ldl {fastmatrix}

The LDL decomposition

Description

Compute the LDL decomposition of a real symmetric matrix.

Usage

ldl(x)

Arguments

x

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

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}.

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)