Matrix (version 0.999375-42)

CHMfactor-class: CHOLMOD-based Cholesky Factorizations

Description

The virtual class "CHMfactor" is a class of CHOLMOD-based Cholesky factorizations of symmetric, sparse, compressed, column-oriented matrices. Such a factorization is simplicial (virtual class "CHMsimpl") or supernodal (virtual class "CHMsuper"). Objects that inherit from these classes are either numeric factorizations (classes "dCHMsimpl" and "dCHMsuper") or symbolic factorizations (classes "nCHMsimpl" and "nCHMsuper").

Usage

## S3 method for class 'CHMfactor':
update(object, parent, mult = 0, \dots)
isLDL(x)

Arguments

object,x

a "CHMfactor" object.

parent

a "dsCMatrix" matrix or "dgCMatrix" object with the same nonzero pattern as the matrix that generated object. If parent is a symmetric m

mult

a numeric scalar (default 0). mult times the identity matrix is (implicitly) added to parent or tcrossprod(parent) before updating the decomposition object.

...

Optional additional arguments to the methods.

Objects from the Class

Objects can be created by calls of the form new("dCHMsuper", ...) but are more commonly created via Cholesky(), applied to dsCMatrix or lsCMatrix objects.

See Also

Cholesky, also for examples; class dgCMatrix.

Examples

## An example for the expand() method
n <- 1000; m <- 200; nnz <- 2000
set.seed(1)
M1 <- spMatrix(n, m,
               i = sample(n, nnz, replace = TRUE),
               j = sample(m, nnz, replace = TRUE),
               x = round(rnorm(nnz),1))
XX <- crossprod(M1)
CX <- Cholesky(XX)
isLDL(CX)
str(CX) ## a "dCHMsimpl" object
r <- expand(CX)
L.P <- with(r, crossprod(L,P))  ## == L'P
PLLP <- crossprod(L.P)          ## == (L'P)' L'P == P'LL'P
b <- sample(m)
stopifnot(all.equal(PLLP, XX),          all(as.vector(solve(CX, b, system="P" )) == r$P %*% b),
          all(as.vector(solve(CX, b, system="Pt")) == t(r$P) %*% b) )

   ## [ See  help(Cholesky)  for more examples ]