Occasionally I have had to solve large systems of differential equations which result in matlab running out of memory during evaluation. Odesplit breaks up the simulation period into a series of chunks to ease this problem. At each split point in the evaluation a function specified by the user is called with the current set of results to do whatever is necessary with the ouput. The next section is then evaluated using the final value of the previous section as the new starting point.
This behaviour differs from matlab's odextend as it allows you operate only on small sections of the solution, whereas odeextend always returns the full solution from the original start time to the specified final time. With odesplit, you could also choose to extract only particular solution components of interest, but which depend on the full solution, saving more resources.
Example:
Create the ode function described in Example 1 of the documentation for
ode45 (doc ode45)
function dy = rigid(t,y)
dy = zeros(3,1); % a column vector
dy(1) = y(2) * y(3);
dy(2) = -y(1) * y(3);
dy(3) = -0.51 * y(1) * y(2);
Create a function to be called at each split point
function results = rigidspfcn(results, sol)
if nargin == 0
results.iters = 0;
else
save(['rigidodesave_', int2str(results.iters), '.mat'], 'sol');
results.iters = results.iters + 1;
end
Set the options etc. and call odesplit, splitting the computation into
three blocks
odeoptions = odeset('RelTol',1e-4,'AbsTol',[1e-4 1e-4 1e-5]);
odefcn = @ode45;
odeevfcn = @rigid;
tspan = [0, 30];
y0 = [0 1 1];
spfcn = @rigidspfcn;
[results, tspan] = odesplit(odefcn, odeevfcn, tspan, ...
y0, odeoptions, spfcn, 'Blocks', 3)
In this case, odesplit evaluate the ode and saves the results of each section to disk. However, we could have done anything we wished with this section of data, such as appending solution components of interest to 'results'. The 'results' variable is maintained throughout the calculation in odesplit and returned at the end.
If you ask it to, odesplit will also look out for an out-of-memory error and restart the calculation with a greater number of split points. |