KiK {qfratio}

Matrix square root and generalized inverse

Description

This internal function calculates the decomposition \mathbf{S} = \mathbf{K} \mathbf{K}^T for an n \times n covariance matrix \mathbf{S}, so that \mathbf{K} is an n \times m matrix with m being the rank of \mathbf{S}. Returns this \mathbf{K} and its generalized inverse, \mathbf{K}^-, in a list.

Usage

KiK(S, tol = .Machine$double.eps * 100)

Arguments

S

Covariance matrix. Symmetry and positive (semi-)definiteness are checked.

tol

Tolerance to determine the rank of \mathbf{S}. Eigenvalues smaller than this value are considered zero.

Details

At present, this utilizes svd(), although there may be better alternatives.

Value

List with K and iK, with the latter being \mathbf{K}^-