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solve(<CHMfactor>, <numeric>) and related
\name{CHMfactor-class}
\title{CHOLMOD-based Cholesky Factorizations}
\docType{class}
\alias{CHMfactor-class}% "mother" virtual
\alias{CHMsimpl-class}% virtual
\alias{CHMsuper-class}% virtual
\alias{dCHMsimpl-class}
\alias{nCHMsimpl-class}
\alias{dCHMsuper-class}
\alias{nCHMsuper-class}
%
\alias{coerce,CHMfactor,Matrix-method}
\alias{coerce,CHMfactor,sparseMatrix-method}
\alias{solve,CHMfactor,ddenseMatrix-method}
\alias{solve,CHMfactor,dsparseMatrix-method}
\alias{solve,CHMfactor,numeric-method}
\alias{solve,CHMfactor,matrix-method}
\alias{solve,CHMfactor,ANY-method}
%
\description{The virtual class \code{"CHMfactor"} is a class of
CHOLMOD-based Cholesky factorizations of symmetric, sparse,
compressed, column-oriented matrices.  Such a factorization is
simplicial (virtual class \code{"CHMsimpl"}) or supernodal (virtual
class \code{"CHMsuper"}).  Objects that inherit from these classes are
either numeric factorizations (classes \code{"dCHMsimpl"} and
\code{"dCHMsuper"}) or symbolic factorizations (classes
\code{"nCHMsimpl"} and \code{"nCHMsuper"}).
}
\section{Objects from the Class}{
Objects can be created by calls of the form \code{new("dCHMsuper", ...)}
but are more commonly created via \code{\link{Cholesky}()}.
applied to  \code{\linkS4class{dsCMatrix}} or
\code{\linkS4class{lsCMatrix}} objects.
}
\section{Slots}{
of \code{"CHMfactor"} and all classes inheriting from it:
\describe{
\item{\code{perm}:}{An integer vector giving the 0-based
permutation of the rows and columns chosen to reduce fill-in and
for post-ordering.}
\item{\code{colcount}:}{Object of class \code{"integer"} .... }%% FIXME
\item{\code{type}:}{Object of class \code{"integer"} .... }
}

Slots of the non virtual classes \dQuote{[dl]CHM(super|simpl)}:
\describe{
\item{\code{p}:}{Object of class \code{"integer"} of pointers, one
for each column, to the initial (zero-based) index of elements in
the column. Only present in classes that contain \code{"CHMsimpl"}.}
\item{\code{i}:}{Object of class \code{"integer"} of length nnzero
(number of non-zero elements).  These are the row numbers for
each non-zero element in the matrix.  Only present in classes that
contain \code{"CHMsimpl"}.}
\item{\code{x}:}{For the \code{"d*"} classes: \code{"numeric"} - the
non-zero elements of the matrix.}
}
}
\section{Methods}{
\describe{
\item{coerce}{\code{signature(from = "CHMfactor", to = "sparseMatrix")}}
\item{image}{\code{signature(x = "CHMfactor")}}

\item{solve}{\code{signature(a = "CHMfactor", b = "ddenseMatrix")}
The \code{solve} methods for a \code{"CHMfactor"} object take an
optional third argument \code{system} whose value can be one of the
character strings \code{"A"}, \code{"LDLt"}, \code{"LD"},
\code{"DLt"}, \code{"L"}, \code{"Lt"}, \code{"D"}, \code{"P"} or
\code{"Pt"}.  This argument describes the system to be solved.  The
default is to solve \code{Ax = b} for \code{x} where \code{A} is
sparse, positive-definite matrix that was factored to produce
\code{"a"}.}
\item{solve}{\code{signature(a = "CHMfactor", b = "matrix")}, and}
\item{solve}{\code{signature(a = "CHMfactor", b = "numeric")} call
the above \code{signature(*, b = "ddenseMatrix")} method.}

\item{solve}{\code{signature(a = "CHMfactor", b = "dsparseMatrix")}
takes the same third argument \code{system} and calls the
corresponding sparse CHOLMOD algorithm.}
}
}
%\references{}
%\author{}
%\note{}
\seealso{
\code{\link{Cholesky}}, also for examples;
class \code{\linkS4class{dgCMatrix}}.
}
%\examples{} are in ./Cholesky.Rd
\keyword{classes}
\keyword{algebra}


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