comparison DEPENDENCIES/mingw32/Python27/Lib/site-packages/numpy/lib/shape_base.py @ 87:2a2c65a20a8b

Add Python libs and headers

+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 `(r0*s0, r1*s1, ..., 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)