Optimizing computing double integrals by elementwise matrix operations

Hi all,

I wrote my own function to calculate the double integral of a function, here referred to as 'fun(x,y)' between the boundaries x=[a,b] and y=[c,d]:

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function [ I ] = mydblquad( fun,a, b, c, d )
%MYDBLQUAD Summary of this function goes here
%   Detailed explanation goes here

myquad = @(fun_int,a,b,tol,trace,varargin)quadgk(@(x)fun_int(x,varargin{:}),a,b,'AbsTol',tol);
I=dblquad(fun,a,b,c,d,1e-5,myquad);

end

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However, as the function I have to integrate is also function of two parameters 'n' and 'm', and as I have to compute this integral over a big set of values for 'n' and 'm', it becomes computationally ineffecient to compute all the integrals in two for-loops over 'n' and 'm'. Is there another possibility, such as computing dblquad not on one function, but on a set of functions arranged in a matrix depeding on 'n' and 'm'? A first try-out did not work.

What I would like to get is something like: I( n x m ) = mydblquad ( F( n x m) ), whereby you integrate over x and y

Thanks,

Bart

Answer 1

[Sean de Wolski]

If you are using R2012a, consider using integral2

doc integral2

[Bart Boesman]

I use both R2012a and R2011b. I used this quad function because I have to integrate from -Inf to Inf. Is there an alternative for R2011b?

Answer 2

[Bart Boesman]

Hi,

As far as I've tried, using integral2 does not solve to problem. As I suspected you can't input a matrix to the function. Any other ideas to optimize this integral loops?

Thanks,

Bart

[Mike Hosea]

What you are trying to do requires a lot of work, and it is going to take some time. The computational efficiency of loops is NOT the problem. The problem is the problem. You can't speed this sort of thing up by vectorizing it. You can, however speed it up by parallelizing it, and it sounds to me like your problem is what we call "embarrassingly parallel".