Diagonal Create Diagonal Matrix Object

Description

Create a diagonal matrix object, i.e., an object inheriting from diagonalMatrix (or a “standard” CsparseMatrix diagonal matrix in cases that is prefered).

Usage

Diagonal(n, x = NULL)

   .symDiagonal(n, x = rep.int(1,n), uplo = "U",   kind)
    .trDiagonal(n, x = 1,            uplo = "U", unitri=TRUE, kind)
.sparseDiagonal(n, x = 1,            uplo = "U",
                shape = if(missing(cols)) "t" else "g",
	        unitri, kind, cols = if(n) 0:(n - 1L) else integer(0))

Arguments

n	integer specifying the dimension of the (square) matrix. If missing, length(x) is used.
x	numeric or logical; if missing, a unit diagonal n x n matrix is created.
uplo	for .symDiagonal (.trDiagonal), the resulting sparse symmetricMatrix (or triangularMatrix) will have slot uplo set from this argument, either "U" or "L". Only rarely will it make sense to change this from the default.
shape	string of 1 character, one of c("t","s","g"), to choose a triangular, symmetric or general result matrix.
unitri	optional logical indicating if a triangular result should be “unit-triangular”, i.e., with diag = "U" slot, if possible. The default, missing, is the same as TRUE.
kind	string of 1 character, one of c("d","l","n"), to choose the storage mode of the result, from classes dsparseMatrix, lsparseMatrix, or nsparseMatrix, respectively.
cols	integer vector with values from 0:(n-1), denoting the columns to subselect conceptually, i.e., get the equivalent of Diagonal(n,*)[, cols + 1].

Value

Diagonal() returns an object of class ddiMatrix or ldiMatrix (with “superclass” diagonalMatrix).

.symDiagonal() returns an object of class dsCMatrix or lsCMatrix, i.e., a sparse symmetric matrix. Analogously, .triDiagonal gives a sparse triangularMatrix. This can be more efficient than Diagonal(n) when the result is combined with further symmetric (sparse) matrices, e.g., in kronecker, however not for matrix multiplications where Diagonal() is clearly preferred.

.sparseDiagonal(), the workhorse of .symDiagonal and .trDiagonal returns a CsparseMatrix (the resulting class depending on shape and kind) representation of Diagonal(n), or, when cols are specified, of Diagonal(n)[, cols+1].

Author(s)

Martin Maechler

See Also

the generic function diag for extraction of the diagonal from a matrix works for all “Matrices”.

bandSparse constructs a banded sparse matrix from its non-zero sub-/super - diagonals. band(A) returns a band matrix containing some sub-/super - diagonals of A.

Matrix for general matrix construction; further, class diagonalMatrix.

Examples

Diagonal(3)
Diagonal(x = 10^(3:1))
Diagonal(x = (1:4) >= 2)#-> "ldiMatrix"

## Use Diagonal() + kronecker() for "repeated-block" matrices:
M1 <- Matrix(0+0:5, 2,3)
(M <- kronecker(Diagonal(3), M1))

(S <- crossprod(Matrix(rbinom(60, size=1, prob=0.1), 10,6)))
(SI <- S + 10*.symDiagonal(6)) # sparse symmetric still
stopifnot(is(SI, "dsCMatrix"))
(I4 <- .sparseDiagonal(4, shape="t"))# now (2012-10) unitriangular
stopifnot(I4@diag == "U", all(I4 == diag(4)))