Doing a nested numerical integral in Matlab

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L'O.G. 2022년 12월 28일
편집: Torsten 2022년 12월 29일
How do I do the following nested integral in Matlab? The goal is to evaluate the following:
where the function ϕ is defined as
where . The notation seems a bit weird to me since the argument of ϕ in the second equation is only part of the argument where it appears in the first equation. I imagine that just means μ is re-defined in terms of itself. Assuming that's correct, how do I do this nested integral?

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Torsten 2022년 12월 28일
mu = -20:0.01:20;
f = @(mu) integral2(@(u,sigma) sin(mu*sqrt(1-sigma.^2).*cos(pi/2*u)).*(sin(mu*sigma/2)).^2,0,1,0,1);
P = arrayfun(@(mu)f(mu),mu);
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L'O.G. 2022년 12월 29일
arrayfun is slow, is there a faster option?
Torsten 2022년 12월 29일
편집: Torsten 2022년 12월 29일
Yes, a for-loop over the elements of mu.
But I don't think that "arrayfun" is the time-consuming part - it's "integral2".

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