How to write a function which includes numerical integration?

Question

I need to calculate the integration in many points. So,

f = f(r,theta,k,phi); 
q =integral2(f,0,1,0,2*pi,'AbsTol',0,'RelTol',1e-10); % integration should be by k and phi

I want the q to be a function of r and theta that I can call it anytime to calculate the integration in the given r and theta point. How can I do this? The problem is that I couldn't use the indefinite @ function or matlabFunction() methods, because it seems that the integration is done first and when Matlab detects that it doesn't have all arguments defined, it brings some errors.

Answer 1

Is this all you're looking for (I still don't know what f returns)?:

r = ...     % Define
theta = ... % Define
g = @(k,phi)f(r,theta,k,phi); % g is now a function of k and phi
q = integral2(g,0,1,0,2*pi,'AbsTol',0,'RelTol',1e-10);

This creates an anonymous function g where the values of r and theta are captured as parameters and k and theta are still arguments. This concept is known as a closure in computer science.

If you want to turn the whole thing into a function of r and theta that returns q you can can create the following anonymous function:

q = @(r,theta)integral2(@(k,phi)f(r,theta,k,phi),0,1,0,2*pi,'AbsTol',0,'RelTol',1e-10);

that you can call with q(r,theta). Of course you could equally just use normal functions (which are usually faster and make your code easier to understand by others).