Setting an element of an array to a value

Question

This may be a simple syntax question, but for some reason I've been having trouble with it. Suppose we have an array arr, and we want to set one of the elements to a particular value (say, 7). It's easy to do this manually:

arr = {{1, 2}, {3, 4}};
arr[[1, 2]] = 7;
arr

Out: {{1, 7}, {3, 4}}

How do we do this when the index we want to modify is stored as a list? It's easy to use Extract to return the current element at that location:

indices = {2, 2};
Extract[arr, indices]

Out: 4

But attempting to set it equal to a value (say, 13) gives errors:

Extract[arr, indices] = 13

Out: Set::write: Tag Extract in Extract[{{1,7},{3,4}},{2,2}] is Protected. >>

Similarly, using Part gives errors when done the naive way:

arr[[##]] & @@ indices = 13

Out: Set::write: Tag Apply in (arr[[##1]]&)@@{2,2} is Protected. >>

Of course, I can sort of do it manually in the following way:

arr[[indices[[1]], indices[[2]]]] = 13
arr

Out: {{1, 7}, {3, 13}}

But this becomes cumbersome when dealing with arrays which are very deep. So the question is, is there a way to set an element in an array to a value without having to enter the expression manually?

Answer 1

Single level indices (your example):

arr = {{1, 2}, {3, 4}}; indices = {2, 2};
(arr[[#1, #2]] = 13;) & @@ indices
arr

{{1, 2}, {3, 13}}

Double level indices (in case you need to replace more than one element)

arr = {{1, 2}, {3, 4}}; indices = {{1, 2}, {2, 2}}; newValues = {56, 78};
(arr[[#1, #2]] = newValues[[Position[indices, {#1, #2}][[1, 1]]]];) & @@@ indices
arr

{{1, 56}, {3, 78}}

Answer 2

another approach:

arr = {{1, 2}, {3, 4}};
indices = {{1, 2}, {2, 2}};
newValues = {56, 78};

arr = ReplacePart[arr, Thread[indices -> newValues]]

{{1, 56}, {3, 78}}

or

(arr[[##2]] = #) & @@@ Join[List /@ newValues, indices, 2];
arr

{{1, 56}, {3, 78}}