trichol: Choleski decomposition of a tri-diagonal matrix
In mgcv: Mixed GAM Computation Vehicle with Automatic Smoothness Estimation

trichol

R Documentation

Choleski decomposition of a tri-diagonal matrix

Description

Computes Choleski decomposition of a (symmetric positive definite) tri-diagonal matrix stored as a leading diagonal and sub/super diagonal.

Usage

trichol(ld,sd)

Arguments

`ld`	leading diagonal of matrix
`sd`	sub-super diagonal of matrix

Details

Calls dpttrf from LAPACK. The point of this is that it has O(n) computational cost, rather than the O(n^3) required by dense matrix methods.

Value

A list with elements ld and sd. ld is the leading diagonal and sd is the super diagonal of bidiagonal matrix \bf B where {\bf B}^T{\bf B} = {\bf T} and \bf T is the original tridiagonal matrix.

Author(s)

Simon N. Wood simon.wood@r-project.org

References

Anderson, E., Bai, Z., Bischof, C., Blackford, S., Dongarra, J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A. and Sorensen, D., 1999. LAPACK Users' guide (Vol. 9). Siam.

Examples

require(mgcv)
## simulate some diagonals...
set.seed(19); k <- 7
ld <- runif(k)+1
sd <- runif(k-1) -.5

## get diagonals of chol factor...
trichol(ld,sd)

## compare to dense matrix result...
A <- diag(ld);for (i in 1:(k-1)) A[i,i+1] <- A[i+1,i] <- sd[i]
R <- chol(A)
diag(R);diag(R[,-1])

mgcv documentation built on May 29, 2024, 4:34 a.m.