double summation without a loop

I have an anonymous function f that has two indices, i and t. i runs from 1 to n; t runs from 1 to m != n. For example:

   f       = @(delta,i,t)  exp( - delta(i).*t );
    delta   = rand(1:n);

Obviously, I can sum f with respect to either t or i,

     sum(f(delta,1:n,t))
     sum(f(delta,i,1:m))

But I'd like to compute, in one step, sum_i=1^n (sum_t=1^m f(delta,i,t)) , without writing a loop. Is this possible? thanks very much for any advice!

Answer 1

[Jan]

f = @(delta,i,t)  exp(bsxfun(@times, -delta(i), t.'))
result = sum(reshape(f(delta, 1:n, 1:m), 1, []))

[Leo Simon]

Perfect, thanks, Jan. Could you please explain the "." in t.'? I tried this with and without the . and got the same answer...

[Stephen23]

In general operations with a period character . are elementwise operations, whereas the operations without are standard linear algebra operations.

In this case:

• ' is the complex conjugate transpose of the matrix.
• .' is the non-conjugate tranpose of the matrix (elementwise transpose).

Jan Simon used the non-conjugate transpose in their answer, and this is the one you should use too.

[Jan]

@Stephen: In their answer? I'm aware that the name Jan can be male and female and Simon is a common first name also, but we are at least only one person. So I'd prefer his ;-)