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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: Bunch-Kaufman Decomposition Methods</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 BunchKaufman-methods {Matrix}"><tr><td>BunchKaufman-methods {Matrix}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>Bunch-Kaufman Decomposition Methods</h2> <h3>Description</h3> <p>The Bunch-Kaufman Decomposition of a square symmetric matrix <i>A</i> is <i>A = P LDL' P'</i> where <i>P</i> is a permutation matrix, <i>L</i> is <em>unit</em>-lower triangular and <i>D</i> is <em>block</em>-diagonal with blocks of dimension <i>1 x 1</i> or <i>2 x 2</i>. </p> <h3>Usage</h3> <pre> BunchKaufman(x, ...) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>x</code></td> <td> <p>a symmetric square matrix.</p> </td></tr> <tr valign="top"><td><code>...</code></td> <td> <p>potentially further arguments passed to methods.</p> </td></tr> </table> <h3>Value</h3> <p>an object of class <code><a href="Cholesky-class.html">BunchKaufman</a></code>, which can also be used as a (triangular) matrix directly. </p> <h3>Methods</h3> <p>Currently, only methods for <b>dense</b> numeric symmetric matrices are implemented. </p> <dl> <dt><code>x = "dspMatrix"</code></dt><dd><p>uses Lapack routine <code>dsptrf</code>,</p> </dd> <dt><code>x = "dsyMatrix"</code></dt><dd><p>uses Lapack routine <code>dsytrf</code>, computing the Bunch-Kaufman decomposition.</p> </dd> </dl> <h3>References</h3> <p>The original LAPACK source code, including documentation; <a href="http://www.netlib.org/lapack/double/dsytrf.f">http://www.netlib.org/lapack/double/dsytrf.f</a> and <a href="http://www.netlib.org/lapack/double/dsptrf.f">http://www.netlib.org/lapack/double/dsptrf.f</a> </p> <h3>See Also</h3> <p>The resulting class, <code><a href="Cholesky-class.html">BunchKaufman</a></code>. Related decompositions are the LU, <code><a href="lu.html">lu</a></code>, and the Cholesky, <code><a href="chol.html">chol</a></code> (and for <em>sparse</em> matrices, <code><a href="Cholesky.html">Cholesky</a></code>). </p> <h3>Examples</h3> <pre> data(CAex) dim(CAex) isSymmetric(CAex)# TRUE CAs <- as(CAex, "symmetricMatrix") if(FALSE) # no method defined yet for *sparse* : bk. <- BunchKaufman(CAs) ## does apply to *dense* symmetric matrices: bkCA <- BunchKaufman(as(CAs, "denseMatrix")) bkCA image(bkCA)# shows how sparse it is, too str(R.CA <- as(bkCA, "sparseMatrix")) ## an upper triangular 72x72 matrix with only 144 non-zero entries </pre> <hr /><div style="text-align: center;">[Package <em>Matrix</em> version 1.2-17 <a href="00Index.html">Index</a>]</div> </body></html>