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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><title>R: Positive-Definite Block Diagonal Matrix</title> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <link rel="stylesheet" type="text/css" href="R.css" /> </head><body> <table width="100%" summary="page for pdBlocked {nlme}"><tr><td>pdBlocked {nlme}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>Positive-Definite Block Diagonal Matrix</h2> <h3>Description</h3> <p>This function is a constructor for the <code>pdBlocked</code> 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 <code>pdMat</code> object. When <code>value</code> is <code>numeric(0)</code>, a list of uninitialized <code>pdMat</code> objects, a list of one-sided formulas, or a list of vectors of character strings, <code>object</code> is returned as an uninitialized <code>pdBlocked</code> object (with just some of its attributes and its class defined) and needs to have its coefficients assigned later, generally using the <code>coef</code> or <code>matrix</code> replacement functions. If <code>value</code> is a list of initialized <code>pdMat</code> objects, <code>object</code> will be constructed from the list obtained by applying <code>as.matrix</code> to each of the <code>pdMat</code> elements of <code>value</code>. Finally, if <code>value</code> 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. </p> <h3>Usage</h3> <pre> pdBlocked(value, form, nam, data, pdClass) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>value</code></td> <td> <p>an optional list with elements to be used as the <code>value</code> argument to other <code>pdMat</code> constructors. These include: <code>pdMat</code> 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 <code>numeric(0)</code>, corresponding to an uninitialized object.</p> </td></tr> <tr valign="top"><td><code>form</code></td> <td> <p>an optional list of one-sided linear formulas specifying the row/column names for the block-diagonal elements of the matrix represented by <code>object</code>. Because factors may be present in <code>form</code>, the formulas needs to be evaluated on a data.frame to resolve the names they define. This argument is ignored when <code>value</code> is a list of one-sided formulas. Defaults to <code>NULL</code>.</p> </td></tr> <tr valign="top"><td><code>nam</code></td> <td> <p>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 <code>value</code> is a list of vector of character strings. Defaults to <code>NULL</code>.</p> </td></tr> <tr valign="top"><td><code>data</code></td> <td> <p>an optional data frame in which to evaluate the variables named in <code>value</code> and <code>form</code>. It is used to obtain the levels for <code>factors</code>, which affect the dimensions and the row/column names of the underlying matrix. If <code>NULL</code>, no attempt is made to obtain information on any <code>factors</code> appearing in the formulas. Defaults to the parent frame from which the function was called.</p> </td></tr> <tr valign="top"><td><code>pdClass</code></td> <td> <p>an optional vector of character strings naming the <code>pdMat</code> 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 <code>value</code> is missing, or its elements are not <code>pdMat</code> objects. Defaults to <code>"pdSymm"</code>.</p> </td></tr> </table> <h3>Value</h3> <p>a <code>pdBlocked</code> object representing a positive-definite block-diagonal matrix, also inheriting from class <code>pdMat</code>. </p> <h3>Author(s)</h3> <p>José Pinheiro and Douglas Bates <a href="mailto:bates@stat.wisc.edu">bates@stat.wisc.edu</a></p> <h3>References</h3> <p>Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models in S and S-PLUS", Springer, esp. p. 162. </p> <h3>See Also</h3> <p><code><a href="as.matrix.pdMat.html">as.matrix.pdMat</a></code>, <code><a href="coef.pdMat.html">coef.pdMat</a></code>, <code><a href="pdClasses.html">pdClasses</a></code>, <code><a href="Matrix.pdMat.html">matrix<-.pdMat</a></code> </p> <h3>Examples</h3> <pre> pd1 <- pdBlocked(list(diag(1:2), diag(c(0.1, 0.2, 0.3))), nam = list(c("A","B"), c("a1", "a2", "a3"))) pd1 </pre> <hr /><div style="text-align: center;">[Package <em>nlme</em> version 3.1-139 <a href="00Index.html">Index</a>]</div> </body></html>