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//opt/alt/python27/lib64/python2.7/site-packages/numpy/lib/shape_base.py
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 -------- 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. 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)) 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 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 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 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 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]]) """ try: tup = tuple(reps) except TypeError: tup = (reps,) d = len(tup) if all(x == 1 for x in tup) and isinstance(A, _nx.ndarray): # 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 return _nx.array(A, copy=True, subok=True, ndmin=d) 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. c = _nx.array(A, copy=False, subok=True, ndmin=d) if (d < c.ndim): tup = (1,)*(c.ndim-d) + tup shape_out = tuple(s*t for s, t in zip(c.shape, tup)) n = c.size if n > 0: for dim_in, nrep in zip(c.shape, tup): if nrep != 1: c = c.reshape(-1, n).repeat(nrep, 0) n //= dim_in return c.reshape(shape_out)
