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

bandSparse {Matrix}

R Documentation

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.

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!
)