R/cholesky.R

In cmna: Computational Methods for Numerical Analysis

## Copyright (c) 2016, James P. Howard, II <jh@jameshoward.us>
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#' @title Cholesky Decomposition
#'
#' @description
#' Decompose a matrix into the Cholesky
#'
#' @param m a matrix
#'
#' @details
#' \code{choleskymatrix} decomposes the matrix \code{m} into the LU
#' decomposition, such that m == L %*% L*.
#'
#' @return the matrix L
#'
#' @family linear
#'
#' @examples
#' (A <- matrix(c(5, 1, 2, 1, 9, 3, 2, 3, 7), 3))
#' (L <- choleskymatrix(A))
#' t(L) %*% L
#'
#' @export
choleskymatrix <- function(m) {
    count.rows <- nrow(m)
    count.cols <- ncol(m)

    L = diag(0, count.rows)
    for(i in 1:count.rows) {
        for(k in 1:i) {
            p.sum <- 0
            for(j in 1:k)
                p.sum <- p.sum + L[j, i] * L[j, k]
            if(i == k)
                L[k, i] <- sqrt(m[i, i] - p.sum)
            else
                L[k, i] <- (m[k, i] - p.sum) / L[k, k]
        }
    }
    return(L)
}