sparseMatrix {Matrix}

General Sparse Matrix Construction from Nonzero Entries

Description

User-friendly construction of sparse matrices (inheriting from virtual class CsparseMatrix, RsparseMatrix, or TsparseMatrix) from the positions and values of their nonzero entries.

This interface is recommended over direct construction via calls such as new("..[CRT]Matrix", ...).

Usage

sparseMatrix(i, j, p, x, dims, dimnames,
             symmetric = FALSE, triangular = FALSE, index1 = TRUE,
             repr = c("C", "R", "T"), giveCsparse,
             check = TRUE, use.last.ij = FALSE)

Arguments

i, j

integer vectors of equal length specifying the positions (row and column indices) of the nonzero (or non-TRUE) entries of the matrix. Note that, when x is non-missing, the x_k corresponding to repeated pairs (i_k,j_k) are added, for consistency with the definition of class TsparseMatrix, unless use.last.ij is TRUE, in which case only the last such x_k is used.

p

integer vector of pointers, one for each column (or row), to the initial (zero-based) index of elements in the column (or row). Exactly one of i, j, and p must be missing.

x

optional, typically nonzero values for the matrix entries. If specified, then the length must equal that of i (or j) or equal 1, in which case x is recycled as necessary. If missing, then the result is a nonzero pattern matrix, i.e., inheriting from class nsparseMatrix.

dims

optional length-2 integer vector of matrix dimensions. If missing, then !index1+c(max(i),max(j)) is used.

dimnames

optional list of dimnames; if missing, then NULL ones are used.

symmetric

logical indicating if the resulting matrix should be symmetric. In that case, (i,j,p) should specify only one triangle (upper or lower).

triangular

logical indicating if the resulting matrix should be triangular. In that case, (i,j,p) should specify only one triangle (upper or lower).

index1

logical. If TRUE (the default), then i and j are interpreted as 1-based indices, following the R convention. That is, counting of rows and columns starts at 1. If FALSE, then they are interpreted as 0-based indices.

repr

character string, one of "C", "R", and "T", specifying the representation of the sparse matrix result, i.e., specifying one of the virtual classes CsparseMatrix, RsparseMatrix, and TsparseMatrix.

giveCsparse

(deprecated, replaced by repr) logical indicating if the result should inherit from CsparseMatrix or TsparseMatrix. Note that operations involving CsparseMatrix are very often (but not always) more efficient.

check

logical indicating whether to check that the result is formally valid before returning. Do not set to FALSE unless you know what you are doing!

use.last.ij

logical indicating if, in the case of repeated (duplicated) pairs (i_k,j_k), only the last pair should be used. FALSE (the default) is consistent with the definiton of class TsparseMatrix.

Details

Exactly one of the arguments i, j and p must be missing.

In typical usage, p is missing, i and j are vectors of positive integers and x is a numeric vector. These three vectors, which must have the same length, form the triplet representation of the sparse matrix.

If i or j is missing then p must be a non-decreasing integer vector whose first element is zero. It provides the compressed, or “pointer” representation of the row or column indices, whichever is missing. The expanded form of p, rep(seq_along(dp),dp) where dp <- diff(p), is used as the (1-based) row or column indices.

You cannot set both singular and triangular to true; rather use Diagonal() (or its alternatives, see there).

The values of i, j, p and index1 are used to create 1-based index vectors i and j from which a TsparseMatrix is constructed, with numerical values given by x, if non-missing. Note that in that case, when some pairs (i_k,j_k) are repeated (aka “duplicated”), the corresponding x_k are added, in consistency with the definition of the TsparseMatrix class, unless use.last.ij is set to true.

By default, when repr = "C", the CsparseMatrix derived from this triplet form is returned, where repr = "R" now allows to directly get an RsparseMatrix and repr = "T" leaves the result as TsparseMatrix.

The reason for returning a CsparseMatrix object instead of the triplet format by default is that the compressed column form is easier to work with when performing matrix operations. In particular, if there are no zeros in x then a CsparseMatrix is a unique representation of the sparse matrix.

Value

A sparse matrix, by default in compressed sparse column format and (formally) without symmetric or triangular structure, i.e., by default inheriting from both CsparseMatrix and generalMatrix.

Note

You do need to use index1 = FALSE (or add + 1 to i and j) if you want use the 0-based i (and j) slots from existing sparse matrices.

See Also

Matrix(*, sparse=TRUE) for the constructor of such matrices from a dense matrix. That is easier in small sample, but much less efficient (or impossible) for large matrices, where something like sparseMatrix() is needed. Further bdiag and Diagonal for (block-)diagonal and bandSparse for banded sparse matrix constructors.

Random sparse matrices via rsparsematrix().

The standard R xtabs(*, sparse=TRUE), for sparse tables and sparse.model.matrix() for building sparse model matrices.

Consider CsparseMatrix and similar class definition help files.

Examples

## simple example
i <- c(1,3:8); j <- c(2,9,6:10); x <- 7 * (1:7)
(A <- sparseMatrix(i, j, x = x))                    ##  8 x 10 "dgCMatrix"
summary(A)
str(A) # note that *internally* 0-based row indices are used

(sA <- sparseMatrix(i, j, x = x, symmetric = TRUE)) ## 10 x 10 "dsCMatrix"
(tA <- sparseMatrix(i, j, x = x, triangular= TRUE)) ## 10 x 10 "dtCMatrix"
stopifnot( all(sA == tA + t(tA)) ,
           identical(sA, as(tA + t(tA), "symmetricMatrix")))

## dims can be larger than the maximum row or column indices
(AA <- sparseMatrix(c(1,3:8), c(2,9,6:10), x = 7 * (1:7), dims = c(10,20)))
summary(AA)

## i, j and x can be in an arbitrary order, as long as they are consistent
set.seed(1); (perm <- sample(1:7))
(A1 <- sparseMatrix(i[perm], j[perm], x = x[perm]))
stopifnot(identical(A, A1))

## The slots are 0-index based, so
try( sparseMatrix(i=A@i, p=A@p, x= seq_along(A@x)) )
## fails and you should say so: 1-indexing is FALSE:
     sparseMatrix(i=A@i, p=A@p, x= seq_along(A@x), index1 = FALSE)

## the (i,j) pairs can be repeated, in which case the x's are summed
(args <- data.frame(i = c(i, 1), j = c(j, 2), x = c(x, 2)))
(Aa <- do.call(sparseMatrix, args))
## explicitly ask for elimination of such duplicates, so
## that the last one is used:
(A. <- do.call(sparseMatrix, c(args, list(use.last.ij = TRUE))))
stopifnot(Aa[1,2] == 9, # 2+7 == 9
          A.[1,2] == 2) # 2 was *after* 7

## for a pattern matrix, of course there is no "summing":
(nA <- do.call(sparseMatrix, args[c("i","j")]))

dn <- list(LETTERS[1:3], letters[1:5])
## pointer vectors can be used, and the (i,x) slots are sorted if necessary:
m <- sparseMatrix(i = c(3,1, 3:2, 2:1), p= c(0:2, 4,4,6), x = 1:6, dimnames = dn)
m
str(m)
stopifnot(identical(dimnames(m), dn))

sparseMatrix(x = 2.72, i=1:3, j=2:4) # recycling x
sparseMatrix(x = TRUE, i=1:3, j=2:4) # recycling x, |--> "lgCMatrix"

## no 'x' --> patter*n* matrix:
(n <- sparseMatrix(i=1:6, j=rev(2:7)))# -> ngCMatrix

## an empty sparse matrix:
(e <- sparseMatrix(dims = c(4,6), i={}, j={}))

## a symmetric one:
(sy <- sparseMatrix(i= c(2,4,3:5), j= c(4,7:5,5), x = 1:5,
                    dims = c(7,7), symmetric=TRUE))
stopifnot(isSymmetric(sy),
          identical(sy, ## switch i <-> j {and transpose }
    t( sparseMatrix(j= c(2,4,3:5), i= c(4,7:5,5), x = 1:5,
                    dims = c(7,7), symmetric=TRUE))))

## rsparsematrix() calls sparseMatrix() :
M1 <- rsparsematrix(1000, 20, nnz = 200)
summary(M1)

## pointers example in converting from other sparse matrix representations.
if(requireNamespace("SparseM") &&
   packageVersion("SparseM") >= "0.87" &&
   nzchar(dfil <- system.file("extdata", "rua_32_ax.rua", package = "SparseM"))) {
  X <- SparseM::model.matrix(SparseM::read.matrix.hb(dfil))
  XX <- sparseMatrix(j = X@ja, p = X@ia - 1L, x = X@ra, dims = X@dimension)
  validObject(XX)

  ## Alternatively, and even more user friendly :
  X. <- as(X, "Matrix")  # or also
  X2 <- as(X, "sparseMatrix")
  stopifnot(identical(XX, X.), identical(X., X2))
}