dsyMatrix-class | R Documentation |

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

or `new("dspMatrix", ...)`

, respectively.

`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.

`"dsyMatrix"`

extends class `"dgeMatrix"`

, directly, whereas

`"dspMatrix"`

extends class `"ddenseMatrix"`

, directly.

Both extend class `"symmetricMatrix"`

, directly,
and class `"Matrix"`

and others, *in*directly, use
`showClass("dsyMatrix")`

, e.g., for details.

- 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.

The *positive (Semi-)definite* dense (packed or non-packed
numeric matrix classes `dpoMatrix`

,
`dppMatrix`

and `corMatrix`

,

Classes `dgeMatrix`

and `Matrix`

;
`solve`

, `norm`

, `rcond`

,
`t`

```
## 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)))
str(t(sy2)) # uplo = "L", and the lower tri. (i.e. NA is replaced).
chol(sy2) #-> "Cholesky" matrix
(sp2 <- pack(sy2)) # a "dspMatrix"
## 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
## 4x4 example
m <- matrix(0,4,4); m[upper.tri(m)] <- 1:6
(sym <- m+t(m)+diag(11:14, 4))
(S1 <- pack(sym))
(S2 <- t(S1))
stopifnot(all(S1 == S2)) # equal "seen as matrix", but differ internally :
str(S1)
S2@x
```

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