how can i use integral2 for a vector-valued function ?

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meysam esmaeeli
meysam esmaeeli 2015-9-5
评论： 祥宇 崔 2023-4-10
for example i wrote this code:
% code
f=@(x,y)x+y;
g=@(x,y)x^2+y^2;
h=@(x,y)x/y+y/x;
w=@(x,y)sin(x)+cos(y);
box=@(x,y)[f(x,y) g(x,y);h(x,y) w(x,y)];
answers=integral2(box,1,2,1,2)
i expected answers to be a 2*2 scalar matrix but i got only error... what to do?

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Star Strider
Star Strider 2015-9-5
编辑：Star Strider 2015-9-5
They’re not 'ArrayValued' in the sense integral understands, and only integral — and not integral2 — can handle array-valued arguments. Otherwise, you could just use integral twice, the second time on the result of the first.
They’re also essentially independent of each other, so integrate them individually using integral2 and then put them together in a matrix at the end.
Specifically:
% Vectorised Equations:
f = @(x,y)x+y;
g = @(x,y)x.^2+y.^2;
h = @(x,y)x./y+y./x;
w = @(x,y)sin(x)+cos(y);
intf = integral2(f,1,2,1,2);
intg = integral2(g,1,2,1,2);
inth = integral2(h,1,2,1,2);
intw = integral2(w,1,2,1,2);
answers = [intf intg; inth intw]
answers =
3.0000 4.6667
2.0794 1.0243
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祥宇 崔
祥宇 崔 2023-4-10
@Star Strider
Thanks! As you suggested, we can use 'integral' for twice only when these two variables are independent to each other. But what if we can't seperate them? For instance:
fun = @(n,x,y) sin(n*x-y).*sqrt(x-n*y);
for i=1:1e3
integral2(@(x,y) fun(i,x,y),0,2*pi,0,2*pi);
end
Is there anaway to speed it up by vectorizing it?
祥宇 崔
祥宇 崔 2023-4-10
@Star Strider
If you got any idea, here is my question.
Thanks!
https://ww2.mathworks.cn/matlabcentral/answers/1944314-how-to-vectorize-integral2

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