| ldl {fastmatrix} | R Documentation |
Compute the LDL decomposition of a real symmetric matrix.
ldl(x)
x |
a symmetric numeric matrix whose LDL decomposition is to be computed. |
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 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}. |
Golub, G.H., Van Loan, C.F. (1996). Matrix Computations, 3rd Edition. John Hopkins University Press.
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)