MATLAB: How to implement Parfor loop with nested for loops

nested for loopsParallel Computing Toolboxparforsimulink

Hi
I'm doing a Brute Force search by varying 5 parameters, running a Simulink model and then calculating a cost function.
I have a Matlab script which contains the following:
simTime = 2;  %2 seconds simulation time
N = 5;        % number of time step
brakeRange = 0:1/(10-1):1; % Vector of possible brake value (percent)
timeVec = 0:simTime/(N-1):simTime;
leng = length(brakeRange);
data = zeros(leng^N,N+1);
a =1;
tic
for i = 1: leng
  s = sprintf('\n Percentage complete =  %s % ',num2str((a/leng^N)*100));
  disp(s);
  for j = 1: leng
      for k = 1: leng
          for l = 1: leng
              for m = 1: leng
                  % Index input vector
                  inVec = [brakeRange(i) brakeRange(j) brakeRange(k)           brakeRange(l) brakeRange(m)];
                    % run simulation
                    simOut =   sim(mdl,'SimulationMode','Accelerator','ReturnWorkspaceOutputs', 'on');
                    % Get cost from simulation
                    tempJ  = simOut.get('cost');
                    %packing data struct
                    data(a,:) = horzcat(tempJ(end), inVec);
                    % increment counter
                    a = a +1;
                end
            end
        end
    end
end
Unfortunately, the code is very slow, so I decided to purchase the Parallel Computing Toolbox. I tried to use Parfor, but I get the error message "the PARFOR loop cannot runt due to the way data is used." I get the same message for the variable 'a'.
I think the problem has to do with sliced variables (?) but I'm not sure as I'm new to Parallel Computing. How does one implement parfor loops with nested for loops?

Best Answer

While you and I can clearly see that each simulation and access into 'data' is independent, unfortunately PARFOR doesn't understand the way you've written things. In general, output variables in PARFOR must be indexed using the loop variable and constant terms only. I would suggest that you should be able to flatten your multiply-nest loop, and then it will be simple to get PARFOR to understand.
The key to flattening in this case is to use MATLAB's IND2SUB which can be used to convert a single counter into a series of subscripts. So, you need something like this
% simSpace is the size of the space you're exploring
simSpace = [leng, leng, leng, leng, leng];
% calculate the total number of simulations
numSims  = prod(simSpace);
% pre-allocate data
data = zeros(numSims,N+1);
parfor idx = 1:numSims
  % convert scalar index into subscripts
  [i, j, k, l, m] = ind2sub(simSpace, idx);
  % Index input vector (you should be able to use a single vector
  % subscript here, as shown)
  inVec = brakeRange([i, j, k, l, m]);
  simOut = ...;
  data(idx, :) = ...;
end
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