How to speed up this loops?

Hi,

Is there a way to speed up this?

maxN = 120;
x = -30:0.1:30;
xElements = numel(x);
u_mn = zeros(xElements, xElements);

for m = -maxN:2:maxN
    for i = 1 : xElements
        for j = 1 : xElements
            u_mn(i, j) = sqrt((n+1)/pi) * besselj(m+1, 2*sqrt(x(i)^2 + x(j)^2)) / sqrt(x(i)^2 + x(j)^2)^(m+1) * (x(i) + 1i*x(j))^m;
        end
    end
end

Best regards, Alex

[CS Researcher]

What is n here? Is there another loop for it?

[Alex Kurek]

Im sorry, youre right, there is. The entire code is:

x = -30:0.1:30;
xElements = numel(x);
maxN = 120;

parfor n = 0:maxN
    u_mn(:, :, n+1) = firstTestFunct(maxN, xElements, x, n);
end
u_mnSummed = sum(u_mn, 3);

and the function:

function u_mn = firstTestFunct(maxN, xElements, x, n)
u_mn = zeros(xElements, xElements);

for m = -maxN:2:maxN
    for i = 1 : xElements
        for j = 1 : xElements
            u_mn(i, j) = sqrt((n+1)/pi) * besselj(m+1, 2*sqrt(x(i)^2 + x(j)^2)) / sqrt(x(i)^2 + x(j)^2)^(m+1) * (x(i) + 1i*x(j))^m;
        end
    end
end

This is the fastest version I have now.

[Walter Roberson]

You do not store the results for each different m, and you are not summing them or anything like that, so the effect is as if you had only done the final m value.

[Alex Kurek]

Thanky you, obviously, you are right. the middle line in the loops should look like this:

for m = -maxN:2:maxN
    for i = 1 : xElements
        for j = 1 : xElements
            u_mn(i, j) = u_mn(i, j) + sqrt((n+1)/pi) * besselj(m+1, 2*sqrt(x(i)^2 + x(j)^2)) / sqrt(x(i)^2 + x(j)^2)^(m+1) * (x(i) + 1i*x(j))^m;
        end
    end
end

But still, how to speed this up? Its not working to fast right now.

Answer 1

[Ahmed Rashid]

You can create a mex function of your firstTestFunct by

xx = 1;
codegen firstTestFunct -args {xx, xx, xx, xx}

You need to do it only once. It will generate a mex file. To call the generated mex file, you just need to replace firstTestFunct with firstTestFunct_mex .