dpoMatrix-class | R Documentation |

The

`"dpoMatrix"`

class is the class of positive-semidefinite symmetric matrices in nonpacked storage.The

`"dppMatrix"`

class is the same except in packed storage. Only the upper triangle or the lower triangle is required to be available.The

`"corMatrix"`

and`"pcorMatrix"`

classes represent correlation matrices. They extend`"dpoMatrix"`

and`"dppMatrix"`

, respectively, with an additional slot`sd`

allowing restoration of the original covariance matrix.

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

or from `crossprod`

applied to
an `"dgeMatrix"`

object.

`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`

:Object of class

`"integer"`

. The dimensions of the matrix which must be a two-element vector of non-negative integers.`Dimnames`

:inherited from class

`"Matrix"`

`factors`

:Object of class

`"list"`

. A named list of factorizations that have been computed for the matrix.`sd`

:(for

`"corMatrix"`

and`"pcorMatrix"`

) a`numeric`

vector of length`n`

containing the (original)`\sqrt{var(.)}`

entries which allow reconstruction of a covariance matrix from the correlation matrix.

Class `"dsyMatrix"`

, directly.

Classes `"dgeMatrix"`

, `"symmetricMatrix"`

, and many more
by class `"dsyMatrix"`

.

- chol
`signature(x = "dpoMatrix")`

: Returns (and stores) the Cholesky decomposition of`x`

, see`chol`

.- determinant
`signature(x = "dpoMatrix")`

: Returns the`determinant`

of`x`

, via`chol(x)`

, see above.- rcond
`signature(x = "dpoMatrix", norm = "character")`

: Returns (and stores) the reciprocal of the condition number of`x`

. The`norm`

can be`"O"`

for the one-norm (the default) or`"I"`

for the infinity-norm. For symmetric matrices the result does not depend on the norm.- solve
`signature(a = "dpoMatrix", b = "....")`

, and- solve
`signature(a = "dppMatrix", b = "....")`

work via the Cholesky composition, see also the Matrix`solve-methods`

.- Arith
`signature(e1 = "dpoMatrix", e2 = "numeric")`

(and quite a few other signatures): The result of (“elementwise” defined) arithmetic operations is typically*not*positive-definite anymore. The only exceptions, currently, are multiplications, divisions or additions with*positive*`length(.) == 1`

numbers (or`logical`

s).

Currently the validity methods for these classes such as
`getValidity(getClass("dpoMatrix"))`

for efficiency reasons
only check the diagonal entries of the matrix – they may not be negative.
This is only necessary but not sufficient for a symmetric matrix to be
positive semi-definite.

A more reliable (but often more expensive) check for positive
semi-definiteness would look at the signs of `diag(BunchKaufman(.))`

(with some tolerance for very small negative values), and for (strict)
positive definiteness at something like
`!inherits(tryCatch(chol(.), error=identity), "error")`

.
Indeed, when *coercing* to these classes, a version
of `Cholesky()`

or `chol()`

is
typically used, e.g., see ```
selectMethod("coerce",
c(from="dsyMatrix", to="dpoMatrix"))
```

.

Classes `dsyMatrix`

and `dgeMatrix`

;
further, `Matrix`

, `rcond`

,
`chol`

, `solve`

, `crossprod`

.

```
h6 <- Hilbert(6)
rcond(h6)
str(h6)
h6 * 27720 # is ``integer''
solve(h6)
str(hp6 <- pack(h6))
### Note that as(*, "corMatrix") *scales* the matrix
(ch6 <- as(h6, "corMatrix"))
stopifnot(all.equal(as(h6 * 27720, "dsyMatrix"), round(27720 * h6),
tolerance = 1e-14),
all.equal(ch6@sd^(-2), 2*(1:6)-1,
tolerance = 1e-12))
chch <- Cholesky(ch6, perm = FALSE)
stopifnot(identical(chch, ch6@factors$Cholesky),
all(abs(crossprod(as(chch, "dtrMatrix")) - ch6) < 1e-10))
```

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