Choleski decomposition of a tri-diagonal matrix
Computes Choleski decomposition of a (symmetric positive definite) tri-diagonal matrix stored as a leading diagonal and sub/super diagonal.
trichol(ld,sd)
ld |
leading diagonal of matrix |
sd |
sub-super diagonal of matrix |
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.
A list with elements ld and sd. ld is the leading diagonal and sd is the super diagonal of bidiagonal matrix B where B'B=T and T is the original tridiagonal matrix.
Simon N. Wood simon.wood@r-project.org
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.
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])
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