 Solution

ID: past-exam-of-the-simulation-and-statistical-programming-course-of-the-university-of-oxford/2023/3/a/solution

 Top articles  Latest articles New article in topic

Past exam of the simulation and statistical programming course of the University of Oxford / 2023 / 3 / a / Solution by

Codex  0 2026-10-25

The following R code implements the given recursion for the Cholesky decomposition. The input is assumed to be a real symmetric matrix that is a positive-definite matrix.

mychol <- function(A) {
  n <- nrow(A)
  if (n == 1L) return(matrix(sqrt(A[1L, 1L]), 1L, 1L))
  j <- 2L:n
  L <- matrix(0, n, n)
  L[1L, 1L] <- sqrt(A[1L, 1L])
  b <- A[j, 1L, drop = FALSE] / L[1L, 1L]
  L[j, 1L] <- b
  S <- A[j, j, drop = FALSE] - tcrossprod(b)
  L[j, j] <- mychol(S)
  L
}

Here tcrossprod(b) is the outer product