ode45 mex文件运行缓慢

Question

This is the function trial2 which creates the system of differential equations:

function xdot=trial2(t,x) 
delta=0.1045;epsilon=0.0048685; 
xdot=[x(2);(-delta-epsilon*cos(t))*x(1)-0.7*delta*abs(x(1))];

Then, I try and solve this using ode45 :

[t,x]=ode45('trial2',[0 10000000],[0;1]);
plot(t,x(:,1),'r');

But, this takes approximately 15 minutes. So I tried to improve the run time by creating a mex file. I found an ode45 mex equivalent function ode45eq.c . Then, I tried to solve by:

mex ode45eq.c;
[t,x]=ode45eq('trial2',[0 10000000],[0;1]);
plot(t,x(:,1),'r');

But this seems to run even slower. What could be the reason and how can I improve the run time to 2–3 minutes? I have to perform a lot of these computations. Also, is it worth creating a standalone C++ file to solve the problem faster?

Also, I am running this on an Intel i5 processor 64-bit system with 8 gb RAM. How much gain in speed do you think I can get if I move to a better processor with say 16 gb RAM?

Answer 1

With current versions of Matlab, it's very unlikely that you'll see any performance improvement by compiling ode45 to C/C++ mex . In fact, the compiled version will almost certainly be slower as you found. There's a good reason that ode45 is written in pure Matlab, as opposed to being compiled down to a native C function: it has to call user functions written in Matlab on every iteration. Additionally, Matlab's ode45 is a very dynamic function that is capable of interacting with the Matlab environment in many ways during the course of integration (plotting output functions, event detection, interpolation, etc.). It's also probably more straightforward to safely handle dynamic memory allocation in Matlab, than in C.

Your C code calls your user function via mexCallMATLAB . This function is not really meant for repeated calls , especially if they transfer data back and forth. Doing what you're trying to do would likely require new mex APIs and possibly changes to the Matlab language.

If you want faster numerical integration, you're going to have to give up the convenience of being able to write your integrations functions (ie, trial2 in your example) in Matlab. You'll need to "hard code" your integration functions and compile them along with the integration scheme itself. With a detailed knowledge about your problem, and decent programming skills, you can write a tight integration loop and it may be possible to achieve an order of magnitude speedup in some cases.

Lastly, your trial2 function has an absolute value as well as an oscillating trigonometric function in it. Is this differential equation stiff ? Have you tried other solvers, eg, ode15s ? Compare the outputs even over a shorter time period. And you may find that you get a bit of a speed-up (~25% on my machine) if you use the modern way of passing function handles instead of strings to ode45 :

[t,x] = ode45(@trial2,[0 10000000],[0;1]);

The trial2 function can still be in a separate M-file or it can be a sub-function in the same file with your call to ode45 (this file need to be a function file, not a script of course).

Answer 2

What you did is basically replacing the todays implementation with the implementation of 1993, you have shown that mathworks did a great job improving the performance of the ode45 solver.

I don't see any possibility to improve the performance in this case, you can assume that such a fundamental part of MATLAB like ode45 is implemented in a optimal way, replacing it with some other code to mex it is not the solution. Everything you could gain using a mex function is cutting of the overhead of input/output handling which is implemented in m. Probably less than 0.1s execution time.