R: isTriangular() and isDiagonal() Methods

isTriangular {Matrix}

R Documentation

isTriangular() and isDiagonal() Methods

Description

isTriangular(M) returns a logical indicating if M is a triangular matrix. Analogously, isDiagonal(M) is true iff M is a diagonal matrix.

Contrary to isSymmetric(), these two functions are generically from package Matrix, and hence also define methods for traditional (class "matrix") matrices.

By our definition, triangular, diagonal and symmetric matrices are all square, i.e. have the same number of rows and columns.

Usage

isDiagonal(object)

isTriangular(object, upper = NA, ...)

Arguments

`object`	any R object, typically a matrix (traditional or Matrix package).
`upper`	logical, one of `NA` (default), `FALSE`, or `TRUE` where the last two cases require a lower or upper triangular `object` to result in `TRUE`.
`...`	potentially further arguments for other methods.

Value

a (“scalar”) logical, TRUE or FALSE, never NA. For isTriangular(), if the result is TRUE, it may contain an attribute (see attributes "kind", either "L" or "U" indicating if it is a lower or upper triangular matrix.

Examples

isTriangular(Diagonal(4))
## is TRUE: a diagonal matrix is also (both upper and lower) triangular
(M <- Matrix(c(1,2,0,1), 2,2))
isTriangular(M) # TRUE (*and* of formal class "dtrMatrix")
isTriangular(as(M, "dgeMatrix")) # still triangular, even if not "formally"
isTriangular(crossprod(M)) # FALSE

isDiagonal(matrix(c(2,0,0,1), 2,2)) # TRUE