diagonalMatrix-class | R Documentation |

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

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

`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.

Class `"sparseMatrix"`

, directly.

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 \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.

`Diagonal()`

as constructor of these matrices, and
`isDiagonal`

.
`ddiMatrix`

and `ldiMatrix`

are
“actual” classes extending `"diagonalMatrix"`

.

```
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))
```

Matrix documentation built on Nov. 14, 2023, 5:06 p.m.

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