On Wed, Apr 30, 2008 at 9:16 PM, Anne Archibald <[EMAIL PROTECTED]> wrote:
> 2008/4/30 Charles R Harris <[EMAIL PROTECTED]>: > > > Some operations on stacks of small matrices are easy to get, for > instance, > > +,-,*,/, and matrix multiply. The last is the interesting one. If A and > B > > are stacks of matrices with the same number of dimensions with the > matrices > > stored in the last two indices, then > > > > sum(A[...,:,:,newaxis]*B[...,newaxis,:,:], axis=-2) > > > > is the matrix-wise multiplication of the two stacks. If B is replaced by > a > > stack of 1D vectors, x, it is even simpler: > > > > sum(A[...,:,:]*x[...,newaxis,:], axis=-1) > > > > This doesn't go through BLAS, but for large stacks of small matrices it > > might be even faster than BLAS because BLAS is kinda slow for small > > matrices. > > Yes and no. For the first operation, you have to create a temporary > that is larger than either of the two input arrays. These invisible > (potentially) gigantic temporaries are the sort of thing that puzzle > users when as their problem size grows they suddenly find they hit a > massive slowdown because it starts swapping to disk, and then a > failure because the temporary can't be allocated. This is one reason > we have dot() and tensordot() even though they can be expressed like > this. (The other is of course that it lets us use optimized BLAS.) > But it is interesting that you can multiply stacks of matrices that way, is it not? I haven't seen it mentioned elsewhere. Chuck
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