Matrix (version 1.4-1)

band: Extract bands of a matrix

Description

Returns a new matrix formed by extracting the lower triangle (tril) or the upper triangle (triu) or a general band relative to the diagonal (band), and setting other elements to zero. The general forms of these functions include integer arguments to specify how many diagonal bands above or below the main diagonal are not set to zero.

Usage

band(x, k1, k2, ...)
tril(x, k = 0, ...)
triu(x, k = 0, ...)

Value

An object of an appropriate matrix class. The class of the value of

tril or triu inherits from

triangularMatrix when appropriate. Note that the result is of class sparseMatrix only if x is.

Arguments

x

a matrix-like object

k,k1,k2

integers specifying the diagonal bands that will not be set to zero. These are given relative to the main diagonal, which is k=0. A negative value of k indicates a diagonal below the main diagonal and a positive value indicates a diagonal above the main diagonal.

...

Optional arguments used by specific methods. (None used at present.)

Methods

x = "CsparseMatrix"

method for compressed, sparse, column-oriented matrices.

x = "TsparseMatrix"

method for sparse matrices in triplet format.

x = "RsparseMatrix"

method for compressed, sparse, row-oriented matrices.

x = "ddenseMatrix"

method for dense numeric matrices, including packed numeric matrices.

See Also

bandSparse for the construction of a banded sparse matrix directly from its non-zero diagonals.

Examples

## A random sparse matrix :
set.seed(7)
m <- matrix(0, 5, 5)
m[sample(length(m), size = 14)] <- rep(1:9, length=14)
(mm <- as(m, "CsparseMatrix"))

tril(mm)        # lower triangle
tril(mm, -1)    # strict lower triangle
triu(mm,  1)    # strict upper triangle
band(mm, -1, 2) # general band
(m5 <- Matrix(rnorm(25), nc = 5))
tril(m5)        # lower triangle
tril(m5, -1)    # strict lower triangle
triu(m5, 1)     # strict upper triangle
band(m5, -1, 2) # general band
(m65 <- Matrix(rnorm(30), nc = 5))  # not square
triu(m65)       # result not "dtrMatrix" unless square
(sm5 <- crossprod(m65)) # symmetric
   band(sm5, -1, 1)# "dsyMatrix": symmetric band preserves symmetry property
as(band(sm5, -1, 1), "sparseMatrix")# often preferable
(sm <- round(crossprod(triu(mm/2)))) # sparse symmetric ("dsC*")
band(sm, -1,1) # remains "dsC", *however*
band(sm, -2,1) # -> "dgC"



 ## this uses special methods
(x.x <- crossprod(mm))
tril(x.x)
xx <- tril(x.x) + triu(x.x, 1) ## the same as x.x (but stored differently):
txx <- t(as(xx, "symmetricMatrix"))
stopifnot(identical(triu(x.x), t(tril(x.x))),
	  identical(class(x.x), class(txx)),
	  identical(as(x.x, "generalMatrix"), as(txx, "generalMatrix")))