Returns the pseudo square root of a real symmetric matrix
Given a matrix $ M $, the result $ S $ is defined as the matrix such that $ S S^T = M. $ If the matrix is not positive semi definite, it can return an approximation of the pseudo square root using a (user selected) salvaging algorithm.
For more information see: R. Rebonato and P. Jäckel, The most general methodology to create a valid correlation matrix for risk management and option pricing purposes, The Journal of Risk, 2(2), Winter 1999/2000. http://www.rebonato.com/correlationmatrix.pdf
Revised and extended in "Monte Carlo Methods in Finance", by Peter Jäckel, Chapter 6.
the given matrix must be symmetric.
relates Matrix
warning Higham algorithm only works for correlation matrices.
test
Returns the rank-reduced pseudo square root of a real symmetric matrix
The result matrix has rank<=maxRank. If maxRank>=size, then the specified percentage of eigenvalues out of the eigenvalues' sum is retained.
If the input matrix is not positive semi definite, it can return an approximation of the pseudo square root using a (user selected) salvaging algorithm.
the given matrix must be symmetric.
relates Matrix
Optimization function for hypersphere and lower-diagonal algorithm