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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: Matrix Exponential</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 expm {Matrix}"><tr><td>expm {Matrix}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>Matrix Exponential</h2> <h3>Description</h3> <p>Compute the exponential of a matrix. </p> <h3>Usage</h3> <pre> expm(x) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>x</code></td> <td> <p>a matrix, typically inheriting from the <code><a href="dMatrix-class.html">dMatrix</a></code> class.</p> </td></tr> </table> <h3>Details</h3> <p>The exponential of a matrix is defined as the infinite Taylor series <code>expm(A) = I + A + A^2/2! + A^3/3! + ...</code> (although this is definitely not the way to compute it). The method for the <code>dgeMatrix</code> class uses Ward's diagonal Pade' approximation with three step preconditioning. </p> <h3>Value</h3> <p>The matrix exponential of <code>x</code>. </p> <h3>Note</h3> <p>The <a href="https://CRAN.R-project.org/package=expm"><span class="pkg">expm</span></a> package contains newer (partly faster and more accurate) algorithms for <code>expm()</code> and includes <code><a href="../../expm/html/logm.html">logm</a></code> and <code><a href="../../expm/html/sqrtm.html">sqrtm</a></code>. </p> <h3>Author(s)</h3> <p>This is a translation of the implementation of the corresponding Octave function contributed to the Octave project by A. Scottedward Hodel <a href="mailto:A.S.Hodel@Eng.Auburn.EDU">A.S.Hodel@Eng.Auburn.EDU</a>. A bug in there has been fixed by Martin Maechler. </p> <h3>References</h3> <p><a href="http://en.wikipedia.org/wiki/Matrix_exponential">http://en.wikipedia.org/wiki/Matrix_exponential</a> </p> <p>Cleve Moler and Charles Van Loan (2003) Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. <em>SIAM Review</em> <b>45</b>, 1, 3–49. </p> <p>Eric W. Weisstein et al. (1999) <em>Matrix Exponential</em>. From MathWorld, <a href="http://mathworld.wolfram.com/MatrixExponential.html">http://mathworld.wolfram.com/MatrixExponential.html</a> </p> <h3>See Also</h3> <p><code><a href="Schur.html">Schur</a></code>; additionally, <code><a href="../../expm/html/expm.html">expm</a></code>, <code><a href="../../expm/html/logm.html">logm</a></code>, etc in package <a href="https://CRAN.R-project.org/package=expm"><span class="pkg">expm</span></a>. </p> <h3>Examples</h3> <pre> (m1 <- Matrix(c(1,0,1,1), nc = 2)) (e1 <- expm(m1)) ; e <- exp(1) stopifnot(all.equal(e1@x, c(e,0,e,e), tolerance = 1e-15)) (m2 <- Matrix(c(-49, -64, 24, 31), nc = 2)) (e2 <- expm(m2)) (m3 <- Matrix(cbind(0,rbind(6*diag(3),0))))# sparse! (e3 <- expm(m3)) # upper triangular </pre> <hr /><div style="text-align: center;">[Package <em>Matrix</em> version 1.2-17 <a href="00Index.html">Index</a>]</div> </body></html>