Efficient way to perform loops of matrix multiplications

Hello,

I have an implementation that involves multiplying matrices, summing them up, and storing them. It goes like this,

A = 0;
for i=1:1225
  % Load operator A_i of size NxN
  A_i = load('A_i.mat');
  % z_i is some variable of size Nx1 that I compute in this loop
  % x is some variable of size Nx1 calculated above this loop 
  % I have to perform some operations like these two
  y_i = A_i*(z_i + x);
  A = A + A_i*A_i'
end

My problem is the large amount of simulation time being consumed by the above code. Even when the operations inside the loop are efficient (let's say ~0.01mins), the entire looped implementation still consumes about ~12-13mins. Can somebody please help me out and suggest an efficient way to do this? Thanks so much!

[Walter Roberson]

You are loading the same file each time. You probably want

A_i = load( sprintf('A_%d.mat', i) );

Note that A_i will be a struct with one field for each variable stored in the file.

Question: how long does it take to execute

for i = 1 : 1225
  A_i = load( sprintf('A_%d.mat', i) );
end

[AA]

Hello,

Thanks for your response. Yes, you are right; I just showed it as some sort of pseudo-code.

My code is

 tic
 ... load A_i operator 
 A_i_obj = load([path_temp,'A_',num2str(i),'.mat']);
 A_i     = (A_i_obj.A);
 toc

Takes roughly ~0.14secs for every A_i.

Thanks again!

[Lukas]

You can check, which operation is the most costly in your code with the profiler. In my experience, saving and loading can take significant more time than calculations. You can maybe avoid this by loading all data at once.

[AA]

Hello,

Thanks for your reply. One of the side problems that I have is the amount of A_is. I have >1k of these operators of size NxN (N is of order 300^2-400^2). Although, they are sparse matrices, storing them together in the memory eats up all my RAM. So, that't the reason I pre-compute them offline and load them one by one.

Thanks again!

[Walter Roberson]

Potentially you could load them in batches (to avoid filling memory) using parfor (to load in parallel.) However, using parfor often turns out to be slower, especially when you take into account the time to start the pool.

[AA]

Hello,

Thanks for your response. Yes, in my case, parfor is not able to help. As you rightly pointed out, the time taken to start the pool overwhelms any time savings thereafter. Unfortunately, I faced the same problem while working on gpuArrays. The time taken for transferring the data is large, and shows no overall improvement. I am currently stuck and have no good way to get it done within some practical time.

Thanks for your help again!

[David Goodmanson]

Hi AA,

If N stays constant, when you compute them offline could you stack them into sets of 3d arrays, no one of which is large enough to overrun RAM? That way you would have to load stuff a lot less often.