fastmatrix (version 0.5-7721)

ldl: The LDL decomposition

Description

Compute the LDL decomposition of a real symmetric matrix.

Usage

ldl(x)

Value

The factorization has the form \(\bold{X} = \bold{LDL}^T\), where \(\bold{D}\)

is a diagonal matrix and \(\bold{L}\) is unitary lower triangular.

The LDL decomposition of \(\bold{x}\) is returned as a list with components:

lower

the unitary lower triangular factor \(\bold{L}\).

d

a vector containing the diagonal elements of \(\bold{D}\).

Arguments

x

a symmetric numeric matrix whose LDL decomposition is to be computed.

References

Golub, G.H., Van Loan, C.F. (1996). Matrix Computations, 3rd Edition. John Hopkins University Press.

See Also

chol

Examples

a <- matrix(c(2,-1,0,-1,2,-1,0,-1,1), ncol = 3)
z <- ldl(a)
z # information of LDL factorization

# computing det(a)
prod(z$d) # product of diagonal elements of D

# a non-positive-definite matrix
m <- matrix(c(5,-5,-5,3), ncol = 2)
try(chol(m)) # fails
ldl(m)