Using nested for loops inside parfor

Hi,

I have upper triangle portion of n by n matrix to fill with s sample values (consider undirected and fully connected network without repeating edges). Sample values are drawn from designated pools unique to each entry of the upper triangle. For the simplicity, I am just putting in random values in the sample code below. Since I am taking a very large number of samples, and this is the major bottleneck in running time, I have decided to use parfor. However, I keep getting this error message saying "The PARFOR loop cannot run due to the way variable 'a' is used". I have read parfor documentation several times and understood required structures, sliced variables, and etc, but I can't figure this out. Any help would be greatly appreciated! Thanks,

%Create the matrix and assign preallocate zeros on the upper triangle portion to fill with sample values
matrix = cell(n,n);
for i = 1:n
  for j = i+1:n
      a{i,j} = zeros(s,1);
  end
end

parfor k = 1:s
  for i = 1:n
      for j = i+1:n
          a{i,j}(k) = rand; %Instead of rand there will be some specific function
      end
  end
end

Answer 1

[Guillaume]

In the statement

A{i, j}(k) = something

with k scalar, something has to be scalar for it to work. So, you could just as well do:

parfor k = 1:s
   a{k} = zeros(n);
   for i = 1:n
      for j=i+1:n
         a{k}(i,j) = rand; %or whatever scalar is returned by your function
      end
   end
end
a = cat(3, a{:}) %3d matrix rather than cell array

If you really want a cell array at the end, after the cat:

a = num2cell(a, 3);

[Louis]

Thank you. This works!

Answer 2

[Matt J]

I agree the documentation doesn't make it obvious what the problem is. But I think the problem is you are trying to slice a variable in the 2nd level of indexing. One fix, at least for the example you've shown, is to make "a" into a 3D numeric array instead of a cell array,

    a=zeros(s,n,n);

    parfor k = 1:s
      for i = 1:n
          for j = i+1:n
              a(k,i,j)=rand;
          end
      end
    end

a=num2cell(a,1); %post-convert to cell if needed

[Louis]

Thank you for replying. I ran the following toy example and am getting the following error:

Error: The variable a in a parfor cannot be classified. See Parallel for Loops in MATLAB, "Overview".

a = zeros(100,10,10);

parfor k = 1:100
    for i = 1:10
        for j = i+1:10
            a(k,i,j) = rand;
        end
    end
end

[Matt J]

This appears to fix it.

    parfor k = 1:100
        for i = 1:10
            for j = 1:10
                if j>=i+1
                 a(k,i,j) = rand;
                end
            end
        end
    end

[Louis]

Thank you!