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Optimize the construction of a function for quadrature purposes

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pluton schmidt
pluton schmidt 2023-2-15
编辑： Torsten 2023-2-15
Hello,
I want to compute the integral of a function which is the linear combination of some known function family (here, Fourier functions):
MyInt = integral(@(t) myfun(t), 0, 2*pi);
My function myfun(t) is built as follows:
function Output = myfun(t)
Output = 0;
for p = 1:20
Output = Output + 1/p.*cos(p*t);
Output = Output + 1/(2*p).*sin(p*t);
end
I can't think of a way to vectorize what's above without the for loop? Can we do better?
Thank you

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采纳的回答

Torsten
Torsten 2023-2-15
编辑：Torsten 2023-2-15
Ran in:
MyInt = integral(@myfun, 0, 2*pi)
MyInt = -5.5511e-16
function Output = myfun(t)
p = (1:20).';
Output = sum(1./p.*cos(p.*t) + 1./(2*p).*sin(p.*t),1);
end

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