How to replace use of cell storage with use of arrays?

Thanks for taking the time to read this. This is a part of the script I'm working on:

resultX0=cell(length(n),length(q), ntrials);
resultY0=cell(length(n),length(q), ntrials);
resultG=cell(length(n),length(q), ntrials);

for i=1:length(n)
  for j=1:length(q)
      for k=1:1:ntrials
          [G,X0,Y0]=matrix_plantsubm(M,N,c,n(i),p,q(j));
          resultX0{i,j,k}=X0;
          resultY0{i,j,k}=Y0;
          resultG{i,j,k}=G;
      end
  end
end

I would like to replace use of cell storage with use of arrays (e.g. resultG{i,j,k} = G). I want to run the function 10 times (in this case ntrials) for each value q and n. How can I do that?

Thanks

[James Tursa]

It is not clear why you want to do this. What are the sizes of G, X0, and Y0?

[POLLY]

I want to do that because saving and accessing the cells is what is causing the experiment to take long time(it has to save a massive file at the end of each simulation). I am working on HPC and cells are not the best way

[aepound]

What are the dimensions of G, X0 and Y0? Are they scalars? Are they variable for each i,j,k?

[POLLY]

They are the matrices 500*500 that were randomly generated for each i,j,k

[James Tursa]

What code do you currently use to save and access the cells?

Answer 1

[Nicole Peltier]

According to a previous time you posted about matrix_plantsubm.m on Matlab Answers (thanks Google!), it looks like G, X0, and Y0 are all MxN matrices. Therefore, you could declare resultX0, resultY0, and resultG as follows:

resultX0 = zeros(length(n), length(q), ntrials, M, N);
resultY0 = zeros(length(n), length(q), ntrials, M, N);
resultG = zeros(length(n), length(q), ntrials, M, N);

Then your for-loops should look like this:

for i=1:length(n)
  for j=1:length(q)
      for k=1:ntrials
          [G,X0,Y0]=matrix_plantsubm(M,N,c,n(i),p,q(j));
          resultX0(i,j,k,:,:)=X0;
          resultY0(i,j,k,:,:)=Y0;
          resultG(i,j,k,:,:)=G;
      end
  end
end

Hope this helps!

[POLLY]

Thanks for your answer. But why do we use 5-D array?

[Nicole Peltier]

I don't know the purpose of n or q in your code, so I can't answer that concretely. But your loops run such that new 2-D matrices are created for G, X0, and Y0 for each element in n and in q, and for each trial. A 2-D matrix computed within 3 nested for-loops requires a storage matrix that is 5-D.

[Another way to think about it is to build up to it: If G were a scalar (just 1 number), resultG should be 3-D. If G were a vector (a 1-D list of numbers), resultG should be 4-D. Since G is a 2-D matrix, resultG should be 5-D.]

[POLLY]

Thanks for your clarification.

Also, once I have all results from the given part of script , I need to use resultG as an input for a different function that again is run 10 times(ntrials) for each q and n. Will it be like that:

resultX=zeros(length(n),length(q), ntrials, M, N);
resultY=zeros(length(n),length(q), ntrials, M, N);
for i=1:length(n)
  for j=1:length(q)

        gamma = 6/((q(j) - p)*n(i));

        for k=1:1:ntrials

            [X,Y,Q, iter] = ADMM(resultG(i,j,k),c, n(i), gamma,tau, opt_tol, verbose);
            resultX(i,j,k, :, :)=X;
            resultY(i,j,k, :, :)=Y;

Or how can I define indices for resultG? Thanks

I really appreciate your help!

[Nicole Peltier]

Is there a reason why this loop must be separate from the previous one? If not, I'd recommend combining the loops like this:

% Declare all variables here
resultX0 = zeros(length(n), length(q), ntrials, M, N);
resultY0 = zeros(length(n), length(q), ntrials, M, N);
resultG = zeros(length(n), length(q), ntrials, M, N);
resultX=zeros(length(n),length(q), ntrials, M, N);
resultY=zeros(length(n),length(q), ntrials, M, N);

for i=1:length(n)
  for j=1:length(q)
    gamma = 6/((q(j) - p)*n(i));

      for k=1:ntrials

        % The following code is from the first loop
        [G,X0,Y0]=matrix_plantsubm(M,N,c,n(i),p,q(j));
        resultX0(i,j,k,:,:)=X0;
        resultY0(i,j,k,:,:)=Y0;
        resultG(i,j,k,:,:)=G;

        % Consolidate code from second loop into first one
        [X,Y,Q, iter] = ADMM(G, c, n(i), gamma, tau, opt_tol, verbose);
        resultX(i,j,k, :, :)=X;
        resultY(i,j,k, :, :)=Y;

      end
    end
  end

This way, you can use the variable G which you've already calculated instead of having to select the correct index out of resultG. (Otherwise you'll have to use resultG(i,j,k,:,:) as your input argument to ADMM.)

[Stephen23]

You might also like to consider ordering the dimensions slightly differently, to keep the matrices as the first two dimensions:

(M, N, length(n), length(q), ntrials)

That might make processing/accessing the data easier later.