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\name{nsparseMatrix-class}
\title{Sparse "pattern" Matrices}
%
\docType{class}
\keyword{array}
\keyword{classes}
%
\alias{nsparseMatrix-class}
\alias{nsparseMatrix-classes} % used by package 'arules'
\alias{ngCMatrix-class}
\alias{ngRMatrix-class}
\alias{ngTMatrix-class}
\alias{ntCMatrix-class}
\alias{ntRMatrix-class}
\alias{ntTMatrix-class}
\alias{nsCMatrix-class}
\alias{nsRMatrix-class}
\alias{nsTMatrix-class}
% nsparse
\alias{!,nsparseMatrix-method}
\alias{-,nsparseMatrix,missing-method}
\alias{Arith,nsparseMatrix,Matrix-method}
\alias{Arith,dsparseMatrix,nsparseMatrix-method}
\alias{Arith,lsparseMatrix,nsparseMatrix-method}
\alias{Arith,nsparseMatrix,dsparseMatrix-method}
\alias{Arith,nsparseMatrix,lsparseMatrix-method}
\alias{Ops,nsparseMatrix,dsparseMatrix-method}
\alias{Ops,nsparseMatrix,lsparseMatrix-method}
\alias{Ops,nsparseMatrix,sparseMatrix-method}
\alias{coerce,matrix,nsparseMatrix-method}
\alias{coerce,nsparseMatrix,indMatrix-method}
\alias{coerce,nsparseMatrix,pMatrix-method}
\alias{coerce,vector,nsparseMatrix-method}
\alias{which,nsparseMatrix-method}
% ngC
% ngR
% ngT
% ntC
% ntR
% ntT
% nsC
% nsR
% nsT
%
\description{The \code{nsparseMatrix} class is a virtual class of sparse
\emph{\dQuote{pattern}} matrices, i.e., binary matrices conceptually
with \code{TRUE}/\code{FALSE} entries. Only the positions of the
elements that are \code{TRUE} are stored.
These can be stored in the \dQuote{triplet} form
(\code{\linkS4class{TsparseMatrix}}, subclasses \code{ngTMatrix},
\code{nsTMatrix}, and \code{ntTMatrix} which really contain pairs, not
triplets) or in compressed column-oriented form (class
\code{\linkS4class{CsparseMatrix}}, subclasses \code{ngCMatrix},
\code{nsCMatrix}, and \code{ntCMatrix}) or--\emph{rarely}--in
compressed row-oriented form (class \code{\linkS4class{RsparseMatrix}},
subclasses \code{ngRMatrix}, \code{nsRMatrix}, and \code{ntRMatrix}).
The second letter in the name of these non-virtual classes indicates
\code{g}eneral, \code{s}ymmetric, or \code{t}riangular.
}
\section{Objects from the Class}{
Objects can be created by calls of the form \code{new("ngCMatrix",
...)} and so on. More frequently objects are created by coercion of
a numeric sparse matrix to the pattern form for use in
the symbolic analysis phase
of an algorithm involving sparse matrices. Such algorithms often
involve two phases: a symbolic phase wherein the positions of the
non-zeros in the result are determined and a numeric phase wherein the
actual results are calculated. During the symbolic phase only the
positions of the non-zero elements in any operands are of interest,
hence numeric sparse matrices can be treated as sparse pattern
matrices.
}
\section{Slots}{
\describe{
\item{\code{uplo}:}{Object of class \code{"character"}. Must be
either "U", for upper triangular, and "L", for lower
triangular. Present in the triangular and symmetric classes but not
in the general class.}
\item{\code{diag}:}{Object of class \code{"character"}. Must be
either \code{"U"}, for unit triangular (diagonal is all ones), or
\code{"N"} for non-unit. The implicit diagonal elements are not
explicitly stored when \code{diag} is \code{"U"}. Present in the
triangular classes only.}
\item{\code{p}:}{Object of class \code{"integer"} of pointers, one
for each column (row), to the initial (zero-based) index of elements in
the column. Present in compressed column-oriented and compressed
row-oriented forms only.}
\item{\code{i}:}{Object of class \code{"integer"} of length nnzero
(number of non-zero elements). These are the row numbers for
each TRUE element in the matrix. All other elements are FALSE.
Present in triplet and compressed column-oriented forms only.}
\item{\code{j}:}{Object of class \code{"integer"} of length nnzero
(number of non-zero elements). These are the column numbers for
each TRUE element in the matrix. All other elements are FALSE.
Present in triplet and compressed row-oriented forms only.}
\item{\code{Dim}:}{Object of class \code{"integer"} - the dimensions
of the matrix.}
}
}
\section{Methods}{
\describe{
\item{coerce}{\code{signature(from = "dgCMatrix", to =
"ngCMatrix")}, and many similar ones; typically you should
coerce to \code{"nsparseMatrix"} (or \code{"nMatrix"}). Note that
coercion to a sparse pattern matrix records all the potential
non-zero entries, i.e., explicit (\dQuote{non-structural}) zeroes
are coerced to \code{TRUE}, not \code{FALSE}, see the example.
}
\item{t}{\code{signature(x = "ngCMatrix")}: returns the transpose
of \code{x}}
\item{which}{\code{signature(x = "lsparseMatrix")}, semantically
equivalent to \pkg{base} function \code{\link{which}(x, arr.ind)};
for details, see the \code{\linkS4class{lMatrix}} class documentation.}
}
}
%\references{}
%\author{}
%\note{}
\seealso{
the class \code{\linkS4class{dgCMatrix}}
}
\examples{
\dontshow{ % for R_DEFAULT_PACKAGES=NULL
library(utils, pos = "package:base", verbose = FALSE)
}
(m <- Matrix(c(0,0,2:0), 3,5, dimnames=list(LETTERS[1:3],NULL)))
## ``extract the nonzero-pattern of (m) into an nMatrix'':
nm <- as(m, "nsparseMatrix") ## -> will be a "ngCMatrix"
str(nm) # no 'x' slot
nnm <- !nm # no longer sparse
## consistency check:
stopifnot(xor(as( nm, "matrix"),
as(nnm, "matrix")))
## low-level way of adding "non-structural zeros" :
nnm <- as(nnm, "lsparseMatrix") # "lgCMatrix"
nnm@x[2:4] <- c(FALSE, NA, NA)
nnm
as(nnm, "nMatrix") # NAs *and* non-structural 0 |---> 'TRUE'
data(KNex, package = "Matrix")
nmm <- as(KNex $ mm, "nMatrix")
str(xlx <- crossprod(nmm))# "nsCMatrix"
stopifnot(isSymmetric(xlx))
image(xlx, main=paste("crossprod(nmm) : Sparse", class(xlx)))
}
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