I want to eliminate the for loop from the code below and vectorize it, but it is a 2 dimensional operation. Can you please help me.
for i=1:10 savingsFull(i,:) = distances(i,9)+distances(9,knnIdx(i,:))-distances(i,knnIdx(i,:)); end here, "distances" is a 10x10 symmetric matrix and "knnIdx" is a 10x2 matrix as below:
1 10 2 10 3 8 4 8 5 4 6 5 7 2 8 4 9 8 10 1 "savingsFull" is also a 10x2 matrix.
Following code should help:
savingsFull = distances(:, [9 9]) + [distances(9, knnIdx(:, 1)).', distances(9, knnIdx(:, 2)).'] - [diag(distances(:, knnIdx(:, 1))), diag(distances(:, knnIdx(:, 2)))] If first column of knnIdx are consequent numbers from 1 to 10, then you can simplify to
savingsFull = distances(:, [9 9]) + [distances(9, knnIdx(:, 1)).', distances(9, knnIdx(:, 2)).'] - [diag(distances), diag(distances(:, knnIdx(:, 2)))] 
' and .' operators is that .' transposes a matrix and ' only changes dimensions. So there is a simple relation between them: A' = conj(A.');. So distances(9, knnIdx(:, 1)).' leads to a column-vector instead of row-vector. So, assuming that distance is real-valued, there should be no difference between ' and .'.
bsxfunto vectorize