How to optimize matrix multiplication speed?

Hi all,

I'd like to increase computation speed of a matrix multiplication that occures many times in my code.

P = PHI*(P + Q)*PHI' + Q;
% P and Q are symetric positive  50x50 matrices
% PHI is a 50x50 matrix

Is there a way to optimize this code?

thanks!

Answer 1

[John D'Errico]

Do this:

P = PHI*(P + Q)*PHI' + Q;

While it may look exactly like the line of code you wrote, in fact, it is the same. Matrix multiplies are already pretty well optimized in MATLAB.

Do you have the parallel processing toolbox, as well as GPU that is accessible to it? If so, then I believe you will get some gain by using gpuArray, as then the array multiplies can be done using your GPU.

Answer 2

[James Tursa]

This looks like a covariance matrix update to me. The matrix multiplies are already done by highly optimized multi-threaded compiled BLAS library code, so you will not be able to improve on that. The only thing that might help you is the symmetry part, but unfortunately there are no symmetric BLAS routines to do your specific multiply. Also, since the multiplies will be done with generic matrix multiply routines, the result will likely not be exactly symmetric. If this makes a difference to you, you will have to manually correct the result. E.g., P = (P + P')/2