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I am trying to sum over specific indices in a matrix.

For example, if I have the matrix

a = 1, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 9, 1, 5, 9, 7

i need to sum the index 2, 1 and 4, 3 , i.e 4 + 9 = 13 automatically.

I try the code

Sum[a[[ii]][[jj]], ii, 2, 4, 2, jj, 1, 4 , 2]

and this is equals to 20. (WTF) (i think this shows the result of 4+6+1+9) Why?

In a general form I need to compute the sum of indices 2, 1, 4, 3, 6, 5, 8, 7, 10, 9, 12, 11, 14,13, 16,15 for a 16x16 square matrix.

Thanks for the help

Regards

a = 1, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 9, 1, 5, 9, 7;
positions = 2, 1, 4, 3;
Total@Extract[a, positions]

To see why it doesn't work as you expected, look at the indices that you generated.

Table[ii, jj, ii, 2, 4, 2, jj, 1, 4, 2]

(* 2, 1, 2, 3, 4, 1, 4, 3 *)

You generated four indices so the sum was over four entries. Use

a = 1, 2, 3, 3, 4, 5, 6, 6, 7, 8, 9, 9, 1, 5, 9, 7;

Sum[a[[Sequence @@ i]], i, 2, 1, 4, 3]

(* 13 *)

I would have used Extract if Alan had not posted it first.

So, here is a way to use Sum:

Sum[a[[## & @@ i]], i, 2, 1, 4, 3]

13

But that is also posted a minute earlier by Bob Hanlon.

That leaves

☺ = ♯, ♯♯ [Function] +## & @@ (♯[[##]] & @@@ ♯♯);
☺[a, 2, 1, 4, 3]

13

and

☺☺ = +## & @@ (♯ [Function] #[[## & @@ ♯]]) /@ #2 &;
☺☺[a, 2, 1, 4, 3]

13