[Numpy-discussion] untenable matrix behavior in SVN
Charles R Harris
charlesr.harris@gmail....
Wed Apr 30 23:41:27 CDT 2008
On Wed, Apr 30, 2008 at 9:16 PM, Anne Archibald <peridot.faceted@gmail.com>
wrote:
> 2008/4/30 Charles R Harris <charlesr.harris@gmail.com>:
>
> > 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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