trichol {mgcv} 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.

bandchol

### 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])



[Package mgcv version 1.9-0 Index]