Thanks a lot Matti. It makes a lot more sense now. ________________________________ From: NumPy-Discussion <numpy-discussion-bounces+jeffsaremi=hotmail....@python.org> on behalf of Matti Picus <matti.pi...@gmail.com> Sent: Monday, July 9, 2018 10:54 AM To: numpy-discussion@python.org Subject: Re: [Numpy-discussion] Looking for description/insight/documentation on matmul
On 09/07/18 09:48, jeff saremi wrote: > Is there any resource available or anyone who's able to describe > matmul operation of matrices when n > 2? > > The only description i can find is: "If either argument is N-D, N > 2, > it is treated as a stack of matrices residing in the last two indexes > and broadcast accordingly." which is very cryptic to me. > Could someone break this down please? > when a [2 3 5 6] is multiplied by a [7 8 9] what are the resulting > dimensions? is there one answer to that? Is it deterministic? > What does "residing in the last two indices" mean? What is broadcast > and where? > thanks > jeff > You could do np.matmul(np.ones((2, 3, 4, 5, 6)), np.ones((2, 3, 4, 6, 7))).shape which yields (2, 3, 4, 5, 7). When ndim >= 2 in both operands, matmul uses the last two dimensions as (..., n, m) @ (...., m, p) -> (..., n, p). Note the repeating "m", so your example would not work: n1=5, m1=6 in the first operand and m2=8, p2=9 in the second so m1 != m2. The "broadcast" refers only to the "..." dimensions, if in either of the operands you replace the 2 or 3 or 4 with 1 then that operand will broadcast (repeat itself) across that dimension to fit the other operand. Also if one of the three first dimensions is missing in one of the operands it will broadcast. When ndim < 2 for one of the operands only, it will be interpreted as "m", and the other dimension "n" or "p" will not appear on the output, so the signature is (..., n, m),(m) -> (..., n) or (m),(..., m, p)->(..., p) When ndim < 2 for both of the operands, it is the same as a dot product and will produce a scalar. You didn't ask, but I will complete the picture: np.dot is different for the case of n>=2. The result will extend (combine? broadcast across?) both sets of ... dimensions, so np.dot(np.ones((2,3,4,5,6)), np.ones((8, 9, 6, 7))).shape which yields (2, 6, 4, 5, 8, 9, 7). The (2, 3, 4) dimensions are followed by (8, 9) Matti _______________________________________________ NumPy-Discussion mailing list NumPy-Discussion@python.org https://mail.python.org/mailman/listinfo/numpy-discussion
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