How to pass a function handle of an anonymous function into ode45 function in matlab?

I need to pass an inline anonymous function into ode45 function in matlab but i have not managed to to that. I have looked through the help of matlab but didn't help me. let's give a code example to clarify:

I have a matrix function as follows: f_xyz = @(x,y,z) [-1 1 0;2 -1 -x;0 y -3]*[x;y;z];

and i would like to pass it into ode45 function with such syntax:

[T Y] = ode45(ode_function,time_interval,initial_values);

I checked many forums to get some hints but i didnt work please advise me how to do that?

P.S. :I know how to do that if we have a m-file function but i need it to be as an anonymous function.

Answer 1

[Cedric]

Assuming that your problem has 3 dimensions, so you have for example

 x0 = [10; 5; 7] ;           % [x1(0), x2(0), x3(0)], or 
                             % [x(0), y(0), z(0)] with your notation.

where 10 is the initial condition for dim 1, etc, ODE45 will call the function f that it receives as 1st arg, referenced by its handle @f, with the following parameters:

f( t, x, ... )

where ... symbolize extra parameters that can be defined as extra parameters in the call to ODE45, or through an appropriate definition of the function/handle that you pass as 1st argument. You have therefore to pass a function which takes t and x in this order. If you have the freedom to define f_xyz, you should then define it as follows

 f_xyz = @(t, x) [-1 1 0;2 -1 -x(1);0 x(2) -3] * x ;

If you cannot modify f_xyz, you can pass a handle on an intermediary anonymous function which plays the role of interface, adjusting parameters orders/structure:

 % f_xyz defined elsewhere, you cannot access/modify it.
 f_xyz = @(x,y,z) [-1 1 0;2 -1 -x;0 y -3]*[x;y;z];      

 % Call to ODE45 using an "interface" anonymous function.
 [t, x_t] = ode45( @(t, x) f_xyz(x(1), x(2), x(3)), ... ) ;

Note that you can give a name to this interface function if you prefer not to deal with anonymous functions (but you'll often see people using anonymous functions here)..

 interf   = @(t, x) f_xyz(x(1), x(2), x(3)) ;
 [t, x_t] = ode45( interf, ... ) ;

Hope it helps