Re: Multiply matrix slices

[Parsiad Azimzadeh]

On Sun, Nov 22, 2015 at 7:21 AM, Nicholas Jankowski <address@hidden> wrote:
> On Sun, Nov 22, 2015 at 2:05 AM, Parsiad Azimzadeh
> <address@hidden> wrote:
>>
>> A triply-nested loop in an octave-financial routine I wrote renders it
>> fairly slow:
>> http://sourceforge.net/p/octave/financial/ci/default/tree/inst/@sde/simByEuler.m.
>>
>> This could be fixed through a _native_ routine to multiply slices. That
>> is, if A and B are 3-dimensional real arrays, C = multiply_slices(A,B) would
>> give:
>>
>> C(:, :, 1) == A(:, :, 1)*B(:, :, 1),
>> ...,
>> C(:, :, k) == A(:, :, k)*B(:, :, k).
>>
>> I am guessing no such routine exists in the core. I may also be
>> overlooking other possible solutions. Has anyone run into a similar
>> problem/have advice?
>>
>> Thanks,
>> Parsiad
>
>
>
> Are your matrices always a predictable size?  I was doing an eigenvector
> based program over the summer that worked with n-D arrays of 2x2 matrices.
> Had to do the 'multiply by slice' problem you mentioned quite a bit. The
> fastest way to do it, since my matrix size was fixed, was to 'unroll the
> multiply and do vectorized multiplication of each element. I don't think
> there is a good vectorized way to do it without knowing the size apriori,
> though. Found a speed comparison somewhere on stackexchange I think.
>
> Code below, and m-fie attached. It works for any set of 2 x 2 x n x m x p x
> ...  as long as they are the same size.  It's far from 'Octave core' worthy,
> though.
>
>
> ------------------------------
> function C = twobytwoarraymult(A,B)
>    %either A and B should be 2x2 matrices. either or both can be a 2x2xn
> matrix array,
>    %but if both are arrays, they must have the same n.  Output
>    %will be matrix multiplication of 2x2 matrices along 3rd dimentsion in A
> and B.
>    %either A or B will be broadcast in 3rd dimension if it is only a single
> matrix,
>    %otherwise it needs to be the same size as A.
>    %will work for higher dimensions than three. the : will recast them as 3D
> arrays for
>    %the multiply, and C will be returned with the intended multidimensional
> size.
>
>
>    if (ndims(A)>=ndims(B))
>     C = zeros(size(A));
>   else
>     C = zeros(size(B));
>   end
>
>   C(1,1,:) = A(1,1,:).*B(1,1,:) + A(1,2,:).*B(2,1,:);
>   C(1,2,:) = A(1,1,:).*B(1,2,:) + A(1,2,:).*B(2,2,:);
>   C(2,1,:) = A(2,1,:).*B(1,1,:) + A(2,2,:).*B(2,1,:);
>   C(2,2,:) = A(2,1,:).*B(1,2,:) + A(2,2,:).*B(2,2,:);
> end
>
> ------------------------------
>

Thanks for the code. Unfortunately, the matrices are of variable size.