R: Class "diagonalMatrix" of Diagonal Matrices

diagonalMatrix-class {Matrix} | R Documentation

## Class "diagonalMatrix" of Diagonal Matrices

### Description

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`:

  code"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 `NA`s, we implicitly use 0 / x = 0, hence differing from traditional R arithmetic (where 0/0 |-> 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

    # an unusual way to construct a band matrix:
    rbind2(cbind2(I5, D5),
           cbind2(D5, I5))

[Package Matrix version 1.2-12 Index]