Positive-Definite Block Diagonal Matrix - R Documentation

`pdBlocked` Positive-Definite Block Diagonal Matrix

Description

This function is a constructor for the pdBlocked class, representing a positive-definite block-diagonal matrix. Each block-diagonal element of the underlying matrix is itself a positive-definite matrix and is represented internally as an individual pdMat object. When value is numeric(0), a list of uninitialized pdMat objects, a list of one-sided formulas, or a list of vectors of character strings, object is returned as an uninitialized pdBlocked 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 a list of initialized pdMat objects, object will be constructed from the list obtained by applying as.matrix to each of the pdMat elements of value. Finally, if value is a list of numeric vectors, they are assumed to represent the unrestricted coefficients of the block-diagonal elements of the underlying positive-definite matrix.

Usage

pdBlocked(value, form, nam, data, pdClass)

Arguments

`value`	an optional list with elements to be used as the `value` argument to other `pdMat` constructors. These include: `pdMat` objects, positive-definite matrices, one-sided linear formulas, vectors of character strings, or numeric vectors. All elements in the list must be similar (e.g. all one-sided formulas, or all numeric vectors). Defaults to `numeric(0)`, corresponding to an uninitialized object.
`form`	an optional list of one-sided linear formulas specifying the row/column names for the block-diagonal elements of the matrix represented by `object`. Because factors may be present in `form`, the formulas needs to be evaluated on a data.frame to resolve the names they define. This argument is ignored when `value` is a list of one-sided formulas. Defaults to `NULL`.
`nam`	an optional list of vector of character strings specifying the row/column names for the block-diagonal elements of the matrix represented by object. Each of its components must have length equal to the dimension of the corresponding block-diagonal element and unreplicated elements. This argument is ignored when `value` is a list of vector of character strings. Defaults to `NULL`.
`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 any `factors` appearing in the formulas. Defaults to the parent frame from which the function was called.
`pdClass`	an optional vector of character strings naming the `pdMat` classes to be assigned to the individual blocks in the underlying matrix. If a single class is specified, it is used for all block-diagonal elements. This argument will only be used when `value` is missing, or its elements are not `pdMat` objects. Defaults to `"pdSymm"`.

Value

a pdBlocked object representing a positive-definite block-diagonal matrix, also inheriting from class pdMat.

Author(s)

José Pinheiro and Douglas Bates [email protected]

References

Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models in S and S-PLUS", Springer, esp. p. 162.

Examples

pd1 <- pdBlocked(list(diag(1:2), diag(c(0.1, 0.2, 0.3))),
                 nam = list(c("A","B"), c("a1", "a2", "a3")))
pd1

pdBlocked Positive-Definite Block Diagonal Matrix