Method for finding the nearest positive semi-definite matrix

To ensure valid covariance matrices, the GSN algorithm involves finding the nearest (in the sense of the Frobenius norm) symmetric positive semi-definite matrix to a given matrix (see PSD() in Steps 5 and 7). This is accomplished using the method proposed by Higham (^{Higham, 1988}). Our implementation is as follows (constructnearestpsdcovariance.{m,py}):

Note that this method is equivalent to performing an eigendecomposition of C and setting negative eigenvalues to zero.