calculating trace of matrix without calculating the matrix itself

Let's say I have this matrix

tmp = magic(10);

and then I have

 vecx= [1,2]
 vecy=[3,4]

If I write tmp(vecx,vecy) it generates the matrix of

A= [tmp(1,3), tmp(1,4); tmp(2,3), tmp(2,4)]

but what I want to get is

B=[tmp(1,3), tmp(2,4)].

I understand B= trace(A), but the problem is in my actually code, I can't calculate A, because it is too large and I go out of memory.

How can I calculate B without explicitly calculating A?

Thanks,

[James Tursa]

We can't answer unless we know what A is and how it is currently calculated. Until we know that, how can we possibly tell you how to calculate only the trace elements of it?

Answer 1

[Roger Stafford]

Let tmp be an n by n matrix.

B = tmp(vecx+n*(vecy-1)).';

(Note: The ‘trace’ is the sum of the diagonal elements of A, not their vector.)

[Walter Roberson]

The above is pretty much the internal formula used by sub2ind, but calling sub2ind() specifically can be easier to read and understand (but direct calculation can sometimes be much faster.)