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.
USAGE:
pdKron(value, form, nam, data, pdClass, groups)
REQUIRED ARGUMENTS:
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.
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.
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.
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.
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".
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.
VALUE:
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
.
SEE ALSO:
EXAMPLES:
pd1 <- pdKron(3*diag(2)+1, form = ~day, data = Pixel, groups = ~Side)
pd1