Kronecker-Product Positive-Definite Matrix

DESCRIPTION:

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