What is the fastest way to do repeated element wise matrix multiplication?

Given a matrix `A`, I need to multiply with another constant vector `B`, N times (N > 1 million). The size of `A` is `9000x1` and `B` is `9000x1000`.

The code is currently evaluated in the following way (random values taken for example):

B = rand(9000,1000); % B is fixed, does not depend on i
N = 1000000;
for i=1:N
    
    rand('seed',i);
    A = rand(9000,1); % A is 9000x1 matrix which varies with i
    
    % prod = A.*B; % prod is 9000 x 1000 matrix
    
    % sum_temp = sum(product); % sum_temp is 1 x 1000 matrix
    
    % Edit
    sum_temp = A.' * B;
    
    % do multiple pperations with sum_temp
    % result(i) = some_constant;
end

I used Profiler to see which line is taking the most time and it is the 2nd line (prod = A.*R;). The problem is that N is very large and the code is taking over several days to complete.

I am about to try the parallel computing toolbox (GPU computing), but are there any suggestions on what I can do in the basic version?

How can I reduce the run-time of such codes in MATLAB?

Answer 1

[Stephen23]

Reduce the number of operations inside the loop by replacing TIMES and SUM with MTIMES (of course adjusting the matrix/vector orientations to suit).

[Aravind Varma Dantuluri]

@Stephen23, do you mean by the Edit I added in the code? That definitely helped. It reduced runtime by ~ 33%!. But it still is the most time-taking line. Are there any more suggestions ?

[Stephen23]

"do you mean by the Edit I added in the code?", basically yes. I would avoid the transpose on A as well: either create A with correct orientation in the first place (if possible), or transpose B before the loop.

You might also be interested to read about:

https://www.mathworks.com/help/matlab/ref/pagemtimes.html

[Aravind Varma Dantuluri]

Ok. Thanks. Can you add your comments as an answer so that I can accept it?

[Stephen23]

@Aravind Varma Dantuluri: did that make enough difference to the speed?

Another possibilty would be to look at some kind of parallel processing:

https://www.mathworks.com/help/parallel-computing/parfor.html

[Aravind Varma Dantuluri]

@Stephen23, using MTIMES definitely helped. Now I am checking out pagemtimes and then will check parallel computing capabilities. Thanks for your help!