MATLAB Answers

Efficient ODE with function handles

4 views (last 30 days)
Stefan Weichert
Stefan Weichert on 3 Sep 2021
Edited: Stefan Weichert on 3 Sep 2021
I am solving an ODE very often, so efficiency is important. The ODE I am solving calls other functions, because the ode is very general, but the details depend on the problem.
What I am doing now is this ( not working code, but the relevant snippets)
% just some parameters that are passed. This does not impact performance
params = {1,2,3};
% function handle of function that changes the ode in question
h1 = @f_function;
% function handle of the ode
%h_dydt = @(t,y)f_dydt(t,y,params); % aproach 1)
h_dydt = @(t,y)f_dydt(t,y,params,h1); % aproach 2)
solution = ode45(h_dydt,...)
Where the ode function is
%function [dydt] = f_dydt(t,y,params,h)% aproach 1)
function [dydt] = f_dydt(t,y,params,h) % aproach 2)
% a = f_function(y,params); % aproach 1)
a = h(y,params); % aproach 2)
%the rest is not important,but could be
dydt = y*t*a;
The problem is, that aproach 2) takes 60% more time than aproach 1), and I wonder if there is a way to have the same flexibility without the huge added cost. As it is now, I have to do aproach 1) and write a separate dydt function for each problem.
Thanks for looking into this!

Answers (2)

Bjorn Gustavsson
Bjorn Gustavsson on 3 Sep 2021
Edited: Bjorn Gustavsson on 3 Sep 2021
If the function-handle-argument is too costly and you still want "some general flexibility" you might try to simply extend the ODE-function with a switch-selecting between the different drivers? Something like this:
%function [dydt] = f_dydt(t,X,params,h)% aproach 1)
function [dydt] = f_dydt(t,X,params,n_RHS) % aproach 1.5)
% a = f_function(x,y,params); % aproach 1)
switch n_RHS
case 1
a = h1(X,params); % aproach 1.5)
case 2
a = h2(X,params); % aproach 1.5)
a = 12;
%the rest is not important,but could be
dydt = y*t*a;
This should fall somewhere inbetween your two aproaches, and might be good enough as a solution to both issues. It will require some effort on writing the documentation of your function to provide "easy use".
  1 Comment
Stefan Weichert
Stefan Weichert on 3 Sep 2021
thanks a lot for your suggestion. This is indeed a possibility.

Sign in to comment.

Steven Lord
Steven Lord on 3 Sep 2021
Does f_function expect to be called with two input arguments or three?
x = [1; 2; 3];
y = [4; 5; 6];
value1 = min([x, y], 4) % This works
value1 = 3×2
1 4 2 4 3 4
value2 = min(x, y, 4) % This does not work
Error using min
Dimension argument is not supported when two input arrays are provided.
How are the X input argument with which ode45 calls your function related to the two variables x and y whose definitions you've elided from your code?
I suspect you're comparing apples and oranges here, though with the limited information you've provided I can't be certain.
  1 Comment
Stefan Weichert
Stefan Weichert on 3 Sep 2021
I see I mixed x and y after reducing the complexity of the functions to declutter the code.
Fixed it now. Thanks.
But the problem with efficiency remains.

Sign in to comment.




Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!