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Optimizing computing double integrals by elementwise matrix operations

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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]:
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);
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


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Accepted Answer

Sean de Wolski
Sean de Wolski on 14 Aug 2012
If you are using R2012a, consider using integral2

  1 Comment

Bart Boesman
Bart Boesman on 14 Aug 2012
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?

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More Answers (1)

Bart Boesman
Bart Boesman on 16 Aug 2012
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?

  1 Comment

Mike Hosea
Mike Hosea on 21 Aug 2012
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".

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