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Tue Jan 15 10:16:29 2008 UTC (11 years, 7 months ago) by maechler
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solve(<CHMfactor>, <numeric>) and related
\title{CHOLMOD-based Cholesky Factorizations}
\alias{CHMfactor-class}% "mother" virtual
\alias{CHMsimpl-class}% virtual
\alias{CHMsuper-class}% virtual
\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.
  of \code{"CHMfactor"} and all classes inheriting from it:
    \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)}:
    \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.}
    \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
    \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.}
  \code{\link{Cholesky}}, also for examples;
  class \code{\linkS4class{dgCMatrix}}.
%\examples{} are in ./Cholesky.Rd
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