Parallel ODE solve using parfor-loop

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Danila Zharenkov
Danila Zharenkov 2013-5-3
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?

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Edric Ellis
Edric Ellis 2013-5-3
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(:);
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Edric Ellis
Edric Ellis 2013-5-7
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
Danila Zharenkov 2013-5-11
Thank you. And are there any other solutions for parallel ode system solving?

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