In RcppCore/RcppArmadillo: 'Rcpp' Integration for the 'Armadillo' Templated Linear Algebra Library
library(RcppArmadillo)
library(Matrix)
\setcounter{tocdepth}{2}
\tableofcontents
Introduction
The documentation is intended for the convenience of RcppArmadillo sparse matrix users based on
integration of the documentation of library
Matrix \citep{CRAN:Matrix} and
Armadillo
\citep{Sanderson:2010:Armadillo,Sanderson+Curtin:2016}.
There are 31 types of sparse matrices in the Matrix
package that can be used directly. But for now, only 12 of them are supported in RcppArmadillo:
dgCMatrix, dtCMatrix, dsCMatrix, dgTMatrix, dtTMatrix, dsTMatrix, dgRMatrix,
dtRMatrix, dsRMatrix, indMatrix, pMatrix, ddiMatrix.
In the Armadillo library, sparse matrix content is
currently stored as
CSC
format. Such kind of format is quite similar to numeric column-oriented sparse matrix in the library
Matrix (including dgCMatrix, dtCMatrix and
dsCMatrix). When a sparse matrix from the package
Matrix is passed through the
RcppArmadillo) package
\citep{Eddelbuettel+Sanderson:2014:RcppArmadillo,CRAN:RcppArmadillo}, it will be converted or mapped to
CSC format, then undertaken operations on, and finally ouput as a dgCMatrix in R.
In what follows, we will always assume this common header:
#include <RcppArmadillo.h>
// [[Rcpp::depends(RcppArmadillo)]]
using namespace Rcpp;
using namespace arma;
but not generally show it.
Sparse Matrix
dgCMatrix
Synopsis
- Description: general column-oriented numeric sparse matrix.
- Constructor\
new("dgCMatrix", ...) \Matrix(*, sparse = TRUE) \sparseMatrix()
- Coercion\
as(*, "CsparseMatrix") \as(*, "dgCMatrix") \
C++ Code
// [[Rcpp::export]]
sp_mat sqrt_(sp_mat X) {
return sqrt(X);
}
R Code
R> i <- c(1,3:8)
R> j <- c(2,9,6:10)
R> x <- 7 * (1:7)
R> A <- sparseMatrix(i, j, x = x)
R> sqrt_(A)
8 x 10 sparse Matrix of class "dgCMatrix"
[1,] . 2.645751 . . . . . . . .
[2,] . . . . . . . . . .
[3,] . . . . . . . . 3.741657 .
[4,] . . . . . 4.582576 . . . .
[5,] . . . . . . 5.291503 . . .
[6,] . . . . . . . 5.91608 . .
[7,] . . . . . . . . 6.480741 .
[8,] . . . . . . . . . 7
dtCMatrix
Synopsis
- Description: triangular column-oriented numeric sparse matrix.
- Constructor\
new("dtCMatrix", ...) \Matrix(*, sparse = TRUE) \sparseMatrix(*, triangular=TRUE)
- Coercion\
as(*, "triangularMatrix") \as(*, "dtCMatrix")
C++ Code
// [[Rcpp::export]]
sp_mat symmatl_(sp_mat X) {
return symmatl(X);
}
R Code
R> dtC <- new("dtCMatrix", Dim = c(5L, 5L), uplo = "L",
x = c(10, 1, 3, 10, 1, 10, 1, 10, 10),
i = c(0L, 2L, 4L, 1L, 3L,2L, 4L, 3L, 4L),
p = c(0L, 3L, 5L, 7:9))
R> symmatl_(dtC)
5 x 5 sparse Matrix of class "dtCMatrix"
[1,] 10 . 1 . 3
[2,] . 10 . 1 .
[3,] 1 . 10 . 1
[4,] . 1 . 10 .
[5,] 3 . 1 . 10
dsCMatrix
Synopsis
- Description: symmetric column-oriented numeric sparse matrix.
- Constructor\
new("dsCMatrix", ...) \Matrix(*, sparse = TRUE) \sparseMatrix(*, symmetric = TRUE)
- Coercion\
as(*, "symmetricMatrix")\as(*, "dsCMatrix")
C++ Code
// [[Rcpp::export]]
sp_mat trimatu_(sp_mat X) {
return trimatu(X);
}
R Code
R> i <- c(1,3:8)
R> j <- c(2,9,6:10)
R> x <- 7 * (1:7)
R> dsC <- sparseMatrix(i, j, x = x, symmetric = TRUE)
R> trimatu_(dsC)
10 x 10 sparse Matrix of class "dgCMatrix"
[1,] . 7 . . . . . . . .
[2,] . . . . . . . . . .
[3,] . . . . . . . . 14 .
[4,] . . . . . 21 . . . .
[5,] . . . . . . 28 . . .
[6,] . . . . . . . 35 . .
[7,] . . . . . . . . 42 .
[8,] . . . . . . . . . 49
[9,] . . . . . . . . . .
[10,] . . . . . . . . . .
dgTMatrix
Synopsis
- Description: general numeric sparse matrix in triplet form.
- Constructor\
new("dgTMatrix", ...) \sparseMatrix(*, giveCsparse=FALSE) \spMatrix()
- Coercion\
as(*, "TsparseMatrix")\as(*, "dgTMatrix")
C++ Code
// [[Rcpp::export]]
sp_mat multiply(sp_mat A, sp_mat B) {
return A * B;
}
// [[Rcpp::export]]
sp_mat trans_(sp_mat X) {
return trans(X);
}
// [[Rcpp::export]]
int trace_(sp_mat X) {
return trace(X);
}
R Code
R> dgT <- new("dgTMatrix",
i = c(1L,1L,0L,3L,3L),
j = c(2L,2L,4L,0L,0L),
x=10*1:5, Dim=4:5)
R> dgT_t <- trans_(dgT)
R> prod <- multiply(dgT, dgT_t)
R> trace_(prod)
[1] 9900
dtTMatrix
Synopsis
- Description: triangular numeric sparse matrix in triplet form.
- Constructor \
new("dtTMatrix", ...) \code{sparseMatrix(*, triangular=TRUE, giveCsparse=FALSE)
- Coercion\
as(*, "triangularMatrix")\as(*, "dtTMatrix")\
C++ Code
// [[Rcpp::export]]
sp_mat diag_ones(sp_mat X) {
X.diag().ones();
return X;
}
R Code
R> dtT <- new("dtTMatrix", x= c(3,7),
i= 0:1, j=3:2, Dim= as.integer(c(4,4)))
R> diag_ones(dtT)
4 x 4 sparse Matrix of class "dgCMatrix"
[1,] 1 . . 3
[2,] . 1 7 .
[3,] . . 1 .
[4,] . . . 1
dsTMatrix
Synopsis
- Description: symmetric numeric sparse matrix in triplet form.
- Constructor \
new("dsTMatrix", ...) \sparseMatrix(*, symmetric=TRUE, giveCsparse=FALSE)
- Coercion\
as(*, "symmetricMatrix")\as(*, "dsTMatrix")\
C++ Code
// [[Rcpp::export]]
int trace_(sp_mat X) {
return trace(X);
}
R Code
R> mm <- Matrix(toeplitz(c(10, 0, 1, 0, 3)),
sparse = TRUE)
R> mT <- as(mm, "dgTMatrix")
R> dsT <- as(mT, "symmetricMatrix")
R> trace_(dsT)
[1] 50
dgRMatrix
Synopsis
- Description: general row-oriented numeric sparse matrix.
- Constructor\
new("dgRMatrix", ...)
- Coercion\
as(*, "RsparseMatrix")\as(*, "dgRatrix") \
C++ Code
// [[Rcpp::export]]
sp_mat square_(sp_mat X) {
return square(X);
}
R Code
R> dgR <- new("dgRMatrix", j=c(0L,2L,1L,3L),
p=c(0L,2L,3L,3L,4L),
x=c(3,1,2,1),
Dim=rep(4L,2))
R> square_(dgR)
4 x 4 sparse Matrix of class "dgCMatrix"
[1,] 9 . 1 .
[2,] . 4 . .
[3,] . . . .
[4,] . . . 1
dtRMatrix
Synopsis
- Description: triangular row-oriented numeric sparse matrix.
- Constructor\
new("dtRMatrix", ...) \
C++ Code
// [[Rcpp::export]]
sp_mat repmat_(sp_mat X, int i, int j) {
return repmat(X, i, j);
}
R Code
R> dtR <- new("dtRMatrix", Dim = c(2L,2L),
x = c(5, 1:2), p = c(0L,2:3), j= c(0:1,1L))
R> repmat_(dtR, 2, 2)
4 x 4 sparse Matrix of class "dgCMatrix"
[1,] 5 1 5 1
[2,] . 2 . 2
[3,] 5 1 5 1
[4,] . 2 . 2
dsRMatrix
Synopsis
- Description: symmetric row-oriented numeric sparse matrix.
- Constructor \
new("dsRMatrix", ...)
- Coercion \
as("dsCMatrix", "dsRMatrix")
C++ Code
// [[Rcpp::export]]
sp_mat sign_(sp_mat X) {
return sign(X);
}
R Code
R> dsR <- new("dsRMatrix", Dim = c(2L,2L),
x = c(-3,1), j = c(1L,1L), p = 0:2)
R> sign_(dsR)
2 x 2 sparse Matrix of class "dgCMatrix"
[1,] . -1
[2,] -1 1
indMatrix
Synopsis
- Description: index matrix.
- Constructor \
- new("indMatrix", ...)\
- Coercion \
as(*, "indMatrix")\
C++ Code
// [[Rcpp::export]]
sp_mat multiply(sp_mat A, sp_mat B) {
return A * B;
}
R Code
R> ind <- as(2:4, "indMatrix")
R> dgT <- new("dgTMatrix",
i = c(1L,1L,0L,3L,3L),
j = c(2L,2L,4L,0L,0L),
x=10*1:5, Dim=4:5)
R> multiply(ind, dgT)
3 x 5 sparse Matrix of class "dgCMatrix"
[1,] . . 30 . .
[2,] . . . . .
[3,] 90 . . . .
pMatrix
Synopsis
- Description: permutation matrix.
- Constructor\
new("pMatrix", ...)
- Coercion \
as(*, "pMatrix")
C++ Code
// [[Rcpp::export]]
sp_mat multiply(sp_mat A, sp_mat B) {
return A * B;
}
R Code
R> pM <- as(c(2,3,1,4), "pMatrix")
R> dgT <- new("dgTMatrix",
i = c(1L,1L,0L,3L,3L),
j = c(2L,2L,4L,0L,0L),
x=10*1:5, Dim=4:5)
R> multiply(pM, dgT)
4 x 5 sparse Matrix of class "dgCMatrix"
[1,] . . 30 . .
[2,] . . . . .
[3,] . . . . 30
[4,] 90 . . . .
ddiMatrix
Synopsis
- Description: numeric diagonal Matrix.
- Constructor\
new("ddiMatrix", ...)\Diagonal(*)\
C++ Code
// [[Rcpp::export]]
sp_mat multiply(sp_mat A, sp_mat B) {
return A * B;
}
R Code
R> ddi <- Diagonal(4)
R> dgR <- new("dgRMatrix", j=c(0L,2L,1L,3L),
p=c(0L,2L,3L,3L,4L),
x=c(3,1,2,1),
Dim=rep(4L,2))
R> multiply(ddi, dgR)
4 x 4 sparse Matrix of class "dgCMatrix"
[1,] 3 . 1 .
[2,] . 2 . .
[3,] . . . .
[4,] . . . 1
RcppCore/RcppArmadillo documentation built on April 12, 2024, 3:26 p.m.
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library(RcppArmadillo) library(Matrix)
\setcounter{tocdepth}{2} \tableofcontents
Introduction
The documentation is intended for the convenience of RcppArmadillo sparse matrix users based on integration of the documentation of library Matrix \citep{CRAN:Matrix} and Armadillo \citep{Sanderson:2010:Armadillo,Sanderson+Curtin:2016}.
There are 31 types of sparse matrices in the Matrix
package that can be used directly. But for now, only 12 of them are supported in RcppArmadillo:
dgCMatrix, dtCMatrix, dsCMatrix, dgTMatrix, dtTMatrix, dsTMatrix, dgRMatrix,
dtRMatrix, dsRMatrix, indMatrix, pMatrix, ddiMatrix.
In the Armadillo library, sparse matrix content is
currently stored as
CSC
format. Such kind of format is quite similar to numeric column-oriented sparse matrix in the library
Matrix (including dgCMatrix, dtCMatrix and
dsCMatrix). When a sparse matrix from the package
Matrix is passed through the
RcppArmadillo) package
\citep{Eddelbuettel+Sanderson:2014:RcppArmadillo,CRAN:RcppArmadillo}, it will be converted or mapped to
CSC format, then undertaken operations on, and finally ouput as a dgCMatrix in R.
In what follows, we will always assume this common header:
#include <RcppArmadillo.h> // [[Rcpp::depends(RcppArmadillo)]] using namespace Rcpp; using namespace arma;
but not generally show it.
Sparse Matrix
dgCMatrix
Synopsis
- Description: general column-oriented numeric sparse matrix.
- Constructor\
new("dgCMatrix", ...)\Matrix(*, sparse = TRUE)\sparseMatrix()
- Coercion\
as(*, "CsparseMatrix")\as(*, "dgCMatrix")\
C++ Code
// [[Rcpp::export]] sp_mat sqrt_(sp_mat X) { return sqrt(X); }
R Code
R> i <- c(1,3:8) R> j <- c(2,9,6:10) R> x <- 7 * (1:7) R> A <- sparseMatrix(i, j, x = x) R> sqrt_(A) 8 x 10 sparse Matrix of class "dgCMatrix" [1,] . 2.645751 . . . . . . . . [2,] . . . . . . . . . . [3,] . . . . . . . . 3.741657 . [4,] . . . . . 4.582576 . . . . [5,] . . . . . . 5.291503 . . . [6,] . . . . . . . 5.91608 . . [7,] . . . . . . . . 6.480741 . [8,] . . . . . . . . . 7
dtCMatrix
Synopsis
- Description: triangular column-oriented numeric sparse matrix.
- Constructor\
new("dtCMatrix", ...)\Matrix(*, sparse = TRUE)\sparseMatrix(*, triangular=TRUE)
- Coercion\
as(*, "triangularMatrix")\as(*, "dtCMatrix")
C++ Code
// [[Rcpp::export]] sp_mat symmatl_(sp_mat X) { return symmatl(X); }
R Code
R> dtC <- new("dtCMatrix", Dim = c(5L, 5L), uplo = "L", x = c(10, 1, 3, 10, 1, 10, 1, 10, 10), i = c(0L, 2L, 4L, 1L, 3L,2L, 4L, 3L, 4L), p = c(0L, 3L, 5L, 7:9)) R> symmatl_(dtC) 5 x 5 sparse Matrix of class "dtCMatrix" [1,] 10 . 1 . 3 [2,] . 10 . 1 . [3,] 1 . 10 . 1 [4,] . 1 . 10 . [5,] 3 . 1 . 10
dsCMatrix
Synopsis
- Description: symmetric column-oriented numeric sparse matrix.
- Constructor\
new("dsCMatrix", ...)\Matrix(*, sparse = TRUE)\sparseMatrix(*, symmetric = TRUE)
- Coercion\
as(*, "symmetricMatrix")\as(*, "dsCMatrix")
C++ Code
// [[Rcpp::export]] sp_mat trimatu_(sp_mat X) { return trimatu(X); }
R Code
R> i <- c(1,3:8) R> j <- c(2,9,6:10) R> x <- 7 * (1:7) R> dsC <- sparseMatrix(i, j, x = x, symmetric = TRUE) R> trimatu_(dsC) 10 x 10 sparse Matrix of class "dgCMatrix" [1,] . 7 . . . . . . . . [2,] . . . . . . . . . . [3,] . . . . . . . . 14 . [4,] . . . . . 21 . . . . [5,] . . . . . . 28 . . . [6,] . . . . . . . 35 . . [7,] . . . . . . . . 42 . [8,] . . . . . . . . . 49 [9,] . . . . . . . . . . [10,] . . . . . . . . . .
dgTMatrix
Synopsis
- Description: general numeric sparse matrix in triplet form.
- Constructor\
new("dgTMatrix", ...)\sparseMatrix(*, giveCsparse=FALSE)\spMatrix()
- Coercion\
as(*, "TsparseMatrix")\as(*, "dgTMatrix")
C++ Code
// [[Rcpp::export]] sp_mat multiply(sp_mat A, sp_mat B) { return A * B; } // [[Rcpp::export]] sp_mat trans_(sp_mat X) { return trans(X); } // [[Rcpp::export]] int trace_(sp_mat X) { return trace(X); }
R Code
R> dgT <- new("dgTMatrix", i = c(1L,1L,0L,3L,3L), j = c(2L,2L,4L,0L,0L), x=10*1:5, Dim=4:5) R> dgT_t <- trans_(dgT) R> prod <- multiply(dgT, dgT_t) R> trace_(prod) [1] 9900
dtTMatrix
Synopsis
- Description: triangular numeric sparse matrix in triplet form.
- Constructor \
new("dtTMatrix", ...)\code{sparseMatrix(*, triangular=TRUE, giveCsparse=FALSE)
- Coercion\
as(*, "triangularMatrix")\as(*, "dtTMatrix")\
C++ Code
// [[Rcpp::export]] sp_mat diag_ones(sp_mat X) { X.diag().ones(); return X; }
R Code
R> dtT <- new("dtTMatrix", x= c(3,7), i= 0:1, j=3:2, Dim= as.integer(c(4,4))) R> diag_ones(dtT) 4 x 4 sparse Matrix of class "dgCMatrix" [1,] 1 . . 3 [2,] . 1 7 . [3,] . . 1 . [4,] . . . 1
dsTMatrix
Synopsis
- Description: symmetric numeric sparse matrix in triplet form.
- Constructor \
new("dsTMatrix", ...)\sparseMatrix(*, symmetric=TRUE, giveCsparse=FALSE)
- Coercion\
as(*, "symmetricMatrix")\as(*, "dsTMatrix")\
C++ Code
// [[Rcpp::export]] int trace_(sp_mat X) { return trace(X); }
R Code
R> mm <- Matrix(toeplitz(c(10, 0, 1, 0, 3)), sparse = TRUE) R> mT <- as(mm, "dgTMatrix") R> dsT <- as(mT, "symmetricMatrix") R> trace_(dsT) [1] 50
dgRMatrix
Synopsis
- Description: general row-oriented numeric sparse matrix.
- Constructor\
new("dgRMatrix", ...)
- Coercion\
as(*, "RsparseMatrix")\as(*, "dgRatrix")\
C++ Code
// [[Rcpp::export]] sp_mat square_(sp_mat X) { return square(X); }
R Code
R> dgR <- new("dgRMatrix", j=c(0L,2L,1L,3L), p=c(0L,2L,3L,3L,4L), x=c(3,1,2,1), Dim=rep(4L,2)) R> square_(dgR) 4 x 4 sparse Matrix of class "dgCMatrix" [1,] 9 . 1 . [2,] . 4 . . [3,] . . . . [4,] . . . 1
dtRMatrix
Synopsis
- Description: triangular row-oriented numeric sparse matrix.
- Constructor\
new("dtRMatrix", ...)\
C++ Code
// [[Rcpp::export]] sp_mat repmat_(sp_mat X, int i, int j) { return repmat(X, i, j); }
R Code
R> dtR <- new("dtRMatrix", Dim = c(2L,2L), x = c(5, 1:2), p = c(0L,2:3), j= c(0:1,1L)) R> repmat_(dtR, 2, 2) 4 x 4 sparse Matrix of class "dgCMatrix" [1,] 5 1 5 1 [2,] . 2 . 2 [3,] 5 1 5 1 [4,] . 2 . 2
dsRMatrix
Synopsis
- Description: symmetric row-oriented numeric sparse matrix.
- Constructor \
new("dsRMatrix", ...)
- Coercion \
as("dsCMatrix", "dsRMatrix")
C++ Code
// [[Rcpp::export]] sp_mat sign_(sp_mat X) { return sign(X); }
R Code
R> dsR <- new("dsRMatrix", Dim = c(2L,2L), x = c(-3,1), j = c(1L,1L), p = 0:2) R> sign_(dsR) 2 x 2 sparse Matrix of class "dgCMatrix" [1,] . -1 [2,] -1 1
indMatrix
Synopsis
- Description: index matrix.
- Constructor \
- new("indMatrix", ...)\
- Coercion \
as(*, "indMatrix")\
C++ Code
// [[Rcpp::export]] sp_mat multiply(sp_mat A, sp_mat B) { return A * B; }
R Code
R> ind <- as(2:4, "indMatrix") R> dgT <- new("dgTMatrix", i = c(1L,1L,0L,3L,3L), j = c(2L,2L,4L,0L,0L), x=10*1:5, Dim=4:5) R> multiply(ind, dgT) 3 x 5 sparse Matrix of class "dgCMatrix" [1,] . . 30 . . [2,] . . . . . [3,] 90 . . . .
pMatrix
Synopsis
- Description: permutation matrix.
- Constructor\
new("pMatrix", ...)
- Coercion \
as(*, "pMatrix")
C++ Code
// [[Rcpp::export]] sp_mat multiply(sp_mat A, sp_mat B) { return A * B; }
R Code
R> pM <- as(c(2,3,1,4), "pMatrix") R> dgT <- new("dgTMatrix", i = c(1L,1L,0L,3L,3L), j = c(2L,2L,4L,0L,0L), x=10*1:5, Dim=4:5) R> multiply(pM, dgT) 4 x 5 sparse Matrix of class "dgCMatrix" [1,] . . 30 . . [2,] . . . . . [3,] . . . . 30 [4,] 90 . . . .
ddiMatrix
Synopsis
- Description: numeric diagonal Matrix.
- Constructor\
new("ddiMatrix", ...)\Diagonal(*)\
C++ Code
// [[Rcpp::export]] sp_mat multiply(sp_mat A, sp_mat B) { return A * B; }
R Code
R> ddi <- Diagonal(4) R> dgR <- new("dgRMatrix", j=c(0L,2L,1L,3L), p=c(0L,2L,3L,3L,4L), x=c(3,1,2,1), Dim=rep(4L,2)) R> multiply(ddi, dgR) 4 x 4 sparse Matrix of class "dgCMatrix" [1,] 3 . 1 . [2,] . 2 . . [3,] . . . . [4,] . . . 1
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