Symmetric Dense (Packed or Unpacked) Numeric Matrices

The "dsyMatrix" class is the class of symmetric, dense matrices in non-packed storage and
"dspMatrix" is the class of symmetric dense matrices in packed storage, see pack(). Only the upper triangle or the lower triangle is stored.

Objects from the Class

Objects can be created by calls of the form new("dsyMatrix", ...) or new("dspMatrix", ...), respectively.

Slots

uplo:: Object of class "character". Must be either "U", for upper triangular, and "L", for lower triangular.
x:: Object of class "numeric". The numeric values that constitute the matrix, stored in column-major order.
Dim,Dimnames:: The dimension (a length-2 "integer") and corresponding names (or NULL), see the Matrix.
factors:: Object of class "list". A named list of factorizations that have been computed for the matrix.

Extends

"dsyMatrix" extends class "dgeMatrix", directly, whereas
"dspMatrix" extends class "ddenseMatrix", directly.

Both extend class "symmetricMatrix", directly, and class "Matrix" and others, indirectly, use showClass("dsyMatrix"), e.g., for details.

Methods

norm: signature(x = "dspMatrix", type = "character"), or x = "dsyMatrix" or type = "missing": Computes the matrix norm of the desired type, see, norm.
rcond: signature(x = "dspMatrix", type = "character"), or x = "dsyMatrix" or type = "missing": Computes the reciprocal condition number, rcond().
solve: signature(a = "dspMatrix", b = "...."), and
solve: signature(a = "dsyMatrix", b = "...."): x <- solve(a,b) solves \(A x = b\) for \(x\); see solve-methods.
t: signature(x = "dsyMatrix"): Transpose; swaps from upper triangular to lower triangular storage, i.e., the uplo slot from "U" to "L" or vice versa, the same as for all symmetric matrices.

Examples

## Only upper triangular part matters (when uplo == "U" as per default)
(sy2 <- new("dsyMatrix", Dim = as.integer(c(2,2)), x = c(14, NA,32,77)))
#> 2 x 2 Matrix of class "dsyMatrix"
#>      [,1] [,2]
#> [1,]   14   32
#> [2,]   32   77
str(t(sy2)) # uplo = "L", and the lower tri. (i.e. NA is replaced).
#> Formal class 'dsyMatrix' [package "Matrix"] with 5 slots
#>   ..@ Dim     : int [1:2] 2 2
#>   ..@ Dimnames:List of 2
#>   .. ..$ : NULL
#>   .. ..$ : NULL
#>   ..@ x       : num [1:4] 14 32 NA 77
#>   ..@ uplo    : chr "L"
#>   ..@ factors : list()

chol(sy2) #-> "Cholesky" matrix
#> 2 x 2 Matrix of class "dtrMatrix"
#>      [,1]     [,2]    
#> [1,] 3.741657 8.552360
#> [2,]        . 1.963961
(sp2 <- pack(sy2)) # a "dspMatrix"
#> 2 x 2 Matrix of class "dspMatrix"
#>      [,1] [,2]
#> [1,]   14   32
#> [2,]   32   77

## Coercing to dpoMatrix gives invalid object:
sy3 <- new("dsyMatrix", Dim = as.integer(c(2,2)), x = c(14, -1, 2, -7))
try(as(sy3, "dpoMatrix")) # -> error: not positive definite
#> Error in asMethod(object) : 
#>   not a positive definite matrix (and positive semidefiniteness is not checked)

## 4x4 example
m <- matrix(0,4,4); m[upper.tri(m)] <- 1:6
(sym <- m+t(m)+diag(11:14, 4))
#>      [,1] [,2] [,3] [,4]
#> [1,]   11    1    2    4
#> [2,]    1   12    3    5
#> [3,]    2    3   13    6
#> [4,]    4    5    6   14
(S1 <- pack(sym))
#> 4 x 4 Matrix of class "dspMatrix"
#>      [,1] [,2] [,3] [,4]
#> [1,]   11    1    2    4
#> [2,]    1   12    3    5
#> [3,]    2    3   13    6
#> [4,]    4    5    6   14
(S2 <- t(S1))
#> 4 x 4 Matrix of class "dspMatrix"
#>      [,1] [,2] [,3] [,4]
#> [1,]   11    1    2    4
#> [2,]    1   12    3    5
#> [3,]    2    3   13    6
#> [4,]    4    5    6   14
stopifnot(all(S1 == S2)) # equal "seen as matrix", but differ internally :
str(S1)
#> Formal class 'dspMatrix' [package "Matrix"] with 5 slots
#>   ..@ uplo    : chr "U"
#>   ..@ Dim     : int [1:2] 4 4
#>   ..@ Dimnames:List of 2
#>   .. ..$ : NULL
#>   .. ..$ : NULL
#>   ..@ x       : num [1:10] 11 1 12 2 3 13 4 5 6 14
#>   ..@ factors : list()
S2@x
#>  [1] 11  1  2  4 12  3  5 13  6 14