如何有效地在matlab中创建这个矩阵？没有for循环？

Question

我想用这个函数创建一个N * N矩阵A：

其中x和y是N-d向量。我可以通过4嵌套for循环创建，但如何更有效地实现它？有没有for循环的方法吗？

非常感谢。

Answer 1

using element-wise .* operations will be dramatically faster than 4 nested for loops. I think you want something like this:

M = 100;
K = 100;
N = 40;
x = linspace(0,1,N);
y = linspace(0,1,N);

%order reversed matches i,j notation in question
[Y,X] = meshgrid(y,x);
A = zeros(size(X));

for m = 1:M
    for k = 1:K

        A = A + sqrt(m^2 + k^2)*sin(m*X).*cos(k*Y);

    end 
end