EVOLUTION-MANAGER
Edit File: pdLogChol.html
<!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: General Positive-Definite 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 pdLogChol {nlme}"><tr><td>pdLogChol {nlme}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>General Positive-Definite Matrix</h2> <h3>Description</h3> <p>This function is a constructor for the <code>pdLogChol</code> class, representing a general positive-definite matrix. If the matrix associated with <code>object</code> is of dimension <i>n</i>, it is represented by <i>n*(n+1)/2</i> unrestricted parameters, using the log-Cholesky parametrization described in Pinheiro and Bates (1996). </p> <ul> <li><p> When <code>value</code> is <code>numeric(0)</code>, an uninitialized <code>pdMat</code> object, a one-sided formula, or a character vector, <code>object</code> is returned as an <em>uninitialized</em> <code>pdLogChol</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. </p> </li> <li><p> If <code>value</code> is an <em>initialized</em> <code>pdMat</code> object, <code>object</code> will be constructed from <code>as.matrix(value)</code>. </p> </li> <li><p> Finally, if <code>value</code> is a numeric vector, it is assumed to represent the unrestricted coefficients of the matrix-logarithm parametrization of the underlying positive-definite matrix. </p> </li></ul> <h3>Usage</h3> <pre> pdLogChol(value, form, nam, data) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>value</code></td> <td> <p>an optional initialization value, which can be any of the following: a <code>pdMat</code> object, a positive-definite matrix, a one-sided linear formula (with variables separated by <code>+</code>), a vector of character strings, or a numeric vector. 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 one-sided linear formula specifying the row/column names for the matrix represented by <code>object</code>. Because factors may be present in <code>form</code>, the formula needs to be evaluated on a data frame to resolve the names it defines. This argument is ignored when <code>value</code> is a one-sided formula. Defaults to <code>NULL</code>.</p> </td></tr> <tr valign="top"><td><code>nam</code></td> <td> <p>an optional character vector specifying the row/column names for the matrix represented by object. It must have length equal to the dimension of the underlying positive-definite matrix and unreplicated elements. This argument is ignored when <code>value</code> is a character vector. 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 <code>factor</code>s appearing in the formulas. Defaults to the parent frame from which the function was called.</p> </td></tr> </table> <h3>Details</h3> <p>Internally, the <code>pdLogChol</code> representation of a symmetric positive definite matrix is a vector starting with the logarithms of the diagonal of the Choleski factorization of that matrix followed by its upper triangular portion. </p> <h3>Value</h3> <p>a <code>pdLogChol</code> object representing a general positive-definite 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. (1996) Unconstrained Parametrizations for Variance-Covariance Matrices, <em>Statistics and Computing</em> <b>6</b>, 289–296. </p> <p>Pinheiro, J.C., and Bates, D.M. (2000) <em>Mixed-Effects Models in S and S-PLUS</em>, Springer. </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 <- pdLogChol(diag(1:3), nam = c("A","B","C"))) (pd4 <- pdLogChol(1:6)) (pd4c <- chol(pd4)) # -> upper-tri matrix with off-diagonals 4 5 6 pd4c[upper.tri(pd4c)] log(diag(pd4c)) # 1 2 3 </pre> <hr /><div style="text-align: center;">[Package <em>nlme</em> version 3.1-139 <a href="00Index.html">Index</a>]</div> </body></html>