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"""
Utilities that manipulate strides to achieve desirable effects.
An explanation of strides can be found in the "ndarray.rst" file in the
NumPy reference guide.
"""
from __future__ import division, absolute_import, print_function
import numpy as np
__all__ = ['broadcast_arrays']
class DummyArray(object):
"""Dummy object that just exists to hang __array_interface__ dictionaries
and possibly keep alive a reference to a base array.
"""
def __init__(self, interface, base=None):
self.__array_interface__ = interface
self.base = base
def as_strided(x, shape=None, strides=None):
""" Make an ndarray from the given array with the given shape and strides.
"""
interface = dict(x.__array_interface__)
if shape is not None:
interface['shape'] = tuple(shape)
if strides is not None:
interface['strides'] = tuple(strides)
array = np.asarray(DummyArray(interface, base=x))
# Make sure dtype is correct in case of custom dtype
if array.dtype.kind == 'V':
array.dtype = x.dtype
return array
def broadcast_arrays(*args):
"""
Broadcast any number of arrays against each other.
Parameters
----------
`*args` : array_likes
The arrays to broadcast.
Returns
-------
broadcasted : list of arrays
These arrays are views on the original arrays. They are typically
not contiguous. Furthermore, more than one element of a
broadcasted array may refer to a single memory location. If you
need to write to the arrays, make copies first.
Examples
--------
>>> x = np.array([[1,2,3]])
>>> y = np.array([[1],[2],[3]])
>>> np.broadcast_arrays(x, y)
[array([[1, 2, 3],
[1, 2, 3],
[1, 2, 3]]), array([[1, 1, 1],
[2, 2, 2],
[3, 3, 3]])]
Here is a useful idiom for getting contiguous copies instead of
non-contiguous views.
>>> [np.array(a) for a in np.broadcast_arrays(x, y)]
[array([[1, 2, 3],
[1, 2, 3],
[1, 2, 3]]), array([[1, 1, 1],
[2, 2, 2],
[3, 3, 3]])]
"""
args = [np.asarray(_m) for _m in args]
shapes = [x.shape for x in args]
if len(set(shapes)) == 1:
# Common case where nothing needs to be broadcasted.
return args
shapes = [list(s) for s in shapes]
strides = [list(x.strides) for x in args]
nds = [len(s) for s in shapes]
biggest = max(nds)
# Go through each array and prepend dimensions of length 1 to each of
# the shapes in order to make the number of dimensions equal.
for i in range(len(args)):
diff = biggest - nds[i]
if diff > 0:
shapes[i] = [1] * diff + shapes[i]
strides[i] = [0] * diff + strides[i]
# Chech each dimension for compatibility. A dimension length of 1 is
# accepted as compatible with any other length.
common_shape = []
for axis in range(biggest):
lengths = [s[axis] for s in shapes]
unique = set(lengths + [1])
if len(unique) > 2:
# There must be at least two non-1 lengths for this axis.
raise ValueError("shape mismatch: two or more arrays have "
"incompatible dimensions on axis %r." % (axis,))
elif len(unique) == 2:
# There is exactly one non-1 length. The common shape will take
# this value.
unique.remove(1)
new_length = unique.pop()
common_shape.append(new_length)
# For each array, if this axis is being broadcasted from a
# length of 1, then set its stride to 0 so that it repeats its
# data.
for i in range(len(args)):
if shapes[i][axis] == 1:
shapes[i][axis] = new_length
strides[i][axis] = 0
else:
# Every array has a length of 1 on this axis. Strides can be
# left alone as nothing is broadcasted.
common_shape.append(1)
# Construct the new arrays.
broadcasted = [as_strided(x, shape=sh, strides=st) for (x, sh, st) in
zip(args, shapes, strides)]
return broadcasted
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