Efficient method to set Matrix values based on position

Question

I have a matrix, a list of positions, and a vector.

I want a new matrix with the values of the vector inserted into the original matrix based upon the list of positions.

For example:

oldMatrix = {{a1, a2, a3, a4}, {b1, b2, b3, b4}, 
             {c1, c2, c3, c4}, {d1, d2, d3, d4}};

positions = {{1, 1}, {2, 3}, {3, 2}, {4, 1}}

newElements = {A1, B3, C2, D1}

Then I want the new matrix to be

Mathematica graphics

If I was working with a vector rather than a matrix this would be easy:

newVector                = oldVector
newVector[[{positions}]] = newElements

as vectors support a list when indexing.

This will not work with matrices.

I have searched and read with interest this answer but it doesn't fit this problem.

The best I have been able to come up with is:

setMatrix[matrix_, positionsMatrix_, vector_] := Module[
  {
   vectorF,
   positionsVector,
   row,
   column
   },

  vectorF = Flatten[matrix];
  {row, column} = Dimensions[matrix];

  positionsVector = Map[(#[[1]] - 1)*row + #[[2]] &,
    positionsMatrix];

  vectorF[[positionsVector]] = vector;

  Partition[vectorF, row]
  ]

but I would hope there was a simpler, more elegant and efficient approach.

score 5 · Accepted Answer · answered Sep 13 '15 at 17:04

oldMatrix = {{a1, a2, a3, a4}, {b1, b2, b3, b4}, {c1, c2, c3, 
    c4}, {d1, d2, d3, d4}};

positions = {{1, 1}, {2, 3}, {3, 2}, {4, 1}};

newElements = {A1, B3, C2, D1};

(newMatrix = 
   ReplacePart[oldMatrix, 
    Thread[positions -> newElements]]) // MatrixForm

Efficient method to set Matrix values based on position

1 Answers1