How can I improve this really slow code, which consists of several nested for loops?

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Noob on 28 Sep 2020
Commented: Noob on 29 Sep 2020
So I've written these nested for loops, but it takes a very long time to execute this code:
for T = linspace( 1, 5, 10 )
for xdot_0 = linspace( -3, 3, 10 )
for ydot_0 = linspace( 16, 20, 10 )
for thetadot_0 = linspace( -5, 0, 10 )
z = DifferenceMap( xdot_0, ydot_0, thetadot_0, T );
if norm(z) < 1e-3
disp( xdot_0, ydot_0, thetadot_0, T )
disp( z )
The DifferenceMap( ) function calls another function that gives solutions from the ode45 solver at final time, T.
Is there a better way to write this code so that it's faster?
Sindar on 29 Sep 2020
There are definitely diminishing returns. parfor is easy to implement, but if you figure out lower-level parallelization (esp. vectorization), it has a good chance to be more effective

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Accepted Answer

Walter Roberson
Walter Roberson on 29 Sep 2020
If you can, arrange DifferenceMap to accept a vector of T values. In the ode45() call, instead of passing in the two-element vector [0 T] for scalar T, pass in [0 vector_of_T] . ode45() will report back results at only those times. Discard the first row (corresponding to T = 0) and the rest of the rows hold the results required for each of the values in the vector of T values.
At present, your code is evaluating the same system of ode equations for a number of different T values, but at quite different times -- you do not do T = 1.4 until you have finished all of the T = 1 cases. But in order to simulate to T = 1.4, ode45 would have to integrate starting from scratch, from 0, re-doing the integrations done for time 0 to 1. And then eventually T would become 1.9 and ode45 would have to integrate the same system from scratch again, going all the way through starting from 0 to 1.4 .
My proposal is to do all the times in the same call for a given configuration, so that within the same call after making the prediction for T = 1, it would be able to use the data it already has in order to move on to T = 1.4, and through to T = 1.9 and so on, not needing to re-do the [0 1], [0 1.4] and so on integrations.

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