How can I get the elements from a matrix and use them as the coordinates in another matrix

I have a matrix

W=[1 3 4 1

1 2 3 1

1 2 4 1]

and I want to get the values of another matrix

C=[0 3 7 8

3 0 1 4

7 1 0 2

8 4 2 0].

That is, I want to take firstly the values of C which exist in (1,3) position, (3,4) position and (4,1) position (the first row of W), i.e. 7,2 and 8 respectively in matrix C and the sum of these values (18). The same indeed for all the rows.

Answer 1

[Matt J]

D = C(  sub2ind(  size(C), W(:,1:end-1), W(:,2:end)  )  ),

sum(D,2)

[giorgos kazas]

Thank you very much!