How to vectorize a two matrices in row-wise multiplication (optimization)?

Hi Matlab users,

I have the following code where N = 20000, "prt1" and "P" are both matrices of (20000x20000). As can be seen in the code I want to multiply each row of "prt1" from 1st to 20000th row in row 1 of "P" and then all rows of "prt1" in row 2 of "P" and so on. Every time sum them up and put in the matrix of "S". Unfortunately, This takes me great deal of time. Any way that I can optimize this such vectorization?

Here is the code:

for r = 1:N
    for c = 1:N
        S(r,c) = sum (prt1(c,:).*P(r,:));
    end
end

Thank you very much for your hint.

All the best....

MhD

[Jan]

Did you pre-allocate S?

[M G]

Yes I did. However, still runs for hours!

Answer 1

[Jan]

For N = 1000 I get 1.7 sec instead of 21 sec of the original version:

S = zeros(N, N);
for r = 1:N
   S(r, :) = prt1 * P(r, :)';
end

But with 0.14 seconds even faster:

S = P * ptr1';

A speedup of factor 150, fine.