LDL Decomposition of a Matrix

Description

Function ldl computes the LDL decomposition of a positive semidefinite matrix.

Usage

ldl(x, tol)

Arguments

Value

Transformed matrix with D in diagonal, L in strictly lower diagonal and zeros on upper diagonal.

Examples

# Positive semidefinite matrix, example matrix taken from ?chol
x <- matrix(c(1:5, (1:5)^2), 5, 2)
x <- cbind(x, x[, 1] + 3*x[, 2])
m <- crossprod(x)
l <- ldl(m)
d <- diag(diag(l))
diag(l) <- 1
all.equal(l %*% d %*% t(l), m, tol = 1e-15)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(KFAS)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/KFAS/ldl.Rd_%03d_medium.png", width=480, height=480)
> ### Name: ldl
> ### Title: LDL Decomposition of a Matrix
> ### Aliases: ldl
> 
> ### ** Examples
> 
> # Positive semidefinite matrix, example matrix taken from ?chol
> x <- matrix(c(1:5, (1:5)^2), 5, 2)
> x <- cbind(x, x[, 1] + 3*x[, 2])
> m <- crossprod(x)
> l <- ldl(m)
> d <- diag(diag(l))
> diag(l) <- 1
> all.equal(l %*% d %*% t(l), m, tol = 1e-15)
[1] TRUE
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>