MATLAB: Parallel ODE solve using parfor-loop

odeparallel computingParallel Computing Toolboxparfor

Hello, I'm trying to solve my parallel ODE system, because very a small step and high tolerance are necessary here. Here is the code:
    n = 4
    matlabpool('open',n)
    X0=[0.0046   10.9820   15.3579]
    tend=5000;
    parfor i=0:100
      options = odeset('RelTol', 1e-2,'MaxStep', 1e-4);
      [T(i*50:(i+1)*50),X(i*50:(i+1)*50)] = ode45(@rightpart,[50*i  50*(i+1)],X0,options);
    end
   matlabool close;
   figure
   plot(T,X(:,1),'-',T,X(:,2),'-.',T,X(:,3),'.')
   figure
   plot3(X(:,1),X(:,2),X(:,3))  
   end
Matlab doesn't allow to use [T,X] after parfor-loop. How can I modify this code? Or are there any other solutions for this problem?

Best Answer

The problem is that PARFOR doesn't know how to 'slice' your variables T and X because the indexing expression you're using is too complicated. There are more details on this page, but basically I think it should work to do this:
% pre-allocate rectangular T and X.
T = zeros(50, 101);
X = zeros(50, 101);
parfor i = 1:101
  ...
  % Assign whole columns of T and X using 'i' as the slicing index
  [T(:, i), X(:, i)] = ode45(...);
end
% Convert T and X back to single columns
T = T(:);
X = X(:);
Related Question