# Diagonal

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##### Create Diagonal Matrix Object

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

Keywords
algebra, array
##### 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 $n \times n$ 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].

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.

##### Aliases
• Diagonal
• .sparseDiagonal
• .symDiagonal
• .trDiagonal
##### Examples
# NOT RUN {
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)))
# }

Documentation reproduced from package Matrix, version 1.2-18, License: GPL (>= 2) | file LICENCE

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