Changing multiple elements (of known coordinates) of a matrix without a for loop

Question

I have a matrix say

Z = [1 2 3;
     4 5 6;
     7 8 9]

I have to change its values, say at positions (2,2) and (3,1), to some specified v

Answer 1

Use sub2ind with multiple entries for rows and columns

Z(sub2ind(size(Z), rowNos, colNos))=0

Example:

Z = [1 2 3;
    4 5 6;
    7 8 9];

rowNos = [2, 3];
colNos = [2, 1];

Z(sub2ind(size(Z), rowNos, colNos))=0

Z =

     1     2     3
     4     0     6
     0     8     9

Answer 2

Use sub2ind, it'll convert your sub-indices to linear indices, which is a number pointing at one exact spot in the matrix (more info).

Z = [ 1 2 3 ; 4 5 6 ; 7 8 9];
rowNos = [2, 3];
colNos = [2, 1];

lin_idcs = sub2ind(size(Z), rowNos, colNos)

If you want to operate on all elements on a specific row and column (elements in higher dimensions that is), you can also address them using linear indexing. It only becomes a bit trickier of calculating them:

Z = reshape(1:4*4*3,[4 4 3]);
rowNos = [2, 3];
colNos = [2, 1];

siz = size(Z);
lin_idcs = sub2ind(siz, rowNos, colNos,ones(size(rowNos))); % just the first element of the remaining dimensions
lin_idcs_all = bsxfun(@plus,lin_idcs',prod(siz(1:2))*(0:prod(siz(3:end))-1)); % all of them
lin_idcs_all = lin_idcs_all(:);

Z(lin_idcs_all) = 0;

experiment a bit with sub2ind, and go through my code step-by-step to understand it.

It would've been easier if it was the first dimension you wanted to take all elements off, then you could have used the colon operator :

Z = reshape(1:3*4*4,[3 4 4]);
rowNos = [2, 3];
colNos = [2, 1];

siz = size(Z);
lin_idcs = sub2ind(siz(2:end),rowNos,colNos);
Z(:,lin_idcs) = 0;

Answer 3

You would like to do this

z(rowNos, colNos)

but you can not - MATLAB does a Cartesian product of the indices. You can do this trick

idx=(colNos-1)*size(z, 1)+rowNos;
z(idx)=0

Flatten the z-matrix and access it through a linear index, which is a combination of rowNos and colNos. Remember that MATLAB flattens the matrix by columns (column-based matrix storage).