How to fastly compute a double integral of a self-defined function?

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Tmat 2020-2-26

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/507569-how-to-fastly-compute-a-double-integral-of-a-self-defined-function

评论： Tmat 2020-2-27

采纳的回答： Steven Lord

在 MATLAB Online 中打开

Hi everyone,

I need to compute

, where

is my self-defined function, M is infinity and in actual calculation I set it to be a large number and

is the probability density function of standard bivariate normal. My code for a simple example looks as follows (here

clear;
tic
step=0.01; 
grid=-100:step:100; lg=length(grid);
x=repmat(grid',1,lg);
y=repmat(grid,lg,1);
tempz=[x(:) y(:)];
z=tempz(:,1).*tempz(:,2);
fz=mvnpdf(tempz);
t=sum(z.*fz);
toc

This simple example already takes me 30 seconds on a computing node of our university. In the real application

is much more complex and defined by a separate function file. I'm wondering if there are any more efficient ways of doing this?

采纳的回答

Steven Lord 2020-2-26

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https://ww2.mathworks.cn/matlabcentral/answers/507569-how-to-fastly-compute-a-double-integral-of-a-self-defined-function#answer_417361

Use the integral2 function.

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Steven Lord 2020-2-26

在 MATLAB Online 中打开

fh = @(x, y) reshape(mvnpdf([x(:), y(:)]), size(x));
integral2(fh, -Inf, Inf, -Inf, Inf)

fh combines the two coordinate vectors integral2 will pass into it into the coordinate matrix mvnpdf requires, evaluates the PDF, and uses reshape to make the PDF values vector the same shape as the input.

Tmat 2020-2-27