fastest way for multiplication of symmetric matrix and sparse matrix

I am doing a multiplication as: P=A*P*A'

where size of A and P are 6640x6640. The nonzero element of A and P is 309028 and 0. P is symmetric.

If I use sparse matrix for A, the time to calculate A*P*A' is twice as if I use dense matrix for A.

I want to reduce the computational time for this calculation, can you recommend a method? I am planning to use PARDISO solver from https://www.pardiso-project.org/

Thank you!

Answer 1

[Matt J]

If I use sparse matrix for A, the time to calculate A*P*A' is twice as if I use dense matrix for A.

You have a strange computer. I see very much the opposite. One thing you can check is whether nzmax(A)=nnz(A). You can also shave off some time by precomputing A'.

N=6640/2;

A=sprand(N,N,.007);
At=A;
P=rand(N); P=P+P.';
Af=full(A);
Aft=Af';

tic
A*P*A';
toc

Elapsed time is 0.738674 seconds.

tic
A*P*At;
toc

Elapsed time is 0.631558 seconds.

tic;
 Af*P*Aft;
toc;

Elapsed time is 2.053788 seconds.

[Nguyen Van Hieu]

precomputing A' works for my calculation. Thank you so much!!!