Nearest block diagonal matrix to a given matrix

[cpp6f]

Suppose I have a matrix that I want to reduce to block diagonal form. Obviously, the block diagonal form is not unique as each of the diagonal blocks is defined only to within a unitary rotation. So I want to find the block diagonal matrix that is closest to the original matrix in terms of the Frobenius norm.

This problem arises in a quantum chemistry manuscript I am putting together. If anyone can point me to a solution for this, I would be more than happy to acknowledge them in the manuscript.

Thanks!

 

[cpp6f]

Okay, I figured it out myself. After thinking about it for a week, I solve it right after posting!