Matrix (version 1.4-1)

# sparseMatrix: General Sparse Matrix Construction from Nonzero Entries

## Description

User friendly construction of a compressed, column-oriented, sparse matrix, inheriting from `class` `'>CsparseMatrix` (or `'>TsparseMatrix` if `giveCsparse` is false), from locations (and values) of its non-zero entries.

This is the recommended user interface rather than direct `new("***Matrix", ....)` calls.

## Usage

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

## Arguments

i,j

integer vectors of the same length specifying the locations (row and column indices) of the non-zero (or non-`TRUE`) entries of the matrix. Note that for repeated pairs \((i_k,j_k)\), when `x` is not missing, the corresponding \(x_k\) are added, in consistency with the definition of the `"'>TsparseMatrix"` class, unless `use.last.ij` is true, in which case only the last of the corresponding \((i_k, j_k, x_k)\) triplet is used.

p

numeric (integer valued) 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` or `p` must be missing.

x

optional values of the matrix entries. If specified, must be of the same length as `i` / `j`, or of length one where it will be recycled to full length. If missing, the resulting matrix will be a 0/1 pattern matrix, i.e., extending class `'>nsparseMatrix`.

dims

optional, non-negative, integer, dimensions vector of length 2. Defaults to `c(max(i), max(j))`.

dimnames

optional list of `dimnames`; if not specified, none, i.e., `NULL` ones, are used.

symmetric

logical indicating if the resulting matrix should be symmetric. In that case, only the lower or upper triangle needs to be specified via \((i/j/p)\).

triangular

logical indicating if the resulting matrix should be triangular. In that case, the lower or upper triangle needs to be specified via \((i/j/p)\).

index1

logical scalar. If `TRUE`, the default, the index vectors `i` and/or `j` are 1-based, as is the convention in R. That is, counting of rows and columns starts at 1. If `FALSE` the index vectors are 0-based so counting of rows and columns starts at 0; this corresponds to the internal representation.

repr

`character` string, one of `"C"`, `"T"`, or `"R"`, specifying the sparse representation to be used for the result, i.e., one from the super classes `'>CsparseMatrix`, `'>TsparseMatrix`, or `'>RsparseMatrix`.

giveCsparse

(deprecated, replaced with `repr`): logical indicating if the result should be a `'>CsparseMatrix` or a `'>TsparseMatrix`, where the default was `TRUE`, and now is determined from `repr`; very often Csparse matrices are more efficient subsequently, but not always.

check

logical indicating if a validity check is performed; do not set to `FALSE` unless you know what you're doing!

use.last.ij

logical indicating if in the case of repeated, i.e., duplicated pairs \((i_k, j_k)\) only the last one should be used. The default, `FALSE`, corresponds to the `"'>TsparseMatrix"` definition.

## Value

A sparse matrix, by default (from `repr = "C"`) in compressed, column-oriented form, as an R object inheriting from both `'>CsparseMatrix` and `'>generalMatrix`.

## 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
```# NOT RUN {
## 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"))) {
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))
}
# }
# NOT RUN {
<!-- % if -->
# }
```

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