scipy.stats._multivariate:random_correlation_gen._givens_to_1

Extended Summary

The input matrix is a 2x2 symmetric matrix M = [ aii aij ; aij ajj ].

The output matrix g is a 2x2 anti-symmetric matrix of the form [ c s ; -s c ]; the elements c and s are returned.

Applying the output matrix to the input matrix (as b=g.T M g) results in a matrix with bii=1, provided tr(M) - det(M) >= 1 and floating point issues do not occur. Otherwise, some other valid rotation is returned. When tr(M)==2, also bjj=1.