https://github.com/cran/Matrix
Tip revision: 13baa504e0e1ede81c41388d01ae28662acf62d8 authored by Martin Maechler on 27 November 2019, 14:20:02 UTC
version 1.2-18
version 1.2-18
Tip revision: 13baa50
dtCMatrix-class.Rd
\name{dtCMatrix-class}
\title{Triangular, (compressed) sparse column matrices}
\docType{class}
\alias{dtCMatrix-class}% C and
\alias{dtTMatrix-class}% T
%
\alias{coerce,dtCMatrix,dgCMatrix-method}
\alias{coerce,dtCMatrix,dgeMatrix-method}
\alias{coerce,dtCMatrix,dgTMatrix-method}
\alias{coerce,dtCMatrix,dsCMatrix-method}
\alias{coerce,dtCMatrix,dtTMatrix-method}
\alias{coerce,dtCMatrix,dtrMatrix-method}
\alias{coerce,dtCMatrix,ltCMatrix-method}
\alias{coerce,dtCMatrix,ntCMatrix-method}
\alias{coerce,dtCMatrix,TsparseMatrix-method}
\alias{coerce,dtCMatrix,denseMatrix-method}
\alias{coerce,dtCMatrix,matrix-method}
\alias{coerce,dtTMatrix,dgTMatrix-method}
\alias{coerce,dtTMatrix,dgeMatrix-method}
\alias{coerce,dtTMatrix,dtCMatrix-method}
\alias{coerce,dtTMatrix,dtrMatrix-method}
%no longer\alias{coerce,dtTMatrix,ltTMatrix-method}
%no longer\alias{coerce,dtTMatrix,ntTMatrix-method}
\alias{coerce,dtTMatrix,generalMatrix-method}
\alias{coerce,dtTMatrix,matrix-method}
\alias{coerce,matrix,dtCMatrix-method}
\alias{coerce,matrix,dtTMatrix-method}
%% Group methods
\alias{Arith,dtCMatrix,dtCMatrix-method}
%
%\alias{solve,dtCMatrix,...-method}%--> solve-methods.Rd
\alias{t,dtCMatrix-method}
\alias{t,dtTMatrix-method}
\description{The \code{"dtCMatrix"} class is a class of triangular, sparse
matrices in the compressed, column-oriented format. In this
implementation the non-zero elements in the columns are sorted into
increasing row order.
The \code{"dtTMatrix"} class is a class of triangular, sparse matrices
in triplet format.
}
\section{Objects from the Class}{
Objects can be created by calls of the form \code{new("dtCMatrix",
...)} or calls of the form \code{new("dtTMatrix", ...)}, but more
typically automatically via \code{\link{Matrix}()} or coercion such as
\code{as(x, "triangularMatrix")}, or \code{as(x, "dtCMatrix")}.
}
\section{Slots}{
\describe{
\item{\code{uplo}:}{Object of class \code{"character"}. Must be
either "U", for upper triangular, and "L", for lower triangular.}
\item{\code{diag}:}{Object of class \code{"character"}. Must be
either \code{"U"}, for unit triangular (diagonal is all ones), or
\code{"N"}; see \code{\linkS4class{triangularMatrix}}.}
\item{\code{p}:}{(only present in \code{"dtCMatrix"}:) an
\code{\link{integer}} vector for providing pointers, one for each
column, see the detailed description in \code{\linkS4class{CsparseMatrix}}.}
\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.}
\item{\code{j}:}{Object of class \code{"integer"} of length nnzero
(number of non-zero elements). These are the column numbers for
each non-zero element in the matrix. (Only present in the
\code{dtTMatrix} class.)}
\item{\code{x}:}{Object of class \code{"numeric"} - the non-zero
elements of the matrix.}
\item{\code{Dim},\code{Dimnames}:}{The dimension (a length-2
\code{"integer"}) and corresponding names (or \code{NULL}),
inherited from the \code{\linkS4class{Matrix}}, see there.}
}
}
\section{Extends}{
Class \code{"dgCMatrix"}, directly.
Class \code{"triangularMatrix"}, directly.
Class \code{"dMatrix"}, \code{"sparseMatrix"}, and more by class
\code{"dgCMatrix"} etc, see the examples.
}
\section{Methods}{
\describe{
\item{coerce}{\code{signature(from = "dtCMatrix", to = "dgTMatrix")}}
\item{coerce}{\code{signature(from = "dtCMatrix", to = "dgeMatrix")}}
\item{coerce}{\code{signature(from = "dtTMatrix", to = "dgeMatrix")}}
\item{coerce}{\code{signature(from = "dtTMatrix", to = "dtrMatrix")}}
\item{coerce}{\code{signature(from = "dtTMatrix", to = "matrix")}}
\item{solve}{\code{signature(a = "dtCMatrix", b = "....")}:
sparse triangular solve (aka \dQuote{backsolve} or
\dQuote{forwardsolve}), see \code{\link{solve-methods}}.}
\item{t}{\code{signature(x = "dtCMatrix")}: returns the transpose of
\code{x}}
\item{t}{\code{signature(x = "dtTMatrix")}: returns the transpose of
\code{x}}
}
}
%\references{}
%\author{}
%\note{}
\seealso{
Classes \code{\linkS4class{dgCMatrix}}, \code{\linkS4class{dgTMatrix}},
\code{\linkS4class{dgeMatrix}}, and \code{\linkS4class{dtrMatrix}}.
}
\examples{
showClass("dtCMatrix")
showClass("dtTMatrix")
t1 <- new("dtTMatrix", x= c(3,7), i= 0:1, j=3:2, Dim= as.integer(c(4,4)))
t1
## from 0-diagonal to unit-diagonal {low-level step}:
tu <- t1 ; tu@diag <- "U"
tu
(cu <- as(tu, "dtCMatrix"))
str(cu)# only two entries in @i and @x
stopifnot(cu@i == 1:0,
all(2 * symmpart(cu) == Diagonal(4) + forceSymmetric(cu)))
t1[1,2:3] <- -1:-2
diag(t1) <- 10*c(1:2,3:2)
t1 # still triangular
(it1 <- solve(t1))
t1. <- solve(it1)
all(abs(t1 - t1.) < 10 * .Machine$double.eps)
## 2nd example
U5 <- new("dtCMatrix", i= c(1L, 0:3), p=c(0L,0L,0:2, 5L), Dim = c(5L, 5L),
x = rep(1, 5), diag = "U")
U5
(iu <- solve(U5)) # contains one '0'
validObject(iu2 <- solve(U5, Diagonal(5)))# failed in earlier versions
I5 <- iu \%*\% U5 # should equal the identity matrix
i5 <- iu2 \%*\% U5
m53 <- matrix(1:15, 5,3, dimnames=list(NULL,letters[1:3]))
asDiag <- function(M) as(drop0(M), "diagonalMatrix")
stopifnot(
all.equal(Diagonal(5), asDiag(I5), tolerance=1e-14) ,
all.equal(Diagonal(5), asDiag(i5), tolerance=1e-14) ,
identical(list(NULL, dimnames(m53)[[2]]), dimnames(solve(U5, m53)))
)
\dontshow{%
i5. <- I5; colnames(i5.) <- LETTERS[11:15]
M53 <- as(m53, "dgeMatrix")
stopifnot(
identical((dns <- dimnames(solve(i5., M53))),
dimnames(solve(as.matrix(i5.), as.matrix(M53)))) ,
identical(dns, dimnames(solve(i5., as.matrix(M53))))
)
}%dont
}
\keyword{classes}
\keyword{algebra}