ref:`BFGS <optimize.minimize-bfgs>` uses the quasi-Newton
+    method of Broyden, Fletcher, Goldfarb, and Shanno (BFGS) [5]_
+    pp. 136. It uses the first derivatives only. BFGS has proven good
+    performance even for non-smooth optimizations. This method also
+    returns an approximation of the Hessian inverse, stored as
+    `hess_inv` in the OptimizeResult object.
+
+    Method :ref:`Newton-CG <optimize.minimize-newtoncg>` uses a
+    Newton-CG algorithm [5]_ pp. 168 (also known as the truncated
+    Newton method). It uses a CG method to the compute the search
+    direction. See also *TNC* method for a box-constrained
+    minimization with a similar algorithm. Suitable for large-scale
+    problems.
+
+    Method :ref:`dogleg <optimize.minimize-dogleg>` uses the dog-leg
+    trust-region algorithm [5]_ for unconstrained minimization. This
+    algorithm requires the gradient and Hessian; furthermore the
+    Hessian is required to be positive definite.
+
+    Method :ref:`trust-ncg <optimize.minimize-trustncg>` uses the
+    Newton conjugate gradient trust-region algorithm [5]_ for
+    unconstrained minimization. This algorithm requires the gradient
+    and either the Hessian or a function that computes the product of
+    the Hessian with a given vector. Suitable for large-scale problems.
+
+    Method :ref:`trust-krylov <optimize.minimize-trustkrylov>` uses
+    the Newton GLTR trust-region algorithm [14]_, [15]_ for unconstrained
+    minimization. This algorithm requires the gradient
+    and either the Hessian or a function that computes the product of
+    the Hessian with a given vector. Suitable for large-scale problems.
+    On indefinite problems it requires usually less iterations than the
+    `trust-ncg` method and is recommended for medium and large-scale problems.
+
+    Method :ref:`trust-exact <optimize.minimize-trustexact>`
+    is a trust-region method for unconstrained minimization in which
+    quadratic subproblems are solved almost exactly [13]_. This
+    algorithm requires the gradient and the Hessian (which is
+    *not* required to be positive definite). It is, in many
+    situations, the Newton method to converge in fewer iterations
+    and the most recommended for small and medium-size problems.
+
+    **Bound-Constrained minimization**
+
+    Method :ref:`Nelder-Mead <optimize.minimize-neldermead>` uses the
+    Simplex algorithm [1]_, [2]_. This algorithm is robust in many
+    applications. However, if numerical computation of derivative can be
+    trusted, other algorithms using the first and/or second derivatives
+    information might be preferred for their better performance in
+    general.
+
+    Method :ref:`L-BFGS-B <optimize.minimize-lbfgsb>` uses the L-BFGS-B
+    algorithm [6]_, [7]_ for bound constrained minimization.
+
+    Method :ref:`Powell <optimize.minimize-powell>` is a modification
+    of Powell's method [3]_, [4]_ which is a conjugate direction
+    method. It performs sequential one-dimensional minimizations along
+    each vector of the directions set (`direc` field in `options` and
+    `info`), which is updated at each iteration of the main
+    minimization loop. The function need not be differentiable, and no
+    derivatives are taken. If bounds are not provided, then an
+    unbounded line search will be used. If bounds are provided and
+    the initial guess is within the bounds, then every function
+    evaluation throughout the minimization procedure will be within
+    the bounds. If bounds are provided, the initial guess is outside
+    the bounds, and `direc` is full rank (default has full rank), then
+    some function evaluations during the first iteration may be
+    outside the bounds, but every function evaluation after the first
+    iteration will be within the bounds. If `direc` is not full rank,
+    then some parameters may not be optimized and the solution is not
+    guaranteed to be within the bounds.
+
+    Method :ref:`TNC <optimize.minimize-tnc>` uses a truncated Newton
+    algorithm [5]_, [8]_ to minimize a function with variables subject
+    to bounds. This algorithm uses gradient information; it is also
+    called Newton Conjugate-Gradient. It differs from the *Newton-CG*
+    method described above as it wraps a C implementation and allows
+    each variable to be given upper and lower bounds.
+
+    **Constrained Minimization**
+
+    Method :ref:`COBYLA <optimize.minimize-cobyla>` uses the
+    Constrained Optimization BY Linear Approximation (COBYLA) method
+    [9]_, [10]_, [11]_. The algorithm is based on linear
+    approximations to the objective function and each constraint. The
+    method wraps a FORTRAN implementation of the algorithm. The
+    constraints functions 'fun' may return either a single number
+    or an array or list of numbers.
+
+    Method :ref:`COBYQA <optimize.minimize-cobyqa>` uses the Constrained
+    Optimization BY Quadratic Approximations (COBYQA) method [18]_. The
+    algorithm is a derivative-free trust-region SQP method based on quadratic
+    approximations to the objective function and each nonlinear constraint. The
+    bounds are treated as unrelaxable constraints, in the sense that the
+    algorithm always respects them throughout the optimization process.
+
+    Method :ref:`SLSQP <optimize.minimize-slsqp>` uses Sequential
+    Least SQuares Programming to minimize a function of several
+    variables with any combination of bounds, equality and inequality
+    constraints. The method wraps the SLSQP Optimization subroutine
+    originally implemented by Dieter Kraft [12]_. Note that the
+    wrapper handles infinite values in bounds by converting them into
+    large floating values.
+
+    Method :ref:`trust-constr <optimize.minimize-trustconstr>` is a
+    trust-region algorithm for constrained optimization. It switches
+    between two implementations depending on the problem definition.
+    It is the most versatile constrained minimization algorithm
+    implemented in SciPy and the most appropriate for large-scale problems.
+    For equality constrained problems it is an implementation of Byrd-Omojokun
+    Trust-Region SQP method described in [17]_ and in [5]_, p. 549. When
+    inequality constraints are imposed as well, it switches to the trust-region
+    interior point method described in [16]_. This interior point algorithm,
+    in turn, solves inequality constraints by introducing slack variables
+    and solving a sequence of equality-constrained barrier problems
+    for progressively smaller values of the barrier parameter.
+    The previously described equality constrained SQP method is
+    used to solve the subproblems with increasing levels of accuracy
+    as the iterate gets closer to a solution.
+
+    **Finite-Difference Options**
+
+    For Method :ref:`trust-constr <optimize.minimize-trustconstr>`
+    the gradient and the Hessian may be approximated using
+    three finite-difference schemes: {'2-point', '3-point', 'cs'}.
+    The scheme 'cs' is, potentially, the most accurate but it
+    requires the function to correctly handle complex inputs and to
+    be differentiable in the complex plane. The scheme '3-point' is more
+    accurate than '2-point' but requires twice as many operations. If the
+    gradient is estimated via finite-differences the Hessian must be
+    estimated using one of the quasi-Newton strategies.
+
+    **Method specific options for the** `hess` **keyword**
+
+    +--------------+------+----------+-------------------------+-----+
+    | method/Hess  | None | callable | '2-point/'3-point'/'cs' | HUS |
+    +==============+======+==========+=========================+=====+
+    | Newton-CG    | x    | (n, n)   | x                       | x   |
+    |              |      | LO       |                         |     |
+    +--------------+------+----------+-------------------------+-----+
+    | dogleg       |      | (n, n)   |                         |     |
+    +--------------+------+----------+-------------------------+-----+
+    | trust-ncg    |      | (n, n)   | x                       | x   |
+    +--------------+------+----------+-------------------------+-----+
+    | trust-krylov |      | (n, n)   | x                       | x   |
+    +--------------+------+----------+-------------------------+-----+
+    | trust-exact  |      | (n, n)   |                         |     |
+    +--------------+------+----------+-------------------------+-----+
+    | trust-constr | x    | (n, n)   |  x                      | x   |
+    |              |      | LO       |                         |     |
+    |              |      | sp       |                         |     |
+    +--------------+------+----------+-------------------------+-----+
+
+    where LO=LinearOperator, sp=Sparse matrix, HUS=HessianUpdateStrategy
+
+    **Custom minimizers**
+
+    It may be useful to pass a custom minimization method, for example
+    when using a frontend to this method such as `scipy.optimize.basinhopping`
+    or a different library.  You can simply pass a callable as the ``method``
+    parameter.
+
+    The callable is called as ``method(fun, x0, args, **kwargs, **options)``
+    where ``kwargs`` corresponds to any other parameters passed to `minimize`
+    (such as `callback`, `hess`, etc.), except the `options` dict, which has
+    its contents also passed as `method` parameters pair by pair.  Also, if
+    `jac` has been passed as a bool type, `jac` and `fun` are mangled so that
+    `fun` returns just the function values and `jac` is converted to a function
+    returning the Jacobian.  The method shall return an `OptimizeResult`
+    object.
+
+    The provided `method` callable must be able to accept (and possibly ignore)
+    arbitrary parameters; the set of parameters accepted by `minimize` may
+    expand in future versions and then these parameters will be passed to
+    the method.  You can find an example in the scipy.optimize tutorial.
+
+    References
+    ----------
+    .. [1] Nelder, J A, and R Mead. 1965. A Simplex Method for Function
+        Minimization. The Computer Journal 7: 308-13.
+    .. [2] Wright M H. 1996. Direct search methods: Once scorned, now
+        respectable, in Numerical Analysis 1995: Proceedings of the 1995
+        Dundee Biennial Conference in Numerical Analysis (Eds. D F
+        Griffiths and G A Watson). Addison Wesley Longman, Harlow, UK.
+        191-208.
+    .. [3] Powell, M J D. 1964. An efficient method for finding the minimum of
+       a function of several variables without calculating derivatives. The
+       Computer Journal 7: 155-162.
+    .. [4] Press W, S A Teukolsky, W T Vetterling and B P Flannery.
+       Numerical Recipes (any edition), Cambridge University Press.
+    .. [5] Nocedal, J, and S J Wright. 2006. Numerical Optimization.
+       Springer New York.
+    .. [6] Byrd, R H and P Lu and J. Nocedal. 1995. A Limited Memory
+       Algorithm for Bound Constrained Optimization. SIAM Journal on
+       Scientific and Statistical Computing 16 (5): 1190-1208.
+    .. [7] Zhu, C and R H Byrd and J Nocedal. 1997. L-BFGS-B: Algorithm
+       778: L-BFGS-B, FORTRAN routines for large scale bound constrained
+       optimization. ACM Transactions on Mathematical Software 23 (4):
+       550-560.
+    .. [8] Nash, S G. Newton-Type Minimization Via the Lanczos Method.
+       1984. SIAM Journal of Numerical Analysis 21: 770-778.
+    .. [9] Powell, M J D. A direct search optimization method that models
+       the objective and constraint functions by linear interpolation.
+       1994. Advances in Optimization and Numerical Analysis, eds. S. Gomez
+       and J-P Hennart, Kluwer Academic (Dordrecht), 51-67.
+    .. [10] Powell M J D. Direct search algorithms for optimization
+       calculations. 1998. Acta Numerica 7: 287-336.
+    .. [11] Powell M J D. A view of algorithms for optimization without
+       derivatives. 2007.Cambridge University Technical Report DAMTP
+       2007/NA03
+    .. [12] Kraft, D. A software package for sequential quadratic
+       programming. 1988. Tech. Rep. DFVLR-FB 88-28, DLR German Aerospace
+       Center -- Institute for Flight Mechanics, Koln, Germany.
+    .. [13] Conn, A. R., Gould, N. I., and Toint, P. L.
+       Trust region methods. 2000. Siam. pp. 169-200.
+    .. [14] F. Lenders, C. Kirches, A. Potschka: "trlib: A vector-free
+       implementation of the GLTR method for iterative solution of
+       the trust region problem", :arxiv:`1611.04718`
+    .. [15] N. Gould, S. Lucidi, M. Roma, P. Toint: "Solving the
+       Trust-Region Subproblem using the Lanczos Method",
+       SIAM J. Optim., 9(2), 504--525, (1999).
+    .. [16] Byrd, Richard H., Mary E. Hribar, and Jorge Nocedal. 1999.
+        An interior point algorithm for large-scale nonlinear  programming.
+        SIAM Journal on Optimization 9.4: 877-900.
+    .. [17] Lalee, Marucha, Jorge Nocedal, and Todd Plantega. 1998. On the
+        implementation of an algorithm for large-scale equality constrained
+        optimization. SIAM Journal on Optimization 8.3: 682-706.
+    .. [18] Ragonneau, T. M. *Model-Based Derivative-Free Optimization Methods
+        and Software*. PhD thesis, Department of Applied Mathematics, The Hong
+        Kong Polytechnic University, Hong Kong, China, 2022. URL:
+        https://theses.lib.polyu.edu.hk/handle/200/12294.
+
+    Examples
+    --------
+    Let us consider the problem of minimizing the Rosenbrock function. This
+    function (and its respective derivatives) is implemented in `rosen`
+    (resp. `rosen_der`, `rosen_hess`) in the `scipy.optimize`.
+
+    >>> from scipy.optimize import minimize, rosen, rosen_der
+
+    A simple application of the *Nelder-Mead* method is:
+
+    >>> x0 = [1.3, 0.7, 0.8, 1.9, 1.2]
+    >>> res = minimize(rosen, x0, method='Nelder-Mead', tol=1e-6)
+    >>> res.x
+    array([ 1.,  1.,  1.,  1.,  1.])
+
+    Now using the *BFGS* algorithm, using the first derivative and a few
+    options:
+
+    >>> res = minimize(rosen, x0, method='BFGS', jac=rosen_der,
+    ...                options={'gtol': 1e-6, 'disp': True})
+    Optimization terminated successfully.
+             Current function value: 0.000000
+             Iterations: 26
+             Function evaluations: 31
+             Gradient evaluations: 31
+    >>> res.x
+    array([ 1.,  1.,  1.,  1.,  1.])
+    >>> print(res.message)
+    Optimization terminated successfully.
+    >>> res.hess_inv
+    array([
+        [ 0.00749589,  0.01255155,  0.02396251,  0.04750988,  0.09495377],  # may vary
+        [ 0.01255155,  0.02510441,  0.04794055,  0.09502834,  0.18996269],
+        [ 0.02396251,  0.04794055,  0.09631614,  0.19092151,  0.38165151],
+        [ 0.04750988,  0.09502834,  0.19092151,  0.38341252,  0.7664427 ],
+        [ 0.09495377,  0.18996269,  0.38165151,  0.7664427,   1.53713523]
+    ])
+
+
+    Next, consider a minimization problem with several constraints (namely
+    Example 16.4 from [5]_). The objective function is:
+
+    >>> fun = lambda x: (x[0] - 1)**2 + (x[1] - 2.5)**2
+
+    There are three constraints defined as:
+
+    >>> cons = ({'type': 'ineq', 'fun': lambda x:  x[0] - 2 * x[1] + 2},
+    ...         {'type': 'ineq', 'fun': lambda x: -x[0] - 2 * x[1] + 6},
+    ...         {'type': 'ineq', 'fun': lambda x: -x[0] + 2 * x[1] + 2})
+
+    And variables must be positive, hence the following bounds:
+
+    >>> bnds = ((0, None), (0, None))
+
+    The optimization problem is solved using the SLSQP method as:
+
+    >>> res = minimize(fun, (2, 0), method='SLSQP', bounds=bnds,
+    ...                constraints=cons)
+
+    It should converge to the theoretical solution (1.4 ,1.7).
+
+    """
+    x0 = np.atleast_1d(np.asarray(x0))
+
+    if x0.ndim != 1:
+        raise ValueError("'x0' must only have one dimension.")
+
+    if x0.dtype.kind in np.typecodes["AllInteger"]:
+        x0 = np.asarray(x0, dtype=float)
+
+    if not isinstance(args, tuple):
+        args = (args,)
+
+    if method is None:
+        # Select automatically
+        if constraints:
+            method = 'SLSQP'
+        elif bounds is not None:
+            method = 'L-BFGS-B'
+        else:
+            method = 'BFGS'
+
+    if callable(method):
+        meth = "_custom"
+    else:
+        meth = method.lower()
+
+    if options is None:
+        options = {}
+    # check if optional parameters are supported by the selected method
+    # - jac
+    if meth in ('nelder-mead', 'powell', 'cobyla', 'cobyqa') and bool(jac):
+        warn('Method %s does not use gradient information (jac).' % method,
+             RuntimeWarning, stacklevel=2)
+    # - hess
+    if meth not in ('newton-cg', 'dogleg', 'trust-ncg', 'trust-constr',
+                    'trust-krylov', 'trust-exact', '_custom') and hess is not None:
+        warn('Method %s does not use Hessian information (hess).' % method,
+             RuntimeWarning, stacklevel=2)
+    # - hessp
+    if meth not in ('newton-cg', 'trust-ncg', 'trust-constr',
+                    'trust-krylov', '_custom') \
+       and hessp is not None:
+        warn('Method %s does not use Hessian-vector product '
+             'information (hessp).' % method,
+             RuntimeWarning, stacklevel=2)
+    # - constraints or bounds
+    if (meth not in ('cobyla', 'cobyqa', 'slsqp', 'trust-constr', '_custom') and
+            np.any(constraints)):
+        warn('Method %s cannot handle constraints.' % method,
+             RuntimeWarning, stacklevel=2)
+    if meth not in (
+            'nelder-mead', 'powell', 'l-bfgs-b', 'cobyla', 'cobyqa', 'slsqp',
+            'tnc', 'trust-constr', '_custom') and bounds is not None:
+        warn('Method %s cannot handle bounds.' % method,
+             RuntimeWarning, stacklevel=2)
+    # - return_all
+    if (meth in ('l-bfgs-b', 'tnc', 'cobyla', 'cobyqa', 'slsqp') and
+            options.get('return_all', False)):
+        warn('Method %s does not support the return_all option.' % method,
+             RuntimeWarning, stacklevel=2)
+
+    # check gradient vector
+    if callable(jac):
+        pass
+    elif jac is True:
+        # fun returns func and grad
+        fun = MemoizeJac(fun)
+        jac = fun.derivative
+    elif (jac in FD_METHODS and
+          meth in ['trust-constr', 'bfgs', 'cg', 'l-bfgs-b', 'tnc', 'slsqp']):
+        # finite differences with relative step
+        pass
+    elif meth in ['trust-constr']:
+        # default jac calculation for this method
+        jac = '2-point'
+    elif jac is None or bool(jac) is False:
+        # this will cause e.g. LBFGS to use forward difference, absolute step
+        jac = None
+    else:
+        # default if jac option is not understood
+        jac = None
+
+    # set default tolerances
+    if tol is not None:
+        options = dict(options)
+        if meth == 'nelder-mead':
+            options.setdefault('xatol', tol)
+            options.setdefault('fatol', tol)
+        if meth in ('newton-cg', 'powell', 'tnc'):
+            options.setdefault('xtol', tol)
+        if meth in ('powell', 'l-bfgs-b', 'tnc', 'slsqp'):
+            options.setdefault('ftol', tol)
+        if meth in ('bfgs', 'cg', 'l-bfgs-b', 'tnc', 'dogleg',
+                    'trust-ncg', 'trust-exact', 'trust-krylov'):
+            options.setdefault('gtol', tol)
+        if meth in ('cobyla', '_custom'):
+            options.setdefault('tol', tol)
+        if meth == 'cobyqa':
+            options.setdefault('final_tr_radius', tol)
+        if meth == 'trust-constr':
+            options.setdefault('xtol', tol)
+            options.setdefault('gtol', tol)
+            options.setdefault('barrier_tol', tol)
+
+    if meth == '_custom':
+        # custom method called before bounds and constraints are 'standardised'
+        # custom method should be able to accept whatever bounds/constraints
+        # are provided to it.
+        return method(fun, x0, args=args, jac=jac, hess=hess, hessp=hessp,
+                      bounds=bounds, constraints=constraints,
+                      callback=callback, **options)
+
+    constraints = standardize_constraints(constraints, x0, meth)
+
+    remove_vars = False
+    if bounds is not None:
+        # convert to new-style bounds so we only have to consider one case
+        bounds = standardize_bounds(bounds, x0, 'new')
+        bounds = _validate_bounds(bounds, x0, meth)
+
+        if meth in {"tnc", "slsqp", "l-bfgs-b"}:
+            # These methods can't take the finite-difference derivatives they
+            # need when a variable is fixed by the bounds. To avoid this issue,
+            # remove fixed variables from the problem.
+            # NOTE: if this list is expanded, then be sure to update the
+            # accompanying tests and test_optimize.eb_data. Consider also if
+            # default OptimizeResult will need updating.
+
+            # determine whether any variables are fixed
+            i_fixed = (bounds.lb == bounds.ub)
+
+            if np.all(i_fixed):
+                # all the parameters are fixed, a minimizer is not able to do
+                # anything
+                return _optimize_result_for_equal_bounds(
+                    fun, bounds, meth, args=args, constraints=constraints
+                )
+
+            # determine whether finite differences are needed for any grad/jac
+            fd_needed = (not callable(jac))
+            for con in constraints:
+                if not callable(con.get('jac', None)):
+                    fd_needed = True
+
+            # If finite differences are ever used, remove all fixed variables
+            # Always remove fixed variables for TNC; see gh-14565
+            remove_vars = i_fixed.any() and (fd_needed or meth == "tnc")
+            if remove_vars:
+                x_fixed = (bounds.lb)[i_fixed]
+                x0 = x0[~i_fixed]
+                bounds = _remove_from_bounds(bounds, i_fixed)
+                fun = _remove_from_func(fun, i_fixed, x_fixed)
+                if callable(callback):
+                    callback = _remove_from_func(callback, i_fixed, x_fixed)
+                if callable(jac):
+                    jac = _remove_from_func(jac, i_fixed, x_fixed, remove=1)
+
+                # make a copy of the constraints so the user's version doesn't
+                # get changed. (Shallow copy is ok)
+                constraints = [con.copy() for con in constraints]
+                for con in constraints:  # yes, guaranteed to be a list
+                    con['fun'] = _remove_from_func(con['fun'], i_fixed,
+                                                   x_fixed, min_dim=1,
+                                                   remove=0)
+                    if callable(con.get('jac', None)):
+                        con['jac'] = _remove_from_func(con['jac'], i_fixed,
+                                                       x_fixed, min_dim=2,
+                                                       remove=1)
+        bounds = standardize_bounds(bounds, x0, meth)
+
+    callback = _wrap_callback(callback, meth)
+
+    if meth == 'nelder-mead':
+        res = _minimize_neldermead(fun, x0, args, callback, bounds=bounds,
+                                   **options)
+    elif meth == 'powell':
+        res = _minimize_powell(fun, x0, args, callback, bounds, **options)
+    elif meth == 'cg':
+        res = _minimize_cg(fun, x0, args, jac, callback, **options)
+    elif meth == 'bfgs':
+        res = _minimize_bfgs(fun, x0, args, jac, callback, **options)
+    elif meth == 'newton-cg':
+        res = _minimize_newtoncg(fun, x0, args, jac, hess, hessp, callback,
+                                 **options)
+    elif meth == 'l-bfgs-b':
+        res = _minimize_lbfgsb(fun, x0, args, jac, bounds,
+                               callback=callback, **options)
+    elif meth == 'tnc':
+        res = _minimize_tnc(fun, x0, args, jac, bounds, callback=callback,
+                            **options)
+    elif meth == 'cobyla':
+        res = _minimize_cobyla(fun, x0, args, constraints, callback=callback,
+                               bounds=bounds, **options)
+    elif meth == 'cobyqa':
+        res = _minimize_cobyqa(fun, x0, args, bounds, constraints, callback,
+                               **options)
+    elif meth == 'slsqp':
+        res = _minimize_slsqp(fun, x0, args, jac, bounds,
+                              constraints, callback=callback, **options)
+    elif meth == 'trust-constr':
+        res = _minimize_trustregion_constr(fun, x0, args, jac, hess, hessp,
+                                           bounds, constraints,
+                                           callback=callback, **options)
+    elif meth == 'dogleg':
+        res = _minimize_dogleg(fun, x0, args, jac, hess,
+                               callback=callback, **options)
+    elif meth == 'trust-ncg':
+        res = _minimize_trust_ncg(fun, x0, args, jac, hess, hessp,
+                                  callback=callback, **options)
+    elif meth == 'trust-krylov':
+        res = _minimize_trust_krylov(fun, x0, args, jac, hess, hessp,
+                                     callback=callback, **options)
+    elif meth == 'trust-exact':
+        res = _minimize_trustregion_exact(fun, x0, args, jac, hess,
+                                          callback=callback, **options)
+    else:
+        raise ValueError('Unknown solver %s' % method)
+
+    if remove_vars:
+        res.x = _add_to_array(res.x, i_fixed, x_fixed)
+        res.jac = _add_to_array(res.jac, i_fixed, np.nan)
+        if "hess_inv" in res:
+            res.hess_inv = None  # unknown
+
+    if getattr(callback, 'stop_iteration', False):
+        res.success = False
+        res.status = 99
+        res.message = "`callback` raised `StopIteration`."
+
+    return res
+
+
+def minimize_scalar(fun, bracket=None, bounds=None, args=(),
+                    method=None, tol=None, options=None):
+    """Local minimization of scalar function of one variable.
+
+    Parameters
+    ----------
+    fun : callable
+        Objective function.
+        Scalar function, must return a scalar.
+    bracket : sequence, optional
+        For methods 'brent' and 'golden', `bracket` defines the bracketing
+        interval and is required.
+        Either a triple ``(xa, xb, xc)`` satisfying ``xa < xb < xc`` and
+        ``func(xb) < func(xa) and  func(xb) < func(xc)``, or a pair
+        ``(xa, xb)`` to be used as initial points for a downhill bracket search
+        (see `scipy.optimize.bracket`).
+        The minimizer ``res.x`` will not necessarily satisfy
+        ``xa <= res.x <= xb``.
+    bounds : sequence, optional
+        For method 'bounded', `bounds` is mandatory and must have two finite
+        items corresponding to the optimization bounds.
+    args : tuple, optional
+        Extra arguments passed to the objective function.
+    method : str or callable, optional
+        Type of solver.  Should be one of:
+
+            - :ref:`Brent <optimize.minimize_scalar-brent>`
+            - :ref:`Bounded <optimize.minimize_scalar-bounded>`
+            - :ref:`Golden <optimize.minimize_scalar-golden>`
+            - custom - a callable object (added in version 0.14.0), see below
+
+        Default is "Bounded" if bounds are provided and "Brent" otherwise.
+        See the 'Notes' section for details of each solver.
+
+    tol : float, optional
+        Tolerance for termination. For detailed control, use solver-specific
+        options.
+    options : dict, optional
+        A dictionary of solver options.
+
+            maxiter : int
+                Maximum number of iterations to perform.
+            disp : bool
+                Set to True to print convergence messages.
+
+        See :func:`show_options()` for solver-specific options.
+
+    Returns
+    -------
+    res : OptimizeResult
+        The optimization result represented as a ``OptimizeResult`` object.
+        Important attributes are: ``x`` the solution array, ``success`` a
+        Boolean flag indicating if the optimizer exited successfully and
+        ``message`` which describes the cause of the termination. See
+        `OptimizeResult` for a description of other attributes.
+
+    See also
+    --------
+    minimize : Interface to minimization algorithms for scalar multivariate
+        functions
+    show_options : Additional options accepted by the solvers
+
+    Notes
+    -----
+    This section describes the available solvers that can be selected by the
+    'method' parameter. The default method is the ``"Bounded"`` Brent method if
+    `bounds` are passed and unbounded ``"Brent"`` otherwise.
+
+    Method :ref:`Brent <optimize.minimize_scalar-brent>` uses Brent's
+    algorithm [1]_ to find a local minimum.  The algorithm uses inverse
+    parabolic interpolation when possible to speed up convergence of
+    the golden section method.
+
+    Method :ref:`Golden <optimize.minimize_scalar-golden>` uses the
+    golden section search technique [1]_. It uses analog of the bisection
+    method to decrease the bracketed interval. It is usually
+    preferable to use the *Brent* method.
+
+    Method :ref:`Bounded <optimize.minimize_scalar-bounded>` can
+    perform bounded minimization [2]_ [3]_. It uses the Brent method to find a
+    local minimum in the interval x1 < xopt < x2.
+
+    Note that the Brent and Golden methods do not guarantee success unless a
+    valid ``bracket`` triple is provided. If a three-point bracket cannot be
+    found, consider `scipy.optimize.minimize`. Also, all methods are intended
+    only for local minimization. When the function of interest has more than
+    one local minimum, consider :ref:`global_optimization`.
+
+    **Custom minimizers**
+
+    It may be useful to pass a custom minimization method, for example
+    when using some library frontend to minimize_scalar. You can simply
+    pass a callable as the ``method`` parameter.
+
+    The callable is called as ``method(fun, args, **kwargs, **options)``
+    where ``kwargs`` corresponds to any other parameters passed to `minimize`
+    (such as `bracket`, `tol`, etc.), except the `options` dict, which has
+    its contents also passed as `method` parameters pair by pair.  The method
+    shall return an `OptimizeResult` object.
+
+    The provided `method` callable must be able to accept (and possibly ignore)
+    arbitrary parameters; the set of parameters accepted by `minimize` may
+    expand in future versions and then these parameters will be passed to
+    the method. You can find an example in the scipy.optimize tutorial.
+
+    .. versionadded:: 0.11.0
+
+    References
+    ----------
+    .. [1] Press, W., S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery.
+           Numerical Recipes in C. Cambridge University Press.
+    .. [2] Forsythe, G.E., M. A. Malcolm, and C. B. Moler. "Computer Methods
+           for Mathematical Computations." Prentice-Hall Series in Automatic
+           Computation 259 (1977).
+    .. [3] Brent, Richard P. Algorithms for Minimization Without Derivatives.
+           Courier Corporation, 2013.
+
+    Examples
+    --------
+    Consider the problem of minimizing the following function.
+
+    >>> def f(x):
+    ...     return (x - 2) * x * (x + 2)**2
+
+    Using the *Brent* method, we find the local minimum as:
+
+    >>> from scipy.optimize import minimize_scalar
+    >>> res = minimize_scalar(f)
+    >>> res.fun
+    -9.9149495908
+
+    The minimizer is:
+
+    >>> res.x
+    1.28077640403
+
+    Using the *Bounded* method, we find a local minimum with specified
+    bounds as:
+
+    >>> res = minimize_scalar(f, bounds=(-3, -1), method='bounded')
+    >>> res.fun  # minimum
+    3.28365179850e-13
+    >>> res.x  # minimizer
+    -2.0000002026
+
+    """
+    if not isinstance(args, tuple):
+        args = (args,)
+
+    if callable(method):
+        meth = "_custom"
+    elif method is None:
+        meth = 'brent' if bounds is None else 'bounded'
+    else:
+        meth = method.lower()
+    if options is None:
+        options = {}
+
+    if bounds is not None and meth in {'brent', 'golden'}:
+        message = f"Use of `bounds` is incompatible with 'method={method}'."
+        raise ValueError(message)
+
+    if tol is not None:
+        options = dict(options)
+        if meth == 'bounded' and 'xatol' not in options:
+            warn("Method 'bounded' does not support relative tolerance in x; "
+                 "defaulting to absolute tolerance.",
+                 RuntimeWarning, stacklevel=2)
+            options['xatol'] = tol
+        elif meth == '_custom':
+            options.setdefault('tol', tol)
+        else:
+            options.setdefault('xtol', tol)
+
+    # replace boolean "disp" option, if specified, by an integer value.
+    disp = options.get('disp')
+    if isinstance(disp, bool):
+        options['disp'] = 2 * int(disp)
+
+    if meth == '_custom':
+        res = method(fun, args=args, bracket=bracket, bounds=bounds, **options)
+    elif meth == 'brent':
+        res = _recover_from_bracket_error(_minimize_scalar_brent,
+                                          fun, bracket, args, **options)
+    elif meth == 'bounded':
+        if bounds is None:
+            raise ValueError('The `bounds` parameter is mandatory for '
+                             'method `bounded`.')
+        res = _minimize_scalar_bounded(fun, bounds, args, **options)
+    elif meth == 'golden':
+        res = _recover_from_bracket_error(_minimize_scalar_golden,
+                                          fun, bracket, args, **options)
+    else:
+        raise ValueError('Unknown solver %s' % method)
+
+    # gh-16196 reported inconsistencies in the output shape of `res.x`. While
+    # fixing this, future-proof it for when the function is vectorized:
+    # the shape of `res.x` should match that of `res.fun`.
+    res.fun = np.asarray(res.fun)[()]
+    res.x = np.reshape(res.x, res.fun.shape)[()]
+    return res
+
+
+def _remove_from_bounds(bounds, i_fixed):
+    """Removes fixed variables from a `Bounds` instance"""
+    lb = bounds.lb[~i_fixed]
+    ub = bounds.ub[~i_fixed]
+    return Bounds(lb, ub)  # don't mutate original Bounds object
+
+
+def _remove_from_func(fun_in, i_fixed, x_fixed, min_dim=None, remove=0):
+    """Wraps a function such that fixed variables need not be passed in"""
+    def fun_out(x_in, *args, **kwargs):
+        x_out = np.zeros_like(i_fixed, dtype=x_in.dtype)
+        x_out[i_fixed] = x_fixed
+        x_out[~i_fixed] = x_in
+        y_out = fun_in(x_out, *args, **kwargs)
+        y_out = np.array(y_out)
+
+        if min_dim == 1:
+            y_out = np.atleast_1d(y_out)
+        elif min_dim == 2:
+            y_out = np.atleast_2d(y_out)
+
+        if remove == 1:
+            y_out = y_out[..., ~i_fixed]
+        elif remove == 2:
+            y_out = y_out[~i_fixed, ~i_fixed]
+
+        return y_out
+    return fun_out
+
+
+def _add_to_array(x_in, i_fixed, x_fixed):
+    """Adds fixed variables back to an array"""
+    i_free = ~i_fixed
+    if x_in.ndim == 2:
+        i_free = i_free[:, None] @ i_free[None, :]
+    x_out = np.zeros_like(i_free, dtype=x_in.dtype)
+    x_out[~i_free] = x_fixed
+    x_out[i_free] = x_in.ravel()
+    return x_out
+
+
+def _validate_bounds(bounds, x0, meth):
+    """Check that bounds are valid."""
+
+    msg = "An upper bound is less than the corresponding lower bound."
+    if np.any(bounds.ub < bounds.lb):
+        raise ValueError(msg)
+
+    msg = "The number of bounds is not compatible with the length of `x0`."
+    try:
+        bounds.lb = np.broadcast_to(bounds.lb, x0.shape)
+        bounds.ub = np.broadcast_to(bounds.ub, x0.shape)
+    except Exception as e:
+        raise ValueError(msg) from e
+
+    return bounds
+
+def standardize_bounds(bounds, x0, meth):
+    """Converts bounds to the form required by the solver."""
+    if meth in {'trust-constr', 'powell', 'nelder-mead', 'cobyla', 'cobyqa',
+                'new'}:
+        if not isinstance(bounds, Bounds):
+            lb, ub = old_bound_to_new(bounds)
+            bounds = Bounds(lb, ub)
+    elif meth in ('l-bfgs-b', 'tnc', 'slsqp', 'old'):
+        if isinstance(bounds, Bounds):
+            bounds = new_bounds_to_old(bounds.lb, bounds.ub, x0.shape[0])
+    return bounds
+
+
+def standardize_constraints(constraints, x0, meth):
+    """Converts constraints to the form required by the solver."""
+    all_constraint_types = (NonlinearConstraint, LinearConstraint, dict)
+    new_constraint_types = all_constraint_types[:-1]
+    if constraints is None:
+        constraints = []
+    elif isinstance(constraints, all_constraint_types):
+        constraints = [constraints]
+    else:
+        constraints = list(constraints)  # ensure it's a mutable sequence
+
+    if meth in ['trust-constr', 'cobyqa', 'new']:
+        for i, con in enumerate(constraints):
+            if not isinstance(con, new_constraint_types):
+                constraints[i] = old_constraint_to_new(i, con)
+    else:
+        # iterate over copy, changing original
+        for i, con in enumerate(list(constraints)):
+            if isinstance(con, new_constraint_types):
+                old_constraints = new_constraint_to_old(con, x0)
+                constraints[i] = old_constraints[0]
+                constraints.extend(old_constraints[1:])  # appends 1 if present
+
+    return constraints
+
+
+def _optimize_result_for_equal_bounds(
+        fun, bounds, method, args=(), constraints=()
+):
+    """
+    Provides a default OptimizeResult for when a bounded minimization method
+    has (lb == ub).all().
+
+    Parameters
+    ----------
+    fun: callable
+    bounds: Bounds
+    method: str
+    constraints: Constraint
+    """
+    success = True
+    message = 'All independent variables were fixed by bounds.'
+
+    # bounds is new-style
+    x0 = bounds.lb
+
+    if constraints:
+        message = ("All independent variables were fixed by bounds at values"
+                   " that satisfy the constraints.")
+        constraints = standardize_constraints(constraints, x0, 'new')
+
+    maxcv = 0
+    for c in constraints:
+        pc = PreparedConstraint(c, x0)
+        violation = pc.violation(x0)
+        if np.sum(violation):
+            maxcv = max(maxcv, np.max(violation))
+            success = False
+            message = (f"All independent variables were fixed by bounds, but "
+                       f"the independent variables do not satisfy the "
+                       f"constraints exactly. (Maximum violation: {maxcv}).")
+
+    return OptimizeResult(
+        x=x0, fun=fun(x0, *args), success=success, message=message, nfev=1,
+        njev=0, nhev=0,
+    )

llava_next/lib/python3.10/site-packages/scipy/optimize/_nnls.py

@@ -0,0 +1,164 @@
+import numpy as np
+from scipy.linalg import solve, LinAlgWarning
+import warnings
+
+__all__ = ['nnls']
+
+
+def nnls(A, b, maxiter=None, *, atol=None):
+    """
+    Solve ``argmin_x || Ax - b ||_2`` for ``x>=0``.
+
+    This problem, often called as NonNegative Least Squares, is a convex
+    optimization problem with convex constraints. It typically arises when
+    the ``x`` models quantities for which only nonnegative values are
+    attainable; weight of ingredients, component costs and so on.
+
+    Parameters
+    ----------
+    A : (m, n) ndarray
+        Coefficient array
+    b : (m,) ndarray, float
+        Right-hand side vector.
+    maxiter: int, optional
+        Maximum number of iterations, optional. Default value is ``3 * n``.
+    atol: float
+        Tolerance value used in the algorithm to assess closeness to zero in
+        the projected residual ``(A.T @ (A x - b)`` entries. Increasing this
+        value relaxes the solution constraints. A typical relaxation value can
+        be selected as ``max(m, n) * np.linalg.norm(a, 1) * np.spacing(1.)``.
+        This value is not set as default since the norm operation becomes
+        expensive for large problems hence can be used only when necessary.
+
+    Returns
+    -------
+    x : ndarray
+        Solution vector.
+    rnorm : float
+        The 2-norm of the residual, ``|| Ax-b ||_2``.
+
+    See Also
+    --------
+    lsq_linear : Linear least squares with bounds on the variables
+
+    Notes
+    -----
+    The code is based on [2]_ which is an improved version of the classical
+    algorithm of [1]_. It utilizes an active set method and solves the KKT
+    (Karush-Kuhn-Tucker) conditions for the non-negative least squares problem.
+
+    References
+    ----------
+    .. [1] : Lawson C., Hanson R.J., "Solving Least Squares Problems", SIAM,
+       1995, :doi:`10.1137/1.9781611971217`
+    .. [2] : Bro, Rasmus and de Jong, Sijmen, "A Fast Non-Negativity-
+       Constrained Least Squares Algorithm", Journal Of Chemometrics, 1997,
+       :doi:`10.1002/(SICI)1099-128X(199709/10)11:5<393::AID-CEM483>3.0.CO;2-L`
+
+     Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.optimize import nnls
+    ...
+    >>> A = np.array([[1, 0], [1, 0], [0, 1]])
+    >>> b = np.array([2, 1, 1])
+    >>> nnls(A, b)
+    (array([1.5, 1. ]), 0.7071067811865475)
+
+    >>> b = np.array([-1, -1, -1])
+    >>> nnls(A, b)
+    (array([0., 0.]), 1.7320508075688772)
+
+    """
+
+    A = np.asarray_chkfinite(A)
+    b = np.asarray_chkfinite(b)
+
+    if len(A.shape) != 2:
+        raise ValueError("Expected a two-dimensional array (matrix)" +
+                         f", but the shape of A is {A.shape}")
+    if len(b.shape) != 1:
+        raise ValueError("Expected a one-dimensional array (vector)" +
+                         f", but the shape of b is {b.shape}")
+
+    m, n = A.shape
+
+    if m != b.shape[0]:
+        raise ValueError(
+                "Incompatible dimensions. The first dimension of " +
+                f"A is {m}, while the shape of b is {(b.shape[0], )}")
+
+    x, rnorm, mode = _nnls(A, b, maxiter, tol=atol)
+    if mode != 1:
+        raise RuntimeError("Maximum number of iterations reached.")
+
+    return x, rnorm
+
+
+def _nnls(A, b, maxiter=None, tol=None):
+    """
+    This is a single RHS algorithm from ref [2] above. For multiple RHS
+    support, the algorithm is given in  :doi:`10.1002/cem.889`
+    """
+    m, n = A.shape
+
+    AtA = A.T @ A
+    Atb = b @ A  # Result is 1D - let NumPy figure it out
+
+    if not maxiter:
+        maxiter = 3*n
+    if tol is None:
+        tol = 10 * max(m, n) * np.spacing(1.)
+
+    # Initialize vars
+    x = np.zeros(n, dtype=np.float64)
+    s = np.zeros(n, dtype=np.float64)
+    # Inactive constraint switches
+    P = np.zeros(n, dtype=bool)
+
+    # Projected residual
+    w = Atb.copy().astype(np.float64)  # x=0. Skip (-AtA @ x) term
+
+    # Overall iteration counter
+    # Outer loop is not counted, inner iter is counted across outer spins
+    iter = 0
+
+    while (not P.all()) and (w[~P] > tol).any():  # B
+        # Get the "most" active coeff index and move to inactive set
+        k = np.argmax(w * (~P))  # B.2
+        P[k] = True  # B.3
+
+        # Iteration solution
+        s[:] = 0.
+        # B.4
+        with warnings.catch_warnings():
+            warnings.filterwarnings('ignore', message='Ill-conditioned matrix',
+                                    category=LinAlgWarning)
+            s[P] = solve(AtA[np.ix_(P, P)], Atb[P], assume_a='sym', check_finite=False)
+
+        # Inner loop
+        while (iter < maxiter) and (s[P].min() < 0):  # C.1
+            iter += 1
+            inds = P * (s < 0)
+            alpha = (x[inds] / (x[inds] - s[inds])).min()  # C.2
+            x *= (1 - alpha)
+            x += alpha*s
+            P[x <= tol] = False
+            with warnings.catch_warnings():
+                warnings.filterwarnings('ignore', message='Ill-conditioned matrix',
+                                        category=LinAlgWarning)
+                s[P] = solve(AtA[np.ix_(P, P)], Atb[P], assume_a='sym',
+                             check_finite=False)
+            s[~P] = 0  # C.6
+
+        x[:] = s[:]
+        w[:] = Atb - AtA @ x
+
+        if iter == maxiter:
+            # Typically following line should return
+            # return x, np.linalg.norm(A@x - b), -1
+            # however at the top level, -1 raises an exception wasting norm
+            # Instead return dummy number 0.
+            return x, 0., -1
+
+    return x, np.linalg.norm(A@x - b), 1

llava_next/lib/python3.10/site-packages/scipy/optimize/_numdiff.py

@@ -0,0 +1,779 @@
+"""Routines for numerical differentiation."""
+import functools
+import numpy as np
+from numpy.linalg import norm
+
+from scipy.sparse.linalg import LinearOperator
+from ..sparse import issparse, csc_matrix, csr_matrix, coo_matrix, find
+from ._group_columns import group_dense, group_sparse
+from scipy._lib._array_api import atleast_nd, array_namespace
+
+
+def _adjust_scheme_to_bounds(x0, h, num_steps, scheme, lb, ub):
+    """Adjust final difference scheme to the presence of bounds.
+
+    Parameters
+    ----------
+    x0 : ndarray, shape (n,)
+        Point at which we wish to estimate derivative.
+    h : ndarray, shape (n,)
+        Desired absolute finite difference steps.
+    num_steps : int
+        Number of `h` steps in one direction required to implement finite
+        difference scheme. For example, 2 means that we need to evaluate
+        f(x0 + 2 * h) or f(x0 - 2 * h)
+    scheme : {'1-sided', '2-sided'}
+        Whether steps in one or both directions are required. In other
+        words '1-sided' applies to forward and backward schemes, '2-sided'
+        applies to center schemes.
+    lb : ndarray, shape (n,)
+        Lower bounds on independent variables.
+    ub : ndarray, shape (n,)
+        Upper bounds on independent variables.
+
+    Returns
+    -------
+    h_adjusted : ndarray, shape (n,)
+        Adjusted absolute step sizes. Step size decreases only if a sign flip
+        or switching to one-sided scheme doesn't allow to take a full step.
+    use_one_sided : ndarray of bool, shape (n,)
+        Whether to switch to one-sided scheme. Informative only for
+        ``scheme='2-sided'``.
+    """
+    if scheme == '1-sided':
+        use_one_sided = np.ones_like(h, dtype=bool)
+    elif scheme == '2-sided':
+        h = np.abs(h)
+        use_one_sided = np.zeros_like(h, dtype=bool)
+    else:
+        raise ValueError("`scheme` must be '1-sided' or '2-sided'.")
+
+    if np.all((lb == -np.inf) & (ub == np.inf)):
+        return h, use_one_sided
+
+    h_total = h * num_steps
+    h_adjusted = h.copy()
+
+    lower_dist = x0 - lb
+    upper_dist = ub - x0
+
+    if scheme == '1-sided':
+        x = x0 + h_total
+        violated = (x < lb) | (x > ub)
+        fitting = np.abs(h_total) <= np.maximum(lower_dist, upper_dist)
+        h_adjusted[violated & fitting] *= -1
+
+        forward = (upper_dist >= lower_dist) & ~fitting
+        h_adjusted[forward] = upper_dist[forward] / num_steps
+        backward = (upper_dist < lower_dist) & ~fitting
+        h_adjusted[backward] = -lower_dist[backward] / num_steps
+    elif scheme == '2-sided':
+        central = (lower_dist >= h_total) & (upper_dist >= h_total)
+
+        forward = (upper_dist >= lower_dist) & ~central
+        h_adjusted[forward] = np.minimum(
+            h[forward], 0.5 * upper_dist[forward] / num_steps)
+        use_one_sided[forward] = True
+
+        backward = (upper_dist < lower_dist) & ~central
+        h_adjusted[backward] = -np.minimum(
+            h[backward], 0.5 * lower_dist[backward] / num_steps)
+        use_one_sided[backward] = True
+
+        min_dist = np.minimum(upper_dist, lower_dist) / num_steps
+        adjusted_central = (~central & (np.abs(h_adjusted) <= min_dist))
+        h_adjusted[adjusted_central] = min_dist[adjusted_central]
+        use_one_sided[adjusted_central] = False
+
+    return h_adjusted, use_one_sided
+
+
+@functools.lru_cache
+def _eps_for_method(x0_dtype, f0_dtype, method):
+    """
+    Calculates relative EPS step to use for a given data type
+    and numdiff step method.
+
+    Progressively smaller steps are used for larger floating point types.
+
+    Parameters
+    ----------
+    f0_dtype: np.dtype
+        dtype of function evaluation
+
+    x0_dtype: np.dtype
+        dtype of parameter vector
+
+    method: {'2-point', '3-point', 'cs'}
+
+    Returns
+    -------
+    EPS: float
+        relative step size. May be np.float16, np.float32, np.float64
+
+    Notes
+    -----
+    The default relative step will be np.float64. However, if x0 or f0 are
+    smaller floating point types (np.float16, np.float32), then the smallest
+    floating point type is chosen.
+    """
+    # the default EPS value
+    EPS = np.finfo(np.float64).eps
+
+    x0_is_fp = False
+    if np.issubdtype(x0_dtype, np.inexact):
+        # if you're a floating point type then over-ride the default EPS
+        EPS = np.finfo(x0_dtype).eps
+        x0_itemsize = np.dtype(x0_dtype).itemsize
+        x0_is_fp = True
+
+    if np.issubdtype(f0_dtype, np.inexact):
+        f0_itemsize = np.dtype(f0_dtype).itemsize
+        # choose the smallest itemsize between x0 and f0
+        if x0_is_fp and f0_itemsize < x0_itemsize:
+            EPS = np.finfo(f0_dtype).eps
+
+    if method in ["2-point", "cs"]:
+        return EPS**0.5
+    elif method in ["3-point"]:
+        return EPS**(1/3)
+    else:
+        raise RuntimeError("Unknown step method, should be one of "
+                           "{'2-point', '3-point', 'cs'}")
+
+
+def _compute_absolute_step(rel_step, x0, f0, method):
+    """
+    Computes an absolute step from a relative step for finite difference
+    calculation.
+
+    Parameters
+    ----------
+    rel_step: None or array-like
+        Relative step for the finite difference calculation
+    x0 : np.ndarray
+        Parameter vector
+    f0 : np.ndarray or scalar
+    method : {'2-point', '3-point', 'cs'}
+
+    Returns
+    -------
+    h : float
+        The absolute step size
+
+    Notes
+    -----
+    `h` will always be np.float64. However, if `x0` or `f0` are
+    smaller floating point dtypes (e.g. np.float32), then the absolute
+    step size will be calculated from the smallest floating point size.
+    """
+    # this is used instead of np.sign(x0) because we need
+    # sign_x0 to be 1 when x0 == 0.
+    sign_x0 = (x0 >= 0).astype(float) * 2 - 1
+
+    rstep = _eps_for_method(x0.dtype, f0.dtype, method)
+
+    if rel_step is None:
+        abs_step = rstep * sign_x0 * np.maximum(1.0, np.abs(x0))
+    else:
+        # User has requested specific relative steps.
+        # Don't multiply by max(1, abs(x0) because if x0 < 1 then their
+        # requested step is not used.
+        abs_step = rel_step * sign_x0 * np.abs(x0)
+
+        # however we don't want an abs_step of 0, which can happen if
+        # rel_step is 0, or x0 is 0. Instead, substitute a realistic step
+        dx = ((x0 + abs_step) - x0)
+        abs_step = np.where(dx == 0,
+                            rstep * sign_x0 * np.maximum(1.0, np.abs(x0)),
+                            abs_step)
+
+    return abs_step
+
+
+def _prepare_bounds(bounds, x0):
+    """
+    Prepares new-style bounds from a two-tuple specifying the lower and upper
+    limits for values in x0. If a value is not bound then the lower/upper bound
+    will be expected to be -np.inf/np.inf.
+
+    Examples
+    --------
+    >>> _prepare_bounds([(0, 1, 2), (1, 2, np.inf)], [0.5, 1.5, 2.5])
+    (array([0., 1., 2.]), array([ 1.,  2., inf]))
+    """
+    lb, ub = (np.asarray(b, dtype=float) for b in bounds)
+    if lb.ndim == 0:
+        lb = np.resize(lb, x0.shape)
+
+    if ub.ndim == 0:
+        ub = np.resize(ub, x0.shape)
+
+    return lb, ub
+
+
+def group_columns(A, order=0):
+    """Group columns of a 2-D matrix for sparse finite differencing [1]_.
+
+    Two columns are in the same group if in each row at least one of them
+    has zero. A greedy sequential algorithm is used to construct groups.
+
+    Parameters
+    ----------
+    A : array_like or sparse matrix, shape (m, n)
+        Matrix of which to group columns.
+    order : int, iterable of int with shape (n,) or None
+        Permutation array which defines the order of columns enumeration.
+        If int or None, a random permutation is used with `order` used as
+        a random seed. Default is 0, that is use a random permutation but
+        guarantee repeatability.
+
+    Returns
+    -------
+    groups : ndarray of int, shape (n,)
+        Contains values from 0 to n_groups-1, where n_groups is the number
+        of found groups. Each value ``groups[i]`` is an index of a group to
+        which ith column assigned. The procedure was helpful only if
+        n_groups is significantly less than n.
+
+    References
+    ----------
+    .. [1] A. Curtis, M. J. D. Powell, and J. Reid, "On the estimation of
+           sparse Jacobian matrices", Journal of the Institute of Mathematics
+           and its Applications, 13 (1974), pp. 117-120.
+    """
+    if issparse(A):
+        A = csc_matrix(A)
+    else:
+        A = np.atleast_2d(A)
+        A = (A != 0).astype(np.int32)
+
+    if A.ndim != 2:
+        raise ValueError("`A` must be 2-dimensional.")
+
+    m, n = A.shape
+
+    if order is None or np.isscalar(order):
+        rng = np.random.RandomState(order)
+        order = rng.permutation(n)
+    else:
+        order = np.asarray(order)
+        if order.shape != (n,):
+            raise ValueError("`order` has incorrect shape.")
+
+    A = A[:, order]
+
+    if issparse(A):
+        groups = group_sparse(m, n, A.indices, A.indptr)
+    else:
+        groups = group_dense(m, n, A)
+
+    groups[order] = groups.copy()
+
+    return groups
+
+
+def approx_derivative(fun, x0, method='3-point', rel_step=None, abs_step=None,
+                      f0=None, bounds=(-np.inf, np.inf), sparsity=None,
+                      as_linear_operator=False, args=(), kwargs={}):
+    """Compute finite difference approximation of the derivatives of a
+    vector-valued function.
+
+    If a function maps from R^n to R^m, its derivatives form m-by-n matrix
+    called the Jacobian, where an element (i, j) is a partial derivative of
+    f[i] with respect to x[j].
+
+    Parameters
+    ----------
+    fun : callable
+        Function of which to estimate the derivatives. The argument x
+        passed to this function is ndarray of shape (n,) (never a scalar
+        even if n=1). It must return 1-D array_like of shape (m,) or a scalar.
+    x0 : array_like of shape (n,) or float
+        Point at which to estimate the derivatives. Float will be converted
+        to a 1-D array.
+    method : {'3-point', '2-point', 'cs'}, optional
+        Finite difference method to use:
+            - '2-point' - use the first order accuracy forward or backward
+                          difference.
+            - '3-point' - use central difference in interior points and the
+                          second order accuracy forward or backward difference
+                          near the boundary.
+            - 'cs' - use a complex-step finite difference scheme. This assumes
+                     that the user function is real-valued and can be
+                     analytically continued to the complex plane. Otherwise,
+                     produces bogus results.
+    rel_step : None or array_like, optional
+        Relative step size to use. If None (default) the absolute step size is
+        computed as ``h = rel_step * sign(x0) * max(1, abs(x0))``, with
+        `rel_step` being selected automatically, see Notes. Otherwise
+        ``h = rel_step * sign(x0) * abs(x0)``. For ``method='3-point'`` the
+        sign of `h` is ignored. The calculated step size is possibly adjusted
+        to fit into the bounds.
+    abs_step : array_like, optional
+        Absolute step size to use, possibly adjusted to fit into the bounds.
+        For ``method='3-point'`` the sign of `abs_step` is ignored. By default
+        relative steps are used, only if ``abs_step is not None`` are absolute
+        steps used.
+    f0 : None or array_like, optional
+        If not None it is assumed to be equal to ``fun(x0)``, in this case
+        the ``fun(x0)`` is not called. Default is None.
+    bounds : tuple of array_like, optional
+        Lower and upper bounds on independent variables. Defaults to no bounds.
+        Each bound must match the size of `x0` or be a scalar, in the latter
+        case the bound will be the same for all variables. Use it to limit the
+        range of function evaluation. Bounds checking is not implemented
+        when `as_linear_operator` is True.
+    sparsity : {None, array_like, sparse matrix, 2-tuple}, optional
+        Defines a sparsity structure of the Jacobian matrix. If the Jacobian
+        matrix is known to have only few non-zero elements in each row, then
+        it's possible to estimate its several columns by a single function
+        evaluation [3]_. To perform such economic computations two ingredients
+        are required:
+
+        * structure : array_like or sparse matrix of shape (m, n). A zero
+          element means that a corresponding element of the Jacobian
+          identically equals to zero.
+        * groups : array_like of shape (n,). A column grouping for a given
+          sparsity structure, use `group_columns` to obtain it.
+
+        A single array or a sparse matrix is interpreted as a sparsity
+        structure, and groups are computed inside the function. A tuple is
+        interpreted as (structure, groups). If None (default), a standard
+        dense differencing will be used.
+
+        Note, that sparse differencing makes sense only for large Jacobian
+        matrices where each row contains few non-zero elements.
+    as_linear_operator : bool, optional
+        When True the function returns an `scipy.sparse.linalg.LinearOperator`.
+        Otherwise it returns a dense array or a sparse matrix depending on
+        `sparsity`. The linear operator provides an efficient way of computing
+        ``J.dot(p)`` for any vector ``p`` of shape (n,), but does not allow
+        direct access to individual elements of the matrix. By default
+        `as_linear_operator` is False.
+    args, kwargs : tuple and dict, optional
+        Additional arguments passed to `fun`. Both empty by default.
+        The calling signature is ``fun(x, *args, **kwargs)``.
+
+    Returns
+    -------
+    J : {ndarray, sparse matrix, LinearOperator}
+        Finite difference approximation of the Jacobian matrix.
+        If `as_linear_operator` is True returns a LinearOperator
+        with shape (m, n). Otherwise it returns a dense array or sparse
+        matrix depending on how `sparsity` is defined. If `sparsity`
+        is None then a ndarray with shape (m, n) is returned. If
+        `sparsity` is not None returns a csr_matrix with shape (m, n).
+        For sparse matrices and linear operators it is always returned as
+        a 2-D structure, for ndarrays, if m=1 it is returned
+        as a 1-D gradient array with shape (n,).
+
+    See Also
+    --------
+    check_derivative : Check correctness of a function computing derivatives.
+
+    Notes
+    -----
+    If `rel_step` is not provided, it assigned as ``EPS**(1/s)``, where EPS is
+    determined from the smallest floating point dtype of `x0` or `fun(x0)`,
+    ``np.finfo(x0.dtype).eps``, s=2 for '2-point' method and
+    s=3 for '3-point' method. Such relative step approximately minimizes a sum
+    of truncation and round-off errors, see [1]_. Relative steps are used by
+    default. However, absolute steps are used when ``abs_step is not None``.
+    If any of the absolute or relative steps produces an indistinguishable
+    difference from the original `x0`, ``(x0 + dx) - x0 == 0``, then a
+    automatic step size is substituted for that particular entry.
+
+    A finite difference scheme for '3-point' method is selected automatically.
+    The well-known central difference scheme is used for points sufficiently
+    far from the boundary, and 3-point forward or backward scheme is used for
+    points near the boundary. Both schemes have the second-order accuracy in
+    terms of Taylor expansion. Refer to [2]_ for the formulas of 3-point
+    forward and backward difference schemes.
+
+    For dense differencing when m=1 Jacobian is returned with a shape (n,),
+    on the other hand when n=1 Jacobian is returned with a shape (m, 1).
+    Our motivation is the following: a) It handles a case of gradient
+    computation (m=1) in a conventional way. b) It clearly separates these two
+    different cases. b) In all cases np.atleast_2d can be called to get 2-D
+    Jacobian with correct dimensions.
+
+    References
+    ----------
+    .. [1] W. H. Press et. al. "Numerical Recipes. The Art of Scientific
+           Computing. 3rd edition", sec. 5.7.
+
+    .. [2] A. Curtis, M. J. D. Powell, and J. Reid, "On the estimation of
+           sparse Jacobian matrices", Journal of the Institute of Mathematics
+           and its Applications, 13 (1974), pp. 117-120.
+
+    .. [3] B. Fornberg, "Generation of Finite Difference Formulas on
+           Arbitrarily Spaced Grids", Mathematics of Computation 51, 1988.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.optimize._numdiff import approx_derivative
+    >>>
+    >>> def f(x, c1, c2):
+    ...     return np.array([x[0] * np.sin(c1 * x[1]),
+    ...                      x[0] * np.cos(c2 * x[1])])
+    ...
+    >>> x0 = np.array([1.0, 0.5 * np.pi])
+    >>> approx_derivative(f, x0, args=(1, 2))
+    array([[ 1.,  0.],
+           [-1.,  0.]])
+
+    Bounds can be used to limit the region of function evaluation.
+    In the example below we compute left and right derivative at point 1.0.
+
+    >>> def g(x):
+    ...     return x**2 if x >= 1 else x
+    ...
+    >>> x0 = 1.0
+    >>> approx_derivative(g, x0, bounds=(-np.inf, 1.0))
+    array([ 1.])
+    >>> approx_derivative(g, x0, bounds=(1.0, np.inf))
+    array([ 2.])
+    """
+    if method not in ['2-point', '3-point', 'cs']:
+        raise ValueError("Unknown method '%s'. " % method)
+
+    xp = array_namespace(x0)
+    _x = atleast_nd(x0, ndim=1, xp=xp)
+    _dtype = xp.float64
+    if xp.isdtype(_x.dtype, "real floating"):
+        _dtype = _x.dtype
+
+    # promotes to floating
+    x0 = xp.astype(_x, _dtype)
+
+    if x0.ndim > 1:
+        raise ValueError("`x0` must have at most 1 dimension.")
+
+    lb, ub = _prepare_bounds(bounds, x0)
+
+    if lb.shape != x0.shape or ub.shape != x0.shape:
+        raise ValueError("Inconsistent shapes between bounds and `x0`.")
+
+    if as_linear_operator and not (np.all(np.isinf(lb))
+                                   and np.all(np.isinf(ub))):
+        raise ValueError("Bounds not supported when "
+                         "`as_linear_operator` is True.")
+
+    def fun_wrapped(x):
+        # send user function same fp type as x0. (but only if cs is not being
+        # used
+        if xp.isdtype(x.dtype, "real floating"):
+            x = xp.astype(x, x0.dtype)
+
+        f = np.atleast_1d(fun(x, *args, **kwargs))
+        if f.ndim > 1:
+            raise RuntimeError("`fun` return value has "
+                               "more than 1 dimension.")
+        return f
+
+    if f0 is None:
+        f0 = fun_wrapped(x0)
+    else:
+        f0 = np.atleast_1d(f0)
+        if f0.ndim > 1:
+            raise ValueError("`f0` passed has more than 1 dimension.")
+
+    if np.any((x0 < lb) | (x0 > ub)):
+        raise ValueError("`x0` violates bound constraints.")
+
+    if as_linear_operator:
+        if rel_step is None:
+            rel_step = _eps_for_method(x0.dtype, f0.dtype, method)
+
+        return _linear_operator_difference(fun_wrapped, x0,
+                                           f0, rel_step, method)
+    else:
+        # by default we use rel_step
+        if abs_step is None:
+            h = _compute_absolute_step(rel_step, x0, f0, method)
+        else:
+            # user specifies an absolute step
+            sign_x0 = (x0 >= 0).astype(float) * 2 - 1
+            h = abs_step
+
+            # cannot have a zero step. This might happen if x0 is very large
+            # or small. In which case fall back to relative step.
+            dx = ((x0 + h) - x0)
+            h = np.where(dx == 0,
+                         _eps_for_method(x0.dtype, f0.dtype, method) *
+                         sign_x0 * np.maximum(1.0, np.abs(x0)),
+                         h)
+
+        if method == '2-point':
+            h, use_one_sided = _adjust_scheme_to_bounds(
+                x0, h, 1, '1-sided', lb, ub)
+        elif method == '3-point':
+            h, use_one_sided = _adjust_scheme_to_bounds(
+                x0, h, 1, '2-sided', lb, ub)
+        elif method == 'cs':
+            use_one_sided = False
+
+        if sparsity is None:
+            return _dense_difference(fun_wrapped, x0, f0, h,
+                                     use_one_sided, method)
+        else:
+            if not issparse(sparsity) and len(sparsity) == 2:
+                structure, groups = sparsity
+            else:
+                structure = sparsity
+                groups = group_columns(sparsity)
+
+            if issparse(structure):
+                structure = csc_matrix(structure)
+            else:
+                structure = np.atleast_2d(structure)
+
+            groups = np.atleast_1d(groups)
+            return _sparse_difference(fun_wrapped, x0, f0, h,
+                                      use_one_sided, structure,
+                                      groups, method)
+
+
+def _linear_operator_difference(fun, x0, f0, h, method):
+    m = f0.size
+    n = x0.size
+
+    if method == '2-point':
+        def matvec(p):
+            if np.array_equal(p, np.zeros_like(p)):
+                return np.zeros(m)
+            dx = h / norm(p)
+            x = x0 + dx*p
+            df = fun(x) - f0
+            return df / dx
+
+    elif method == '3-point':
+        def matvec(p):
+            if np.array_equal(p, np.zeros_like(p)):
+                return np.zeros(m)
+            dx = 2*h / norm(p)
+            x1 = x0 - (dx/2)*p
+            x2 = x0 + (dx/2)*p
+            f1 = fun(x1)
+            f2 = fun(x2)
+            df = f2 - f1
+            return df / dx
+
+    elif method == 'cs':
+        def matvec(p):
+            if np.array_equal(p, np.zeros_like(p)):
+                return np.zeros(m)
+            dx = h / norm(p)
+            x = x0 + dx*p*1.j
+            f1 = fun(x)
+            df = f1.imag
+            return df / dx
+
+    else:
+        raise RuntimeError("Never be here.")
+
+    return LinearOperator((m, n), matvec)
+
+
+def _dense_difference(fun, x0, f0, h, use_one_sided, method):
+    m = f0.size
+    n = x0.size
+    J_transposed = np.empty((n, m))
+    x1 = x0.copy()
+    x2 = x0.copy()
+    xc = x0.astype(complex, copy=True)
+
+    for i in range(h.size):
+        if method == '2-point':
+            x1[i] += h[i]
+            dx = x1[i] - x0[i]  # Recompute dx as exactly representable number.
+            df = fun(x1) - f0
+        elif method == '3-point' and use_one_sided[i]:
+            x1[i] += h[i]
+            x2[i] += 2 * h[i]
+            dx = x2[i] - x0[i]
+            f1 = fun(x1)
+            f2 = fun(x2)
+            df = -3.0 * f0 + 4 * f1 - f2
+        elif method == '3-point' and not use_one_sided[i]:
+            x1[i] -= h[i]
+            x2[i] += h[i]
+            dx = x2[i] - x1[i]
+            f1 = fun(x1)
+            f2 = fun(x2)
+            df = f2 - f1
+        elif method == 'cs':
+            xc[i] += h[i] * 1.j
+            f1 = fun(xc)
+            df = f1.imag
+            dx = h[i]
+        else:
+            raise RuntimeError("Never be here.")
+
+        J_transposed[i] = df / dx
+        x1[i] = x2[i] = xc[i] = x0[i]
+
+    if m == 1:
+        J_transposed = np.ravel(J_transposed)
+
+    return J_transposed.T
+
+
+def _sparse_difference(fun, x0, f0, h, use_one_sided,
+                       structure, groups, method):
+    m = f0.size
+    n = x0.size
+    row_indices = []
+    col_indices = []
+    fractions = []
+
+    n_groups = np.max(groups) + 1
+    for group in range(n_groups):
+        # Perturb variables which are in the same group simultaneously.
+        e = np.equal(group, groups)
+        h_vec = h * e
+        if method == '2-point':
+            x = x0 + h_vec
+            dx = x - x0
+            df = fun(x) - f0
+            # The result is  written to columns which correspond to perturbed
+            # variables.
+            cols, = np.nonzero(e)
+            # Find all non-zero elements in selected columns of Jacobian.
+            i, j, _ = find(structure[:, cols])
+            # Restore column indices in the full array.
+            j = cols[j]
+        elif method == '3-point':
+            # Here we do conceptually the same but separate one-sided
+            # and two-sided schemes.
+            x1 = x0.copy()
+            x2 = x0.copy()
+
+            mask_1 = use_one_sided & e
+            x1[mask_1] += h_vec[mask_1]
+            x2[mask_1] += 2 * h_vec[mask_1]
+
+            mask_2 = ~use_one_sided & e
+            x1[mask_2] -= h_vec[mask_2]
+            x2[mask_2] += h_vec[mask_2]
+
+            dx = np.zeros(n)
+            dx[mask_1] = x2[mask_1] - x0[mask_1]
+            dx[mask_2] = x2[mask_2] - x1[mask_2]
+
+            f1 = fun(x1)
+            f2 = fun(x2)
+
+            cols, = np.nonzero(e)
+            i, j, _ = find(structure[:, cols])
+            j = cols[j]
+
+            mask = use_one_sided[j]
+            df = np.empty(m)
+
+            rows = i[mask]
+            df[rows] = -3 * f0[rows] + 4 * f1[rows] - f2[rows]
+
+            rows = i[~mask]
+            df[rows] = f2[rows] - f1[rows]
+        elif method == 'cs':
+            f1 = fun(x0 + h_vec*1.j)
+            df = f1.imag
+            dx = h_vec
+            cols, = np.nonzero(e)
+            i, j, _ = find(structure[:, cols])
+            j = cols[j]
+        else:
+            raise ValueError("Never be here.")
+
+        # All that's left is to compute the fraction. We store i, j and
+        # fractions as separate arrays and later construct coo_matrix.
+        row_indices.append(i)
+        col_indices.append(j)
+        fractions.append(df[i] / dx[j])
+
+    row_indices = np.hstack(row_indices)
+    col_indices = np.hstack(col_indices)
+    fractions = np.hstack(fractions)
+    J = coo_matrix((fractions, (row_indices, col_indices)), shape=(m, n))
+    return csr_matrix(J)
+
+
+def check_derivative(fun, jac, x0, bounds=(-np.inf, np.inf), args=(),
+                     kwargs={}):
+    """Check correctness of a function computing derivatives (Jacobian or
+    gradient) by comparison with a finite difference approximation.
+
+    Parameters
+    ----------
+    fun : callable
+        Function of which to estimate the derivatives. The argument x
+        passed to this function is ndarray of shape (n,) (never a scalar
+        even if n=1). It must return 1-D array_like of shape (m,) or a scalar.
+    jac : callable
+        Function which computes Jacobian matrix of `fun`. It must work with
+        argument x the same way as `fun`. The return value must be array_like
+        or sparse matrix with an appropriate shape.
+    x0 : array_like of shape (n,) or float
+        Point at which to estimate the derivatives. Float will be converted
+        to 1-D array.
+    bounds : 2-tuple of array_like, optional
+        Lower and upper bounds on independent variables. Defaults to no bounds.
+        Each bound must match the size of `x0` or be a scalar, in the latter
+        case the bound will be the same for all variables. Use it to limit the
+        range of function evaluation.
+    args, kwargs : tuple and dict, optional
+        Additional arguments passed to `fun` and `jac`. Both empty by default.
+        The calling signature is ``fun(x, *args, **kwargs)`` and the same
+        for `jac`.
+
+    Returns
+    -------
+    accuracy : float
+        The maximum among all relative errors for elements with absolute values
+        higher than 1 and absolute errors for elements with absolute values
+        less or equal than 1. If `accuracy` is on the order of 1e-6 or lower,
+        then it is likely that your `jac` implementation is correct.
+
+    See Also
+    --------
+    approx_derivative : Compute finite difference approximation of derivative.
+
+    Examples
+    --------
+    >>> import numpy as np
+    >>> from scipy.optimize._numdiff import check_derivative
+    >>>
+    >>>
+    >>> def f(x, c1, c2):
+    ...     return np.array([x[0] * np.sin(c1 * x[1]),
+    ...                      x[0] * np.cos(c2 * x[1])])
+    ...
+    >>> def jac(x, c1, c2):
+    ...     return np.array([
+    ...         [np.sin(c1 * x[1]),  c1 * x[0] * np.cos(c1 * x[1])],
+    ...         [np.cos(c2 * x[1]), -c2 * x[0] * np.sin(c2 * x[1])]
+    ...     ])
+    ...
+    >>>
+    >>> x0 = np.array([1.0, 0.5 * np.pi])
+    >>> check_derivative(f, jac, x0, args=(1, 2))
+    2.4492935982947064e-16
+    """
+    J_to_test = jac(x0, *args, **kwargs)
+    if issparse(J_to_test):
+        J_diff = approx_derivative(fun, x0, bounds=bounds, sparsity=J_to_test,
+                                   args=args, kwargs=kwargs)
+        J_to_test = csr_matrix(J_to_test)
+        abs_err = J_to_test - J_diff
+        i, j, abs_err_data = find(abs_err)
+        J_diff_data = np.asarray(J_diff[i, j]).ravel()
+        return np.max(np.abs(abs_err_data) /
+                      np.maximum(1, np.abs(J_diff_data)))
+    else:
+        J_diff = approx_derivative(fun, x0, bounds=bounds,
+                                   args=args, kwargs=kwargs)
+        abs_err = np.abs(J_to_test - J_diff)
+        return np.max(abs_err / np.maximum(1, np.abs(J_diff)))

llava_next/lib/python3.10/site-packages/scipy/optimize/_spectral.py

@@ -0,0 +1,260 @@
+"""
+Spectral Algorithm for Nonlinear Equations
+"""
+import collections
+
+import numpy as np
+from scipy.optimize import OptimizeResult
+from scipy.optimize._optimize import _check_unknown_options
+from ._linesearch import _nonmonotone_line_search_cruz, _nonmonotone_line_search_cheng
+
+class _NoConvergence(Exception):
+    pass
+
+
+def _root_df_sane(func, x0, args=(), ftol=1e-8, fatol=1e-300, maxfev=1000,
+                  fnorm=None, callback=None, disp=False, M=10, eta_strategy=None,
+                  sigma_eps=1e-10, sigma_0=1.0, line_search='cruz', **unknown_options):
+    r"""
+    Solve nonlinear equation with the DF-SANE method
+
+    Options
+    -------
+    ftol : float, optional
+        Relative norm tolerance.
+    fatol : float, optional
+        Absolute norm tolerance.
+        Algorithm terminates when ``||func(x)|| < fatol + ftol ||func(x_0)||``.
+    fnorm : callable, optional
+        Norm to use in the convergence check. If None, 2-norm is used.
+    maxfev : int, optional
+        Maximum number of function evaluations.
+    disp : bool, optional
+        Whether to print convergence process to stdout.
+    eta_strategy : callable, optional
+        Choice of the ``eta_k`` parameter, which gives slack for growth
+        of ``||F||**2``.  Called as ``eta_k = eta_strategy(k, x, F)`` with
+        `k` the iteration number, `x` the current iterate and `F` the current
+        residual. Should satisfy ``eta_k > 0`` and ``sum(eta, k=0..inf) < inf``.
+        Default: ``||F||**2 / (1 + k)**2``.
+    sigma_eps : float, optional
+        The spectral coefficient is constrained to ``sigma_eps < sigma < 1/sigma_eps``.
+        Default: 1e-10
+    sigma_0 : float, optional
+        Initial spectral coefficient.
+        Default: 1.0
+    M : int, optional
+        Number of iterates to include in the nonmonotonic line search.
+        Default: 10
+    line_search : {'cruz', 'cheng'}
+        Type of line search to employ. 'cruz' is the original one defined in
+        [Martinez & Raydan. Math. Comp. 75, 1429 (2006)], 'cheng' is
+        a modified search defined in [Cheng & Li. IMA J. Numer. Anal. 29, 814 (2009)].
+        Default: 'cruz'
+
+    References
+    ----------
+    .. [1] "Spectral residual method without gradient information for solving
+           large-scale nonlinear systems of equations." W. La Cruz,
+           J.M. Martinez, M. Raydan. Math. Comp. **75**, 1429 (2006).
+    .. [2] W. La Cruz, Opt. Meth. Software, 29, 24 (2014).
+    .. [3] W. Cheng, D.-H. Li. IMA J. Numer. Anal. **29**, 814 (2009).
+
+    """
+    _check_unknown_options(unknown_options)
+
+    if line_search not in ('cheng', 'cruz'):
+        raise ValueError(f"Invalid value {line_search!r} for 'line_search'")
+
+    nexp = 2
+
+    if eta_strategy is None:
+        # Different choice from [1], as their eta is not invariant
+        # vs. scaling of F.
+        def eta_strategy(k, x, F):
+            # Obtain squared 2-norm of the initial residual from the outer scope
+            return f_0 / (1 + k)**2
+
+    if fnorm is None:
+        def fnorm(F):
+            # Obtain squared 2-norm of the current residual from the outer scope
+            return f_k**(1.0/nexp)
+
+    def fmerit(F):
+        return np.linalg.norm(F)**nexp
+
+    nfev = [0]
+    f, x_k, x_shape, f_k, F_k, is_complex = _wrap_func(func, x0, fmerit,
+                                                       nfev, maxfev, args)
+
+    k = 0
+    f_0 = f_k
+    sigma_k = sigma_0
+
+    F_0_norm = fnorm(F_k)
+
+    # For the 'cruz' line search
+    prev_fs = collections.deque([f_k], M)
+
+    # For the 'cheng' line search
+    Q = 1.0
+    C = f_0
+
+    converged = False
+    message = "too many function evaluations required"
+
+    while True:
+        F_k_norm = fnorm(F_k)
+
+        if disp:
+            print("iter %d: ||F|| = %g, sigma = %g" % (k, F_k_norm, sigma_k))
+
+        if callback is not None:
+            callback(x_k, F_k)
+
+        if F_k_norm < ftol * F_0_norm + fatol:
+            # Converged!
+            message = "successful convergence"
+            converged = True
+            break
+
+        # Control spectral parameter, from [2]
+        if abs(sigma_k) > 1/sigma_eps:
+            sigma_k = 1/sigma_eps * np.sign(sigma_k)
+        elif abs(sigma_k) < sigma_eps:
+            sigma_k = sigma_eps
+
+        # Line search direction
+        d = -sigma_k * F_k
+
+        # Nonmonotone line search
+        eta = eta_strategy(k, x_k, F_k)
+        try:
+            if line_search == 'cruz':
+                alpha, xp, fp, Fp = _nonmonotone_line_search_cruz(f, x_k, d, prev_fs,
+                                                                  eta=eta)
+            elif line_search == 'cheng':
+                alpha, xp, fp, Fp, C, Q = _nonmonotone_line_search_cheng(f, x_k, d, f_k,
+                                                                         C, Q, eta=eta)
+        except _NoConvergence:
+            break
+
+        # Update spectral parameter
+        s_k = xp - x_k
+        y_k = Fp - F_k
+        sigma_k = np.vdot(s_k, s_k) / np.vdot(s_k, y_k)
+
+        # Take step
+        x_k = xp
+        F_k = Fp
+        f_k = fp
+
+        # Store function value
+        if line_search == 'cruz':
+            prev_fs.append(fp)
+
+        k += 1
+
+    x = _wrap_result(x_k, is_complex, shape=x_shape)
+    F = _wrap_result(F_k, is_complex)
+
+    result = OptimizeResult(x=x, success=converged,
+                            message=message,
+                            fun=F, nfev=nfev[0], nit=k, method="df-sane")
+
+    return result
+
+
+def _wrap_func(func, x0, fmerit, nfev_list, maxfev, args=()):
+    """
+    Wrap a function and an initial value so that (i) complex values
+    are wrapped to reals, and (ii) value for a merit function
+    fmerit(x, f) is computed at the same time, (iii) iteration count
+    is maintained and an exception is raised if it is exceeded.
+
+    Parameters
+    ----------
+    func : callable
+        Function to wrap
+    x0 : ndarray
+        Initial value
+    fmerit : callable
+        Merit function fmerit(f) for computing merit value from residual.
+    nfev_list : list
+        List to store number of evaluations in. Should be [0] in the beginning.
+    maxfev : int
+        Maximum number of evaluations before _NoConvergence is raised.
+    args : tuple
+        Extra arguments to func
+
+    Returns
+    -------
+    wrap_func : callable
+        Wrapped function, to be called as
+        ``F, fp = wrap_func(x0)``
+    x0_wrap : ndarray of float
+        Wrapped initial value; raveled to 1-D and complex
+        values mapped to reals.
+    x0_shape : tuple
+        Shape of the initial value array
+    f : float
+        Merit function at F
+    F : ndarray of float
+        Residual at x0_wrap
+    is_complex : bool
+        Whether complex values were mapped to reals
+
+    """
+    x0 = np.asarray(x0)
+    x0_shape = x0.shape
+    F = np.asarray(func(x0, *args)).ravel()
+    is_complex = np.iscomplexobj(x0) or np.iscomplexobj(F)
+    x0 = x0.ravel()
+
+    nfev_list[0] = 1
+
+    if is_complex:
+        def wrap_func(x):
+            if nfev_list[0] >= maxfev:
+                raise _NoConvergence()
+            nfev_list[0] += 1
+            z = _real2complex(x).reshape(x0_shape)
+            v = np.asarray(func(z, *args)).ravel()
+            F = _complex2real(v)
+            f = fmerit(F)
+            return f, F
+
+        x0 = _complex2real(x0)
+        F = _complex2real(F)
+    else:
+        def wrap_func(x):
+            if nfev_list[0] >= maxfev:
+                raise _NoConvergence()
+            nfev_list[0] += 1
+            x = x.reshape(x0_shape)
+            F = np.asarray(func(x, *args)).ravel()
+            f = fmerit(F)
+            return f, F
+
+    return wrap_func, x0, x0_shape, fmerit(F), F, is_complex
+
+
+def _wrap_result(result, is_complex, shape=None):
+    """
+    Convert from real to complex and reshape result arrays.
+    """
+    if is_complex:
+        z = _real2complex(result)
+    else:
+        z = result
+    if shape is not None:
+        z = z.reshape(shape)
+    return z
+
+
+def _real2complex(x):
+    return np.ascontiguousarray(x, dtype=float).view(np.complex128)
+
+
+def _complex2real(z):
+    return np.ascontiguousarray(z, dtype=complex).view(np.float64)

llava_next/lib/python3.10/site-packages/scipy/optimize/_trustregion_ncg.py

@@ -0,0 +1,126 @@
+"""Newton-CG trust-region optimization."""
+import math
+
+import numpy as np
+import scipy.linalg
+from ._trustregion import (_minimize_trust_region, BaseQuadraticSubproblem)
+
+__all__ = []
+
+
+def _minimize_trust_ncg(fun, x0, args=(), jac=None, hess=None, hessp=None,
+                        **trust_region_options):
+    """
+    Minimization of scalar function of one or more variables using
+    the Newton conjugate gradient trust-region algorithm.
+
+    Options
+    -------
+    initial_trust_radius : float
+        Initial trust-region radius.
+    max_trust_radius : float
+        Maximum value of the trust-region radius. No steps that are longer
+        than this value will be proposed.
+    eta : float
+        Trust region related acceptance stringency for proposed steps.
+    gtol : float
+        Gradient norm must be less than `gtol` before successful
+        termination.
+
+    """
+    if jac is None:
+        raise ValueError('Jacobian is required for Newton-CG trust-region '
+                         'minimization')
+    if hess is None and hessp is None:
+        raise ValueError('Either the Hessian or the Hessian-vector product '
+                         'is required for Newton-CG trust-region minimization')
+    return _minimize_trust_region(fun, x0, args=args, jac=jac, hess=hess,
+                                  hessp=hessp, subproblem=CGSteihaugSubproblem,
+                                  **trust_region_options)
+
+
+class CGSteihaugSubproblem(BaseQuadraticSubproblem):
+    """Quadratic subproblem solved by a conjugate gradient method"""
+    def solve(self, trust_radius):
+        """
+        Solve the subproblem using a conjugate gradient method.
+
+        Parameters
+        ----------
+        trust_radius : float
+            We are allowed to wander only this far away from the origin.
+
+        Returns
+        -------
+        p : ndarray
+            The proposed step.
+        hits_boundary : bool
+            True if the proposed step is on the boundary of the trust region.
+
+        Notes
+        -----
+        This is algorithm (7.2) of Nocedal and Wright 2nd edition.
+        Only the function that computes the Hessian-vector product is required.
+        The Hessian itself is not required, and the Hessian does
+        not need to be positive semidefinite.
+        """
+
+        # get the norm of jacobian and define the origin
+        p_origin = np.zeros_like(self.jac)
+
+        # define a default tolerance
+        tolerance = min(0.5, math.sqrt(self.jac_mag)) * self.jac_mag
+
+        # Stop the method if the search direction
+        # is a direction of nonpositive curvature.
+        if self.jac_mag < tolerance:
+            hits_boundary = False
+            return p_origin, hits_boundary
+
+        # init the state for the first iteration
+        z = p_origin
+        r = self.jac
+        d = -r
+
+        # Search for the min of the approximation of the objective function.
+        while True:
+
+            # do an iteration
+            Bd = self.hessp(d)
+            dBd = np.dot(d, Bd)
+            if dBd <= 0:
+                # Look at the two boundary points.
+                # Find both values of t to get the boundary points such that
+                # ||z + t d|| == trust_radius
+                # and then choose the one with the predicted min value.
+                ta, tb = self.get_boundaries_intersections(z, d, trust_radius)
+                pa = z + ta * d
+                pb = z + tb * d
+                if self(pa) < self(pb):
+                    p_boundary = pa
+                else:
+                    p_boundary = pb
+                hits_boundary = True
+                return p_boundary, hits_boundary
+            r_squared = np.dot(r, r)
+            alpha = r_squared / dBd
+            z_next = z + alpha * d
+            if scipy.linalg.norm(z_next) >= trust_radius:
+                # Find t >= 0 to get the boundary point such that
+                # ||z + t d|| == trust_radius
+                ta, tb = self.get_boundaries_intersections(z, d, trust_radius)
+                p_boundary = z + tb * d
+                hits_boundary = True
+                return p_boundary, hits_boundary
+            r_next = r + alpha * Bd
+            r_next_squared = np.dot(r_next, r_next)
+            if math.sqrt(r_next_squared) < tolerance:
+                hits_boundary = False
+                return z_next, hits_boundary
+            beta_next = r_next_squared / r_squared
+            d_next = -r_next + beta_next * d
+
+            # update the state for the next iteration
+            z = z_next
+            r = r_next
+            d = d_next

llava_next/lib/python3.10/site-packages/scipy/optimize/cobyla.py

@@ -0,0 +1,19 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.optimize` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'OptimizeResult',
+    'fmin_cobyla',
+]
+
+def __dir__():
+    return __all__
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="optimize", module="cobyla",
+                                   private_modules=["_cobyla_py"], all=__all__,
+                                   attribute=name)

llava_next/lib/python3.10/site-packages/scipy/optimize/minpack2.py

@@ -0,0 +1,17 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.optimize` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+__all__: list[str] = []
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="optimize", module="minpack2",
+                                   private_modules=["_minpack2"], all=__all__,
+                                   attribute=name)

llava_next/lib/python3.10/site-packages/scipy/optimize/slsqp.py

@@ -0,0 +1,23 @@
+# This file is not meant for public use and will be removed in SciPy v2.0.0.
+# Use the `scipy.optimize` namespace for importing the functions
+# included below.
+
+from scipy._lib.deprecation import _sub_module_deprecation
+
+
+__all__ = [  # noqa: F822
+    'OptimizeResult',
+    'fmin_slsqp',
+    'slsqp',
+    'zeros',
+]
+
+
+def __dir__():
+    return __all__
+
+
+def __getattr__(name):
+    return _sub_module_deprecation(sub_package="optimize", module="slsqp",
+                                   private_modules=["_slsqp_py"], all=__all__,
+                                   attribute=name)

parrot/lib/python3.10/site-packages/gradio_client/__pycache__/media_data.cpython-310.pyc

@@ -0,0 +1,3 @@
+version https://git-lfs.github.com/spec/v1
+oid sha256:b7eb9550628889b4477639bb4c3b301fea459f135cdd6b5b1dc975fdb55a0a43
+size 452036

parrot/lib/python3.10/site-packages/torch/cpu/amp/__init__.py

@@ -0,0 +1,2 @@
+from .autocast_mode import autocast
+from .grad_scaler import GradScaler

parrot/lib/python3.10/site-packages/torch/cpu/amp/autocast_mode.py

@@ -0,0 +1,50 @@
+# mypy: allow-untyped-defs
+from typing import Any
+from typing_extensions import deprecated
+
+import torch
+
+__all__ = ["autocast"]
+
+
+class autocast(torch.amp.autocast_mode.autocast):
+    r"""
+    See :class:`torch.autocast`.
+    ``torch.cpu.amp.autocast(args...)`` is deprecated. Please use ``torch.amp.autocast("cpu", args...)`` instead.
+    """
+
+    @deprecated(
+        "`torch.cpu.amp.autocast(args...)` is deprecated. "
+        "Please use `torch.amp.autocast('cpu', args...)` instead.",
+        category=FutureWarning,
+    )
+    def __init__(
+        self,
+        enabled: bool = True,
+        dtype: torch.dtype = torch.bfloat16,
+        cache_enabled: bool = True,
+    ):
+        if torch._jit_internal.is_scripting():
+            self._enabled = enabled
+            self.device = "cpu"
+            self.fast_dtype = dtype
+            return
+        super().__init__(
+            "cpu", enabled=enabled, dtype=dtype, cache_enabled=cache_enabled
+        )
+
+    def __enter__(self):
+        if torch._jit_internal.is_scripting():
+            return self
+        return super().__enter__()
+
+    # TODO: discuss a unified TorchScript-friendly API for autocast
+    def __exit__(self, exc_type: Any, exc_val: Any, exc_tb: Any):  # type: ignore[override]
+        if torch._jit_internal.is_scripting():
+            return
+        return super().__exit__(exc_type, exc_val, exc_tb)
+
+    def __call__(self, func):
+        if torch._jit_internal.is_scripting():
+            return func
+        return super().__call__(func)

parrot/lib/python3.10/site-packages/torch/cpu/amp/grad_scaler.py

@@ -0,0 +1,34 @@
+from typing_extensions import deprecated
+
+import torch
+
+__all__ = ["GradScaler"]
+
+
+class GradScaler(torch.amp.GradScaler):
+    r"""
+    See :class:`torch.amp.GradScaler`.
+    ``torch.cpu.amp.GradScaler(args...)`` is deprecated. Please use ``torch.amp.GradScaler("cpu", args...)`` instead.
+    """
+
+    @deprecated(
+        "`torch.cpu.amp.GradScaler(args...)` is deprecated. "
+        "Please use `torch.amp.GradScaler('cpu', args...)` instead.",
+        category=FutureWarning,
+    )
+    def __init__(
+        self,
+        init_scale: float = 2.0**16,
+        growth_factor: float = 2.0,
+        backoff_factor: float = 0.5,
+        growth_interval: int = 2000,
+        enabled: bool = True,
+    ) -> None:
+        super().__init__(
+            "cpu",
+            init_scale=init_scale,
+            growth_factor=growth_factor,
+            backoff_factor=backoff_factor,
+            growth_interval=growth_interval,
+            enabled=enabled,
+        )

parrot/lib/python3.10/site-packages/torch/distributed/__init__.py

@@ -0,0 +1,146 @@
+# mypy: allow-untyped-defs
+import os
+import sys
+from enum import Enum
+import pdb
+import io
+
+import torch
+
+def is_available() -> bool:
+    """
+    Return ``True`` if the distributed package is available.
+
+    Otherwise,
+    ``torch.distributed`` does not expose any other APIs. Currently,
+    ``torch.distributed`` is available on Linux, MacOS and Windows. Set
+    ``USE_DISTRIBUTED=1`` to enable it when building PyTorch from source.
+    Currently, the default value is ``USE_DISTRIBUTED=1`` for Linux and Windows,
+    ``USE_DISTRIBUTED=0`` for MacOS.
+    """
+    return hasattr(torch._C, "_c10d_init")
+
+
+if is_available() and not torch._C._c10d_init():
+    raise RuntimeError("Failed to initialize torch.distributed")
+
+# Custom Runtime Errors thrown from the distributed package
+DistError = torch._C._DistError
+DistBackendError = torch._C._DistBackendError
+DistNetworkError = torch._C._DistNetworkError
+DistStoreError = torch._C._DistStoreError
+
+if is_available():
+    from torch._C._distributed_c10d import (
+        Store,
+        FileStore,
+        TCPStore,
+        ProcessGroup as ProcessGroup,
+        Backend as _Backend,
+        PrefixStore,
+        Reducer,
+        Logger,
+        BuiltinCommHookType,
+        GradBucket,
+        Work as _Work,
+        _DEFAULT_FIRST_BUCKET_BYTES,
+        _register_comm_hook,
+        _register_builtin_comm_hook,
+        _broadcast_coalesced,
+        _compute_bucket_assignment_by_size,
+        _verify_params_across_processes,
+        _test_python_store,
+        DebugLevel,
+        get_debug_level,
+        set_debug_level,
+        set_debug_level_from_env,
+        _make_nccl_premul_sum,
+        _ControlCollectives,
+        _StoreCollectives,
+    )
+
+    class _DistributedPdb(pdb.Pdb):
+        """
+        Supports using PDB from inside a multiprocessing child process.
+
+        Usage:
+        _DistributedPdb().set_trace()
+        """
+        def interaction(self, *args, **kwargs):
+            _stdin = sys.stdin
+            try:
+                sys.stdin = open('/dev/stdin')
+                pdb.Pdb.interaction(self, *args, **kwargs)
+            finally:
+                sys.stdin = _stdin
+
+    def breakpoint(rank: int = 0):
+        """
+        Set a breakpoint, but only on a single rank.  All other ranks will wait for you to be
+        done with the breakpoint before continuing.
+
+        Args:
+            rank (int): Which rank to break on.  Default: ``0``
+        """
+        if get_rank() == rank:
+            pdb = _DistributedPdb()
+            pdb.message(
+                "\n!!! ATTENTION !!!\n\n"
+                f"Type 'up' to get to the frame that called dist.breakpoint(rank={rank})\n"
+            )
+            pdb.set_trace()
+        # If Meta/Python keys are in the TLS, we want to make sure that we ignore them
+        # and hit the (default) CPU/CUDA implementation of barrier.
+        meta_in_tls = torch._C._meta_in_tls_dispatch_include()
+        guard = torch._C._DisableTorchDispatch()  # type: ignore[attr-defined]
+        torch._C._set_meta_in_tls_dispatch_include(False)
+        try:
+            barrier()
+        finally:
+            torch._C._set_meta_in_tls_dispatch_include(meta_in_tls)
+            del guard
+
+    if sys.platform != "win32":
+        from torch._C._distributed_c10d import (
+            HashStore,
+            _round_robin_process_groups,
+        )
+
+    from .distributed_c10d import *  # noqa: F403
+
+    # Variables prefixed with underscore are not auto imported
+    # See the comment in `distributed_c10d.py` above `_backend` on why we expose
+    # this.
+
+    from .distributed_c10d import (
+        _all_gather_base,
+        _reduce_scatter_base,
+        _create_process_group_wrapper,
+        _rank_not_in_group,
+        _coalescing_manager,
+        _CoalescingManager,
+        _get_process_group_name,
+        get_node_local_rank,
+    )
+
+    from .rendezvous import (
+        rendezvous,
+        _create_store_from_options,
+        register_rendezvous_handler,
+    )
+
+    from .remote_device import _remote_device
+    from .device_mesh import init_device_mesh, DeviceMesh
+
+    set_debug_level_from_env()
+
+else:
+    # This stub is sufficient to get
+    #   python test/test_public_bindings.py -k test_correct_module_names
+    # working even when USE_DISTRIBUTED=0.  Feel free to add more
+    # stubs as necessary.
+    # We cannot define stubs directly because they confuse pyre
+
+    class _ProcessGroupStub:
+        pass
+    sys.modules["torch.distributed"].ProcessGroup = _ProcessGroupStub  # type: ignore[attr-defined]

parrot/lib/python3.10/site-packages/torch/distributed/_functional_collectives.py

@@ -0,0 +1,1147 @@
+# mypy: allow-untyped-defs
+import sys
+import warnings
+from typing import cast, List, Optional, Tuple, TYPE_CHECKING, Union
+
+import torch
+import torch.distributed as dist
+import torch.distributed.distributed_c10d as c10d
+from torch.distributed.device_mesh import DeviceMesh
+from torch.fx.experimental.proxy_tensor import get_innermost_proxy_mode
+
+from . import _functional_collectives_impl as fun_col_impl
+
+try:
+    from torch.utils._cxx_pytree import tree_map_only
+except ImportError:
+    from torch.utils._pytree import tree_map_only  # type: ignore[no-redef]
+
+
+if torch._running_with_deploy():
+
+    def is_torchdynamo_compiling():
+        """Can't import torchdynamo in torchdeploy builds currently."""
+        return False
+
+else:
+    try:
+        from torch.compiler import is_dynamo_compiling as is_torchdynamo_compiling
+    except Exception:
+        warnings.warn(
+            "Unable to import torchdynamo util `is_torchdynamo_compiling`, so won't support torchdynamo correctly"
+        )
+
+        def is_torchdynamo_compiling():
+            return False
+
+
+"""
+New traceable, functional collectives.
+RFC: https://github.com/pytorch/pytorch/issues/93173
+
+  compiler: trace these ops with plain-old-data schemas, then choose how to lower them.
+  eager: execute these 'functional' ops which in eager return AsyncCollectiveTensor subclasses,
+         automatically calling .wait() on underlying/hidden async 'work' obj only when fed to
+         a downstream op.
+
+Issues:
+* Where should these ops live? Couldn't `import torch` if putting these ops in existing torch.distributed files
+* Proper support for eager requires inplace ops. We should explore having it as an option for the API.
+"""
+
+"""
+Functional collectives are asynchronous only and we perform implicit stream synchronization
+on behalf of the user.
+
+We use AsyncCollectiveTensor to wrap the result tensor of a collective and it lets us witness
+first usage of the tensor and insert cross stream sync at the right place.
+
+The above are the easy bits, the hard one is how we match the Work object returned by
+c10d and the tensor AsyncCollectiveTensor wraps. We alloc the tensor inside the collective
+op implementation (see ``clone()`` call in ``_all_reduce``) and then it's handled by the
+dispatcher which might call other implementations that are allowed to change the returned
+tensor - even return a tensor with a different shape (see ``torch.vmap``).
+
+This means the caller of our ops receives a Tensor that is not guaranteed to be the same
+allocated by our implementations and that makes pairing The AsyncTensor to the original
+tensor a lot harder. This pairing is needed so we can lookup the Work object to use.
+
+Originally, we tried WeakKeyDictionary to map from Tensor to Work, but because Tensor's
+identity is not stable across dispatch, the op caller would end up with a different Tensor
+instance that would not match any in the dictionary.
+
+With Tensor identity out of the question, we decided use the tensor data pointer, which
+should be stable across all the Tensor changes done during dispatch.
+
+We have a dictionary of tensor::data_ptr -> Work that we insert right after we call into c10d.
+
+We use this dictionary when AsyncCollectiveTensor is used to invoke Work::wait()
+
+Finally, we setup a finalizer against the tensor wrapper to observe it getting collected so we
+can clean up stale entries in the dictionary.
+
+To eliminate the possibility of races we have a global version counter that is used by the finalizer.
+
+As a wise man said once: Don't cross the streams (https://www.youtube.com/watch?v=wyKQe_i9yyo)
+
+"""
+
+"""
+Functional collectives can accept any of these types to describe the ranks participating in collectives.
+
+The different types will be desugared to a canonical format
+"""
+RANK_TYPES = Union[
+    List[int],
+    List[List[int]],
+    dist.ProcessGroup,
+    DeviceMesh,
+    Tuple["dist._tensor.DeviceMesh", int],
+    str,
+]
+
+
+"""
+User facing APIs for functional collectives
+-------------------------------------------
+
+These apis are called by user code and expected to work both in eager execution and compilation,
+but there are significant differences to how the two modes are implemented underneath.
+
+Eager execution is 'optimized' using a tensor subclass that schedules the synchronization (via wait_tensor() op)
+just before the tensor is first used.  Compiled tracing currently relies on the compiler to perform this optimization,
+and cannot yet correctly trace the AsyncTensor wrapper class.  In the future, these paths may be unified
+if sufficient subclass support is added in dynamo.
+
+Example: all_reduce is an entrypoint API, and other collectives follow a similar pattern.
+
+Here's how it works under torch.compile/dynamo:
+all_reduce(...)
+  |--> _expand_group(...)               - desugars processgroup into canonical/traceable format
+  |--> c10d_functional.all_reduce(...)  - dynamo captures this op call, doesn't trace deeper
+  |--> _maybe_wrap_tensor(...)          - wait_tensor() op is immediately called, no AsyncTensor subclass needed
+
+And under eager execution:
+all_reduce(...)
+  |--> _expand_group(...)               - same as above, but less critical for eager
+  |--> c10d_functional.all_reduce(...)  - dispatches to real kernel OR records op in trace
+  |--> _maybe_wrap_tensor(...)          - AsyncTensor wrapper applied to returned tensor,
+                                          which issues wait_tensor() at the time of first use
+"""
+
+
+def wait_tensor(tensor):
+    """
+    Wait on a tensor returned by the collectives ops.
+
+    Waiting follows device semantics, which means blocking on CPU and synchronizing streams on CUDA.
+    """
+    return torch.ops._c10d_functional.wait_tensor(tensor)  # type: ignore[attr-defined]
+
+
+def broadcast(self: torch.Tensor, src: int, group: RANK_TYPES, tag: str = ""):
+    """
+    Broadcasts the tensor to all processes in the given process group.
+
+    Args:
+        src (int): Source rank
+        group (ProcessGroup or List[int]): The process group to work on.
+        tag (str, optional): A unique identifier for the collective. Default: empty string
+    """
+    group_name = _resolve_group_name(group, tag)
+    tensor = torch.ops._c10d_functional.broadcast(self, src, group_name)
+    return _maybe_wrap_tensor(tensor)
+
+
+def all_reduce(self: torch.Tensor, reduceOp: str, group: RANK_TYPES, tag: str = ""):
+    """
+    Reduces the tensor data across all machines in such a way that all get
+    the final result.
+
+    The input tensor is left unmodified.
+
+    Group can be one of:
+        List[int]: ranks participating in the collective.
+        List[List[int]]: 2D mesh of ranks taking part of this collective in MPMD.
+        ProcessGroup: Will perform a collective using the ranks and tag of the PG.
+        DeviceMesh: Do a SPMD collective over all ranks of the mesh
+        (DeviceMesh, int): Do a MPMD collective over one dimension of the DeviceMesh
+
+    :: N.B. If you pass a PG or a 1D list to perform a MPMD collective, the compiler won't be able to recover
+    that information and perform collective algebraic optimization. Use other forms of input for that.
+    """
+    group_name = _resolve_group_name(group, tag)
+    tensor = torch.ops._c10d_functional.all_reduce(self, reduceOp.lower(), group_name)
+    return _maybe_wrap_tensor(tensor)
+
+
+def all_gather_tensor(
+    self: torch.Tensor,
+    gather_dim: int,
+    group: RANK_TYPES,
+    tag: str = "",
+):
+    """
+    Gather tensor data across from all machines and concatenate over ``gather_dim``.
+
+    Note that it currently only supports gather_dim = 0.
+
+    The input tensor is left unmodified.
+    Group can be one of:
+        List[int]: ranks participating in the collective.
+        List[List[int]]: 2D mesh of ranks taking part of this collective in MPMD.
+        ProcessGroup: Will perform a collective using the ranks and tag of the PG.
+        DeviceMesh: Do a SPMD collective over all ranks of the mesh
+        (DeviceMesh, int): Do a MPMD collective over one dimension of the DeviceMesh
+
+    :: N.B. If you pass a PG or a 1D list to perform a MPMD collective, the compiler won't be able to recover
+    that information and perform collective algebraic optimization. Use other forms of input for that.
+    """
+    assert self.is_contiguous()
+    group_name = _resolve_group_name(group, tag)
+    group_size = c10d._get_group_size_by_name(group_name)
+    tensor = torch.ops._c10d_functional.all_gather_into_tensor(
+        self, group_size, group_name
+    )
+    res = _maybe_wrap_tensor(tensor)
+    # TODO this should be done inside AsyncCollectiveTensor to delay the wait() call
+    if gather_dim != 0:
+        # torch.cat access the data so we already need to wait here, first do wait
+        # and then chunk + cat avoid us going through ACT dispatching logic again
+        if isinstance(res, AsyncCollectiveTensor):
+            res = res.wait()  # type: ignore[attr-defined]
+        res = torch.cat(torch.chunk(res, group_size, dim=0), dim=gather_dim)
+    return res
+
+
+def all_gather_tensor_autograd(
+    self: torch.Tensor,
+    gather_dim: int,
+    group: RANK_TYPES,
+    tag: str = "",
+):
+    """
+    Gather tensor data across from all machines and concatenate over ``gather_dim``.
+
+    Note that it currently only supports gather_dim = 0.
+
+    This function is the same as all_gather_tensor but will propagate the
+    backwards gradient across workers.
+
+    See all_gather_tensor for more details on usage.
+    """
+    group_name = _resolve_group_name(group, tag)
+    group_size = c10d._get_group_size_by_name(group_name)
+
+    tensor = torch.ops._c10d_functional_autograd.all_gather_into_tensor(
+        self, group_size, group_name
+    )
+    res = _FromTorchTensor.apply(tensor)
+    # TODO this should be done inside AsyncCollectiveTensor to delay the wait() call
+    if gather_dim != 0:
+        # torch.cat access the data so we already need to wait here, first do wait
+        # and then chunk + cat avoid us going through ACT dispatching logic again
+        if isinstance(res, AsyncCollectiveTensor):
+            res = res.wait()  # type: ignore[attr-defined]
+        res = torch.cat(torch.chunk(res, group_size, dim=0), dim=gather_dim)
+    return res
+
+
+def reduce_scatter_tensor(
+    self: torch.Tensor,
+    reduceOp: str,
+    scatter_dim: int,
+    group: RANK_TYPES,
+    tag: str = "",
+):
+    """
+    Reduces the tensor data across all machines in such a way that all get
+    the final result, then scatter the results to corresponding ranks.
+
+
+    The input tensor is left unmodified.
+    Group can be one of:
+        List[int]: ranks participating in the collective.
+        List[List[int]]: 2D mesh of ranks taking part of this collective in MPMD.
+        ProcessGroup: Will perform a collective using the ranks and tag of the PG.
+        DeviceMesh: Do a SPMD collective over all ranks of the mesh
+        (DeviceMesh, int): Do a MPMD collective over one dimension of the DeviceMesh
+    :: N.B. If you pass a PG or a 1D list to perform a MPMD collective, the compiler won't be able to recover
+    that information and perform collective algebraic optimization. Use other forms of input for that.
+    """
+    group_name = _resolve_group_name(group, tag)
+    group_size = c10d._get_group_size_by_name(group_name)
+
+    assert (
+        self.size(scatter_dim) % group_size == 0
+    ), f"input dimension 0 ({self.size(0)} must be a multiple of group_size {group_size}"
+    if scatter_dim != 0:
+        tensor_list = torch.chunk(self, group_size, dim=scatter_dim)
+        self = torch.cat(tensor_list)
+
+    tensor = torch.ops._c10d_functional.reduce_scatter_tensor(
+        self,
+        reduceOp.lower(),
+        group_size,
+        group_name,  # type: ignore[possibly-undefined]
+    )
+    res = _maybe_wrap_tensor(tensor)
+    return res
+
+
+def reduce_scatter_tensor_autograd(
+    self: torch.Tensor,
+    reduceOp: str,
+    scatter_dim: int,
+    group: RANK_TYPES,
+    tag: str = "",
+):
+    """
+    Reduces the tensor data across all machines in such a way that all get
+    the final result, then scatter the results to corresponding ranks.
+
+    This function is the same as reduce_scatter_tensor but will propagate the
+    backwards gradient across workers.
+
+    Currently only the "sum" reduceOp is supported.
+
+    See reduce_scatter_tensor for more details on usage.
+    """
+
+    group_name = _resolve_group_name(group, tag)
+    group_size = c10d._get_group_size_by_name(group_name)
+
+    assert (
+        self.size(scatter_dim) % group_size == 0
+    ), f"input dimension 0 ({self.size(0)} must be a multiple of group_size {group_size}"
+    if scatter_dim != 0:
+        tensor_list = torch.chunk(self, group_size, dim=scatter_dim)
+        self = torch.cat(tensor_list)
+
+    tensor = torch.ops._c10d_functional_autograd.reduce_scatter_tensor(
+        self,
+        reduceOp.lower(),
+        group_size,
+        group_name,  # type: ignore[possibly-undefined]
+    )
+    res = _FromTorchTensor.apply(tensor)
+    return res
+
+
+def all_reduce_coalesced(
+    self: List[torch.Tensor], reduceOp: str, group: RANK_TYPES, tag: str = ""
+) -> List[torch.Tensor]:
+    """
+    Reduces a list of tensors across all machines in such a way that all get
+    the final result.
+
+    The all tensors in the input list are left unmodified.
+
+    Group can be one of:
+        List[int]: ranks participating in the collective.
+        List[List[int]]: 2D mesh of ranks taking part of this collective in MPMD.
+        ProcessGroup: Will perform a collective using the ranks and tag of the PG.
+        DeviceMesh: Do a SPMD collective over all ranks of the mesh
+        (DeviceMesh, int): Do a MPMD collective over one dimension of the DeviceMesh
+
+    :: N.B. If you pass a PG or a 1D list to perform a MPMD collective, the compiler won't be able to recover
+    that information and perform collective algebraic optimization. Use other forms of input for that.
+    """
+    group_name = _resolve_group_name(group, tag)
+    tensor_list = torch.ops._c10d_functional.all_reduce_coalesced(  # type: ignore[attr-defined]
+        self,
+        reduceOp.lower(),
+        group_name,
+    )
+    return list(map(_maybe_wrap_tensor, tensor_list))
+
+
+def all_gather_into_tensor_coalesced(
+    self: List[torch.Tensor], group: RANK_TYPES, tag: str = ""
+) -> List[torch.Tensor]:
+    """
+    Gather a list of tensors across from all machines.
+
+    Note that it currently only supports gather_dim = 0.
+
+    The input tensor is left unmodified.
+    Group can be one of:
+        List[int]: ranks participating in the collective.
+        List[List[int]]: 2D mesh of ranks taking part of this collective in MPMD.
+        ProcessGroup: Will perform a collective using the ranks and tag of the PG.
+        DeviceMesh: Do a SPMD collective over all ranks of the mesh
+        (DeviceMesh, int): Do a MPMD collective over one dimension of the DeviceMesh
+
+    :: N.B. If you pass a PG or a 1D list to perform a MPMD collective, the compiler won't be able to recover
+    that information and perform collective algebraic optimization. Use other forms of input for that.
+    """
+    group_name = _resolve_group_name(group, tag)
+    group_size = c10d._get_group_size_by_name(group_name)
+    tensor_list = torch.ops._c10d_functional.all_gather_into_tensor_coalesced(  # type: ignore[attr-defined]
+        self,
+        group_size,
+        group_name,
+    )
+    return list(map(_maybe_wrap_tensor, tensor_list))
+
+
+def reduce_scatter_tensor_coalesced(
+    inputs: List[torch.Tensor],
+    reduceOp: str,
+    scatter_dim: List[int],
+    group: RANK_TYPES,
+    tag: str = "",
+) -> List[torch.Tensor]:
+    """
+    Reduces a list of tensors across all machines in such a way that all get
+    the final result, then scatter the results to corresponding ranks.
+
+    The input tensors are left unmodified.
+    Group can be one of:
+        List[int]: ranks participating in the collective.
+        List[List[int]]: 2D mesh of ranks taking part of this collective in MPMD.
+        ProcessGroup: Will perform a collective using the ranks and tag of the PG.
+        DeviceMesh: Do a SPMD collective over all ranks of the mesh
+        (DeviceMesh, int): Do a MPMD collective over one dimension of the DeviceMesh
+
+    :: N.B. If you pass a PG or a 1D list to perform a MPMD collective, the compiler won't be able to recover
+    that information and perform collective algebraic optimization. Use other forms of input for that.
+    """
+    group_name = _resolve_group_name(group, tag)
+    group_size = c10d._get_group_size_by_name(group_name)
+
+    assert len(scatter_dim) == len(inputs)
+    for idx, (dim, tensor) in enumerate(zip(scatter_dim, inputs)):
+        assert (
+            tensor.size(dim) % group_size == 0
+        ), f"input dimension {dim} ({tensor.size(dim)} must be a multiple of group_size {group_size} for tensor at index {idx}"
+        if dim != 0:
+            tensor_list = torch.chunk(tensor, group_size, dim=dim)
+            inputs[idx] = torch.cat(tensor_list)
+
+    tensor_list = torch.ops._c10d_functional.reduce_scatter_tensor_coalesced(  # type: ignore[attr-defined]
+        inputs,
+        reduceOp.lower(),
+        group_size,
+        group_name,  # type: ignore[possibly-undefined]
+    )
+
+    return list(map(_maybe_wrap_tensor, tensor_list))
+
+
+# This is a bit unsafe: it checks if the first argument in the schema reports as a non-mutable alias.
+# Today, this maps 1:1 with "aten ops that are views".
+def _is_view_op(tgt):
+    assert isinstance(tgt, torch._ops.OpOverload)
+    schema = tgt._schema
+    if len(schema.arguments) > 0:
+        first_arg = schema.arguments[0]
+        # check if op is a view
+        return first_arg.alias_info is not None and not first_arg.alias_info.is_write
+
+
+def all_to_all_single(
+    self: torch.Tensor,
+    output_split_sizes: Optional[List[int]],
+    input_split_sizes: Optional[List[int]],
+    group: RANK_TYPES,
+    tag: str = "",
+) -> torch.Tensor:
+    """
+    Each process splits input tensor and then scatters the split list
+    to all processes in a group. Then concatenate the received tensors from all
+    the processes in the group and return single output tensor.
+
+    Group can be one of:
+        List[int]: ranks participating in the collective.
+        List[List[int]]: 2D mesh of ranks taking part of this collective in MPMD.
+        ProcessGroup: Will perform a collective using the ranks and tag of the PG.
+        DeviceMesh: Do a SPMD collective over all ranks of the mesh
+        (DeviceMesh, int): Do a MPMD collective over one dimension of the DeviceMesh
+
+    :: N.B. If you pass a PG or a 1D list to perform a MPMD collective, the compiler won't be able to recover
+    that information and perform collective algebraic optimization. Use other forms of input for that.
+    """
+    if output_split_sizes is not None:
+        assert all(
+            isinstance(size, (int, torch.SymInt)) for size in output_split_sizes
+        ), output_split_sizes
+    if input_split_sizes is not None:
+        assert all(
+            isinstance(size, (int, torch.SymInt)) for size in input_split_sizes
+        ), input_split_sizes
+    group_name = _resolve_group_name(group, tag)
+    group_size = c10d._get_group_size_by_name(group_name)
+    if output_split_sizes is None or input_split_sizes is None:
+        assert output_split_sizes is None and input_split_sizes is None, (
+            "output_split_sizes and input_split_sizes must either be "
+            "specified together or both set to None"
+        )
+        output_split_sizes = [self.shape[0] // group_size] * group_size
+        input_split_sizes = output_split_sizes
+    tensor = torch.ops._c10d_functional.all_to_all_single(  # type: ignore[attr-defined]
+        self,
+        output_split_sizes,
+        input_split_sizes,
+        group_name,
+    )
+    return _maybe_wrap_tensor(tensor)
+
+
+def all_to_all_single_autograd(
+    self: torch.Tensor,
+    output_split_sizes: Optional[List[int]],
+    input_split_sizes: Optional[List[int]],
+    group: RANK_TYPES,
+    tag: str = "",
+) -> torch.Tensor:
+    """
+    Same as all_to_all_single but supports autograd.
+    """
+    if output_split_sizes is not None:
+        assert all(
+            isinstance(size, (int, torch.SymInt)) for size in output_split_sizes
+        ), output_split_sizes
+    if input_split_sizes is not None:
+        assert all(
+            isinstance(size, (int, torch.SymInt)) for size in input_split_sizes
+        ), input_split_sizes
+
+    group_name = _resolve_group_name(group, tag)
+    group_size = c10d._get_group_size_by_name(group_name)
+    if output_split_sizes is None or input_split_sizes is None:
+        assert output_split_sizes is None and input_split_sizes is None, (
+            "output_split_sizes and input_split_sizes must either be "
+            "specified together or both set to None"
+        )
+        output_split_sizes = [self.shape[0] // group_size] * group_size
+        input_split_sizes = output_split_sizes
+    tensor = torch.ops._c10d_functional_autograd.all_to_all_single(  # type: ignore[attr-defined]
+        self,
+        output_split_sizes,
+        input_split_sizes,
+        group_name,
+    )
+    return _FromTorchTensor.apply(tensor)
+
+
+def permute_tensor(
+    self: torch.Tensor,
+    src_dst: List[int],
+    group: RANK_TYPES,
+    tag: str = "",
+) -> torch.Tensor:
+    """
+    Permutes the elements of the tensor according to the given source/destination pairs. `src_dst` should
+    be defined such that src_dst[m] == n means m sends to n.
+
+    Group can be one of:
+        List[int]: ranks participating in the collective.
+        List[List[int]]: 2D mesh of ranks taking part of this collective in MPMD.
+        ProcessGroup: Will perform a collective using the ranks and tag of the PG.
+        DeviceMesh: Do a SPMD collective over all ranks of the mesh
+        (DeviceMesh, int): Do a MPMD collective over one
+    """
+    t, rankset, group_size = _expand_group(group, tag)
+    local_pg = c10d._find_or_create_pg_by_ranks_and_tag(t, rankset, group_size)
+
+    output_split_sizes = [0] * group_size
+    input_split_sizes = [0] * group_size
+    for src, dst in enumerate(src_dst):
+        if src == dist.get_rank(local_pg):
+            input_split_sizes[dst] = self.numel()
+        if dst == dist.get_rank(local_pg):
+            output_split_sizes[src] = self.numel()
+
+    return all_to_all_single(self, output_split_sizes, input_split_sizes, group, tag)
+
+
+class AsyncCollectiveTensor(torch.Tensor):
+    r"""
+    A Tensor wrapper subclass that is used to trigger a call to wait
+    prior to first use of the underlying tensor.
+    Use it inside functional collective pytorch wrappers like the following:
+    def functional_collective(self, group, tag):
+        tag, rankset, group_size = _expand_group(group, tag)
+        tensor = torch.ops.c10d_functional.{collective}(self, tag, rankset, group_size)
+        return _maybe_wrap_tensor(tensor)
+    """
+    elem: torch.Tensor
+    completed: bool
+
+    __slots__ = ["elem", "completed"]
+
+    @staticmethod
+    def __new__(cls, elem: torch.Tensor):
+        r = torch.Tensor._make_wrapper_subclass(  # type: ignore[attr-defined]
+            cls,
+            elem.size(),
+            strides=elem.stride(),
+            storage_offset=elem.storage_offset(),
+            dtype=elem.dtype,
+            layout=elem.layout,
+            device=elem.device,
+            requires_grad=elem.requires_grad,
+        )
+        r.elem = elem
+        r.completed = False
+        return r
+
+    def __tensor_flatten__(self):
+        return ["elem"], None
+
+    def tolist(self):
+        return self.trigger_wait().tolist()
+
+    @staticmethod
+    def __tensor_unflatten__(inner_tensors, meta, outer_size, outer_stride):
+        assert meta is None
+        elem = inner_tensors["elem"]
+        return AsyncCollectiveTensor(elem)
+
+    def __repr__(self):
+        return f"AsyncCollectiveTensor({self.trigger_wait()})"
+
+    def trigger_wait(self):
+        if not self.completed:
+            out = wait_tensor(self.elem)
+            self.completed = True
+            return out
+        else:
+            return self.elem
+
+    def wait(self) -> torch.Tensor:
+        return wait_tensor(self.elem)
+
+    def _get_acs_underlying_tensor(self):
+        """This method enables  _functional_collectives_impl to test if a tensor is an ACS"""
+        return self.elem
+
+    @classmethod
+    def __torch_dispatch__(cls, func, types, args=(), kwargs=None):
+        if func == torch.ops.aten.view.default:
+            # Fast handle aten.view as a lot of view related op goes to aten.view
+            # eventually, this avoids pytree slowdown
+            res = func(args[0].elem, args[1])
+            wrapper_res = AsyncCollectiveTensor(res)
+            return wrapper_res
+
+        is_view_op = _is_view_op(func)
+
+        def unwrap(e: AsyncCollectiveTensor):
+            # wait_tensor is idepotent and will do stream sync only once
+            if not is_view_op:
+                return e.trigger_wait()
+            return e.elem
+
+        def wrap(e: torch.Tensor):
+            # wait_tensor is idepotent and will do stream sync only once
+            assert not isinstance(e, AsyncCollectiveTensor)
+            res = AsyncCollectiveTensor(e)
+            return res
+
+        unwrapped_args = tree_map_only(AsyncCollectiveTensor, unwrap, args)
+        unwrapped_kwargs = tree_map_only(AsyncCollectiveTensor, unwrap, kwargs)
+
+        # we don't wrap the result as it doesn't need to be waited on.
+        out = func(*unwrapped_args, **unwrapped_kwargs)
+
+        # View ops dont require a sync, so we should re-wrap the outputs.
+        if is_view_op:
+            out = tree_map_only(torch.Tensor, wrap, out)
+
+        return out
+
+    def numpy(self):
+        return self.wait().numpy()
+
+
+"""
+Utils and infrastructure for tracing support
+"""
+
+
+def _expand_group(group: RANK_TYPES, tag: str = "") -> Tuple[str, List[int], int]:
+    """
+    _expand_group desugars the different RANK_TYPES types into a canonical format that is traceable.
+
+    By having this be part of the explicit eager codepath, we avoid having to specialize behavior inside
+    torchdynamo and can still interoperate with processgroup objects or other untraceable forms.
+    """
+    # had to define this hack _inside_ expand_group to avoid
+    # graph_break [('torch.* op returned non-Tensor int
+    # caused by 'cast_*` functions being treated as 'torch.*' ops (iiuc)
+    if TYPE_CHECKING:
+
+        def cast_listlistint(x):
+            return cast(List[List[int]], x)
+
+        def cast_listint(x):
+            return cast(List[int], x)
+
+    else:
+        # fake cast op for use at runtime since dynamo doesn't support real cast
+        # also, dynamo didn't like encountering 'typing' objects ()
+        # NotImplementedError: argument of type: <class 'typing._GenericAlias'>
+        def cast_listlistint(x):
+            return x
+
+        def cast_listint(x):
+            return x
+
+    rankset: List[int]
+    if isinstance(group, list):
+        if isinstance(group[0], list):
+            nested_list = cast_listlistint(group)
+            rankset = []
+            group_size = -1
+            for rs in nested_list:
+                rankset.extend(rs)
+                if group_size != -1 and group_size != len(rs):
+                    raise ValueError(
+                        f"group sizes must be identical found {group_size} and {len(rs)}"
+                    )
+                group_size = len(rs)
+        else:
+            rankset = cast_listint(group)
+            group_size = len(rankset)
+    elif isinstance(group, dist.ProcessGroup):
+        rankset = dist.get_process_group_ranks(group)
+        group_size = len(rankset)
+        tag = tag or c10d._get_group_tag(group)
+    elif isinstance(group, DeviceMesh):
+        assert (
+            group.ndim == 1
+        ), "Only 1D mesh is supported, pass in (DeviceMesh, int) together if mesh > 1D"
+        # TODO: it should run collective in the whole mesh instead of dim 0
+        tag, rankset, _ = group._dim_group_infos[0]
+        group_size = len(rankset)
+    elif isinstance(group, tuple):
+        if (
+            len(group) == 2
+            and isinstance(group[0], DeviceMesh)
+            and isinstance(group[1], int)
+        ):
+            dmesh = group[0]
+            dim = group[1]
+            tag, rankset, _ = dmesh._dim_group_infos[dim]
+            group_size = len(rankset)
+        else:
+            raise ValueError("Invalid tuple for group must be (DeviceMesh, int)")
+    else:
+        raise ValueError(
+            "Invalid type for group, must be one of List, Processgroup, DeviceMesh or (DeviceMesh, int)."
+        )
+
+    return (tag, rankset, group_size)
+
+
+def _resolve_group_name(group: RANK_TYPES, tag: str = "") -> str:
+    """
+    Given group in RANK_TYPES, return the group name.
+    """
+    # `tag` will be deprecated. See details in:
+    # https://github.com/pytorch/pytorch/issues/93173#issuecomment-1907095208
+    if isinstance(group, dist.ProcessGroup):
+        return group.group_name
+    elif isinstance(group, str):
+        return group
+    elif isinstance(group, DeviceMesh):
+        assert (
+            group.ndim == 1
+        ), "Only 1D mesh is supported, pass in (DeviceMesh, int) together if mesh > 1D"
+        return group._dim_group_infos[0][2]
+    elif isinstance(group, tuple):
+        if (
+            len(group) == 2
+            and isinstance(group[0], DeviceMesh)
+            and isinstance(group[1], int)
+        ):
+            dmesh = group[0]
+            dim = group[1]
+            return dmesh._dim_group_infos[dim][2]
+        else:
+            raise ValueError("Invalid tuple for group must be (DeviceMesh, int)")
+    elif isinstance(group, list):
+        if not is_torchdynamo_compiling():
+            warnings.warn(
+                "The combination of ranks + tag as process group "
+                "identifier has been deprecated. Please switch to "
+                "using ProcessGroup, DeviceMesh, or group name instead.",
+                FutureWarning,
+                stacklevel=3,
+            )
+        return c10d._resolve_group_name_by_ranks_and_tag(cast(List[int], group), tag)
+    else:
+        raise ValueError(f"Unsupported group type: {type(group)}, {group}")
+
+
+class _FromTorchTensor(torch.autograd.Function):
+    """
+    _FromTorchTensor allows autograd to propagate from a normal Tensor to an
+    AsyncCollectiveTensor.
+    """
+
+    @staticmethod
+    def forward(  # type: ignore[override]
+        ctx,  # pyre-ignore[2]: Parameter must be annotated.
+        input: torch.Tensor,
+    ) -> torch.Tensor:
+        return _maybe_wrap_tensor(input)
+
+    @staticmethod
+    def backward(ctx, grad_output: torch.Tensor) -> torch.Tensor:  # type: ignore[override]
+        return grad_output
+
+
+def _are_we_tracing() -> bool:
+    if is_torchdynamo_compiling():
+        return True
+    # If functionalization is turned on, we are almost definitely compiling/tracing.
+    # (In particular, AOTAutograd traces a model once with functionalization on
+    #  but proxy tracing turned of, so this is how we detect it).
+    if (
+        torch._C._get_dispatch_mode(torch._C._TorchDispatchModeKey.FUNCTIONAL)
+        is not None
+    ):
+        return True
+    mode = get_innermost_proxy_mode()
+    if mode is None:
+        return False
+    return mode.tracer is not None
+
+
+def _maybe_wrap_tensor(self) -> torch.Tensor:
+    if _are_we_tracing():
+        return wait_tensor(self)
+    res = AsyncCollectiveTensor(self)
+    return cast(torch.Tensor, res)
+
+
+def _all_gather_into_tensor_coalesced_meta(self, tag, rankset, group_size):
+    def mk_out_tensor(shard):
+        out_size = list(shard.size())
+        out_size[0] *= group_size
+        out_tensor = shard.new_empty(out_size)
+        return out_tensor
+
+    return [mk_out_tensor(t) for t in self]
+
+
+# We now register meta kernels to deal with tracing
+def _broadcast_meta(self, *args):
+    return torch.empty_like(self)
+
+
+def _all_reduce_meta(self, *args):
+    return torch.empty_like(self)
+
+
+def _wait_tensor_meta(self, *args):
+    return torch.empty_like(self)
+
+
+def _all_gather_into_tensor_meta(shard, tag, rankset, group_size):
+    out_size = list(shard.size())
+    out_size[0] *= group_size
+    return shard.new_empty(out_size)
+
+
+def _reduce_scatter_tensor_meta(input, reduce_op, tag, rankset, group_size):
+    out_size = list(input.size())
+    out_size[0] //= group_size
+    return input.new_empty(out_size)
+
+
+def _all_reduce_coalesced_meta(self, *args):
+    return [torch.empty_like(t) for t in self]
+
+
+def _all_reduce__meta(inp, *args):
+    return inp
+
+
+def _broadcast__meta(inp, *args):
+    return inp
+
+
+def _all_reduce_coalesced__meta(inputs, *args):
+    return inputs
+
+
+def _reduce_scatter_tensor_coalesced_meta(inputs, reduceOp, tag, rankset, group_size):
+    def mk_out_tensor(input):
+        out_size = list(input.size())
+        out_size[0] //= group_size
+        out_tensor = input.new_empty(out_size)
+        return out_tensor
+
+    return [mk_out_tensor(t) for t in inputs]
+
+
+# NB: We often say all_to_all has dynamic output size, but this is not
+# technically true: instead, what typically happens is you manually
+# communicate the output_split_sizes ahead of time (which is dynamic),
+# but then you pass those sizes explicitly, and the all to all itself
+# isn't dynamic, it just follows the specified output splits
+def _all_to_all_single_meta(
+    input, output_split_sizes, input_split_sizes, *args, **kwargs
+):
+    if output_split_sizes is None:
+        return input.new_empty(input.size())
+    else:
+        for s in output_split_sizes:
+            torch._check_is_size(s)
+        out_size = list(input.size())
+        out_size[0] = sum(output_split_sizes)
+        return input.new_empty(out_size)
+
+
+def _all_gather_into_tensor_out_native_meta(input, group_size, group_name, *, out):
+    shape = list(input.size())
+    shape[0] *= group_size
+    return input.new_empty(shape)
+
+
+def _all_gather_into_tensor_native_meta(input, group_size, group_name):
+    shape = list(input.size())
+    shape[0] *= group_size
+    return input.new_empty(shape)
+
+
+def _all_gather_into_tensor_coalesced_native_meta(inputs, group_size, group_name):
+    return [
+        _all_gather_into_tensor_native_meta(input, group_size, group_name)
+        for input in inputs
+    ]
+
+
+def _reduce_scatter_tensor_native_meta(inp, reduce_op, group_size, group_name):
+    shape = list(inp.size())
+    shape[0] //= group_size
+    return inp.new_empty(shape)
+
+
+def _reduce_scatter_tensor_coalesced_native_meta(
+    inputs, reduce_op, group_size, group_name
+):
+    return [
+        _reduce_scatter_tensor_native_meta(inp, reduce_op, group_size, group_name)
+        for inp in inputs
+    ]
+
+
+if not torch._running_with_deploy():
+    # Library MUST be defined at module scope or it doesn't work
+    # Creating a "DEF" Library always crashes torch::deploy so we create our
+    # Library instances here guarded against running inside it
+    lib_impl = torch.library.Library("_c10d_functional", "IMPL")
+    lib_impl.impl("all_reduce", _all_reduce_meta, "Meta")
+    lib_impl.impl("all_reduce_", _all_reduce__meta, "Meta")
+    lib_impl.impl("all_reduce_coalesced", _all_reduce_coalesced_meta, "Meta")
+    lib_impl.impl("all_reduce_coalesced_", _all_reduce_coalesced__meta, "Meta")
+    lib_impl.impl("wait_tensor", _wait_tensor_meta, "Meta")
+    lib_impl.impl(
+        "all_gather_into_tensor_out", _all_gather_into_tensor_out_native_meta, "Meta"
+    )
+    lib_impl.impl("all_gather_into_tensor", _all_gather_into_tensor_native_meta, "Meta")
+    lib_impl.impl(
+        "all_gather_into_tensor_coalesced",
+        _all_gather_into_tensor_coalesced_native_meta,
+        "Meta",
+    )
+    lib_impl.impl("reduce_scatter_tensor", _reduce_scatter_tensor_native_meta, "Meta")
+    lib_impl.impl(
+        "reduce_scatter_tensor_coalesced",
+        _reduce_scatter_tensor_coalesced_native_meta,
+        "Meta",
+    )
+    lib_impl.impl("all_to_all_single", _all_to_all_single_meta, "Meta")
+    lib_impl.impl("broadcast", _broadcast_meta, "Meta")
+    lib_impl.impl("broadcast_", _broadcast__meta, "Meta")
+
+    # Register legacy ops for backward compatibility
+    # TODO(yifu): remove these in functional collective beta release
+    legacy_lib = torch.library.Library("c10d_functional", "DEF")
+    legacy_lib_impl = torch.library.Library("c10d_functional", "IMPL")
+    ops_defs = [
+        "broadcast(Tensor self, int src, str tag, int[] ranks, int group_size) -> Tensor",
+        "all_reduce(Tensor self, str reduceOp, str tag, int[] ranks, int group_size) -> Tensor",
+        "all_reduce_coalesced(Tensor[] self, str reduceOp, str tag, int[] ranks, int group_size) -> Tensor[]",
+        "wait_tensor(Tensor self) -> Tensor",
+        "all_gather_into_tensor(Tensor shard, str tag, int[] ranks, int group_size) -> Tensor",
+        "all_gather_into_tensor_coalesced(Tensor[] input, str tag, int[] ranks, int group_size) -> Tensor[]",
+        "reduce_scatter_tensor(Tensor input, str reduceOp, str tag, int[] ranks, int group_size) -> Tensor",
+        "reduce_scatter_tensor_coalesced(Tensor[] inputs, str reduceOp, str tag, int[] ranks, int group_size) -> Tensor[]",
+        "all_to_all_single(Tensor input, SymInt[]? output_split_sizes, SymInt[]? input_split_sizes, str tag, int[] ranks, int group_size) -> Tensor",  # noqa: B950
+    ]
+
+    my_module = sys.modules[__name__]
+    for op_def in ops_defs:
+        op_name = op_def[0 : op_def.index("(")]
+        backend_impl = getattr(fun_col_impl, f"_{op_name}")
+        legacy_lib.define(op_def, tags=torch.Tag.pt2_compliant_tag)
+        legacy_lib_impl.impl(op_name, backend_impl, "CompositeImplicitAutograd")
+
+else:
+    warnings.warn(
+        "PyTorch Distributed functional collectives do not work with torch::deploy."
+    )
+
+
+"""
+Dynamo Remappings allow seamless translation from non-functional collectives of supportable form into
+functional collective calls followed by inplace copy ops, allowing them to be traced into a functional graph.
+
+We implement this by writing a decomposition and teaching dynamo how to associate it to a corresponding op via
+the mapping dict below.
+
+These schemas intentionally match torch.distributed.distributed_c10d.* ops that we are trying to remap from
+"""
+
+
+def all_gather_tensor_inplace(
+    output_tensor: torch.Tensor,
+    input_tensor: torch.Tensor,
+    group,  # TODO add a type,
+    async_op: bool = False,
+    tag: str = "",
+    gather_dim: int = 0,
+):
+    assert (
+        not async_op
+    ), "Can't remap async version of inplace op to functional collective"
+
+    group = group or dist.group.WORLD
+    assert group is not None
+
+    return output_tensor.copy_(all_gather_tensor(input_tensor, gather_dim, group, tag))
+
+
+def reduce_scatter_tensor_inplace(
+    output: torch.Tensor,
+    input: torch.Tensor,
+    op: str = "sum",  # TODO type is actually c10d ReduceOp. is this ok?
+    group=None,  # TODO add a type
+    async_op: bool = False,
+    scatter_dim: int = 0,
+    tag: str = "",
+):
+    assert (
+        not async_op
+    ), "Can't remap async version of inplace op to functional collective"
+
+    group = group or dist.group.WORLD
+    assert group is not None
+
+    return output.copy_(reduce_scatter_tensor(input, op, scatter_dim, group, tag))
+
+
+REDUCE_OP_TO_STR = {
+    dist.ReduceOp.SUM: "sum",
+    dist.ReduceOp.AVG: "avg",
+    dist.ReduceOp.PRODUCT: "product",
+    dist.ReduceOp.MIN: "min",
+    dist.ReduceOp.MAX: "max",
+    dist.ReduceOp.BAND: "band",
+    dist.ReduceOp.BOR: "bor",
+    dist.ReduceOp.BXOR: "bxor",
+}
+
+
+def all_reduce_inplace(
+    tensor: torch.Tensor,
+    op: str = "sum",
+    group=None,
+    async_op: bool = False,
+    tag: str = "",
+):
+    assert (
+        not async_op
+    ), "Can't remap async version of inplace op to functional collective"
+
+    group = group or dist.group.WORLD
+    assert group is not None
+
+    return tensor.copy_(all_reduce(tensor, op, group, tag))
+
+
+def all_to_all_inplace(
+    output: torch.Tensor,
+    input: torch.Tensor,
+    output_split_sizes=None,
+    input_split_sizes=None,
+    group=None,
+    async_op=False,
+    tag: str = "",
+):
+    assert (
+        not async_op
+    ), "Can't remap async version of inplace op to functional collective"
+
+    group = group or dist.group.WORLD
+    assert group is not None
+
+    return output.copy_(
+        all_to_all_single(
+            input,
+            output_split_sizes,
+            input_split_sizes,
+            group,
+            tag,
+        )
+    )
+
+
+def all_gather_inplace(
+    tensor_list: List[torch.Tensor],
+    tensor: torch.Tensor,
+    group=None,
+    async_op=False,
+    tag: str = "",
+):
+    assert (
+        not async_op
+    ), "Can't remap async version of inplace op to functional collective"
+    assert all(
+        t.size(0) == tensor.size(0) for t in tensor_list
+    ), "Remapping variable size all_gather is not yet supported"
+
+    group = group or dist.group.WORLD
+    assert group is not None
+
+    output = all_gather_tensor(tensor, 0, group, tag)
+
+    # Use aten.slice instead of aten.split because the latter causes
+    # tensor.shape(0) to be unnecessarily baked in when it's a SymInt.
+    output_splits = []
+    offset = 0
+    for t in tensor_list:
+        output_splits.append(output[offset : offset + t.size(0)])
+        offset += t.size(0)
+    for dst, src in zip(tensor_list, output_splits):
+        dst.copy_(src)
+    return tensor_list
+
+
+from torch.distributed.distributed_c10d import (
+    _all_gather_base as legacy_all_gather_base,
+    _reduce_scatter_base as legacy_reduce_scatter_base,
+    all_gather as legacy_all_gather,
+    all_gather_into_tensor as legacy_allgather,
+    all_reduce as legacy_allreduce,
+    all_to_all_single as legacy_all_to_all_single,
+    reduce_scatter_tensor as legacy_reducescatter,
+)
+
+# This dict should contain sets of functions that dynamo is allowed to remap.
+# Functions in this set should accept the same args/kwargs 1:1 as their mapping.
+traceable_collective_remaps = {
+    legacy_allgather: all_gather_tensor_inplace,
+    legacy_reducescatter: reduce_scatter_tensor_inplace,
+    legacy_allreduce: all_reduce_inplace,
+    legacy_all_to_all_single: all_to_all_inplace,
+    legacy_all_gather: all_gather_inplace,
+    legacy_reduce_scatter_base: reduce_scatter_tensor_inplace,
+    legacy_all_gather_base: all_gather_tensor_inplace,
+}

parrot/lib/python3.10/site-packages/torch/distributed/_functional_collectives_impl.py

@@ -0,0 +1,116 @@
+# mypy: allow-untyped-defs
+from typing import List, Optional
+
+import torch
+import torch.distributed.distributed_c10d as c10d
+
+"""
+This file contains the op impls for the legacy (c10d_functional) functional collectives.
+These impls simply call into the native (_c10d_functional) functional collectives.
+"""
+
+
+def _broadcast(input, src, tag, ranks, group_size):
+    group_name = c10d._resolve_group_name_by_ranks_and_tag(ranks, tag)
+    return torch.ops._c10d_functional.broadcast(
+        input,
+        src,
+        group_name,
+    )
+
+
+def _all_reduce(input, reduce_op, tag, ranks, group_size):
+    group_name = c10d._resolve_group_name_by_ranks_and_tag(ranks, tag)
+    return torch.ops._c10d_functional.all_reduce(
+        input,
+        reduce_op,
+        group_name,
+    )
+
+
+def _all_reduce_coalesced(inputs, reduce_op, tag, ranks, group_size):
+    group_name = c10d._resolve_group_name_by_ranks_and_tag(ranks, tag)
+    return torch.ops._c10d_functional.all_reduce_coalesced(
+        inputs,
+        reduce_op,
+        group_name,
+    )
+
+
+def _all_gather_into_tensor(input, tag, ranks, group_size):
+    group_name = c10d._resolve_group_name_by_ranks_and_tag(ranks, tag)
+    return torch.ops._c10d_functional.all_gather_into_tensor(
+        input,
+        group_size,
+        group_name,
+    )
+
+
+def _all_gather_into_tensor_coalesced(input, tag, ranks, group_size):
+    group_name = c10d._resolve_group_name_by_ranks_and_tag(ranks, tag)
+    return torch.ops._c10d_functional.all_gather_into_tensor_coalesced(
+        input,
+        group_size,
+        group_name,
+    )
+
+
+def _reduce_scatter_tensor(
+    input: torch.Tensor,
+    reduce_op: str,
+    tag: str,
+    ranks: List[int],
+    group_size: int,
+):
+    group_name = c10d._resolve_group_name_by_ranks_and_tag(ranks, tag)
+    return torch.ops._c10d_functional.reduce_scatter_tensor(
+        input,
+        reduce_op,
+        group_size,
+        group_name,
+    )
+
+
+def _reduce_scatter_tensor_coalesced(
+    inputs: List[torch.Tensor],
+    reduce_op: str,
+    tag: str,
+    ranks: List[int],
+    group_size: int,
+):
+    group_name = c10d._resolve_group_name_by_ranks_and_tag(ranks, tag)
+    return torch.ops._c10d_functional.reduce_scatter_tensor_coalesced(
+        inputs,
+        reduce_op,
+        group_size,
+        group_name,
+    )
+
+
+def _all_to_all_single(
+    input: torch.Tensor,
+    output_split_sizes: Optional[List[int]],
+    input_split_sizes: Optional[List[int]],
+    tag: str,
+    ranks: List[int],
+    group_size: int,
+):
+    if output_split_sizes is None or input_split_sizes is None:
+        assert output_split_sizes is None and input_split_sizes is None, (
+            "output_split_sizes and input_split_sizes must either be "
+            "specified together or both set to None"
+        )
+        output_split_sizes = [input.shape[0] // group_size] * group_size
+        input_split_sizes = output_split_sizes
+
+    group_name = c10d._resolve_group_name_by_ranks_and_tag(ranks, tag)
+    return torch.ops._c10d_functional.all_to_all_single(
+        input,
+        output_split_sizes,
+        input_split_sizes,
+        group_name,
+    )
+
+
+def _wait_tensor(tensor: torch.Tensor) -> torch.Tensor:
+    return torch.ops._c10d_functional.wait_tensor(tensor)

parrot/lib/python3.10/site-packages/torch/distributed/_shard/__init__.py

@@ -0,0 +1,6 @@
+from .api import (
+    _shard_tensor,
+    load_with_process_group,
+    shard_module,
+    shard_parameter,
+)

parrot/lib/python3.10/site-packages/torch/distributed/_shard/_utils.py

@@ -0,0 +1,28 @@
+import torch
+from torch.distributed._shard.metadata import ShardMetadata
+from typing import Sequence
+
+DEPRECATE_MSG = "Please use DTensor instead and we are deprecating ShardedTensor."
+
+def narrow_tensor_by_index(tensor: torch.Tensor, offsets: Sequence[int], sizes: Sequence[int]) -> torch.Tensor:
+    """
+    Narrow the tensor according to ``offsets`` and ``sizes``.
+    """
+    narrowed_tensor = tensor
+    for idx, (offset, size) in enumerate(zip(offsets, sizes)):
+        if size < tensor.size(idx):
+            # Reshape to get shard for this rank and we don't want autograd
+            # recording here for the narrow op and 'local_shard' should be a
+            # leaf variable in the autograd graph.
+            narrowed_tensor = narrowed_tensor.narrow(
+                idx,
+                offset,
+                size
+            )
+    return narrowed_tensor
+
+def narrow_tensor(tensor: torch.Tensor, metadata: ShardMetadata) -> torch.Tensor:
+    """
+    Narrow the tensor according to the metadata
+    """
+    return narrow_tensor_by_index(tensor, metadata.shard_offsets, metadata.shard_sizes)

parrot/lib/python3.10/site-packages/torch/distributed/_shard/checkpoint/__init__.py

@@ -0,0 +1,19 @@
+# Keep old package for BC purposes, this file should be removed once
+# everything moves to the `torch.distributed.checkpoint` package.
+import sys
+import torch
+import warnings
+
+from torch.distributed.checkpoint import *  # noqa: F403
+
+
+with warnings.catch_warnings():
+    warnings.simplefilter("always")
+    warnings.warn(
+        "`torch.distributed._shard.checkpoint` will be deprecated, "
+        "use `torch.distributed.checkpoint` instead",
+        DeprecationWarning,
+        stacklevel=2,
+    )
+
+sys.modules['torch.distributed._shard.checkpoint'] = torch.distributed.checkpoint

parrot/lib/python3.10/site-packages/torch/distributed/_shard/common_op_utils.py

@@ -0,0 +1,62 @@
+# mypy: allow-untyped-defs
+import torch
+from torch.utils import _pytree as pytree
+from typing import Optional
+
+def _basic_validation(op, args=(), kwargs=None):
+    """
+    Common validation across all ops go in here.
+    """
+    from torch.distributed._shard.sharded_tensor import ShardedTensor
+
+    if len(args) == 0 and (kwargs is None or len(kwargs) == 0):
+        raise ValueError(f" No input for '{op.__name__}'!")
+
+    # Validate types
+    has_distributed_tensor = False
+
+    def is_distributed_tensor(e):
+        nonlocal has_distributed_tensor
+        if isinstance(e, ShardedTensor):
+            has_distributed_tensor = True
+
+    pytree.tree_map_(is_distributed_tensor, args)
+    pytree.tree_map_(is_distributed_tensor, kwargs)
+
+    if not has_distributed_tensor:
+        raise TypeError(
+            f"torch function '{op.__name__}', with args: {args} and "
+            f"kwargs: {kwargs} are called without any distributed tensor!"
+        )
+
+    # Validate all distributed tensors use the same PG.
+    cur_pg: Optional[torch.distributed.ProcessGroup] = None
+
+    def validate_pg(e):
+        nonlocal cur_pg
+        if isinstance(e, ShardedTensor):
+            if cur_pg is not None and e._process_group is not cur_pg:
+                raise RuntimeError(
+                    'All distributed tensors should use the '
+                    'same ProcessGroup if used together in an op.'
+                )
+            cur_pg = e._process_group
+
+    pytree.tree_map_(validate_pg, args)
+    pytree.tree_map_(validate_pg, kwargs)
+
+def _register_default_op(op, decorator):
+    @decorator(op)
+    def tensor_default_op(types, args=(), kwargs=None, pg=None):
+        """
+        Handles ``__torch_function__`` dispatch for the default tensor ops that
+        behave the same as ``torch.Tensor`` such as ``torch.Tensor.shape`` or
+        ``torch.Tensor.dtype``. We simply lower to the real op call with
+        DisableTorchFunctionSubclass context like ``torch.Tensor.__torch_function__``
+        to avoid recursions.
+        """
+        if kwargs is None:
+            kwargs = {}
+
+        with torch._C.DisableTorchFunctionSubclass():
+            return op(*args, **kwargs)

parrot/lib/python3.10/site-packages/torch/distributed/_shard/metadata.py

@@ -0,0 +1,62 @@
+# mypy: allow-untyped-defs
+from dataclasses import dataclass
+from typing import List, Union, Optional
+from functools import reduce
+
+from torch.distributed.remote_device import _remote_device
+
+@dataclass
+class ShardMetadata:
+    """
+    Represents a shard of the overall Tensor including its
+    offsets, lengths and device placement.
+
+    Args:
+        shard_offsets(List[int]): Offsets in the original tensor indicating
+            the start offsets for this shard. Should have the same rank as
+            the original tensor.
+        shard_sizes(List[int]): Integers indicating the size of each
+            dimension for this shard. Should have the same rank as the
+            original tensor.
+        placement(:class:`torch.distributed._remote_device`):
+            Specifies the placement of this shard.
+    """
+
+    __slots__ = ['shard_offsets', 'shard_sizes', 'placement']
+
+    shard_offsets: List[int]
+    shard_sizes: List[int]
+    placement: Optional[_remote_device]
+
+    def __init__(
+        self,
+        shard_offsets: List[int],
+        shard_sizes: List[int],
+        placement: Optional[Union[str, _remote_device]] = None
+    ):
+        self.shard_offsets = shard_offsets
+        self.shard_sizes = shard_sizes
+        if isinstance(placement, str):
+            self.placement = _remote_device(placement)
+        else:
+            self.placement = placement
+        if len(self.shard_offsets) != len(self.shard_sizes):
+            raise ValueError(
+                f'shard_offsets and shard_sizes should have '
+                f'the same number of elements, found {len(self.shard_offsets)} '
+                f'and {self.shard_sizes} respectively')
+
+        for i in range(len(self.shard_offsets)):
+            if self.shard_offsets[i] < 0:
+                raise ValueError('shard_offsets should be >=0')
+            if self.shard_sizes[i] < 0:
+                raise ValueError('shard_sizes should be >= 0')
+
+    def __hash__(self):
+        def _hash_reduce(a, b):
+            return (a << 8) + hash(b)
+
+        res = reduce(_hash_reduce, self.shard_offsets, 37)
+        res = reduce(_hash_reduce, self.shard_sizes, res)
+        res = _hash_reduce(res, self.placement)
+        return res

parrot/lib/python3.10/site-packages/torch/distributed/_shard/sharded_optim/api.py

@@ -0,0 +1,98 @@
+# mypy: allow-untyped-defs
+from typing import List, Union, Mapping, Dict, Any
+
+import torch.optim as optim
+from torch import Tensor
+from torch.distributed._shard.sharded_tensor import ShardedTensor
+
+
+class ShardedOptimizer(optim.Optimizer):
+    def __init__(
+        self,
+        named_params: Mapping[str, Union[Tensor, ShardedTensor]],
+        optimizer_class,
+        *optimizer_args,
+        **optimizer_kwargs
+    ):
+        """
+        ShardedOptimizer collects all tensors and local shard tensors of
+        ShardedTensor, then use these tensors as ``params`` for optimizers
+
+        Args:
+            named_params (Dict[str, Union[Tensor, ShardedTensor]]) : a Dict
+                of parameters, where key is the parameter key, value is either
+                Tensor or ShardedTensor parameter.
+            optimizer_class (torch.optim.Optimizer): the Optimizer to use
+                locally, i.e. torch.optim.SGD, torch.optim.Adagrad, etc.
+            *optimizer_args: the arguments to initialize the optimizer.
+            **optimizer_kwargs: the key-word arguments to initialize the optimizer.
+
+        """
+        tensors: List[Tensor] = []
+        for value in named_params.values():
+            if isinstance(value, ShardedTensor):
+                for local_shard in value.local_shards():
+                    tensors.append(local_shard.tensor)
+            else:
+                tensors.append(value)
+
+        self.named_params = named_params
+        self._optim = optimizer_class(tensors, *optimizer_args, **optimizer_kwargs)
+        self.param_groups = self._optim.param_groups
+        self.state = self._optim.state
+
+    def zero_grad(self, set_to_none: bool = True):  # type: ignore[override]
+        r"""Resets the gradients of all optimized :class:`torch.Tensor` s.
+
+        Args:
+            set_to_none (bool): instead of setting to zero, set the grads to None.
+                This will in general have lower memory footprint, and can modestly improve performance.
+                However, it changes certain behaviors. For example:
+                1. When the user tries to access a gradient and perform manual ops on it,
+                a None attribute or a Tensor full of 0s will behave differently.
+                2. If the user requests ``zero_grad(set_to_none=True)`` followed by a backward pass, ``.grad``\ s
+                are guaranteed to be None for params that did not receive a gradient.
+                3. ``torch.optim`` optimizers have a different behavior if the gradient is 0 or None
+                (in one case it does the step with a gradient of 0 and in the other it skips
+                the step altogether).
+        """
+        self._optim.zero_grad(set_to_none)
+
+    def step(self, closure=None):
+        r"""Performs a single optimization step (parameter update).
+
+        Args:
+            closure (Callable): A closure that reevaluates the model and
+                returns the loss. Optional for most optimizers.
+
+        .. note::
+            Unless otherwise specified, this function should not modify the
+            ``.grad`` field of the parameters.
+        """
+        self._optim.step(closure)
+
+    def state_dict(self) -> Dict[str, Any]:
+        """
+        Returned state and param_groups will contain parameter keys
+        instead of parameter indices like torch.optim.Optimizer.
+        This allows for advanced functionality like optimizer re-sharding to be implemented.
+        """
+        # TODO: implement state_dict
+        raise NotImplementedError("ShardedOptimizer state_dict not implemented yet!")
+
+
+    def load_state_dict(self, state_dict: Mapping[str, Any]):
+        r"""Loads the ShardedOptimizer state.
+
+        Args:
+            state_dict (dict): ShardedOptimizer state. Should be an object returned
+                from a call to :meth:`state_dict`.
+        """
+        # TODO: implement load_state_dict
+        raise NotImplementedError("ShardedOptimizer load_state_dict not implemented yet!")
+
+    def add_param_group(self, param_group: Any):
+        r"""Add a new param group
+        """
+        # TODO: implement add_param_group
+        raise NotImplementedError("ShardedOptimizer add_param_group not implemented yet!")

parrot/lib/python3.10/site-packages/torch/distributed/_shard/sharder.py

@@ -0,0 +1,27 @@
+import abc
+import torch.nn as nn
+
+class Sharder(abc.ABC):
+    """
+    This is an interface which allows user to create more advanced
+    sharding strategies that are not easily be composed by the
+    `ShardingSpec`.
+
+    :class:`torch.distributed._shard.sharding_plan.ShardingPlan` could
+    take an object of the `Sharder` and call `shard` to shard the module,
+    then replace the original module with sharded module returned.
+    """
+    @abc.abstractmethod
+    def shard(self, module: nn.Module) -> nn.Module:
+        """
+        Shard a module base on the implementation of this method, and
+        return the sharded version of the module.
+
+        Args:
+            module (:class:`torch.nn.Module`):
+                The module to apply sharding to.
+        Returns:
+            A :class:`torch.nn.Module` object that represents a module
+            that's already been sharded.
+        """
+        pass

parrot/lib/python3.10/site-packages/torch/distributed/argparse_util.py

@@ -0,0 +1,104 @@
+#!/usr/bin/env python3
+# mypy: allow-untyped-defs
+
+# Copyright (c) Facebook, Inc. and its affiliates.
+# All rights reserved.
+#
+# This source code is licensed under the BSD-style license found in the
+# LICENSE file in the root directory of this source tree.
+import os
+from argparse import Action
+
+
+class env(Action):
+    """
+    Get argument values from ``PET_{dest}`` before defaulting to the given ``default`` value.
+
+    For flags (e.g. ``--standalone``)
+    use ``check_env`` instead.
+
+    .. note:: when multiple option strings are specified, ``dest`` is
+              the longest option string (e.g. for ``"-f", "--foo"``
+              the env var to set is ``PET_FOO`` not ``PET_F``)
+
+    Example:
+    ::
+
+     parser.add_argument("-f", "--foo", action=env, default="bar")
+
+     ./program                                      -> args.foo="bar"
+     ./program -f baz                               -> args.foo="baz"
+     ./program --foo baz                            -> args.foo="baz"
+     PET_FOO="env_bar" ./program -f baz    -> args.foo="baz"
+     PET_FOO="env_bar" ./program --foo baz -> args.foo="baz"
+     PET_FOO="env_bar" ./program           -> args.foo="env_bar"
+
+     parser.add_argument("-f", "--foo", action=env, required=True)
+
+     ./program                                      -> fails
+     ./program -f baz                               -> args.foo="baz"
+     PET_FOO="env_bar" ./program           -> args.foo="env_bar"
+     PET_FOO="env_bar" ./program -f baz    -> args.foo="baz"
+    """
+
+    def __init__(self, dest, default=None, required=False, **kwargs) -> None:
+        env_name = f"PET_{dest.upper()}"
+        default = os.environ.get(env_name, default)
+
+        # ``required`` means that it NEEDS to be present  in the command-line args
+        # rather than "this option requires a value (either set explicitly or default"
+        # so if we found default then we don't "require" it to be in the command-line
+        # so set it to False
+        if default:
+            required = False
+
+        super().__init__(dest=dest, default=default, required=required, **kwargs)
+
+    def __call__(self, parser, namespace, values, option_string=None):
+        setattr(namespace, self.dest, values)
+
+
+class check_env(Action):
+    """
+    Check whether the env var ``PET_{dest}`` exists before defaulting to the given ``default`` value.
+
+    Equivalent to
+    ``store_true`` argparse built-in action except that the argument can
+    be omitted from the commandline if the env var is present and has a
+    non-zero value.
+
+    .. note:: it is redundant to pass ``default=True`` for arguments
+              that use this action because a flag should be ``True``
+              when present and ``False`` otherwise.
+
+    Example:
+    ::
+
+     parser.add_argument("--verbose", action=check_env)
+
+     ./program                                  -> args.verbose=False
+     ./program --verbose                        -> args.verbose=True
+     PET_VERBOSE=1 ./program           -> args.verbose=True
+     PET_VERBOSE=0 ./program           -> args.verbose=False
+     PET_VERBOSE=0 ./program --verbose -> args.verbose=True
+
+    Anti-pattern (don't do this):
+
+    ::
+
+     parser.add_argument("--verbose", action=check_env, default=True)
+
+     ./program                                  -> args.verbose=True
+     ./program --verbose                        -> args.verbose=True
+     PET_VERBOSE=1 ./program           -> args.verbose=True
+     PET_VERBOSE=0 ./program           -> args.verbose=False
+
+    """
+
+    def __init__(self, dest, default=False, **kwargs) -> None:
+        env_name = f"PET_{dest.upper()}"
+        default = bool(int(os.environ.get(env_name, "1" if default else "0")))
+        super().__init__(dest=dest, const=True, default=default, nargs=0, **kwargs)
+
+    def __call__(self, parser, namespace, values, option_string=None):
+        setattr(namespace, self.dest, self.const)

parrot/lib/python3.10/site-packages/torch/distributed/autograd/__init__.py

@@ -0,0 +1,53 @@
+# mypy: allow-untyped-defs
+
+import sys
+import torch
+
+
+def is_available():
+    return hasattr(torch._C, "_dist_autograd_init")
+
+
+if is_available() and not torch._C._dist_autograd_init():
+    raise RuntimeError("Failed to initialize torch.distributed.autograd")
+
+if is_available():
+    from torch._C._distributed_autograd import (
+        get_gradients,
+        backward,
+        _init,
+        _new_context,
+        _release_context,
+        _get_max_id,
+        _is_valid_context,
+        _retrieve_context,
+        _current_context,
+        _get_debug_info,
+        DistAutogradContext,
+    )
+
+
+class context:
+    '''
+    Context object to wrap forward and backward passes when using
+    distributed autograd. The ``context_id`` generated in the ``with``
+    statement  is required to uniquely identify a distributed backward pass
+    on all workers. Each worker stores metadata associated with this
+    ``context_id``, which is required to correctly execute a distributed
+    autograd pass.
+
+    Example::
+        >>> # xdoctest: +SKIP
+        >>> import torch.distributed.autograd as dist_autograd
+        >>> with dist_autograd.context() as context_id:
+        >>>     t1 = torch.rand((3, 3), requires_grad=True)
+        >>>     t2 = torch.rand((3, 3), requires_grad=True)
+        >>>     loss = rpc.rpc_sync("worker1", torch.add, args=(t1, t2)).sum()
+        >>>     dist_autograd.backward(context_id, [loss])
+    '''
+    def __enter__(self):
+        self.autograd_context = _new_context()
+        return self.autograd_context._context_id()
+
+    def __exit__(self, type, value, traceback):
+        _release_context(self.autograd_context._context_id())

parrot/lib/python3.10/site-packages/torch/distributed/constants.py

@@ -0,0 +1,23 @@
+from torch._C._distributed_c10d import _DEFAULT_PG_TIMEOUT
+from datetime import timedelta
+from typing import Optional
+
+__all__ = ['default_pg_timeout', 'default_pg_nccl_timeout']
+
+# Default process group wide timeout, if applicable.
+# This only applies to the non-nccl backends
+# To make an attempt at backwards compatibility with THD, we use an
+# extraordinarily high default timeout, given that THD did not have timeouts.
+default_pg_timeout: timedelta = _DEFAULT_PG_TIMEOUT
+# Separate timeout for PGNCCL mainly becuase it's always been that way in the C++ layer, but until recently
+# there was one default that applied across all backends in the python layer.
+# Later, we could consider merging them back together at the c++ layer if we can align on a same value.
+# (only if TORCH_NCCL_BLOCKING_WAIT or TORCH_NCCL_ASYNC_ERROR_HANDLING is set to 1).
+
+try:
+    from torch._C._distributed_c10d import _DEFAULT_PG_NCCL_TIMEOUT
+    default_pg_nccl_timeout: Optional[timedelta] = _DEFAULT_PG_NCCL_TIMEOUT
+except ImportError:
+    # if C++ NCCL support is not compiled, we don't have access to the default nccl value.
+    # if anyone is actually trying to use nccl in this state, it should error.
+    default_pg_nccl_timeout = None

parrot/lib/python3.10/site-packages/torch/distributed/device_mesh.py

@@ -0,0 +1,719 @@
+# mypy: allow-untyped-defs
+# Copyright (c) Meta Platforms, Inc. and affiliates
+import logging
+import math
+import threading
+from typing import Dict, List, Optional, Tuple, TYPE_CHECKING, Union
+
+import torch
+
+from torch.distributed import is_available
+
+from ..utils._typing_utils import not_none
+
+__all__ = ["init_device_mesh", "DeviceMesh"]
+
+
+if not is_available():
+    import sys
+
+    # We need to create the stubs when distributed is not available.
+    # Otherwise, we would fail the doc tests (```./.ci/pytorch/docs-test.sh```),
+    # since it would try to import ``torch.distributed.device_mesh`` or
+    # ``torch.distributed.init_device_mesh`` but cannot find them.
+
+    class _DeviceMeshStub:
+        pass
+
+    def _init_device_mesh_stub():
+        pass
+
+    sys.modules["torch.distributed.device_mesh"].DeviceMesh = _DeviceMeshStub  # type: ignore[attr-defined]
+    sys.modules[
+        "torch.distributed.device_mesh"
+    ].init_device_mesh = _init_device_mesh_stub  # type: ignore[attr-defined]
+
+
+else:
+    from torch.distributed.distributed_c10d import (
+        _find_pg_by_ranks_and_tag,
+        _get_default_group,
+        _get_group_tag,
+        get_process_group_ranks,
+        get_rank,
+        get_world_size,
+        init_process_group,
+        is_initialized,
+        new_group,
+        ProcessGroup,
+    )
+
+    logger = logging.getLogger(__name__)
+
+    # only import numpy typing when type checking
+    if TYPE_CHECKING:
+        try:
+            from numpy.typing import ArrayLike
+        except ImportError:
+            logger.warning(
+                "DeviceMesh requires numpy >= 1.21 to be installed for type checking"
+            )
+
+    class _MeshEnv(threading.local):
+        def __init__(self) -> None:
+            self.mesh_stack: List[DeviceMesh] = []
+            self.child_to_parent_mapping: Dict[DeviceMesh, DeviceMesh] = {}
+            self.mesh_dim_group_options: Dict[
+                int, Tuple[str, Optional[ProcessGroup.Options]]
+            ] = {}
+
+        def get_current_mesh(self) -> "DeviceMesh":
+            if len(self.mesh_stack) == 0:
+                raise RuntimeError("No device mesh is currently active!")
+            return self.mesh_stack[-1]
+
+        def create_child_mesh(
+            self, parent_mesh: "DeviceMesh", submesh_dim_names: Tuple[str, ...]
+        ) -> "DeviceMesh":
+            # submesh_dims are the mesh dimension of the submesh in the parent mesh.
+            submesh_dims = [
+                not_none(parent_mesh.mesh_dim_names).index(mesh_dim_name)
+                for mesh_dim_name in submesh_dim_names
+            ]
+            submesh_dim_sizes = [
+                parent_mesh.mesh.size(mesh_dim) for mesh_dim in submesh_dims
+            ]
+
+            mesh_dims_remained = list(range(parent_mesh.mesh.ndim))
+            for submesh_dim in submesh_dims:
+                mesh_dims_remained.remove(submesh_dim)
+
+            # pg_ranks_by_dim is the size of [number of local ranks of the outermost submesh dimension, *sub_mesh_dims]
+            # This means on each local rank of the outermost slice mesh dim, we have a tensor of submesh size with
+            # the pg ranks of the submesh. From this, we can extract the submesh mesh tensor contains the current rank.
+            pg_ranks_by_dim = parent_mesh.mesh.permute(
+                *mesh_dims_remained, *submesh_dims
+            ).reshape(-1, *submesh_dim_sizes)
+
+            cur_rank = parent_mesh.get_rank()
+            for mesh_nd in pg_ranks_by_dim:
+                submesh = DeviceMesh(
+                    parent_mesh.device_type,
+                    mesh_nd,
+                    mesh_dim_names=submesh_dim_names,
+                    _init_backend=False,
+                )
+                if cur_rank in mesh_nd:
+                    res_submesh = submesh
+
+            res_submesh._parent_mesh = parent_mesh  # type: ignore[possibly-undefined]
+            res_submesh._dim_group_infos = [
+                parent_mesh._dim_group_infos[mesh_dim] for mesh_dim in submesh_dims  # type: ignore[possibly-undefined]
+            ]
+            self.child_to_parent_mapping[res_submesh] = parent_mesh
+
+            return res_submesh
+
+        def get_parent_mesh(self, device_mesh: "DeviceMesh") -> Optional["DeviceMesh"]:
+            return self.child_to_parent_mapping.get(device_mesh, None)
+
+        def get_parent_mesh_dim(self, device_mesh: "DeviceMesh") -> Optional[int]:
+            """
+            Return the index of the mesh dim in the parent mesh.
+            The device_mesh passed in needs to be sliced out from a parent mesh.
+            """
+            parent_mesh = self.get_parent_mesh(device_mesh)
+            child_mesh_dim_names = device_mesh.mesh_dim_names
+            if parent_mesh and child_mesh_dim_names:
+                assert (
+                    len(child_mesh_dim_names) == 1
+                ), "The child mesh can only be a 1D mesh."
+                child_mesh_dim_name = child_mesh_dim_names[0]
+                return self.get_mesh_dim_by_name(parent_mesh, child_mesh_dim_name)
+            return None
+
+        @staticmethod
+        def num_devices_per_host(device_type: str) -> int:
+            return _get_device_handle(device_type).device_count()
+
+        @staticmethod
+        def num_hosts(device_type: str) -> int:
+            # ProcessGroup can't tell us this info so we have to infer it, assume
+            # homogeneous hardware for now
+            return get_world_size() // _MeshEnv.num_devices_per_host(device_type)
+
+        def get_mesh_dim_by_name(
+            self, device_mesh: "DeviceMesh", mesh_dim_name: str
+        ) -> int:
+            if (
+                device_mesh.mesh_dim_names is None
+                or len(device_mesh.mesh_dim_names) == 0
+            ):
+                raise KeyError(
+                    "No `mesh_dim_names` found.",
+                )
+            if mesh_dim_name not in device_mesh.mesh_dim_names:
+                raise KeyError(
+                    f"Mesh dimension '{mesh_dim_name}' does not exist.",
+                    f"Available mesh dimensions are: mesh_dim_names={device_mesh.mesh_dim_names}",
+                )
+            return not_none(device_mesh.mesh_dim_names.index(mesh_dim_name))
+
+        def _set_mesh_dim_group_options(
+            self,
+            dim: int,
+            backend: str,
+            pg_options: Optional[ProcessGroup.Options] = None,
+        ) -> None:
+            self.mesh_dim_group_options[dim] = (backend, pg_options)
+
+    _mesh_resources: _MeshEnv = _MeshEnv()
+
+    def _get_device_handle(device_type: str = "cuda"):
+        """
+        Get the module corresponding to the device_type which is cuda or cuda-like device.
+        For example, when the device_type is cuda, the module `torch.cuda` is returned.
+        Return None when there is no corresponding module for device_type, otherwise
+        return the corresponding module.
+        """
+        return getattr(torch, device_type, None)
+
+    class DeviceMesh:
+        """
+        DeviceMesh represents a mesh of devices, where layout of devices could be
+        represented as a n-d dimension array, and each value of the n-d dimensional
+        array is the global id of the default process group ranks.
+
+        DeviceMesh could be used to describe the layout of devices across the cluster,
+        and serves as a proxy for communication among the device lists within the cluster.
+
+        DeviceMesh can be used as a context manager.
+
+        .. note::
+            DeviceMesh follows SPMD programming model, which means the same PyTorch Python program
+            is running on all processes/ranks in the cluster. Therefore, users need to make sure the
+            `mesh` array (which describes the layout of devices) should be identical across all ranks.
+            Inconsistent `mesh` will lead to silent hang.
+
+        Args:
+            device_type (str): The device type of the mesh. Currently supports: "cpu", "cuda/cuda-like".
+            mesh (ndarray): A multi-dimensional array or an integer tensor describing the layout
+                of devices, where the IDs are global IDs of the default process group.
+
+        Returns:
+            DeviceMesh: A :class:`DeviceMesh` object representing the device layout.
+
+        The following program runs on each process/rank in an SPMD manner. In this example, we have 2
+        hosts with 4 GPUs each.
+        A reduction over the first dimension of mesh will reduce across
+        columns (0, 4), .. and (3, 7), a reduction over the second dimension
+        of mesh reduces across rows (0, 1, 2, 3) and (4, 5, 6, 7).
+
+        Example::
+            >>> # xdoctest: +SKIP("no rank")
+            >>> from torch.distributed.device_mesh import DeviceMesh
+            >>>
+            >>> # Initialize device mesh as (2, 4) to represent the topology
+            >>> # of cross-host(dim 0), and within-host (dim 1).
+            >>> mesh = DeviceMesh(device_type="cuda", mesh=[[0, 1, 2, 3],[4, 5, 6, 7]])
+        """
+
+        device_type: str
+        mesh: torch.Tensor
+        mesh_dim_names: Optional[Tuple[str, ...]]
+
+        def __init__(
+            self,
+            device_type: str,
+            mesh: Union[torch.Tensor, "ArrayLike"],
+            *,
+            mesh_dim_names: Optional[Tuple[str, ...]] = None,
+            _init_backend: bool = True,
+        ) -> None:
+            self.device_type = device_type
+            if isinstance(mesh, torch.Tensor) and mesh.device.type != "cpu":
+                raise ValueError(f"`mesh` must be a CPU tensor, got {mesh}")
+            self.mesh = (
+                mesh.detach().to(dtype=torch.int)
+                if isinstance(mesh, torch.Tensor)
+                else torch.tensor(mesh, device="cpu", dtype=torch.int)
+            )
+            self.mesh_dim_names = tuple(mesh_dim_names) if mesh_dim_names else None
+
+            # private field to pre-generate DeviceMesh's hash
+            self._flatten_mesh_list = tuple(self.mesh.flatten().tolist())
+            self._parent_mesh: Optional[DeviceMesh] = None
+            self._thread_id = threading.get_ident()
+
+            # Skip process group initialization if xla device or init backend is False
+            # TODO(yeounoh) implement DeviceMesh backend and register XLA backend.
+            if device_type != "xla":
+                # always try to create default (world) pg, even if it is not initialized
+                # already. The world pg is used for device mesh identity (rank) on each
+                # process (we need to know if the current global rank is in the mesh or not).
+                if _init_backend:
+                    self._get_or_create_default_group()
+                    self._init_process_groups()
+
+                # calculate the coordinates of the current global rank on the mesh
+                rank_coords = (self.mesh == get_rank()).nonzero()
+                assert rank_coords.size(0) in (0, 1)
+                self._coordinate_on_dim: Optional[List[int]] = (
+                    rank_coords[0].tolist() if rank_coords.size(0) > 0 else None
+                )
+
+        def _get_or_create_default_group(self):
+            default_initialized = is_initialized()
+            if not default_initialized:
+                init_process_group()
+
+            world_size = get_world_size()
+            if self.mesh.numel() > world_size:
+                raise RuntimeError(
+                    f"Mesh should not be bigger than default world size, but found {self.mesh.numel()} ranks!"
+                )
+
+            device_handle = _get_device_handle(self.device_type)
+            # TODO: if user want to pass pg_options, offer a way to do it
+            if not default_initialized and device_handle:
+                # automatically set the current cuda/cuda-like device base on num of gpu devices available in each host
+                # NOTE: This device selection would only work for homogeneous hardware.
+                num_devices_per_host = device_handle.device_count()
+                if (
+                    world_size > num_devices_per_host
+                    and world_size % num_devices_per_host != 0
+                ):
+                    raise RuntimeError(
+                        f"DeviceMesh only support homogeneous hardware, but found "
+                        f"{world_size} ranks and {num_devices_per_host} {self.device_type} devices!"
+                    )
+                device_handle.set_device(get_rank() % num_devices_per_host)
+
+            return _get_default_group()
+
+        def _init_process_groups(self):
+            # tag/ranks/group_name associated with each mesh dimension, each
+            # mesh dimension should have one sub-group per rank
+            #
+            # TODO(yifu): remove tag and ranks once we fully migrate to native
+            # functional collectives. See details in:
+            # https://github.com/pytorch/pytorch/issues/93173#issuecomment-1907095208
+            dim_group_infos: List[Tuple[str, List[int], str]] = []
+
+            if self.mesh.ndim == 1 and self.mesh.numel() == get_world_size():
+                # if the mesh is the same as world_pg, we just append the default
+                # pg to the first dim groups, as new_group cannot have the exact
+                # same ranks as world
+                dim_group_infos.append(
+                    (
+                        _get_group_tag(_get_default_group()),
+                        list(range(get_world_size())),
+                        _get_default_group().group_name,
+                    )
+                )
+            else:
+                # create sub pgs base on the mesh argument specified
+                for dim in range(self.mesh.ndim):
+                    # swap the current dim to the last dim
+                    # then reshape to flatten out other dims
+                    pg_ranks_by_dim = self.mesh.swapdims(-1, dim).reshape(
+                        -1, self.mesh.size(dim)
+                    )
+                    # multi-dim mesh, create subgroups by looping over the pg_ranks
+                    # for each dim and append the groups
+                    for dim_mesh in pg_ranks_by_dim:
+                        subgroup_ranks = dim_mesh.tolist()
+
+                        # Respect dim group options specified via _MeshEnv.set_dim_group_options().
+                        # Inherit from the parent group if no options are specified for the group.
+                        if dim in _mesh_resources.mesh_dim_group_options:
+                            (
+                                backend,
+                                pg_options,
+                            ) = _mesh_resources.mesh_dim_group_options[dim]
+                        else:
+                            backend, pg_options = None, None
+
+                        # We temporarily revert the re-use subgroup, since it breaks two internal tests.
+                        # Temporarily reverting to resolve test timeout while root-causing.
+                        # TODO: Add two tests to cover internal tests scenarios and re-enable reuse subgroup if exists.
+                        dim_group = new_group(
+                            ranks=subgroup_ranks,
+                            backend=backend,
+                            pg_options=pg_options,
+                        )
+
+                        # only add to dim_groups if the current rank in the subgroup
+                        if self.get_rank() in subgroup_ranks:
+                            if len(dim_group_infos) > dim:
+                                raise RuntimeError(
+                                    f"Each device mesh dimension should get only one process group, but got {self.get_rank} "
+                                    f"in {subgroup_ranks}!"
+                                )
+                            dim_group_infos.append(
+                                (
+                                    _get_group_tag(not_none(dim_group)),
+                                    subgroup_ranks,
+                                    dim_group.group_name,
+                                )
+                            )
+            self._dim_group_infos = dim_group_infos
+
+        def __enter__(self) -> "DeviceMesh":
+            # set this mesh as the current mesh in mesh env
+            _mesh_resources.mesh_stack.append(self)
+            return self
+
+        # pyre-fixme[2]: Parameter must be annotated.
+        def __exit__(self, exc_type, exc_value, exc_traceback) -> None:
+            # pop this mesh from mesh env
+            _mesh_resources.mesh_stack.pop()
+
+        def __repr__(self) -> str:
+            device_mesh_repr = (
+                f"DeviceMesh({self.mesh.tolist()})"
+                if not self.mesh_dim_names
+                else f"DeviceMesh({self.mesh.tolist()}, mesh_dim_names={self.mesh_dim_names})"
+            )
+            return device_mesh_repr
+
+        def __hash__(self):
+            # lazily compute hash
+            self._hash = getattr(self, "_hash", None)
+            if not self._hash:
+                self._hash = hash(
+                    (
+                        self._flatten_mesh_list,
+                        self.mesh.shape,
+                        self.device_type,
+                        self.mesh_dim_names,
+                        self._parent_mesh,
+                        self._thread_id,
+                    )
+                )
+            return self._hash
+
+        def __eq__(self, other: object) -> bool:
+            if not isinstance(other, DeviceMesh):
+                return False
+            if id(self) == id(other):
+                return True
+            else:
+                return (
+                    self._flatten_mesh_list == other._flatten_mesh_list
+                    and self.mesh.shape == other.mesh.shape
+                    and self.device_type == other.device_type
+                    and self.mesh_dim_names == other.mesh_dim_names
+                    and self._parent_mesh == other._parent_mesh
+                    and self._thread_id == other._thread_id
+                )
+
+        def __getitem__(
+            self, mesh_dim_names: Union[str, Tuple[str, ...]]
+        ) -> "DeviceMesh":
+            """
+            Slice the current DeviceMesh based on the mesh_dim_name given to create a child
+            DeviceMesh.
+
+            Args:
+                mesh_dim_name (Union[str, Tuple[str]]): the name or the tuple of names of the
+                mesh dimension of the parent DeviceMesh to create the child DeviceMesh for.
+            Returns:
+                A :class:`DeviceMesh` object
+
+            The following program runs on each process/rank in an SPMD manner. In this example, we have 2
+            hosts with 4 GPUs each.
+            Calling mesh["tp"] on rank 0, 1, 2, 3 would return a 1D child DeviceMesh:([0, 1, 2, 3]).
+            Calling mesh["tp"] on rank 4, 5, 6, 7 would return a 1D child DeviceMesh:([4, 5, 6, 7]).
+            Calling mesh["dp"] on rank 0, 4 would return a 1D child DeviceMesh:([0, 4]).
+            Calling mesh["dp"] on rank 1, 5 would return a 1D child DeviceMesh:([1, 5]).
+            Calling mesh["dp"] on rank 2, 6 would return a 1D child DeviceMesh:([2, 6]).
+            Calling mesh["dp"] on rank 3, 7 would return a 1D child DeviceMesh:([3, 7]).
+
+            Example::
+                >>> # xdoctest: +SKIP("no rank")
+                >>> from torch.distributed.device_mesh import DeviceMesh
+                >>>
+                >>> # Initialize device mesh as (2, 4) to represent the topology
+                >>> # of cross-host(dim 0), and within-host (dim 1).
+                >>> mesh = DeviceMesh(device_type="cuda", mesh=[[0, 1, 2, 3],[4, 5, 6, 7]])
+            """
+            if not self.mesh_dim_names:
+                raise RuntimeError("Cannot slice a DeviceMesh without mesh_dim_names!")
+
+            mesh_dim_names = (
+                (mesh_dim_names,) if isinstance(mesh_dim_names, str) else mesh_dim_names
+            )
+
+            error_msg = (
+                f"Invalid mesh_dim_name {mesh_dim_names} specified. "
+                f"Valid mesh_dim_names should be a contiguous subsequence of {self.mesh_dim_names}."
+            )
+
+            if mesh_dim_names == self.mesh_dim_names:
+                return self
+            elif len(mesh_dim_names) > len(self.mesh_dim_names) or not all(
+                mesh_dim_name in self.mesh_dim_names for mesh_dim_name in mesh_dim_names
+            ):
+                raise KeyError(error_msg)
+            # Check if the user-provided slicing is a valid contiguous subsequence of the mesh_dim_names
+            # of the current DeviceMesh.
+            else:
+                outermost_dim_name = mesh_dim_names[0]
+                outermost_dim_idx = self.mesh_dim_names.index(outermost_dim_name)
+                for i, j in zip(
+                    mesh_dim_names,
+                    self.mesh_dim_names[outermost_dim_idx : len(mesh_dim_names)],
+                ):
+                    if i != j:
+                        raise KeyError(error_msg)
+
+            submesh = _mesh_resources.create_child_mesh(self, mesh_dim_names)
+            return submesh
+
+        def get_group(self, mesh_dim: Optional[Union[int, str]] = None) -> ProcessGroup:
+            """
+            Returns the single ProcessGroup specified by mesh_dim, or, if mesh_dim is not specified and the
+            DeviceMesh is 1-dimensional, returns the only ProcessGroup in the mesh.
+
+            Args:
+                mesh_dim (str/int, optional): it can be the name of the mesh dimension or the index
+                of the mesh dimension. Default is None.
+
+            Returns:
+                A :class:`ProcessGroup` object.
+            """
+            if not hasattr(self, "_dim_group_infos"):
+                raise RuntimeError("DeviceMesh process groups not initialized!")
+
+            if self.mesh.ndim > 1 and mesh_dim is None:
+                raise RuntimeError(
+                    f"Found the DeviceMesh have {self.mesh.ndim} dimensions",
+                    "Optional kwarg `mesh_dim` needs to be specified when device_mesh.ndim > 1.",
+                    "If you want to get the list of all the ProcessGroups in the DeviceMesh,"
+                    "please use `get_all_groups()` instead.",
+                )
+
+            if self.mesh.ndim == 1 and mesh_dim is None:
+                mesh_dim = 0
+            else:
+                mesh_dim = (
+                    _mesh_resources.get_mesh_dim_by_name(self, mesh_dim)
+                    if isinstance(mesh_dim, str)
+                    else mesh_dim
+                )
+
+            return not_none(
+                _find_pg_by_ranks_and_tag(*self._dim_group_infos[mesh_dim][:2])  # type: ignore[index]
+            )
+
+        def get_all_groups(self) -> List[ProcessGroup]:
+            """
+            Returns a list of ProcessGroups for all mesh dimensions.
+
+            Returns:
+                A list of :class:`ProcessGroup` object.
+            """
+            return [self.get_group(i) for i in range(self.mesh.ndim)]
+
+        @staticmethod
+        def from_group(
+            group: Union[ProcessGroup, List[ProcessGroup]],
+            device_type: str,
+            mesh: Optional[Union[torch.Tensor, "ArrayLike"]] = None,
+            *,
+            mesh_dim_names: Optional[Tuple[str, ...]] = None,
+        ) -> "DeviceMesh":
+            """
+            Contstructs a :class:`DeviceMesh` with ``device_type`` from an
+            existing :class:`ProcessGroup`.
+
+            The constructed device mesh has number of dimensions equal to the
+            number of groups passed. If more than one group is passed, then the
+            ``mesh`` argument is required.
+            """
+            if isinstance(group, ProcessGroup):
+                group_ranks = get_process_group_ranks(group)
+                if (
+                    isinstance(mesh, torch.Tensor) and mesh.tolist() != group_ranks
+                ) or (mesh is not None and mesh != group_ranks):
+                    raise ValueError(
+                        f"Invalid mesh {str(mesh)} for ProcessGroup with ranks {group_ranks}"
+                    )
+                mesh = torch.tensor(group_ranks, device="cpu", dtype=torch.int)
+                device_mesh = DeviceMesh(
+                    device_type,
+                    mesh,
+                    mesh_dim_names=mesh_dim_names,
+                    _init_backend=False,
+                )
+                device_mesh._dim_group_infos = [
+                    (_get_group_tag(group), group_ranks, group.group_name)
+                ]
+                return device_mesh
+            groups = list(group)
+            if len(groups) == 0:
+                raise ValueError("Expects at least one ProcessGroup to be passed")
+            if mesh is None:
+                raise ValueError("Must pass mesh if passing multiple ProcessGroups")
+            mesh = (
+                mesh.detach().to(dtype=torch.int, device="cpu")
+                if isinstance(mesh, torch.Tensor)
+                else torch.tensor(mesh, device="cpu", dtype=torch.int)
+            )
+            if mesh.ndim != len(groups):
+                raise ValueError(
+                    "Expects mesh with ndim equal to number of ProcessGroups but got "
+                    f"mesh {mesh.tolist()} and {len(groups)} ProcessGroups"
+                )
+            device_mesh = DeviceMesh(
+                device_type, mesh, mesh_dim_names=mesh_dim_names, _init_backend=False
+            )
+            device_mesh._dim_group_infos = [
+                (
+                    _get_group_tag(group),
+                    get_process_group_ranks(group),
+                    group.group_name,
+                )
+                for group in groups
+            ]
+            return device_mesh
+
+        def size(self, mesh_dim: Optional[int] = None) -> int:
+            return self.mesh.numel() if mesh_dim is None else self.mesh.size(mesh_dim)
+
+        @property
+        def ndim(self) -> int:
+            return self.mesh.ndim
+
+        @property
+        def shape(self) -> Tuple[int, ...]:
+            return tuple(self.mesh.shape)
+
+        def get_rank(self) -> int:
+            """
+            Returns the current global rank.
+            """
+            return get_rank()
+
+        def get_local_rank(self, mesh_dim: Optional[Union[int, str]] = None) -> int:
+            """
+            Returns the local rank of the given mesh_dim of the DeviceMesh.
+
+            Args:
+                mesh_dim (str/int, optional): it can be the name of the mesh dimension or the index
+                of the mesh dimension. Default is None.
+
+            Returns:
+                An integer denotes the local rank.
+
+            The following program runs on each process/rank in an SPMD manner. In this example, we have 2
+            hosts with 4 GPUs each.
+            Calling mesh_2d.get_local_rank(mesh_dim=0) on rank 0, 1, 2, 3 would return 0.
+            Calling mesh_2d.get_local_rank(mesh_dim=0) on rank 4, 5, 6, 7 would return 1.
+            Calling mesh_2d.get_local_rank(mesh_dim=1) on rank 0, 4 would return 0.
+            Calling mesh_2d.get_local_rank(mesh_dim=1) on rank 1, 5 would return 1.
+            Calling mesh_2d.get_local_rank(mesh_dim=1) on rank 2, 6 would return 2.
+            Calling mesh_2d.get_local_rank(mesh_dim=1) on rank 3, 7 would return 3.
+
+            Example::
+                >>> # xdoctest: +SKIP("no rank")
+                >>> from torch.distributed.device_mesh import DeviceMesh
+                >>>
+                >>> # Initialize device mesh as (2, 4) to represent the topology
+                >>> # of cross-host(dim 0), and within-host (dim 1).
+                >>> mesh = DeviceMesh(device_type="cuda", mesh=[[0, 1, 2, 3],[4, 5, 6, 7]])
+            """
+            if self.ndim > 1 and mesh_dim is None:
+                raise RuntimeError(
+                    f"Found the DeviceMesh have {self.mesh.ndim} dimensions",
+                    "Optional kwarg `mesh_dim` needs to be specified when device_mesh.ndim > 1.",
+                )
+            elif mesh_dim is None:
+                mesh_dim = 0
+
+            mesh_dim_group = not_none(self.get_group(mesh_dim))
+            assert isinstance(
+                mesh_dim_group, ProcessGroup
+            ), "We expect ProcessGroup before calling `get_rank`!"
+            return not_none(get_rank(mesh_dim_group))
+
+        def get_coordinate(self) -> Optional[List[int]]:
+            """
+            Return the relative indices of this rank relative to all
+            dimensions of the mesh. If this rank is not part of the mesh, return None.
+            """
+            return self._coordinate_on_dim if self._coordinate_on_dim else None
+
+    def init_device_mesh(
+        device_type: str,
+        mesh_shape: Tuple[int, ...],
+        *,
+        mesh_dim_names: Optional[Tuple[str, ...]] = None,
+    ) -> DeviceMesh:
+        """
+        Initializes a `DeviceMesh` based on `device_type`, `mesh_shape`, and `mesh_dim_names` parameters.
+
+        This creates a DeviceMesh with an n-dimensional array layout, where `n` is the length of `mesh_shape`.
+        If `mesh_dim_names` is provided, each dimension is labeled as `mesh_dim_names[i]`.
+
+        .. note::
+            `init_device_mesh` follows SPMD programming model, meaning the same PyTorch Python program
+            runs on all processes/ranks in the cluster. Ensure `mesh_shape` (the dimensions of the nD array
+            describing device layout) is identical across all ranks. Inconsistent `mesh_shape` may lead to hanging.
+
+        .. note::
+            If no process group is found, init_device_mesh will initialize distributed process group/groups
+            required for distributed communications behind the scene.
+
+        Args:
+            device_type (str): The device type of the mesh. Currently supports: "cpu", "cuda/cuda-like".
+                Passing in a device type with a GPU index, such as "cuda:0", is not allowed.
+            mesh_shape (Tuple[int]): A tuple defining the dimensions of the multi-dimensional array
+                describing the layout of devices.
+            mesh_dim_names (Tuple[str], optional): A tuple of mesh dimension names to assign to each dimension
+                of the multi-dimensional array describing the layout of devices. Its length must match the length
+                of `mesh_shape`. Each string in `mesh_dim_names` must be unique.
+
+        Returns:
+            DeviceMesh: A :class:`DeviceMesh` object representing the device layout.
+
+        Example::
+            >>> # xdoctest: +SKIP("no rank")
+            >>> from torch.distributed.device_mesh import init_device_mesh
+            >>>
+            >>> mesh_1d = init_device_mesh("cuda", mesh_shape=(8,))
+            >>> mesh_2d = init_device_mesh("cuda", mesh_shape=(2, 8), mesh_dim_names=("dp", "tp"))
+
+        """
+        if mesh_dim_names is not None:
+            if len(set(mesh_dim_names)) != len(mesh_dim_names):
+                raise RuntimeError(
+                    "Each mesh_dim_name must be unique.",
+                    f"Found repeated mesh_dim_name in mesh_dim_names {mesh_dim_names}",
+                )
+
+            if len(mesh_shape) != len(mesh_dim_names):
+                raise RuntimeError(
+                    "mesh_shape and mesh_dim_names should have same length!",
+                    f"Found len(mesh_dim_names): {len(mesh_dim_names)} and len(mesh_shape):{len(mesh_shape)}.",
+                )
+
+        # assume valid device types are all letters
+        if device_type and not device_type.isalpha():
+            raise RuntimeError(
+                f"Device type with GPU index is not supported but got {device_type}. ",
+                "If you maintained a 'torch.device' object, it's recommended to pass in 'device.type'.",
+            )
+
+        # Always initialize the mesh's tensor on CPU, regardless of what the
+        # external device type has been set to be (e.g. meta)
+        with torch.device("cpu"):
+            mesh = torch.arange(math.prod(mesh_shape), dtype=torch.int).view(mesh_shape)
+        device_mesh = DeviceMesh(
+            device_type=device_type,
+            mesh=mesh,
+            mesh_dim_names=mesh_dim_names,
+        )
+
+        return device_mesh

parrot/lib/python3.10/site-packages/torch/distributed/launch.py

@@ -0,0 +1,208 @@
+# mypy: allow-untyped-defs
+r"""
+Module ``torch.distributed.launch``.
+
+``torch.distributed.launch`` is a module that spawns up multiple distributed
+training processes on each of the training nodes.
+
+.. warning::
+
+    This module is going to be deprecated in favor of :ref:`torchrun <launcher-api>`.
+
+The utility can be used for single-node distributed training, in which one or
+more processes per node will be spawned. The utility can be used for either
+CPU training or GPU training. If the utility is used for GPU training,
+each distributed process will be operating on a single GPU. This can achieve
+well-improved single-node training performance. It can also be used in
+multi-node distributed training, by spawning up multiple processes on each node
+for well-improved multi-node distributed training performance as well.
+This will especially be beneficial for systems with multiple Infiniband
+interfaces that have direct-GPU support, since all of them can be utilized for
+aggregated communication bandwidth.
+
+In both cases of single-node distributed training or multi-node distributed
+training, this utility will launch the given number of processes per node
+(``--nproc-per-node``). If used for GPU training, this number needs to be less
+or equal to the number of GPUs on the current system (``nproc_per_node``),
+and each process will be operating on a single GPU from *GPU 0 to
+GPU (nproc_per_node - 1)*.
+
+**How to use this module:**
+
+1. Single-Node multi-process distributed training
+
+::
+
+    python -m torch.distributed.launch --nproc-per-node=NUM_GPUS_YOU_HAVE
+               YOUR_TRAINING_SCRIPT.py (--arg1 --arg2 --arg3 and all other
+               arguments of your training script)
+
+2. Multi-Node multi-process distributed training: (e.g. two nodes)
+
+
+Node 1: *(IP: 192.168.1.1, and has a free port: 1234)*
+
+::
+
+    python -m torch.distributed.launch --nproc-per-node=NUM_GPUS_YOU_HAVE
+               --nnodes=2 --node-rank=0 --master-addr="192.168.1.1"
+               --master-port=1234 YOUR_TRAINING_SCRIPT.py (--arg1 --arg2 --arg3
+               and all other arguments of your training script)
+
+Node 2:
+
+::
+
+    python -m torch.distributed.launch --nproc-per-node=NUM_GPUS_YOU_HAVE
+               --nnodes=2 --node-rank=1 --master-addr="192.168.1.1"
+               --master-port=1234 YOUR_TRAINING_SCRIPT.py (--arg1 --arg2 --arg3
+               and all other arguments of your training script)
+
+3. To look up what optional arguments this module offers:
+
+::
+
+    python -m torch.distributed.launch --help
+
+
+**Important Notices:**
+
+1. This utility and multi-process distributed (single-node or
+multi-node) GPU training currently only achieves the best performance using
+the NCCL distributed backend. Thus NCCL backend is the recommended backend to
+use for GPU training.
+
+2. In your training program, you must parse the command-line argument:
+``--local-rank=LOCAL_PROCESS_RANK``, which will be provided by this module.
+If your training program uses GPUs, you should ensure that your code only
+runs on the GPU device of LOCAL_PROCESS_RANK. This can be done by:
+
+Parsing the local_rank argument
+
+::
+
+    >>> # xdoctest: +SKIP
+    >>> import argparse
+    >>> parser = argparse.ArgumentParser()
+    >>> parser.add_argument("--local-rank", "--local_rank", type=int)
+    >>> args = parser.parse_args()
+
+Set your device to local rank using either
+
+::
+
+    >>> torch.cuda.set_device(args.local_rank)  # before your code runs
+
+or
+
+::
+
+    >>> with torch.cuda.device(args.local_rank):
+    >>>    # your code to run
+    >>>    ...
+
+.. versionchanged:: 2.0.0
+
+    The launcher will passes the ``--local-rank=<rank>`` argument to your script.
+    From PyTorch 2.0.0 onwards, the dashed ``--local-rank`` is preferred over the
+    previously used underscored ``--local_rank``.
+
+    For backward compatibility, it may be necessary for users to handle both
+    cases in their argument parsing code. This means including both ``"--local-rank"``
+    and ``"--local_rank"`` in the argument parser. If only ``"--local_rank"`` is
+    provided, the launcher will trigger an error: "error: unrecognized arguments:
+    --local-rank=<rank>". For training code that only supports PyTorch 2.0.0+,
+    including ``"--local-rank"`` should be sufficient.
+
+3. In your training program, you are supposed to call the following function
+at the beginning to start the distributed backend. It is strongly recommended
+that ``init_method=env://``. Other init methods (e.g. ``tcp://``) may work,
+but ``env://`` is the one that is officially supported by this module.
+
+::
+
+    >>> torch.distributed.init_process_group(backend='YOUR BACKEND',
+    >>>                                      init_method='env://')
+
+4. In your training program, you can either use regular distributed functions
+or use :func:`torch.nn.parallel.DistributedDataParallel` module. If your
+training program uses GPUs for training and you would like to use
+:func:`torch.nn.parallel.DistributedDataParallel` module,
+here is how to configure it.
+
+::
+
+    >>> model = torch.nn.parallel.DistributedDataParallel(model,
+    >>>                                                   device_ids=[args.local_rank],
+    >>>                                                   output_device=args.local_rank)
+
+Please ensure that ``device_ids`` argument is set to be the only GPU device id
+that your code will be operating on. This is generally the local rank of the
+process. In other words, the ``device_ids`` needs to be ``[args.local_rank]``,
+and ``output_device`` needs to be ``args.local_rank`` in order to use this
+utility
+
+5. Another way to pass ``local_rank`` to the subprocesses via environment variable
+``LOCAL_RANK``. This behavior is enabled when you launch the script with
+``--use-env=True``. You must adjust the subprocess example above to replace
+``args.local_rank`` with ``os.environ['LOCAL_RANK']``; the launcher
+will not pass ``--local-rank`` when you specify this flag.
+
+.. warning::
+
+    ``local_rank`` is NOT globally unique: it is only unique per process
+    on a machine.  Thus, don't use it to decide if you should, e.g.,
+    write to a networked filesystem.  See
+    https://github.com/pytorch/pytorch/issues/12042 for an example of
+    how things can go wrong if you don't do this correctly.
+
+
+
+"""
+
+from typing_extensions import deprecated as _deprecated
+
+from torch.distributed.run import get_args_parser, run
+
+
+def parse_args(args):
+    parser = get_args_parser()
+    parser.add_argument(
+        "--use-env",
+        "--use_env",
+        default=False,
+        action="store_true",
+        help="Use environment variable to pass "
+        "'local rank'. For legacy reasons, the default value is False. "
+        "If set to True, the script will not pass "
+        "--local-rank as argument, and will instead set LOCAL_RANK.",
+    )
+    return parser.parse_args(args)
+
+
+def launch(args):
+    if args.no_python and not args.use_env:
+        raise ValueError(
+            "When using the '--no-python' flag,"
+            " you must also set the '--use-env' flag."
+        )
+    run(args)
+
+
+@_deprecated(
+    "The module torch.distributed.launch is deprecated\n"
+    "and will be removed in future. Use torchrun.\n"
+    "Note that --use-env is set by default in torchrun.\n"
+    "If your script expects `--local-rank` argument to be set, please\n"
+    "change it to read from `os.environ['LOCAL_RANK']` instead. See \n"
+    "https://pytorch.org/docs/stable/distributed.html#launch-utility for \n"
+    "further instructions\n",
+    category=FutureWarning,
+)
+def main(args=None):
+    args = parse_args(args)
+    launch(args)
+
+
+if __name__ == "__main__":
+    main()

parrot/lib/python3.10/site-packages/torch/distributed/optim/__init__.py

@@ -0,0 +1,47 @@
+"""
+:mod:`torch.distributed.optim` exposes DistributedOptimizer, which takes a list
+of remote parameters (:class:`~torch.distributed.rpc.RRef`) and runs the
+optimizer locally on the workers where the parameters live.  The distributed
+optimizer can use any of the local optimizer :ref:`optimizer-algorithms` to
+apply the gradients on each worker.
+"""
+import warnings
+
+import torch
+from torch import optim
+
+from .apply_optimizer_in_backward import (
+    _apply_optimizer_in_backward,
+    _get_in_backward_optimizers,
+)
+from .functional_adadelta import _FunctionalAdadelta
+
+from .functional_adagrad import _FunctionalAdagrad
+from .functional_adam import _FunctionalAdam
+from .functional_adamax import _FunctionalAdamax
+from .functional_adamw import _FunctionalAdamW
+from .functional_rmsprop import _FunctionalRMSprop
+from .functional_rprop import _FunctionalRprop
+from .functional_sgd import _FunctionalSGD
+from .named_optimizer import _NamedOptimizer
+from .utils import as_functional_optim
+
+with warnings.catch_warnings():
+    warnings.simplefilter("always")
+    warnings.warn(
+        "`TorchScript` support for functional optimizers is deprecated "
+        "and will be removed in a future PyTorch release. "
+        "Consider using the `torch.compile` optimizer instead.",
+        DeprecationWarning,
+        stacklevel=2,
+    )
+
+# DistributedOptimizer imports torch.distributed.rpc names, so gate availability
+# based on RPC being available.
+if hasattr(torch._C, "_rpc_init"):
+    from .optimizer import DistributedOptimizer
+
+from .post_localSGD_optimizer import PostLocalSGDOptimizer
+from .zero_redundancy_optimizer import ZeroRedundancyOptimizer
+
+__all__ = ["as_functional_optim", "DistributedOptimizer", "PostLocalSGDOptimizer", "ZeroRedundancyOptimizer"]