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

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Tmat
Tmat 2020-2-26
评论： Tmat 2020-2-27
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?

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Steven Lord
Steven Lord 2020-2-26
Use the integral2 function.
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Steven Lord
Steven Lord 2020-2-26
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.

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