How the implement a 3-fold sum?

Hello,

there are answers for implementing a double sum. But what about a 3-fold sum of the type \sum (x_i*y_j*z_k)*M_{i,j,k} for some given vectors x,y,z and Tensor M.

A naiv implementation would be

SUM=0;
for i=1:length(x)
  for j=1:length(y)
    for k=1:length(z)
      SUM = SUM + x(i)*y(j)*z(k)*M(i,j,k);
    end
  end
end

How to implement this more efficiently in a more compact form?

Thanks for any help!

Answer 1

[David Goodmanson]

Hello Stephen, Here is one way, although you do make three arrays of the same size as M:

[xx yy zz] = ndgrid(x,y,z);
S = xx.*yy.*zz.*m;
SUM = sum(S(:))

Answer 2

[Stephan]

Thanks!