Matrix (version 1.4-1)

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"))

Value

a sparse matrix (of class

CsparseMatrix) of dimension \(n \times m\)

with diagonal “bands” as specified.

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.

See Also

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

Examples

diags <- list(1:30, 10*(1:20), 100*(1:20))
s1 <- bandSparse(13, k = -c(0:2, 6), diag = c(diags, diags[2]), symm=TRUE)
s1
s2 <- bandSparse(13, k =  c(0:2, 6), diag = c(diags, diags[2]), 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!
)