The Choleski Decomposition

Description

Compute the Choleski factorization of a symmetric (Hermitian), positive definite square matrix.

Usage

chol(x)

Arguments

Value

The upper triangular factor of the Choleski decomposition, i.e., the matrix R such that R'R = x (see example).

Note that effectively, only the upper triangular part of x is used such that the above only holds when x is symmetric.

References

Dongarra, J. J., Bunch, J. R., Moler, C. B. and Stewart, G. W. (1978) LINPACK Users Guide. Philadelphia: SIAM Publications.

See Also

chol2inv for its inverse, backsolve for solving linear systems with upper triangular left sides.

qr, svd for related matrix factorizations.

Examples

( m <- matrix(c(5,1,1,3),2,2) )
( cm <- chol(m) )
t(cm) %*% cm  #-- = 'm'
all(abs(m  -  t(cm) %*% cm) < 100* .Machine$double.eps) # TRUE