JayKimDevolved/deepseek

c011401 verified 11 months ago

25.2 kB

	from __future__ import division, absolute_import, print_function

	import warnings

	import numpy.core.numeric as _nx
	from numpy.core.numeric import (
	asarray, zeros, outer, concatenate, isscalar, array, asanyarray
	)
	from numpy.core.fromnumeric import product, reshape
	from numpy.core import vstack, atleast_3d


	__all__ = [
	'column_stack', 'row_stack', 'dstack', 'array_split', 'split',
	'hsplit', 'vsplit', 'dsplit', 'apply_over_axes', 'expand_dims',
	'apply_along_axis', 'kron', 'tile', 'get_array_wrap'
	]


	def apply_along_axis(func1d, axis, arr, args, *kwargs):
	"""
	Apply a function to 1-D slices along the given axis.

	Execute `func1d(a, *args)` where `func1d` operates on 1-D arrays and `a`
	is a 1-D slice of `arr` along `axis`.

	Parameters
	----------
	func1d : function
	This function should accept 1-D arrays. It is applied to 1-D
	slices of `arr` along the specified axis.
	axis : integer
	Axis along which `arr` is sliced.
	arr : ndarray
	Input array.
	args : any
	Additional arguments to `func1d`.
	kwargs: any
	Additional named arguments to `func1d`.

	.. versionadded:: 1.9.0


	Returns
	-------
	apply_along_axis : ndarray
	The output array. The shape of `outarr` is identical to the shape of
	`arr`, except along the `axis` dimension, where the length of `outarr`
	is equal to the size of the return value of `func1d`. If `func1d`
	returns a scalar `outarr` will have one fewer dimensions than `arr`.

	See Also
	--------
	apply_over_axes : Apply a function repeatedly over multiple axes.

	Examples
	--------
	>>> def my_func(a):
	... \"\"\"Average first and last element of a 1-D array\"\"\"
	... return (a[0] + a[-1]) * 0.5
	>>> b = np.array([[1,2,3], [4,5,6], [7,8,9]])
	>>> np.apply_along_axis(my_func, 0, b)
	array([ 4., 5., 6.])
	>>> np.apply_along_axis(my_func, 1, b)
	array([ 2., 5., 8.])

	For a function that doesn't return a scalar, the number of dimensions in
	`outarr` is the same as `arr`.

	>>> b = np.array([[8,1,7], [4,3,9], [5,2,6]])
	>>> np.apply_along_axis(sorted, 1, b)
	array([[1, 7, 8],
	[3, 4, 9],
	[2, 5, 6]])

	"""
	arr = asarray(arr)
	nd = arr.ndim
	if axis < 0:
	axis += nd
	if (axis >= nd):
	raise ValueError("axis must be less than arr.ndim; axis=%d, rank=%d."
	% (axis, nd))
	ind = [0]*(nd-1)
	i = zeros(nd, 'O')
	indlist = list(range(nd))
	indlist.remove(axis)
	i[axis] = slice(None, None)
	outshape = asarray(arr.shape).take(indlist)
	i.put(indlist, ind)
	res = func1d(arr[tuple(i.tolist())], args, *kwargs)
	# if res is a number, then we have a smaller output array
	if isscalar(res):
	outarr = zeros(outshape, asarray(res).dtype)
	outarr[tuple(ind)] = res
	Ntot = product(outshape)
	k = 1
	while k < Ntot:
	# increment the index
	ind[-1] += 1
	n = -1
	while (ind[n] >= outshape[n]) and (n > (1-nd)):
	ind[n-1] += 1
	ind[n] = 0
	n -= 1
	i.put(indlist, ind)
	res = func1d(arr[tuple(i.tolist())], args, *kwargs)
	outarr[tuple(ind)] = res
	k += 1
	return outarr
	else:
	Ntot = product(outshape)
	holdshape = outshape
	outshape = list(arr.shape)
	outshape[axis] = len(res)
	outarr = zeros(outshape, asarray(res).dtype)
	outarr[tuple(i.tolist())] = res
	k = 1
	while k < Ntot:
	# increment the index
	ind[-1] += 1
	n = -1
	while (ind[n] >= holdshape[n]) and (n > (1-nd)):
	ind[n-1] += 1
	ind[n] = 0
	n -= 1
	i.put(indlist, ind)
	res = func1d(arr[tuple(i.tolist())], args, *kwargs)
	outarr[tuple(i.tolist())] = res
	k += 1
	return outarr


	def apply_over_axes(func, a, axes):
	"""
	Apply a function repeatedly over multiple axes.

	`func` is called as `res = func(a, axis)`, where `axis` is the first
	element of `axes`. The result `res` of the function call must have
	either the same dimensions as `a` or one less dimension. If `res`
	has one less dimension than `a`, a dimension is inserted before
	`axis`. The call to `func` is then repeated for each axis in `axes`,
	with `res` as the first argument.

	Parameters
	----------
	func : function
	This function must take two arguments, `func(a, axis)`.
	a : array_like
	Input array.
	axes : array_like
	Axes over which `func` is applied; the elements must be integers.

	Returns
	-------
	apply_over_axis : ndarray
	The output array. The number of dimensions is the same as `a`,
	but the shape can be different. This depends on whether `func`
	changes the shape of its output with respect to its input.

	See Also
	--------
	apply_along_axis :
	Apply a function to 1-D slices of an array along the given axis.

	Notes
	------
	This function is equivalent to tuple axis arguments to reorderable ufuncs
	with keepdims=True. Tuple axis arguments to ufuncs have been availabe since
	version 1.7.0.

	Examples
	--------
	>>> a = np.arange(24).reshape(2,3,4)
	>>> a
	array([[[ 0, 1, 2, 3],
	[ 4, 5, 6, 7],
	[ 8, 9, 10, 11]],
	[[12, 13, 14, 15],
	[16, 17, 18, 19],
	[20, 21, 22, 23]]])

	Sum over axes 0 and 2. The result has same number of dimensions
	as the original array:

	>>> np.apply_over_axes(np.sum, a, [0,2])
	array([[[ 60],
	[ 92],
	[124]]])

	Tuple axis arguments to ufuncs are equivalent:

	>>> np.sum(a, axis=(0,2), keepdims=True)
	array([[[ 60],
	[ 92],
	[124]]])

	"""
	val = asarray(a)
	N = a.ndim
	if array(axes).ndim == 0:
	axes = (axes,)
	for axis in axes:
	if axis < 0:
	axis = N + axis
	args = (val, axis)
	res = func(*args)
	if res.ndim == val.ndim:
	val = res
	else:
	res = expand_dims(res, axis)
	if res.ndim == val.ndim:
	val = res
	else:
	raise ValueError("function is not returning "
	"an array of the correct shape")
	return val

	def expand_dims(a, axis):
	"""
	Expand the shape of an array.

	Insert a new axis, corresponding to a given position in the array shape.

	Parameters
	----------
	a : array_like
	Input array.
	axis : int
	Position (amongst axes) where new axis is to be inserted.

	Returns
	-------
	res : ndarray
	Output array. The number of dimensions is one greater than that of
	the input array.

	See Also
	--------
	doc.indexing, atleast_1d, atleast_2d, atleast_3d

	Examples
	--------
	>>> x = np.array([1,2])
	>>> x.shape
	(2,)

	The following is equivalent to ``x[np.newaxis,:]`` or ``x[np.newaxis]``:

	>>> y = np.expand_dims(x, axis=0)
	>>> y
	array([[1, 2]])
	>>> y.shape
	(1, 2)

	>>> y = np.expand_dims(x, axis=1) # Equivalent to x[:,newaxis]
	>>> y
	array([[1],
	[2]])
	>>> y.shape
	(2, 1)

	Note that some examples may use ``None`` instead of ``np.newaxis``. These
	are the same objects:

	>>> np.newaxis is None
	True

	"""
	a = asarray(a)
	shape = a.shape
	if axis < 0:
	axis = axis + len(shape) + 1
	return a.reshape(shape[:axis] + (1,) + shape[axis:])

	row_stack = vstack

	def column_stack(tup):
	"""
	Stack 1-D arrays as columns into a 2-D array.

	Take a sequence of 1-D arrays and stack them as columns
	to make a single 2-D array. 2-D arrays are stacked as-is,
	just like with `hstack`. 1-D arrays are turned into 2-D columns
	first.

	Parameters
	----------
	tup : sequence of 1-D or 2-D arrays.
	Arrays to stack. All of them must have the same first dimension.

	Returns
	-------
	stacked : 2-D array
	The array formed by stacking the given arrays.

	See Also
	--------
	hstack, vstack, concatenate

	Examples
	--------
	>>> a = np.array((1,2,3))
	>>> b = np.array((2,3,4))
	>>> np.column_stack((a,b))
	array([[1, 2],
	[2, 3],
	[3, 4]])

	"""
	arrays = []
	for v in tup:
	arr = array(v, copy=False, subok=True)
	if arr.ndim < 2:
	arr = array(arr, copy=False, subok=True, ndmin=2).T
	arrays.append(arr)
	return _nx.concatenate(arrays, 1)

	def dstack(tup):
	"""
	Stack arrays in sequence depth wise (along third axis).

	Takes a sequence of arrays and stack them along the third axis
	to make a single array. Rebuilds arrays divided by `dsplit`.
	This is a simple way to stack 2D arrays (images) into a single
	3D array for processing.

	Parameters
	----------
	tup : sequence of arrays
	Arrays to stack. All of them must have the same shape along all
	but the third axis.

	Returns
	-------
	stacked : ndarray
	The array formed by stacking the given arrays.

	See Also
	--------
	vstack : Stack along first axis.
	hstack : Stack along second axis.
	concatenate : Join arrays.
	dsplit : Split array along third axis.

	Notes
	-----
	Equivalent to ``np.concatenate(tup, axis=2)``.

	Examples
	--------
	>>> a = np.array((1,2,3))
	>>> b = np.array((2,3,4))
	>>> np.dstack((a,b))
	array([[[1, 2],
	[2, 3],
	[3, 4]]])

	>>> a = np.array([[1],[2],[3]])
	>>> b = np.array([[2],[3],[4]])
	>>> np.dstack((a,b))
	array([[[1, 2]],
	[[2, 3]],
	[[3, 4]]])

	"""
	return _nx.concatenate([atleast_3d(_m) for _m in tup], 2)

	def _replace_zero_by_x_arrays(sub_arys):
	for i in range(len(sub_arys)):
	if len(_nx.shape(sub_arys[i])) == 0:
	sub_arys[i] = _nx.empty(0, dtype=sub_arys[i].dtype)
	elif _nx.sometrue(_nx.equal(_nx.shape(sub_arys[i]), 0)):
	sub_arys[i] = _nx.empty(0, dtype=sub_arys[i].dtype)
	return sub_arys

	def array_split(ary, indices_or_sections, axis=0):
	"""
	Split an array into multiple sub-arrays.

	Please refer to the ``split`` documentation. The only difference
	between these functions is that ``array_split`` allows
	`indices_or_sections` to be an integer that does not equally
	divide the axis.

	See Also
	--------
	split : Split array into multiple sub-arrays of equal size.

	Examples
	--------
	>>> x = np.arange(8.0)
	>>> np.array_split(x, 3)
	[array([ 0., 1., 2.]), array([ 3., 4., 5.]), array([ 6., 7.])]

	"""
	try:
	Ntotal = ary.shape[axis]
	except AttributeError:
	Ntotal = len(ary)
	try:
	# handle scalar case.
	Nsections = len(indices_or_sections) + 1
	div_points = [0] + list(indices_or_sections) + [Ntotal]
	except TypeError:
	# indices_or_sections is a scalar, not an array.
	Nsections = int(indices_or_sections)
	if Nsections <= 0:
	raise ValueError('number sections must be larger than 0.')
	Neach_section, extras = divmod(Ntotal, Nsections)
	section_sizes = ([0] +
	extras * [Neach_section+1] +
	(Nsections-extras) * [Neach_section])
	div_points = _nx.array(section_sizes).cumsum()

	sub_arys = []
	sary = _nx.swapaxes(ary, axis, 0)
	for i in range(Nsections):
	st = div_points[i]
	end = div_points[i + 1]
	sub_arys.append(_nx.swapaxes(sary[st:end], axis, 0))

	# This "kludge" was introduced here to replace arrays shaped (0, 10)
	# or similar with an array shaped (0,).
	# There seems no need for this, so give a FutureWarning to remove later.
	if sub_arys[-1].size == 0 and sub_arys[-1].ndim != 1:
	warnings.warn("in the future np.array_split will retain the shape of "
	"arrays with a zero size, instead of replacing them by "
	"`array([])`, which always has a shape of (0,).",
	FutureWarning)
	sub_arys = _replace_zero_by_x_arrays(sub_arys)

	return sub_arys

	def split(ary,indices_or_sections,axis=0):
	"""
	Split an array into multiple sub-arrays.

	Parameters
	----------
	ary : ndarray
	Array to be divided into sub-arrays.
	indices_or_sections : int or 1-D array
	If `indices_or_sections` is an integer, N, the array will be divided
	into N equal arrays along `axis`. If such a split is not possible,
	an error is raised.

	If `indices_or_sections` is a 1-D array of sorted integers, the entries
	indicate where along `axis` the array is split. For example,
	``[2, 3]`` would, for ``axis=0``, result in

	- ary[:2]
	- ary[2:3]
	- ary[3:]

	If an index exceeds the dimension of the array along `axis`,
	an empty sub-array is returned correspondingly.
	axis : int, optional
	The axis along which to split, default is 0.

	Returns
	-------
	sub-arrays : list of ndarrays
	A list of sub-arrays.

	Raises
	------
	ValueError
	If `indices_or_sections` is given as an integer, but
	a split does not result in equal division.

	See Also
	--------
	array_split : Split an array into multiple sub-arrays of equal or
	near-equal size. Does not raise an exception if
	an equal division cannot be made.
	hsplit : Split array into multiple sub-arrays horizontally (column-wise).
	vsplit : Split array into multiple sub-arrays vertically (row wise).
	dsplit : Split array into multiple sub-arrays along the 3rd axis (depth).
	concatenate : Join arrays together.
	hstack : Stack arrays in sequence horizontally (column wise).
	vstack : Stack arrays in sequence vertically (row wise).
	dstack : Stack arrays in sequence depth wise (along third dimension).

	Examples
	--------
	>>> x = np.arange(9.0)
	>>> np.split(x, 3)
	[array([ 0., 1., 2.]), array([ 3., 4., 5.]), array([ 6., 7., 8.])]

	>>> x = np.arange(8.0)
	>>> np.split(x, [3, 5, 6, 10])
	[array([ 0., 1., 2.]),
	array([ 3., 4.]),
	array([ 5.]),
	array([ 6., 7.]),
	array([], dtype=float64)]

	"""
	try:
	len(indices_or_sections)
	except TypeError:
	sections = indices_or_sections
	N = ary.shape[axis]
	if N % sections:
	raise ValueError(
	'array split does not result in an equal division')
	res = array_split(ary, indices_or_sections, axis)
	return res

	def hsplit(ary, indices_or_sections):
	"""
	Split an array into multiple sub-arrays horizontally (column-wise).

	Please refer to the `split` documentation. `hsplit` is equivalent
	to `split` with ``axis=1``, the array is always split along the second
	axis regardless of the array dimension.

	See Also
	--------
	split : Split an array into multiple sub-arrays of equal size.

	Examples
	--------
	>>> x = np.arange(16.0).reshape(4, 4)
	>>> x
	array([[ 0., 1., 2., 3.],
	[ 4., 5., 6., 7.],
	[ 8., 9., 10., 11.],
	[ 12., 13., 14., 15.]])
	>>> np.hsplit(x, 2)
	[array([[ 0., 1.],
	[ 4., 5.],
	[ 8., 9.],
	[ 12., 13.]]),
	array([[ 2., 3.],
	[ 6., 7.],
	[ 10., 11.],
	[ 14., 15.]])]
	>>> np.hsplit(x, np.array([3, 6]))
	[array([[ 0., 1., 2.],
	[ 4., 5., 6.],
	[ 8., 9., 10.],
	[ 12., 13., 14.]]),
	array([[ 3.],
	[ 7.],
	[ 11.],
	[ 15.]]),
	array([], dtype=float64)]

	With a higher dimensional array the split is still along the second axis.

	>>> x = np.arange(8.0).reshape(2, 2, 2)
	>>> x
	array([[[ 0., 1.],
	[ 2., 3.]],
	[[ 4., 5.],
	[ 6., 7.]]])
	>>> np.hsplit(x, 2)
	[array([[[ 0., 1.]],
	[[ 4., 5.]]]),
	array([[[ 2., 3.]],
	[[ 6., 7.]]])]

	"""
	if len(_nx.shape(ary)) == 0:
	raise ValueError('hsplit only works on arrays of 1 or more dimensions')
	if len(ary.shape) > 1:
	return split(ary, indices_or_sections, 1)
	else:
	return split(ary, indices_or_sections, 0)

	def vsplit(ary, indices_or_sections):
	"""
	Split an array into multiple sub-arrays vertically (row-wise).

	Please refer to the ``split`` documentation. ``vsplit`` is equivalent
	to ``split`` with `axis=0` (default), the array is always split along the
	first axis regardless of the array dimension.

	See Also
	--------
	split : Split an array into multiple sub-arrays of equal size.

	Examples
	--------
	>>> x = np.arange(16.0).reshape(4, 4)
	>>> x
	array([[ 0., 1., 2., 3.],
	[ 4., 5., 6., 7.],
	[ 8., 9., 10., 11.],
	[ 12., 13., 14., 15.]])
	>>> np.vsplit(x, 2)
	[array([[ 0., 1., 2., 3.],
	[ 4., 5., 6., 7.]]),
	array([[ 8., 9., 10., 11.],
	[ 12., 13., 14., 15.]])]
	>>> np.vsplit(x, np.array([3, 6]))
	[array([[ 0., 1., 2., 3.],
	[ 4., 5., 6., 7.],
	[ 8., 9., 10., 11.]]),
	array([[ 12., 13., 14., 15.]]),
	array([], dtype=float64)]

	With a higher dimensional array the split is still along the first axis.

	>>> x = np.arange(8.0).reshape(2, 2, 2)
	>>> x
	array([[[ 0., 1.],
	[ 2., 3.]],
	[[ 4., 5.],
	[ 6., 7.]]])
	>>> np.vsplit(x, 2)
	[array([[[ 0., 1.],
	[ 2., 3.]]]),
	array([[[ 4., 5.],
	[ 6., 7.]]])]

	"""
	if len(_nx.shape(ary)) < 2:
	raise ValueError('vsplit only works on arrays of 2 or more dimensions')
	return split(ary, indices_or_sections, 0)

	def dsplit(ary, indices_or_sections):
	"""
	Split array into multiple sub-arrays along the 3rd axis (depth).

	Please refer to the `split` documentation. `dsplit` is equivalent
	to `split` with ``axis=2``, the array is always split along the third
	axis provided the array dimension is greater than or equal to 3.

	See Also
	--------
	split : Split an array into multiple sub-arrays of equal size.

	Examples
	--------
	>>> x = np.arange(16.0).reshape(2, 2, 4)
	>>> x
	array([[[ 0., 1., 2., 3.],
	[ 4., 5., 6., 7.]],
	[[ 8., 9., 10., 11.],
	[ 12., 13., 14., 15.]]])
	>>> np.dsplit(x, 2)
	[array([[[ 0., 1.],
	[ 4., 5.]],
	[[ 8., 9.],
	[ 12., 13.]]]),
	array([[[ 2., 3.],
	[ 6., 7.]],
	[[ 10., 11.],
	[ 14., 15.]]])]
	>>> np.dsplit(x, np.array([3, 6]))
	[array([[[ 0., 1., 2.],
	[ 4., 5., 6.]],
	[[ 8., 9., 10.],
	[ 12., 13., 14.]]]),
	array([[[ 3.],
	[ 7.]],
	[[ 11.],
	[ 15.]]]),
	array([], dtype=float64)]

	"""
	if len(_nx.shape(ary)) < 3:
	raise ValueError('dsplit only works on arrays of 3 or more dimensions')
	return split(ary, indices_or_sections, 2)

	def get_array_prepare(*args):
	"""Find the wrapper for the array with the highest priority.

	In case of ties, leftmost wins. If no wrapper is found, return None
	"""
	wrappers = sorted((getattr(x, '__array_priority__', 0), -i,
	x.__array_prepare__) for i, x in enumerate(args)
	if hasattr(x, '__array_prepare__'))
	if wrappers:
	return wrappers[-1][-1]
	return None

	def get_array_wrap(*args):
	"""Find the wrapper for the array with the highest priority.

	In case of ties, leftmost wins. If no wrapper is found, return None
	"""
	wrappers = sorted((getattr(x, '__array_priority__', 0), -i,
	x.__array_wrap__) for i, x in enumerate(args)
	if hasattr(x, '__array_wrap__'))
	if wrappers:
	return wrappers[-1][-1]
	return None

	def kron(a, b):
	"""
	Kronecker product of two arrays.

	Computes the Kronecker product, a composite array made of blocks of the
	second array scaled by the first.

	Parameters
	----------
	a, b : array_like

	Returns
	-------
	out : ndarray

	See Also
	--------
	outer : The outer product

	Notes
	-----
	The function assumes that the number of dimenensions of `a` and `b`
	are the same, if necessary prepending the smallest with ones.
	If `a.shape = (r0,r1,..,rN)` and `b.shape = (s0,s1,...,sN)`,
	the Kronecker product has shape `(r0s0, r1s1, ..., rN*SN)`.
	The elements are products of elements from `a` and `b`, organized
	explicitly by::

	kron(a,b)[k0,k1,...,kN] = a[i0,i1,...,iN] * b[j0,j1,...,jN]

	where::

	kt = it * st + jt, t = 0,...,N

	In the common 2-D case (N=1), the block structure can be visualized::

	[[ a[0,0]b, a[0,1]b, ... , a[0,-1]*b ],
	[ ... ... ],
	[ a[-1,0]b, a[-1,1]b, ... , a[-1,-1]*b ]]


	Examples
	--------
	>>> np.kron([1,10,100], [5,6,7])
	array([ 5, 6, 7, 50, 60, 70, 500, 600, 700])
	>>> np.kron([5,6,7], [1,10,100])
	array([ 5, 50, 500, 6, 60, 600, 7, 70, 700])

	>>> np.kron(np.eye(2), np.ones((2,2)))
	array([[ 1., 1., 0., 0.],
	[ 1., 1., 0., 0.],
	[ 0., 0., 1., 1.],
	[ 0., 0., 1., 1.]])

	>>> a = np.arange(100).reshape((2,5,2,5))
	>>> b = np.arange(24).reshape((2,3,4))
	>>> c = np.kron(a,b)
	>>> c.shape
	(2, 10, 6, 20)
	>>> I = (1,3,0,2)
	>>> J = (0,2,1)
	>>> J1 = (0,) + J # extend to ndim=4
	>>> S1 = (1,) + b.shape
	>>> K = tuple(np.array(I) * np.array(S1) + np.array(J1))
	>>> c[K] == a[I]*b[J]
	True

	"""
	b = asanyarray(b)
	a = array(a, copy=False, subok=True, ndmin=b.ndim)
	ndb, nda = b.ndim, a.ndim
	if (nda == 0 or ndb == 0):
	return _nx.multiply(a, b)
	as_ = a.shape
	bs = b.shape
	if not a.flags.contiguous:
	a = reshape(a, as_)
	if not b.flags.contiguous:
	b = reshape(b, bs)
	nd = ndb
	if (ndb != nda):
	if (ndb > nda):
	as_ = (1,)*(ndb-nda) + as_
	else:
	bs = (1,)*(nda-ndb) + bs
	nd = nda
	result = outer(a, b).reshape(as_+bs)
	axis = nd-1
	for _ in range(nd):
	result = concatenate(result, axis=axis)
	wrapper = get_array_prepare(a, b)
	if wrapper is not None:
	result = wrapper(result)
	wrapper = get_array_wrap(a, b)
	if wrapper is not None:
	result = wrapper(result)
	return result


	def tile(A, reps):
	"""
	Construct an array by repeating A the number of times given by reps.

	If `reps` has length ``d``, the result will have dimension of
	``max(d, A.ndim)``.

	If ``A.ndim < d``, `A` is promoted to be d-dimensional by prepending new
	axes. So a shape (3,) array is promoted to (1, 3) for 2-D replication,
	or shape (1, 1, 3) for 3-D replication. If this is not the desired
	behavior, promote `A` to d-dimensions manually before calling this
	function.

	If ``A.ndim > d``, `reps` is promoted to `A`.ndim by pre-pending 1's to it.
	Thus for an `A` of shape (2, 3, 4, 5), a `reps` of (2, 2) is treated as
	(1, 1, 2, 2).

	Parameters
	----------
	A : array_like
	The input array.
	reps : array_like
	The number of repetitions of `A` along each axis.

	Returns
	-------
	c : ndarray
	The tiled output array.

	See Also
	--------
	repeat : Repeat elements of an array.

	Examples
	--------
	>>> a = np.array([0, 1, 2])
	>>> np.tile(a, 2)
	array([0, 1, 2, 0, 1, 2])
	>>> np.tile(a, (2, 2))
	array([[0, 1, 2, 0, 1, 2],
	[0, 1, 2, 0, 1, 2]])
	>>> np.tile(a, (2, 1, 2))
	array([[[0, 1, 2, 0, 1, 2]],
	[[0, 1, 2, 0, 1, 2]]])

	>>> b = np.array([[1, 2], [3, 4]])
	>>> np.tile(b, 2)
	array([[1, 2, 1, 2],
	[3, 4, 3, 4]])
	>>> np.tile(b, (2, 1))
	array([[1, 2],
	[3, 4],
	[1, 2],
	[3, 4]])

	"""
	try:
	tup = tuple(reps)
	except TypeError:
	tup = (reps,)
	d = len(tup)
	c = _nx.array(A, copy=False, subok=True, ndmin=d)
	shape = list(c.shape)
	n = max(c.size, 1)
	if (d < c.ndim):
	tup = (1,)*(c.ndim-d) + tup
	for i, nrep in enumerate(tup):
	if nrep != 1:
	c = c.reshape(-1, n).repeat(nrep, 0)
	dim_in = shape[i]
	dim_out = dim_in*nrep
	shape[i] = dim_out
	n //= max(dim_in, 1)
	return c.reshape(shape)