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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: Multiplication by Decomposition Factors</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 facmul {Matrix}"><tr><td>facmul {Matrix}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>Multiplication by Decomposition Factors</h2> <h3>Description</h3> <p>Performs multiplication by factors for certain decompositions (and allows explicit formation of those factors). </p> <h3>Usage</h3> <pre> facmul(x, factor, y, transpose, left, ...) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>x</code></td> <td> <p>a matrix decomposition. No missing values or IEEE special values are allowed. </p> </td></tr> <tr valign="top"><td><code>factor</code></td> <td> <p>an indicator for selecting a particular factor for multiplication. </p> </td></tr> <tr valign="top"><td><code>y</code></td> <td> <p>a matrix or vector to be multiplied by the factor or its transpose. No missing values or IEEE special values are allowed. </p> </td></tr> <tr valign="top"><td><code>transpose</code></td> <td> <p>a logical value. When <code>FALSE</code> (the default) the factor is applied. When <code>TRUE</code> the transpose of the factor is applied. </p> </td></tr> <tr valign="top"><td><code>left</code></td> <td> <p>a logical value. When <code>TRUE</code> (the default) the factor is applied from the left. When <code>FALSE</code> the factor is applied from the right. </p> </td></tr> <tr valign="top"><td><code>...</code></td> <td> <p>the method for <code>"qr.Matrix"</code> has additional arguments. </p> </td></tr> </table> <h3>Value</h3> <p>the product of the selected factor (or its transpose) and <code>y</code> </p> <h3>NOTE</h3> <p>Factors for decompositions such as <code>lu</code> and <code>qr</code> can be stored in a compact form. The function <code>facmul</code> allows multiplication without explicit formation of the factors, saving both storage and operations. </p> <h3>References</h3> <p>Golub, G., and Van Loan, C. F. (1989). <em>Matrix Computations,</em> 2nd edition, Johns Hopkins, Baltimore. </p> <h3>Examples</h3> <pre> library(Matrix) x <- Matrix(rnorm(9), 3, 3) ## Not run: qrx <- qr(x) # QR factorization of x y <- rnorm(3) facmul( qr(x), factor = "Q", y) # form Q y ## End(Not run) </pre> <hr /><div style="text-align: center;">[Package <em>Matrix</em> version 1.2-17 <a href="00Index.html">Index</a>]</div> </body></html>