|
asarray, zeros, outer, concatenate, array, asanyarray ) _arrays_for_stack_dispatcher, _warn_for_nonsequence) from numpy.matrixlib.defmatrix import matrix # this raises all the right alarm bells
'column_stack', 'row_stack', 'dstack', 'array_split', 'split', 'hsplit', 'vsplit', 'dsplit', 'apply_over_axes', 'expand_dims', 'apply_along_axis', 'kron', 'tile', 'get_array_wrap', 'take_along_axis', 'put_along_axis' ]
overrides.array_function_dispatch, module='numpy')
# compute dimensions to iterate over raise IndexError('`indices` must be an integer array') raise ValueError( "`indices` and `arr` must have the same number of dimensions")
# build a fancy index, consisting of orthogonal aranges, with the # requested index inserted at the right location else:
return (arr, indices)
def take_along_axis(arr, indices, axis): """ Take values from the input array by matching 1d index and data slices.
This iterates over matching 1d slices oriented along the specified axis in the index and data arrays, and uses the former to look up values in the latter. These slices can be different lengths.
Functions returning an index along an axis, like `argsort` and `argpartition`, produce suitable indices for this function.
.. versionadded:: 1.15.0
Parameters ---------- arr: ndarray (Ni..., M, Nk...) Source array indices: ndarray (Ni..., J, Nk...) Indices to take along each 1d slice of `arr`. This must match the dimension of arr, but dimensions Ni and Nj only need to broadcast against `arr`. axis: int The axis to take 1d slices along. If axis is None, the input array is treated as if it had first been flattened to 1d, for consistency with `sort` and `argsort`.
Returns ------- out: ndarray (Ni..., J, Nk...) The indexed result.
Notes ----- This is equivalent to (but faster than) the following use of `ndindex` and `s_`, which sets each of ``ii`` and ``kk`` to a tuple of indices::
Ni, M, Nk = a.shape[:axis], a.shape[axis], a.shape[axis+1:] J = indices.shape[axis] # Need not equal M out = np.empty(Nk + (J,) + Nk)
for ii in ndindex(Ni): for kk in ndindex(Nk): a_1d = a [ii + s_[:,] + kk] indices_1d = indices[ii + s_[:,] + kk] out_1d = out [ii + s_[:,] + kk] for j in range(J): out_1d[j] = a_1d[indices_1d[j]]
Equivalently, eliminating the inner loop, the last two lines would be::
out_1d[:] = a_1d[indices_1d]
See Also -------- take : Take along an axis, using the same indices for every 1d slice put_along_axis : Put values into the destination array by matching 1d index and data slices
Examples --------
For this sample array
>>> a = np.array([[10, 30, 20], [60, 40, 50]])
We can sort either by using sort directly, or argsort and this function
>>> np.sort(a, axis=1) array([[10, 20, 30], [40, 50, 60]]) >>> ai = np.argsort(a, axis=1); ai array([[0, 2, 1], [1, 2, 0]], dtype=int64) >>> np.take_along_axis(a, ai, axis=1) array([[10, 20, 30], [40, 50, 60]])
The same works for max and min, if you expand the dimensions:
>>> np.expand_dims(np.max(a, axis=1), axis=1) array([[30], [60]]) >>> ai = np.expand_dims(np.argmax(a, axis=1), axis=1) >>> ai array([[1], [0], dtype=int64) >>> np.take_along_axis(a, ai, axis=1) array([[30], [60]])
If we want to get the max and min at the same time, we can stack the indices first
>>> ai_min = np.expand_dims(np.argmin(a, axis=1), axis=1) >>> ai_max = np.expand_dims(np.argmax(a, axis=1), axis=1) >>> ai = np.concatenate([ai_min, ai_max], axis=axis) >> ai array([[0, 1], [1, 0]], dtype=int64) >>> np.take_along_axis(a, ai, axis=1) array([[10, 30], [40, 60]]) """ # normalize inputs arr = arr.flat arr_shape = (len(arr),) # flatiter has no .shape axis = 0 else:
# use the fancy index
return (arr, indices, values)
def put_along_axis(arr, indices, values, axis): """ Put values into the destination array by matching 1d index and data slices.
This iterates over matching 1d slices oriented along the specified axis in the index and data arrays, and uses the former to place values into the latter. These slices can be different lengths.
Functions returning an index along an axis, like `argsort` and `argpartition`, produce suitable indices for this function.
.. versionadded:: 1.15.0
Parameters ---------- arr: ndarray (Ni..., M, Nk...) Destination array. indices: ndarray (Ni..., J, Nk...) Indices to change along each 1d slice of `arr`. This must match the dimension of arr, but dimensions in Ni and Nj may be 1 to broadcast against `arr`. values: array_like (Ni..., J, Nk...) values to insert at those indices. Its shape and dimension are broadcast to match that of `indices`. axis: int The axis to take 1d slices along. If axis is None, the destination array is treated as if a flattened 1d view had been created of it.
Notes ----- This is equivalent to (but faster than) the following use of `ndindex` and `s_`, which sets each of ``ii`` and ``kk`` to a tuple of indices::
Ni, M, Nk = a.shape[:axis], a.shape[axis], a.shape[axis+1:] J = indices.shape[axis] # Need not equal M
for ii in ndindex(Ni): for kk in ndindex(Nk): a_1d = a [ii + s_[:,] + kk] indices_1d = indices[ii + s_[:,] + kk] values_1d = values [ii + s_[:,] + kk] for j in range(J): a_1d[indices_1d[j]] = values_1d[j]
Equivalently, eliminating the inner loop, the last two lines would be::
a_1d[indices_1d] = values_1d
See Also -------- take_along_axis : Take values from the input array by matching 1d index and data slices
Examples --------
For this sample array
>>> a = np.array([[10, 30, 20], [60, 40, 50]])
We can replace the maximum values with:
>>> ai = np.expand_dims(np.argmax(a, axis=1), axis=1) >>> ai array([[1], [0]], dtype=int64) >>> np.put_along_axis(a, ai, 99, axis=1) >>> a array([[10, 99, 20], [99, 40, 50]])
""" # normalize inputs if axis is None: arr = arr.flat axis = 0 arr_shape = (len(arr),) # flatiter has no .shape else: axis = normalize_axis_index(axis, arr.ndim) arr_shape = arr.shape
# use the fancy index arr[_make_along_axis_idx(arr_shape, indices, axis)] = values
return (arr,)
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`.
This is equivalent to (but faster than) the following use of `ndindex` and `s_`, which sets each of ``ii``, ``jj``, and ``kk`` to a tuple of indices::
Ni, Nk = a.shape[:axis], a.shape[axis+1:] for ii in ndindex(Ni): for kk in ndindex(Nk): f = func1d(arr[ii + s_[:,] + kk]) Nj = f.shape for jj in ndindex(Nj): out[ii + jj + kk] = f[jj]
Equivalently, eliminating the inner loop, this can be expressed as::
Ni, Nk = a.shape[:axis], a.shape[axis+1:] for ii in ndindex(Ni): for kk in ndindex(Nk): out[ii + s_[...,] + kk] = func1d(arr[ii + s_[:,] + kk])
Parameters ---------- func1d : function (M,) -> (Nj...) 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 (Ni..., M, Nk...) Input array. args : any Additional arguments to `func1d`. kwargs : any Additional named arguments to `func1d`.
.. versionadded:: 1.9.0
Returns ------- out : ndarray (Ni..., Nj..., Nk...) The output array. The shape of `out` is identical to the shape of `arr`, except along the `axis` dimension. This axis is removed, and replaced with new dimensions equal to the shape of the return value of `func1d`. So if `func1d` returns a scalar `out` 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 returns a 1D array, 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]])
For a function that returns a higher dimensional array, those dimensions are inserted in place of the `axis` dimension.
>>> b = np.array([[1,2,3], [4,5,6], [7,8,9]]) >>> np.apply_along_axis(np.diag, -1, b) array([[[1, 0, 0], [0, 2, 0], [0, 0, 3]], [[4, 0, 0], [0, 5, 0], [0, 0, 6]], [[7, 0, 0], [0, 8, 0], [0, 0, 9]]]) """ # handle negative axes
# arr, with the iteration axis at the end
# compute indices for the iteration axes, and append a trailing ellipsis to # prevent 0d arrays decaying to scalars, which fixes gh-8642
# invoke the function on the first item except StopIteration: raise ValueError('Cannot apply_along_axis when any iteration dimensions are 0')
# build a buffer for storing evaluations of func1d. # remove the requested axis, and add the new ones on the end. # laid out so that each write is contiguous. # for a tuple index inds, buff[inds] = func1d(inarr_view[inds])
# permutation of axes such that out = buff.transpose(buff_permute) buff_dims[0 : axis] + buff_dims[buff.ndim-res.ndim : buff.ndim] + buff_dims[axis : buff.ndim-res.ndim] )
# matrices have a nasty __array_prepare__ and __array_wrap__
# save the first result, then compute and save all remaining results
# wrap the array, to preserve subclasses
# finally, rotate the inserted axes back to where they belong
else: # matrices have to be transposed first, because they collapse dimensions! out_arr = transpose(buff, buff_permute) return res.__array_wrap__(out_arr)
return (a,)
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 available 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
return (a,)
def expand_dims(a, axis): """ Expand the shape of an array.
Insert a new axis that will appear at the `axis` position in the expanded array shape.
.. note:: Previous to NumPy 1.13.0, neither ``axis < -a.ndim - 1`` nor ``axis > a.ndim`` raised errors or put the new axis where documented. Those axis values are now deprecated and will raise an AxisError in the future.
Parameters ---------- a : array_like Input array. axis : int Position in the expanded axes where the new axis is placed.
Returns ------- res : ndarray Output array. The number of dimensions is one greater than that of the input array.
See Also -------- squeeze : The inverse operation, removing singleton dimensions reshape : Insert, remove, and combine dimensions, and resize existing ones 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[:,np.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
""" if isinstance(a, matrix): a = asarray(a) else: a = asanyarray(a)
shape = a.shape if axis > a.ndim or axis < -a.ndim - 1: # 2017-05-17, 1.13.0 warnings.warn("Both axis > a.ndim and axis < -a.ndim - 1 are " "deprecated and will raise an AxisError in the future.", DeprecationWarning, stacklevel=2) # When the deprecation period expires, delete this if block, if axis < 0: axis = axis + a.ndim + 1 # and uncomment the following line. # axis = normalize_axis_index(axis, a.ndim + 1) return a.reshape(shape[:axis] + (1,) + shape[axis:])
return _arrays_for_stack_dispatcher(tup)
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 -------- stack, 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]])
"""
return _arrays_for_stack_dispatcher(tup)
def dstack(tup): """ Stack arrays in sequence depth wise (along third axis).
This is equivalent to concatenation along the third axis after 2-D arrays of shape `(M,N)` have been reshaped to `(M,N,1)` and 1-D arrays of shape `(N,)` have been reshaped to `(1,N,1)`. Rebuilds arrays divided by `dsplit`.
This function makes most sense for arrays with up to 3 dimensions. For instance, for pixel-data with a height (first axis), width (second axis), and r/g/b channels (third axis). The functions `concatenate`, `stack` and `block` provide more general stacking and concatenation operations.
Parameters ---------- tup : sequence of arrays The arrays must have the same shape along all but the third axis. 1-D or 2-D arrays must have the same shape.
Returns ------- stacked : ndarray The array formed by stacking the given arrays, will be at least 3-D.
See Also -------- stack : Join a sequence of arrays along a new axis. vstack : Stack along first axis. hstack : Stack along second axis. concatenate : Join a sequence of arrays along an existing axis. dsplit : Split array along third axis.
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]]])
""" _warn_for_nonsequence(tup) return _nx.concatenate([atleast_3d(_m) for _m in tup], 2)
for i in range(len(sub_arys)): if _nx.ndim(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
return (ary, indices_or_sections)
""" 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. For an array of length l that should be split into n sections, it returns l % n sub-arrays of size l//n + 1 and the rest of size l//n.
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.])]
>>> x = np.arange(7.0) >>> np.array_split(x, 3) [array([ 0., 1., 2.]), array([ 3., 4.]), array([ 5., 6.])]
""" try: Ntotal = ary.shape[axis] except AttributeError: Ntotal = len(ary) try: # handle array 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, dtype=_nx.intp).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))
return sub_arys
return (ary, indices_or_sections)
""" 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 a sequence of arrays along an existing axis. stack : Join a sequence of arrays along a new axis. 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
return (ary, indices_or_sections)
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 _nx.ndim(ary) == 0: raise ValueError('hsplit only works on arrays of 1 or more dimensions') if ary.ndim > 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 _nx.ndim(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 _nx.ndim(ary) < 3: raise ValueError('dsplit only works on arrays of 3 or more dimensions') return split(ary, indices_or_sections, 2)
"""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
"""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
return (a, b)
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 dimensions 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
return (A, reps)
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).
Note : Although tile may be used for broadcasting, it is strongly recommended to use numpy's broadcasting operations and functions.
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. broadcast_to : Broadcast an array to a new shape
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]])
>>> c = np.array([1,2,3,4]) >>> np.tile(c,(4,1)) array([[1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4], [1, 2, 3, 4]]) """ # Fixes the problem that the function does not make a copy if A is a # numpy array and the repetitions are 1 in all dimensions else: # Note that no copy of zero-sized arrays is made. However since they # have no data there is no risk of an inadvertent overwrite. tup = (1,)*(c.ndim-d) + tup |