R: Positive-Definite Block Diagonal Matrix

pdBlocked {nlme} | R Documentation

## 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)

Jose Pinheiro Jose.Pinheiro@pharma.novartis.com and Douglas Bates bates@stat.wisc.edu

### References

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

### See Also

`as.matrix.pdMat`, `coef.pdMat`, `pdClasses`, `matrix<-.pdMat`

### 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

[Package nlme version 3.1-86 Index]