mgcv (version 1.8-31)

trichol: 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

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.

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.

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.

See Also

bandchol

Examples

# NOT RUN {
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])

# }