ldl

The LDL decomposition

Description

Compute the LDL decomposition of a real symmetric matrix.

Usage

ldl(x)

Arguments

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

Value

The factorization has the form \(\mathbf{X} = \mathbf{LDL}^T\) , where \(\mathbf{D}\) is a diagonal matrix and \(\mathbf{L}\) is unitary lower triangular.

The LDL decomposition of x is returned as a list with components:

Value	Description
lower	the unitary lower triangular factor \(\mathbf{L}\).
d	a vector containing the diagonal elements of \(\mathbf{D}\).

Seealso

chol

References

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

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)