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Fix ch.tensordot for numpy 1.14+ (mattloper#2)
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# Up to numpy 1.13, the numpy implementation of tensordot could be | ||
# reinterpreted using chumpy. With numpy 1.14 the implementation started using | ||
# ufunc.multiply.reduce which can't be understood by chumpy. This is the | ||
# chumpy-compatible implementation of tensodrot from numpy 1.13.3. | ||
# | ||
# i.e. | ||
# | ||
# import inspect | ||
# with open('np_tensordot.py', 'w') as f: | ||
# f.write(''.join(inspect.getsourcelines(np.tensordot)[0])) | ||
|
||
""" | ||
Copyright (c) 2005-2017, NumPy Developers. | ||
All rights reserved. | ||
Redistribution and use in source and binary forms, with or without | ||
modification, are permitted provided that the following conditions are | ||
met: | ||
* Redistributions of source code must retain the above copyright | ||
notice, this list of conditions and the following disclaimer. | ||
* Redistributions in binary form must reproduce the above | ||
copyright notice, this list of conditions and the following | ||
disclaimer in the documentation and/or other materials provided | ||
with the distribution. | ||
* Neither the name of the NumPy Developers nor the names of any | ||
contributors may be used to endorse or promote products derived | ||
from this software without specific prior written permission. | ||
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS | ||
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT | ||
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR | ||
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT | ||
OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, | ||
SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT | ||
LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, | ||
DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY | ||
THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT | ||
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE | ||
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. | ||
""" | ||
|
||
def tensordot(a, b, axes=2): | ||
""" | ||
Compute tensor dot product along specified axes for arrays >= 1-D. | ||
Given two tensors (arrays of dimension greater than or equal to one), | ||
`a` and `b`, and an array_like object containing two array_like | ||
objects, ``(a_axes, b_axes)``, sum the products of `a`'s and `b`'s | ||
elements (components) over the axes specified by ``a_axes`` and | ||
``b_axes``. The third argument can be a single non-negative | ||
integer_like scalar, ``N``; if it is such, then the last ``N`` | ||
dimensions of `a` and the first ``N`` dimensions of `b` are summed | ||
over. | ||
Parameters | ||
---------- | ||
a, b : array_like, len(shape) >= 1 | ||
Tensors to "dot". | ||
axes : int or (2,) array_like | ||
* integer_like | ||
If an int N, sum over the last N axes of `a` and the first N axes | ||
of `b` in order. The sizes of the corresponding axes must match. | ||
* (2,) array_like | ||
Or, a list of axes to be summed over, first sequence applying to `a`, | ||
second to `b`. Both elements array_like must be of the same length. | ||
See Also | ||
-------- | ||
dot, einsum | ||
Notes | ||
----- | ||
Three common use cases are: | ||
* ``axes = 0`` : tensor product :math:`a\\otimes b` | ||
* ``axes = 1`` : tensor dot product :math:`a\\cdot b` | ||
* ``axes = 2`` : (default) tensor double contraction :math:`a:b` | ||
When `axes` is integer_like, the sequence for evaluation will be: first | ||
the -Nth axis in `a` and 0th axis in `b`, and the -1th axis in `a` and | ||
Nth axis in `b` last. | ||
When there is more than one axis to sum over - and they are not the last | ||
(first) axes of `a` (`b`) - the argument `axes` should consist of | ||
two sequences of the same length, with the first axis to sum over given | ||
first in both sequences, the second axis second, and so forth. | ||
Examples | ||
-------- | ||
A "traditional" example: | ||
>>> a = np.arange(60.).reshape(3,4,5) | ||
>>> b = np.arange(24.).reshape(4,3,2) | ||
>>> c = np.tensordot(a,b, axes=([1,0],[0,1])) | ||
>>> c.shape | ||
(5, 2) | ||
>>> c | ||
array([[ 4400., 4730.], | ||
[ 4532., 4874.], | ||
[ 4664., 5018.], | ||
[ 4796., 5162.], | ||
[ 4928., 5306.]]) | ||
>>> # A slower but equivalent way of computing the same... | ||
>>> d = np.zeros((5,2)) | ||
>>> for i in range(5): | ||
... for j in range(2): | ||
... for k in range(3): | ||
... for n in range(4): | ||
... d[i,j] += a[k,n,i] * b[n,k,j] | ||
>>> c == d | ||
array([[ True, True], | ||
[ True, True], | ||
[ True, True], | ||
[ True, True], | ||
[ True, True]], dtype=bool) | ||
An extended example taking advantage of the overloading of + and \\*: | ||
>>> a = np.array(range(1, 9)) | ||
>>> a.shape = (2, 2, 2) | ||
>>> A = np.array(('a', 'b', 'c', 'd'), dtype=object) | ||
>>> A.shape = (2, 2) | ||
>>> a; A | ||
array([[[1, 2], | ||
[3, 4]], | ||
[[5, 6], | ||
[7, 8]]]) | ||
array([[a, b], | ||
[c, d]], dtype=object) | ||
>>> np.tensordot(a, A) # third argument default is 2 for double-contraction | ||
array([abbcccdddd, aaaaabbbbbbcccccccdddddddd], dtype=object) | ||
>>> np.tensordot(a, A, 1) | ||
array([[[acc, bdd], | ||
[aaacccc, bbbdddd]], | ||
[[aaaaacccccc, bbbbbdddddd], | ||
[aaaaaaacccccccc, bbbbbbbdddddddd]]], dtype=object) | ||
>>> np.tensordot(a, A, 0) # tensor product (result too long to incl.) | ||
array([[[[[a, b], | ||
[c, d]], | ||
... | ||
>>> np.tensordot(a, A, (0, 1)) | ||
array([[[abbbbb, cddddd], | ||
[aabbbbbb, ccdddddd]], | ||
[[aaabbbbbbb, cccddddddd], | ||
[aaaabbbbbbbb, ccccdddddddd]]], dtype=object) | ||
>>> np.tensordot(a, A, (2, 1)) | ||
array([[[abb, cdd], | ||
[aaabbbb, cccdddd]], | ||
[[aaaaabbbbbb, cccccdddddd], | ||
[aaaaaaabbbbbbbb, cccccccdddddddd]]], dtype=object) | ||
>>> np.tensordot(a, A, ((0, 1), (0, 1))) | ||
array([abbbcccccddddddd, aabbbbccccccdddddddd], dtype=object) | ||
>>> np.tensordot(a, A, ((2, 1), (1, 0))) | ||
array([acccbbdddd, aaaaacccccccbbbbbbdddddddd], dtype=object) | ||
""" | ||
try: | ||
iter(axes) | ||
except: | ||
axes_a = list(range(-axes, 0)) | ||
axes_b = list(range(0, axes)) | ||
else: | ||
axes_a, axes_b = axes | ||
try: | ||
na = len(axes_a) | ||
axes_a = list(axes_a) | ||
except TypeError: | ||
axes_a = [axes_a] | ||
na = 1 | ||
try: | ||
nb = len(axes_b) | ||
axes_b = list(axes_b) | ||
except TypeError: | ||
axes_b = [axes_b] | ||
nb = 1 | ||
|
||
a, b = asarray(a), asarray(b) | ||
as_ = a.shape | ||
nda = a.ndim | ||
bs = b.shape | ||
ndb = b.ndim | ||
equal = True | ||
if na != nb: | ||
equal = False | ||
else: | ||
for k in range(na): | ||
if as_[axes_a[k]] != bs[axes_b[k]]: | ||
equal = False | ||
break | ||
if axes_a[k] < 0: | ||
axes_a[k] += nda | ||
if axes_b[k] < 0: | ||
axes_b[k] += ndb | ||
if not equal: | ||
raise ValueError("shape-mismatch for sum") | ||
|
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# Move the axes to sum over to the end of "a" | ||
# and to the front of "b" | ||
notin = [k for k in range(nda) if k not in axes_a] | ||
newaxes_a = notin + axes_a | ||
N2 = 1 | ||
for axis in axes_a: | ||
N2 *= as_[axis] | ||
newshape_a = (-1, N2) | ||
olda = [as_[axis] for axis in notin] | ||
|
||
notin = [k for k in range(ndb) if k not in axes_b] | ||
newaxes_b = axes_b + notin | ||
N2 = 1 | ||
for axis in axes_b: | ||
N2 *= bs[axis] | ||
newshape_b = (N2, -1) | ||
oldb = [bs[axis] for axis in notin] | ||
|
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at = a.transpose(newaxes_a).reshape(newshape_a) | ||
bt = b.transpose(newaxes_b).reshape(newshape_b) | ||
res = dot(at, bt) | ||
return res.reshape(olda + oldb) |
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Original file line number | Diff line number | Diff line change |
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@@ -15,4 +15,5 @@ dependencies: | |
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test: | ||
override: | ||
- python -c 'import numpy; print numpy.version.version' | ||
- make test |