How to vectorize row-wise diagonalization of a matrix

Question

I have an n-by-m matrix that I want to convert to a mn-by-m matrix, with each m-by-m block of the result containing the diagonal of each row.

For example, if the input i

Answer 1

The easiest way I see to do this is actually quite simple, using simple index referencing and the reshape function:

I = [1 2; 3 4; 5 6];
J(:,[1,4]) = I;
K = reshape(J',2,6)';

If you examine J, it looks like this:

J =
     1     0     0     2
     3     0     0     4
     5     0     0     6

Matrix K is just what wanted:

K =
     1     0
     0     2
     3     0
     0     4
     5     0
     0     6

As Eitan T has noted in the comments, the above is specific to the example, and doesn't cover the general solution. So below is the general solution, with m and n as described in the question.

J(:,1:(m+1):m^2) = I;
K=reshape(J',m,m*n)';

If you want to test it to see it working, just use

I=reshape(1:(m*n),m,n)';

Note: if J already exists, this can cause problems. In this case, you need to also use

J=zeros(n,m^2);