Description Objects from the Class Slots Extends Methods See Also Examples

The `"dtpMatrix"`

class is the class of triangular,
dense, numeric matrices in packed storage. The `"dtrMatrix"`

class is the same except in nonpacked storage.

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

or by coercion from other classes of matrices.

`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. For a packed square matrix of dimension*d * d*,`length(x)`

is of length*d(d+1)/2*(also when`diag == "U"`

!).`Dim`

,`Dimnames`

:The dimension (a length-2

`"integer"`

) and corresponding names (or`NULL`

), inherited from the`Matrix`

, see there.

Class `"ddenseMatrix"`

, directly.
Class `"triangularMatrix"`

, directly.
Class `"dMatrix"`

and more by class `"ddenseMatrix"`

etc, see
the examples.

- %*%
`signature(x = "dtpMatrix", y = "dgeMatrix")`

: Matrix multiplication; ditto for several other signature combinations, see`showMethods("%*%", class = "dtpMatrix")`

.- coerce
`signature(from = "dtpMatrix", to = "dtrMatrix")`

- coerce
`signature(from = "dtpMatrix", to = "matrix")`

- determinant
`signature(x = "dtpMatrix", logarithm = "logical")`

: the`determinant(x)`

trivially is`prod(diag(x))`

, but computed on log scale to prevent over- and underflow.- diag
`signature(x = "dtpMatrix")`

: ...- norm
`signature(x = "dtpMatrix", type = "character")`

: ...- rcond
`signature(x = "dtpMatrix", norm = "character")`

: ...- solve
`signature(a = "dtpMatrix", b = "...")`

: efficiently using internal backsolve or forwardsolve, see`solve-methods`

.- t
`signature(x = "dtpMatrix")`

:`t(x)`

remains a`"dtpMatrix"`

, lower triangular if`x`

is upper triangular, and vice versa.

Class `dtrMatrix`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
showClass("dtrMatrix")
example("dtrMatrix-class", echo=FALSE)
(p1 <- as(T2, "dtpMatrix"))
str(p1)
(pp <- as(T, "dtpMatrix"))
ip1 <- solve(p1)
stopifnot(length(p1@x) == 3, length(pp@x) == 3,
p1 @ uplo == T2 @ uplo, pp @ uplo == T @ uplo,
identical(t(pp), p1), identical(t(p1), pp),
all((l.d <- p1 - T2) == 0), is(l.d, "dtpMatrix"),
all((u.d <- pp - T ) == 0), is(u.d, "dtpMatrix"),
l.d@uplo == T2@uplo, u.d@uplo == T@uplo,
identical(t(ip1), solve(pp)), is(ip1, "dtpMatrix"),
all.equal(as(solve(p1,p1), "diagonalMatrix"), Diagonal(2)))
``` |

```
Class "dtrMatrix" [package "Matrix"]
Slots:
Name: x Dim Dimnames uplo diag
Class: numeric integer list character character
Extends:
Class "ddenseMatrix", directly
Class "triangularMatrix", directly
Class "dMatrix", by class "ddenseMatrix", distance 2
Class "denseMatrix", by class "ddenseMatrix", distance 2
Class "Matrix", by class "triangularMatrix", distance 2
Class "xMatrix", by class "dMatrix", distance 3
Class "mMatrix", by class "Matrix", distance 4
Class "Mnumeric", by class "Matrix", distance 4
Class "replValueSp", by class "Matrix", distance 4
Known Subclasses: "Cholesky", "BunchKaufman"
2 x 2 Matrix of class "dtpMatrix"
[,1] [,2]
[1,] 2 .
[2,] 3 -1
Formal class 'dtpMatrix' [package "Matrix"] with 5 slots
..@ x : num [1:3] 2 3 -1
..@ Dim : int [1:2] 2 2
..@ Dimnames:List of 2
.. ..$ : NULL
.. ..$ : NULL
..@ uplo : chr "L"
..@ diag : chr "N"
2 x 2 Matrix of class "dtpMatrix"
[,1] [,2]
[1,] 2 3
[2,] . -1
```

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