.\" -*- nroff -*- generated from .Rd format
.BG
.FN pdKron
.TL
Kronecker-Product Positive-Definite Matrix
.DN
This function is a constructor for the `pdKron' class,
representing a positive-definite matrix obtained as the Kronecker
product between an identity matrix and a basic positive-definite
matrix. Any `pdMat' object can be used to define the basic pd
matrix. The order of the idientity matrix used in the Kronecker
product is determined by the number of levels of the factor declared
in `groups'. The number of coefficients associated with this
class is equal to the number of coefficients used to represent the
basic `pdMat' object. 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
`pdKron' 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, the basic
`pdMat' object will be constructed from
`as.matrix(value)'. Finally, if `value' 
is a numeric vector, it is assumed to represent the unrestricted
coefficients of the basic `pdMat' object.
.CS
pdKron(value, form, nam, data, pdClass, groups)
.RA
.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 basic matrix used to form the
Kronecker-product 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 basic matrix used to form the
Kronecker-product matrix represented by `object'. It must have
length equal to the dimension of the underlying basic
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', `form', and `groups'. 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 pdClass
an optional character string naming the
`pdMat' class to be assigned to the basic element used to form
the Kronecker product represented by the returned object. This
argument will only be used when `value' is not a `pdMat' 
object. Defaults to `"pdSymm"'.
.AG groups
a one-sided formula specifying the grouping variable
used in forming the Kronecker-product matrix represented by
`object'. Its right hand side must evaluate to a factor in
`data'; the number of levels of the corresponding factor
determines the number of identical block diagonal elements in the
matrix represented by `object'.
.RT
a `pdKron' object representing a positive-definite
matrix obtained as the Kronecker product between an identity matrix
and a basic positive-definite matrix, also inheriting from class
`pdMat'.

.SA
`matrix<-.pdKron'
.EX
pd1 <- pdKron(3*diag(2)+1, form = ~day, data = Pixel, groups = ~Side)
pd1
.KW models
.WR
