Matrix (version 1.5-3)

# sparseMatrix: 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)```

## 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`.

## 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.

`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

Run this code
``````## 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(require(SparseM) && packageVersion("SparseM") >= 0.87 &&
nzchar(dfil <- system.file("extdata", "rua_32_ax.rua", package = "SparseM"))) {