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

Hi,

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 )
     
end
            end
         
        end
         
    end
 
end

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?

Thanks,

[Sindar]

it really depends on the specifics of DifferenceMap. A few possibilities:

• change one of the loops (probably outermost) to a parfor
• look into parallelizing DifferenceMap
• look into parallel versions of ode45 (no familiarity here, but I'd be surprised if there isn't anything)

[VBBV]

T is a vector and loop index. It's also used as last input argument to the function DifferrenceMap.

Did you use any indefinite conditions for while or for loops inside the function ?

[Noob]

Hi Sindar,

Should I do both -- use a parfor and look into paralleizing DifferenceMap -- or are there "diminishing returns", so that doing one of the two is the best I can hope for? (In any case, I'll start reading up on both suggestions.)

Thanks,

[Sindar]

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

Answer 1

[Walter Roberson]

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.

[Noob]

Hi Walter,

This is very interesting. Then that means I can remove the for loop for T, correct?

Should I also specify a step size for ode45, or let the solver do its thing with the adaptive time-stepping?

Thanks,

[Walter Roberson]

Right, you would remove the T loop.

You should let the solve use adaptive time steps.

[Noob]

Ok, I'll try this. Thanks Walter - have a great day / evening.