ۓ,jSrSSjrg)a 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. c[U5 Uup4[U5n[U5n[U5n[U5n[ U5[ U5pUR nURnUR n URn Sn XV:waSn OP[U5HAn XsU XU :waSn O.X<S:a X<==U- ss'XLS:dM5XL==U - ss'MC U (d [S5e[U5V s/sH oU;dM U PM n n X-nSnUH nXU-nM SU4nU Vs/sHnUUPM nn[U 5V s/sH oU;dM U PM n n XM-nSnUH nXU-nM US4nU Vs/sHnU UPM nnURU5RU5nURU5RU5n[UU5nURUU-5$! [[U*S55n[[SU55nGN=f![a U/nSnGNf=f![a U/nSnGNf=fs sn fs snfs sn fs snf)aW 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) TFzshape-mismatch for sum) iterlistrangelen TypeErrorasarrayshapendim ValueError transposereshapedot)abaxesaxes_aaxes_bnanbas_ndabsndbequalknotin newaxes_aN2axis newshape_aolda newaxes_b newshape_boldbatbtress ڡC:\Users\johnn\AppData\Local\Packages\PythonSoftwareFoundation.Python.3.13_qbz5n2kfra8p0\LocalCache\local-packages\Python313\site-packages\chumpy/np_tensordot.py tensordotr,-spt T  [f [f 1:wqzq ''C &&C B &&C E xrA!9~1I.y1} S y1} S  122c 6 1voQ E 6I B $ibJ"' (%$CI%D (c 6 1voQ E 6I B hbJ!& 'BtHD ' Y  ' ' 3B Y  ' ' 3B b"+C ;;td{ ##w&eTE1o&eAtn%    4 7 ) 6 (sQ G2H%H;= I I0I III 2-H"%H87H8;I IN))__doc__r,r+r1sBw$r0