Parallel ODE solve using parfor-loop

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?

Answer 1

[Edric Ellis]

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(:);

[Danila Zharenkov]

Thanks, Edric, great advice. But I have ODE system of 3 equation, so finally X must have 3 columns. Is this variant correct?

   X=zeros(50,300)
   parfor i=1:100
    options = odeset('RelTol', 1e-1,'MaxStep', 1e-1);
    %When i=1, we are filling X's columns from 1 to 3, when i=2, we are filling X's columns from 4 to 6 etc.
    [T(:,i),X(:,3*i-2:3*i)] = ode45(@rightpart,[50*(i-1)  50*i],X0,options);
   end

And how to transform X to 3-column matrix after that? This code works, but is this the easiest solution?

   %Transformation of 50*300 matrix to 5000*3 matrix
   Xn=zeros(5000,3);
   for j=1:100
     Xn(50*j-49:50*j,:)=X(:,i*3-2:i*3)
   end

Thanks.

[Edric Ellis]

Actually, having looked further at what you're doing here, even if you get PARFOR working, you may still have trouble getting the results you wish. It looks like your ODE45 call is starting from successive start times, but using the same initial conditions each time. This probably isn't going to give you the results you're after. The BALLODE example shows how to use different initial conditions as you progress a simulation. Unfortunately, propagating the initial conditions in this way means that the iterations of your loop would no longer be order-independent, and so you would not be able to use PARFOR.

[Danila Zharenkov]

Thank you. And are there any other solutions for parallel ode system solving?