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

Here's a simple vectorized solution, assuming X is the input matrix:

Y = repmat(eye(size(X, 2)), size(X, 1), 1);
Y(find(Y)) = X;

Another alternative is to use sparse, and this can be written as a neat one-liner:

Y = full(sparse(1:numel(X), repmat(1:size(X, 2), 1, size(X, 1)), X'));