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I have a function of two arguments, f[x_,y_], and I want to sum the value of this function for a number of input tuples {x,y} which are in a list. I don't see any way of doing this with Sum. I could write a loop but I'd like to know if there's a better way.

Edit:

Specifically, my function is actually a matrix where the elements are determined by x and y.

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You can just Apply function f:

f[x_, y_] := (x + y)^2;
a = {{1, 2}, {2, 3}, {3, 4}, {4, 5}, {5, 6}};

f @@@ a
(* {9, 25, 49, 81, 121} *)

f @@@ a // Total
(* 285 *)
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  • $\begingroup$ sorry i should have clarified, what if my function is a matrix of functions? Say, f[x_,y_] = {{a[x,y],b[x,y]},{c[x,y],d[x,y]}} $\endgroup$
    – Kai
    Commented Jan 31, 2018 at 22:07
  • $\begingroup$ @Kai It will still work. The result will just be a matrix with sum of elements. $\endgroup$
    – m0nhawk
    Commented Jan 31, 2018 at 22:14
  • $\begingroup$ Thanks, I was having another issue that was preventing it from working but I've got it now $\endgroup$
    – Kai
    Commented Feb 1, 2018 at 1:05
  • $\begingroup$ I have a further question, what if my function is f[x,y,A], where A is an extra vector of parameters? I want to be able to use this in a loop where each time the values in A are updated, but I always pass the same list to the x,y arguments $\endgroup$
    – Kai
    Commented Feb 1, 2018 at 1:39
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    $\begingroup$ I found I can define f[{x_,y_},A_] then perform f[#,Avalues]&/@tuples which seems to work fine. $\endgroup$
    – Kai
    Commented Feb 1, 2018 at 2:03

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