Triangular, dense, numeric matrices

The "dtrMatrix" class is the class of triangular, dense, numeric matrices in nonpacked storage. The "dtpMatrix" class is the same except in packed storage, see pack().

Objects from the Class

Objects can be created by calls of the form new("dtrMatrix", ...).

Slots

uplo:

Object of class "character". Must be either "U", for upper triangular, and "L", for lower triangular.

diag:

Object of class "character". Must be either "U", for unit triangular (diagonal is all ones), or "N"; see triangularMatrix.

x:

Object of class "numeric". The numeric values that constitute the matrix, stored in column-major order.

Dim:

Object of class "integer". The dimensions of the matrix which must be a two-element vector of non-negative integers.

Extends

Class "ddenseMatrix", directly. Class "triangularMatrix", directly. Class "Matrix" and others, by class "ddenseMatrix".

Methods

Among others (such as matrix products, e.g. ?crossprod-methods),

norm

signature(x = "dtrMatrix", type = "character"): ..

rcond

signature(x = "dtrMatrix", norm = "character"): ..

solve

signature(a = "dtrMatrix", b = "...."): efficiently use a “forwardsolve” or backsolve for a lower or upper triangular matrix, respectively, see also solve-methods.

+, -, *, ..., ==, >=, ...

all the Ops group methods are available. When applied to two triangular matrices, these return a triangular matrix when easily possible.

Examples


(m <- rbind(2:3, 0:-1))
#>      [,1] [,2]
#> [1,]    2    3
#> [2,]    0   -1
(M <- as(m, "generalMatrix"))
#> 2 x 2 Matrix of class "dgeMatrix"
#>      [,1] [,2]
#> [1,]    2    3
#> [2,]    0   -1

(T <- as(M, "triangularMatrix")) # formally upper triangular
#> 2 x 2 Matrix of class "dtrMatrix"
#>      [,1] [,2]
#> [1,]    2    3
#> [2,]    .   -1
(T2 <- as(t(M), "triangularMatrix"))
#> 2 x 2 Matrix of class "dtrMatrix"
#>      [,1] [,2]
#> [1,]    2    .
#> [2,]    3   -1
stopifnot(T@uplo == "U", T2@uplo == "L", identical(T2, t(T)))

m <- matrix(0,4,4); m[upper.tri(m)] <- 1:6
(t1 <- Matrix(m+diag(,4)))
#> 4 x 4 Matrix of class "dtrMatrix"
#>      [,1] [,2] [,3] [,4]
#> [1,]    1    1    2    4
#> [2,]    .    1    3    5
#> [3,]    .    .    1    6
#> [4,]    .    .    .    1
str(t1p <- pack(t1))
#> Formal class 'dtpMatrix' [package "Matrix"] with 5 slots
#>   ..@ uplo    : chr "U"
#>   ..@ Dim     : int [1:2] 4 4
#>   ..@ Dimnames:List of 2
#>   .. ..$ : NULL
#>   .. ..$ : NULL
#>   ..@ x       : num [1:10] 1 1 1 2 3 1 4 5 6 1
#>   ..@ diag    : chr "N"
(t1pu <- diagN2U(t1p))
#> 4 x 4 sparse Matrix of class "dtCMatrix" (unitriangular)
#>             
#> [1,] I 1 2 4
#> [2,] . I 3 5
#> [3,] . . I 6
#> [4,] . . . I
stopifnot(exprs = {
   inherits(t1 , "dtrMatrix"); validObject(t1)
   inherits(t1p, "dtpMatrix"); validObject(t1p)
   inherits(t1pu,"dtCMatrix"); validObject(t1pu)
   t1pu@x == 1:6
   all(t1pu == t1p)
   identical((t1pu - t1)@x, numeric())# sparse all-0
})