.\" -*- nroff -*- generated from .Rd format
.BG
.FN pdSymmNat
.TL
General Positive-Definite Matrix in Natural Parameterization
.DN
This function is a constructor for the `pdSymmNat' class,
representing a general positive-definite matrix, using a natural
parameterization . If the matrix associated with `object' is of
dimension n, it is represented by n*(n+1)/2
parameters. Letting S(i,j) denote the ij-th
element of the underlying positive definite matrix and
r(i,j) = S(i,j)/sqrt(S(i,i)S(j,j)), i not equal to j denote the
associated "correlations", if `unconstrained = TRUE', the "natural"
parameters are given by log(Sii), i=1,..,n and
log((1+r(i,j))/(1-r(i,j))), i not equal to j. Note that, in
this case, all  natural parameters are individually unrestricted, but
not jointly unrestricted (meaning that not all unrestricted vectors
would give positive-definite matrices). If `unconstrained =
      FALSE', the S(i,j) are used to parameterize the
returned object. This class does not define an unrestricted
parameterization and, therefore, should NOT be used for
optimization. It is mostly used for deriving 
approximate confidence intervals on parameters following the
optimization of an objective function. When `value' is
`numeric(0)', an uninitialized `pdMat' object, a one-sided
formula, or a vector of character strings, `object' is returned
as an uninitialized `pdSymm' object (with just some of its
attributes and its class defined) and needs to have its coefficients
assigned later, generally using the `coef' or `matrix' replacement
functions. If `value' is an initialized `pdMat' object,
`object' will be constructed from
`as.matrix(value)'. Finally, if `value' is a numeric 
vector, it is assumed to represent the natural parameters of the
underlying positive-definite matrix.
.CS
pdSymmNat(value, form, nam, data, unconstrained)
.OA
.AG value
an optional initialization value, which can be any of the
following: a `pdMat' object, a positive-definite
matrix, a one-sided linear formula (with variables separated by
`+'), a vector of character strings, or a numeric
vector. Defaults to `numeric(0)', corresponding to an
uninitialized object.
.AG form
an optional one-sided linear formula specifying the
row/column names for the matrix represented by `object'. Because
factors may be present in `form', the formula needs to be
evaluated on a data.frame to resolve the names it defines. This
argument is ignored when `value' is a one-sided
formula. Defaults to `NULL'.
.AG nam
an optional vector of character strings specifying the
row/column names for the matrix represented by object. It must have 
length equal to the dimension of the underlying positive-definite
matrix and unreplicated elements. This argument is ignored when
`value' is a vector of character strings. Defaults to
`NULL'.
.AG data
an optional data frame in which to evaluate the variables
named in `value' and `form'. It is used to
obtain the levels for `factors', which affect the
dimensions and the row/column names of the underlying matrix. If
`NULL', no attempt is made to obtain information on 
`factors' appearing in the formulas. Defaults to the
parent frame from which the function was called.
.AG unconstrained
an optional logical value indicating whether an
unconstrained natural parameterization should be used. Defaults to
`TRUE'.
.RT
a `pdSymmNat' object representing a general positive-definite
matrix in natural parameterization, also inheriting from class
`pdMat'.

.SA
`asNatural.pdSymm', `pdSymm'
.EX
pdSymmNat(diag(1:3))
.KW models
.WR
