Sum of a portion of 3D matrix elements

Hello,

I would like to find a sum of 3D matrix elements located in a one tetrahedron. For a matrix A with indices (i, j, k) I need to find a sum of elements with indices (i, j > i, k > j), i.e.

total = 0;
for i = 1:N
    for j = i:N
        for k = j:N
            total = total + A(i,j,k);

Is there a way to do it in a vector/matrix manner without loops?

"Tril/triu" function doesn't work with 3D matricies.

Thanks in advance!

Answer 1

[Matt J]

[I,J,K]=ndgrid(1:N);
total = sum(A(I<=J & J<=K))

[Matt J]

You can conserve some memory by using ndgridVecs instead ( Download )

[I,J,K]=ndgridVecs(1:N);

total = sum(A(I<=J & J<=K))

[Dmitrii Lukashevich]

Thank you a lot