# chlsoi.r                         J F Monahan, June 2008
 #                                 
 # Cholesky factorization and inverse of a positive definite matrix
 A <- matrix(c(4,2,2,4, 2,5,7,0, 2,7,19,11, 4,0,11,25), 4, 4)
 "matrix"
 A
 Lt <- chol(A)
 "Cholesky factor -- transposed to be upper triangular"
 Lt
 AI <- chol2inv(Lt)
 "inverse"
 AI
 "multiply to get identity"
 A %*% AI  
 "solve equations"              
 b <-c( -1, 1, 2.5, .25)
 "Right hand side"
 b
 x <- AI %*% b
 "Solution"
 x
 rm(list=ls())
  q()