Class "diagonalMatrix" of Diagonal Matrices

Class "diagonalMatrix" is the virtual class of all diagonal matrices.

Objects from the Class

A virtual Class: No objects may be created from it.

Slots

diag:

character string, either "U" or "N", where "U" means ‘unit-diagonal’.

Dim:

matrix dimension, and

Dimnames:

the dimnames, a list, see the Matrix class description. Typically list(NULL,NULL) for diagonal matrices.

Extends

Class "sparseMatrix", directly.

Methods

These are just a subset of the signature for which defined methods. Currently, there are (too) many explicit methods defined in order to ensure efficient methods for diagonal matrices.

coerce

signature(from = "matrix", to = "diagonalMatrix"): ...

coerce

signature(from = "Matrix", to = "diagonalMatrix"): ...

coerce

signature(from = "diagonalMatrix", to = "generalMatrix"): ...

coerce

signature(from = "diagonalMatrix", to = "triangularMatrix"): ...

coerce

signature(from = "diagonalMatrix", to = "nMatrix"): ...

coerce

signature(from = "diagonalMatrix", to = "matrix"): ...

coerce

signature(from = "diagonalMatrix", to = "sparseVector"): ...

t

signature(x = "diagonalMatrix"): ...

and many more methods

solve

signature(a = "diagonalMatrix", b, ...): is trivially implemented, of course; see also solve-methods.

which

signature(x = "nMatrix"), semantically equivalent to base function which(x, arr.ind).

"Math"

signature(x = "diagonalMatrix"): all these group methods return a "diagonalMatrix", apart from cumsum() etc which return a vector also for base matrix.

*

signature(e1 = "ddiMatrix", e2="denseMatrix"): arithmetic and other operators from the Ops group have a few dozen explicit method definitions, in order to keep the results diagonal in many cases, including the following:

/

signature(e1 = "ddiMatrix", e2="denseMatrix"): the result is from class ddiMatrix which is typically very desirable. Note that when e2 contains off-diagonal zeros or NAs, we implicitly use \(0 / x = 0\), hence differing from traditional R arithmetic (where \(0 / 0 \mapsto \mbox{NaN}\)), in order to preserve sparsity.

summary

(object = "diagonalMatrix"): Returns an object of S3 class "diagSummary" which is the summary of the vector object@x plus a simple heading, and an appropriate print method.

See also

Diagonal() as constructor of these matrices, and isDiagonal. ddiMatrix and ldiMatrix are “actual” classes extending "diagonalMatrix".

Examples

I5 <- Diagonal(5)
D5 <- Diagonal(x = 10*(1:5))
## trivial (but explicitly defined) methods:
stopifnot(identical(crossprod(I5), I5),
          identical(tcrossprod(I5), I5),
          identical(crossprod(I5, D5), D5),
          identical(tcrossprod(D5, I5), D5),
          identical(solve(D5), solve(D5, I5)),
          all.equal(D5, solve(solve(D5)), tolerance = 1e-12)
          )
solve(D5)# efficient as is diagonal
#> 5 x 5 diagonal matrix of class "ddiMatrix"
#>      [,1] [,2] [,3]       [,4]  [,5]
#> [1,]  0.1    .          .     .    .
#> [2,]    . 0.05          .     .    .
#> [3,]    .    . 0.03333333     .    .
#> [4,]    .    .          . 0.025    .
#> [5,]    .    .          .     . 0.02

# an unusual way to construct a band matrix:
rbind2(cbind2(I5, D5),
       cbind2(D5, I5))
#> 10 x 10 sparse Matrix of class "dgCMatrix"
#>                                    
#>  [1,]  1  .  .  .  . 10  .  .  .  .
#>  [2,]  .  1  .  .  .  . 20  .  .  .
#>  [3,]  .  .  1  .  .  .  . 30  .  .
#>  [4,]  .  .  .  1  .  .  .  . 40  .
#>  [5,]  .  .  .  .  1  .  .  .  . 50
#>  [6,] 10  .  .  .  .  1  .  .  .  .
#>  [7,]  . 20  .  .  .  .  1  .  .  .
#>  [8,]  .  . 30  .  .  .  .  1  .  .
#>  [9,]  .  .  . 40  .  .  .  .  1  .
#> [10,]  .  .  .  . 50  .  .  .  .  1