| chol {Matrix} | R Documentation |
Compute the Choleski factorization of a real symmetric positive-definite square matrix.
chol(x, ...) ## S4 method for signature 'dsCMatrix' chol(x, pivot = FALSE, ...)
x |
a (sparse or dense) square matrix, here inheriting from class
|
pivot |
logical indicating if pivoting is used. |
... |
potentially further arguments passed to methods. |
a matrix of class Cholesky,
i.e., upper triangular: R such that R'R = x.
Use showMethods(chol) to see all; some are worth
mentioning here:
signature(x = "dgeMatrix"): works via
"dpoMatrix", see class dpoMatrix.
signature(x = "dpoMatrix"):
Returns (and stores) the Cholesky decomposition of x, via
LAPACK routines dlacpy and dpotrf.
signature(x = "dppMatrix"):
Returns (and stores) the Cholesky decomposition via LAPACK routine
dpptrf.
signature(x = "dsCMatrix", pivot = "logical"):
Returns (and stores) the Cholesky decomposition of x. If
pivot is TRUE (the default) the Approximate Minimal
Degree (AMD) algorithm is used to create a reordering of the rows
and columns of x so as to reduce fill-in.
Timothy A. Davis (2006) Direct Methods for Sparse Linear Systems, SIAM Series “Fundamentals of Algorithms”.
Tim Davis (1996), An approximate minimal degree ordering algorithm, SIAM J. Matrix Analysis and Applications, 17, 4, 886–905.
The default from base, chol.
showMethods(chol, inherited = FALSE) # show different methods
sy2 <- new("dsyMatrix", Dim = as.integer(c(2,2)), x = c(14, NA,32,77))
(c2 <- chol(sy2))#-> "Cholesky" matrix
stopifnot(all.equal(c2, chol(as(sy2, "dpoMatrix")), tol= 1e-13))
str(c2)
## An example where chol() can't work
(sy3 <- new("dsyMatrix", Dim = as.integer(c(2,2)), x = c(14, -1, 2, -7)))
try(chol(sy3)) # error, since it is not positive definite