prec: Precision matrix parametrization helper functions.

In graphpcor: Models for Correlation Matrices Based on Graphs

Precision matrix parametrization helper functions.

Description

Precision matrix parametrization helper functions.

Usage

Lprec(theta, p, ilowerL)

fillLprec(L, lfi)

theta2Lprec2C(theta, p, ilowerL)

Arguments

theta	numeric vector of length m.
p	numeric giving the dimention of Q. If missing, p = (1+sqrt(1+8*length(theta))) and Q is assumed to be dense.
ilowerL	numeric vector as index to (lower) L to be filled with theta. Default is missing and Q is assumed to be dense.
L	matrix as the lower triangle containing the Cholesky decomposition of a precision matrix
lfi	indicator of fill-in elements

Details

The precision matrix definition consider m parameters for the lower part of L. If Q is dense, then m = p(p-1)/2, else m = length(ilowerL). Then the precision is defined as Q(\theta) = L(\theta)L(\theta)^T

Value

matrix as the Cholesky factor of a precision matrix as the inverse of a correlation

a matrix whose elements at the lower triangle are the filled in elements of the Cholesky decomposition of a precision matrix and diagonal elements as 1:p.

Functions

• fillLprec(): Function to fill-in a Cholesky matrix

• theta2Lprec2C(): Internal function to build C

Examples

theta1 <- c(1, -1, -2)
Lprec(theta1)
theta2 <- c(0.5, -0.5, -1, -1)
Lprec(theta2, 4, c(2,4,7,12))

graphpcor documentation built on June 8, 2025, 10:37 a.m.