Matrix (version 1.4-0)

# bandSparse: Construct Sparse Banded Matrix from (Sup-/Super-) Diagonals

## Description

Construct a sparse banded matrix by specifying its non-zero sup- and super-diagonals.

## Usage

bandSparse(n, m = n, k, diagonals, symmetric = FALSE,
repr = "C", giveCsparse = (repr == "C"))

## Arguments

n,m

the matrix dimension $$(n,m) = (nrow, ncol)$$.

k

integer vector of “diagonal numbers”, with identical meaning as in band(*, k), i.e., relative to the main diagonal, which is k=0.

diagonals

optional list of sub-/super- diagonals; if missing, the result will be a pattern matrix, i.e., inheriting from class '>nMatrix.

diagonals can also be $$n' \times d$$ matrix, where d <- length(k) and $$n' >= min(n,m)$$. In that case, the sub-/super- diagonals are taken from the columns of diagonals, where only the first several rows will be used (typically) for off-diagonals.

symmetric

logical; if true the result will be symmetric (inheriting from class '>symmetricMatrix) and only the upper or lower triangle must be specified (via k and diagonals).

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.

## Value

a sparse matrix (of class '>CsparseMatrix) of dimension $$n \times m$$ with diagonal “bands” as specified.

band, for extraction of matrix bands; bdiag, diag, sparseMatrix, Matrix.

## Examples

Run this code
# NOT RUN {
diags <- list(1:30, 10*(1:20), 100*(1:20))
s1 <- bandSparse(13, k = -c(0:2, 6), diag = c(diags, diags), symm=TRUE)
s1
s2 <- bandSparse(13, k =  c(0:2, 6), diag = c(diags, diags), symm=TRUE)
stopifnot(identical(s1, t(s2)), is(s1,"dsCMatrix"))

## a pattern Matrix of *full* (sub-)diagonals:
bk <- c(0:4, 7,9)
(s3 <- bandSparse(30, k = bk, symm = TRUE))

## If you want a pattern matrix, but with "sparse"-diagonals,
## you currently need to go via logical sparse:
lLis <- lapply(list(rpois(20, 2), rpois(20,1), rpois(20,3))[c(1:3,2:3,3:2)],
as.logical)
(s4 <- bandSparse(20, k = bk, symm = TRUE, diag = lLis))
(s4. <- as(drop0(s4), "nsparseMatrix"))

n <- 1e4
bk <- c(0:5, 7,11)
bMat <- matrix(1:8, n, 8, byrow=TRUE)
bLis <- as.data.frame(bMat)
B  <- bandSparse(n, k = bk, diag = bLis)
Bs <- bandSparse(n, k = bk, diag = bLis, symmetric=TRUE)
B [1:15, 1:30]
Bs[1:15, 1:30]
## can use a list *or* a matrix for specifying the diagonals:
stopifnot(identical(B,  bandSparse(n, k = bk, diag = bMat)),
identical(Bs, bandSparse(n, k = bk, diag = bMat, symmetric=TRUE))
, inherits(B, "dtCMatrix") # triangular!
)
# }


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