Matlab: parfor loop and cell arrays not working

Question

I get the following error: "The variable X_bs in a parfor cannot be classified" when trying to run the following parfor loop:

  y = zeros(1000,1)
        parfor bb = 1:1000
            rng(bb)
            % deleted line: X_bs{8} = [];
            for ii = 1:8
                ind = ceil(N(ii)*rand(N(ii),1));
                X_bs{ii} = X{ii}(ind,:);
            end 

           y(bb) = another_function(X_bs)

        end

X is a 1x8 cell array, each cell containing a N(ii)x4 matrix (N(ii) changes). The code re-samples rows of X and creates a cell array called X_bs. I pass X_bs through a function that outputs the variable that I am interested in, y(bb).

Why am I getting this error? How do I get around this?

Here is an example:

 X{1} = [1 ; 2 ; 3]
 X{2} = [4 ; 5 ; 6; 7]
 N(1) = 3 % size of X{1}
 N(2) = 4 % size of X{2}
    parfor bb=1:10
        rng(bb)
        for ii = 1:2
            X_bs{ii} = zeros(N(ii),1);
            ind = ceil(N(ii)*rand(N(ii),1));
            X_bs{ii} = X{ii}(ind,:);
        end
        % Output is a function of X_bs.  For illustration, say it is the sum
        y(bb) = sum(X_bs{1}) + sum(X_bs{2});
    end

The above code gets the same error as earlier: "The variable X_bs in a parfor cannot be classified". Here is a simpler version that does work and does not use cell structures:

X = [1 ; 2 ; 3]
N = 3; %size of X
parfor bb=1:10
    rng(bb)
    X_bs = zeros(N,1);
    ind = ceil(N*rand(N,1));
    X_bs= X(ind,:);
    y(bb) = sum(X_bs) 
end

The problem (I think) lies within overriding the cell structure. Perhaps parfor treats cellstructures as a slicing variables rather than temporary variables. Any thoughts?

Update: Adriaan suggested that there is a problem with the random vector ind and the cell structure X_bs{ii}. Here is a simpler example that does not invoke the random vector ind and still has the same error:

X{1} = [1 ; 2 ; 3]
 X{2} = [4 ; 5 ; 6; 7]
 N(1) = 3 % size of X{1}
 N(2) = 4 % size of X{2}
    parfor bb=1:10
        for ii = 1:2
            X_bs{ii} = X{ii};
        end
        % Output is a function of X_bs.  For illustration, say it is the sum
        y(bb) = sum(X_bs{1}) + sum(X_bs{2});
    end

Therefore, I am fairly certain MatLab isn't treating the cell structure, X_bs{ii} , as a temporary variable.

Answer 1

A solution (thanks to Andriaan's comment) is to put the forloop that generates X_bs in a nested function, randomize_X. See below for a solution to the working example:

X{1} = [1 ; 2 ; 3]
X{2} = [4 ; 5 ; 6; 7]
N(1) = 3 % size of X{1}
N(2) = 4 % size of X{2}
parfor bb=1:10
    [X_bs] = randomize_X(X,N)
    % Output is a function of X_bs.  For illustration, say it is the sum
    y(bb) = sum(X_bs{1}) + sum(X_bs{2});
end

where

function [X_bs] = randomize_X(X,N)
  for ii = 1:2
      X_bs{ii} = zeros(N(ii),1);
      ind = ceil(N(ii)*rand(N(ii),1));
      X_bs{ii} = X{ii}(ind,:);
  end
end

I'm fairly certain that the parfor loop treats cell structures as slicing variables, so it needs to be specified beforehand and cannot be overwritten within the parfor loop. To get around this, a simple trick is send the computation of cell structures to another function. The parfoor loop has similar problems with the optimization toolbox CVX. The same trick can be employed - call CVX in a subroutine within parfor.