Vectorize a nested loop

Hi all,

is there a way to vectorize the following loop?

for RIPETIZIONE = 1:10
    %for k = 1:size(lambda_tol_vector.Value,1)
    parfor (k = 1:size(lambda_tol_vector.Value,1))
        %fprintf('Completion using nuclear norm regularization... \n');
        [CompletedMat,flag] = matrix_completion_nuclear_GG_vec( ...
               A.Value.*double(B), double(B), N, lambda_tol_vector.Value(k), tol);
        if flag==1
            CompletedMat_parvec{RIPETIZIONE,k}=zeros(size(A));
        end
        CompletedMat_parvec{RIPETIZIONE,k}=CompletedMat;
    end
end

[Jan]

Move the PARFOR loops outside. Starting a parallel loop inside another loop is expensive.

The main part happens inside matrix_completion_nuclear_GG_vec(), so post this code instead of the outer loops.

What are the input values? If B is a large array, creating a copy in double format can be expensive already. Then doing this once only can increase the speed already. A.Value.*double(B) is a constand also. So do not claculate it repeatedly, but once before the loops.

What is the purpose of checking the values of flag?

if flag==1
    CompletedMat_parvec{RIPETIZIONE,k}=zeros(size(A));
end
CompletedMat_parvec{RIPETIZIONE,k}=CompletedMat;

This wasted time only, because if flag equals 1, the output is filled by a zero array, but overwritten directly. Maybe you want:

if flag==1
    CompletedMat_parvec{RIPETIZIONE,k}=zeros(size(A));
else
   CompletedMat_parvec{RIPETIZIONE,k}=CompletedMat;
end

If CompletedMat_parvec pre-allocated?

[federico nutarelli]

Hi @Jan aand thnks for the reply.

Yes CompletedMat_parvec is pre-allocated as a cell array: CompletedMat_parvec={};

However there is a huge time expense when I use the outer for loop.

Please, refer to this thred to see the matrix_completion_nuclear_GG_vec function

As far as the input are concerned you can use these:

clear

%reduce the size of A if necessary.
A=rand(646,200);
B=int8(rand(size(A,1),size(A,2))>0.5);
lambda_tol=0.000000000000004;
N=10;

[Jan]

"Yes CompletedMat_parvec is pre-allocated as a cell array: CompletedMat_parvec={};" - This is not a pre-allocation. Pre-allocating means, to create the array with the final size instead of letting it grow iteratively.

I do not find the code of matrix_completion_nuclear_GG_vec in the other thread, but only matrix_completion_nuclear_GG_alt. Please do not let the readers guess, which code you are using.

By the way, avoid overdoing when naming functions. Too long functions names let you loose the overview.

[federico nutarelli]

Oh sorry @Jan.

I will attach the function here.

As for pre-allocation I will check the best way to pre-allocate vell arrays.

[federico nutarelli]

Oh @Jan another thing that I am nnoticing when putting the arfor loop on the outer one, is tht the final results in term of CompletedMat_parvec is different from the same result when I use only for loos (both outer and inner). Is there a way to make the two results equal?

Answer 1

[Matt J]

EDITED:

R=10; 

K=size(lambda_tol_vector.Value,1);

CompletedMat_parvec=cell(R,K);

B=double(B);

parfor n=1:R*K
    
       [RIPETIZIONE,k]=ind2sub([R,K],n);
    
        %fprintf('Completion using nuclear norm regularization... \n');
        [CompletedMat,flag] = matrix_completion_nuclear_GG_vec( ...
               A.Value.*B,B, N, lambda_tol_vector.Value(k), tol);
        
        if ~flag
         CompletedMat_parvec{n}=CompletedMat;
        end

end


idx=cellfun('isempty', CompletedMat_parvec);
CompletedMat_parvec(idx)={zeros(size(A))};

[federico nutarelli]

@Matt J thank you for the kind reply.

There is however a red flag in CompletedMat_parvec stating that valid indices for the latter are restricted in parfor loops:

Explanation

For MATLAB to execute parfor loops efficiently, the amount of data sent to the MATLAB workers must be minimal. One of the ways MATLAB achieves this is by restricting the way variables can be indexed in parfor iterations. The indicated variable is indexed in a way that is incompatible with parfor.

Suggested Action

Fix the indexing. For a description of the indexing restrictions, see Sliced Variables.

Maybe this line CompletedMat_parvec(1:R,1:K)={zeros(size(A))}; should be substituted by this one:

N_RIPETIZIONI=10;

L=size(lambda_tol_vector.Value,1);
CompletedMat_parvec= cell(N_RIPETIZIONI,L);

?

[Matt J]

Try this replacement,

R=10; %

K=size(lambda_tol_vector.Value,1);

CompletedMat_parvec=cell(R,K);

B=double(B);

parfor n=1:R*K
    
       [RIPETIZIONE,k]=ind2sub([R,K],n);
    
        %fprintf('Completion using nuclear norm regularization... \n');
        [CompletedMat,flag] = matrix_completion_nuclear_GG_vec( ...
               A.Value.*B,B, N, lambda_tol_vector.Value(k), tol);
        
        if ~flag
         CompletedMat_parvec{n}=CompletedMat;
        end

end


idx=cellfun('isempty', CompletedMat_parvec);
CompletedMat_parvec(idx)={zeros(size(A))};

[federico nutarelli]

@Matt J same problem unfortunately. Maaybe we should index it by n? Thhough I don't think so since ideally I need CompletedMat_parvec{RIPETIZIONE,k}=...;

Furthermore it looks like the variable n is not creted when evaluaating the parfor loop.

[Matt J]

Yes! Sorry, you should be indexing by n,

        if ~flag
         CompletedMat_parvec{n}=CompletedMat;
        end

It is equivalent to,

        CompletedMat_parvec{RIPETIZIONE,k}=CompletedMat;