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<div class="title">MatrixExponential.h</div> </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// for linear algebra.</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="comment">//</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span> <span class="comment">// Copyright (C) 2009, 2010 Jitse Niesen <jitse@maths.leeds.ac.uk></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">// Copyright (C) 2011 Chen-Pang He <jdh8@ms63.hinet.net></span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">//</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> </div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor">#ifndef EIGEN_MATRIX_EXPONENTIAL</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_MATRIX_EXPONENTIAL</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor">#include "StemFunction.h"</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> </div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="keyword">namespace </span>Eigen {</div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> </div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00024"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixExponential.html"> 24</a></span> <span class="keyword">class </span><a class="code" href="classEigen_1_1MatrixExponential.html">MatrixExponential</a> {</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span> </div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> </div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <a class="code" href="classEigen_1_1MatrixExponential.html#ab95539bf1dcb956849da615f292aa6b1">MatrixExponential</a>(<span class="keyword">const</span> MatrixType &M);</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span> </div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> ResultType> </div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixExponential.html#a37407499d669c7dd9af708e7dd6f9217">compute</a>(ResultType &result);</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span> </div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keyword">private</span>:</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span> </div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="comment">// Prevent copying</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <a class="code" href="classEigen_1_1MatrixExponential.html#ab95539bf1dcb956849da615f292aa6b1">MatrixExponential</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixExponential.html">MatrixExponential</a>&);</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <a class="code" href="classEigen_1_1MatrixExponential.html">MatrixExponential</a>& operator=(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixExponential.html">MatrixExponential</a>&);</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span> </div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="keywordtype">void</span> pade3(<span class="keyword">const</span> MatrixType &A);</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> </div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keywordtype">void</span> pade5(<span class="keyword">const</span> MatrixType &A);</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span> </div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keywordtype">void</span> pade7(<span class="keyword">const</span> MatrixType &A);</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span> </div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="keywordtype">void</span> pade9(<span class="keyword">const</span> MatrixType &A);</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span> </div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keywordtype">void</span> pade13(<span class="keyword">const</span> MatrixType &A);</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span> </div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="keywordtype">void</span> pade17(<span class="keyword">const</span> MatrixType &A);</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span> </div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="keywordtype">void</span> computeUV(<span class="keywordtype">double</span>);</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span> </div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keywordtype">void</span> computeUV(<span class="keywordtype">float</span>);</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  </div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keywordtype">void</span> computeUV(<span class="keywordtype">long</span> <span class="keywordtype">double</span>);</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span> </div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::traits<MatrixType>::Scalar Scalar;</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> NumTraits<Scalar>::Real RealScalar;</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> std::complex<RealScalar> ComplexScalar;</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span> </div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="keyword">typename</span> internal::nested<MatrixType>::type m_M;</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span> </div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  MatrixType m_U;</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span> </div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  MatrixType m_V;</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span> </div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  MatrixType m_tmp1;</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span> </div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  MatrixType m_tmp2;</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span> </div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  MatrixType m_Id;</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span> </div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="keywordtype">int</span> m_squarings;</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span> </div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  RealScalar m_l1norm;</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span> };</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span> </div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00163"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixExponential.html#ab95539bf1dcb956849da615f292aa6b1"> 163</a></span> <a class="code" href="classEigen_1_1MatrixExponential.html#ab95539bf1dcb956849da615f292aa6b1">MatrixExponential<MatrixType>::MatrixExponential</a>(<span class="keyword">const</span> MatrixType &M) :</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  m_M(M),</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  m_U(M.rows(),M.cols()),</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  m_V(M.rows(),M.cols()),</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  m_tmp1(M.rows(),M.cols()),</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  m_tmp2(M.rows(),M.cols()),</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  m_Id(MatrixType::Identity(M.rows(), M.cols())),</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  m_squarings(0),</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  m_l1norm(M.cwiseAbs().colwise().sum().maxCoeff())</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span> {</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <span class="comment">/* empty body */</span></div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span> }</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span> </div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span> <span class="keyword">template</span> <<span class="keyword">typename</span> ResultType> </div>
<div class="line"><a name="l00178"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixExponential.html#a37407499d669c7dd9af708e7dd6f9217"> 178</a></span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixExponential.html#a37407499d669c7dd9af708e7dd6f9217">MatrixExponential<MatrixType>::compute</a>(ResultType &result)</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span> {</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span> <span class="preprocessor">#if LDBL_MANT_DIG > 112 // rarely happens</span></div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span> <span class="preprocessor"></span> <span class="keywordflow">if</span>(<span class="keyword">sizeof</span>(RealScalar) > 14) {</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  result = m_M.matrixFunction(<a class="code" href="classEigen_1_1StdStemFunctions.html">StdStemFunctions<ComplexScalar>::exp</a>);</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  }</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span> <span class="preprocessor"></span> computeUV(RealScalar());</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  m_tmp1 = m_U + m_V; <span class="comment">// numerator of Pade approximant</span></div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  m_tmp2 = -m_U + m_V; <span class="comment">// denominator of Pade approximant</span></div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  result = m_tmp2.partialPivLu().solve(m_tmp1);</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i=0; i<m_squarings; i++)</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  result *= result; <span class="comment">// undo scaling by repeated squaring</span></div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span> }</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span> </div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span> EIGEN_STRONG_INLINE <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1MatrixExponential.html">MatrixExponential<MatrixType>::pade3</a>(<span class="keyword">const</span> MatrixType &A)</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span> {</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <span class="keyword">const</span> RealScalar b[] = {120., 60., 12., 1.};</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  m_tmp1.noalias() = A * A;</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  m_tmp2 = b[3]*m_tmp1 + b[1]*m_Id;</div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  m_U.noalias() = A * m_tmp2;</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  m_V = b[2]*m_tmp1 + b[0]*m_Id;</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span> }</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span> </div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span> EIGEN_STRONG_INLINE <span class="keywordtype">void</span> MatrixExponential<MatrixType>::pade5(<span class="keyword">const</span> MatrixType &A)</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span> {</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  <span class="keyword">const</span> RealScalar b[] = {30240., 15120., 3360., 420., 30., 1.};</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  MatrixType A2 = A * A;</div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  m_tmp1.noalias() = A2 * A2;</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  m_tmp2 = b[5]*m_tmp1 + b[3]*A2 + b[1]*m_Id;</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  m_U.noalias() = A * m_tmp2;</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  m_V = b[4]*m_tmp1 + b[2]*A2 + b[0]*m_Id;</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span> }</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span> </div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span> EIGEN_STRONG_INLINE <span class="keywordtype">void</span> MatrixExponential<MatrixType>::pade7(<span class="keyword">const</span> MatrixType &A)</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span> {</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="keyword">const</span> RealScalar b[] = {17297280., 8648640., 1995840., 277200., 25200., 1512., 56., 1.};</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  MatrixType A2 = A * A;</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  MatrixType A4 = A2 * A2;</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  m_tmp1.noalias() = A4 * A2;</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  m_tmp2 = b[7]*m_tmp1 + b[5]*A4 + b[3]*A2 + b[1]*m_Id;</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  m_U.noalias() = A * m_tmp2;</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  m_V = b[6]*m_tmp1 + b[4]*A4 + b[2]*A2 + b[0]*m_Id;</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span> }</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span> </div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span> EIGEN_STRONG_INLINE <span class="keywordtype">void</span> MatrixExponential<MatrixType>::pade9(<span class="keyword">const</span> MatrixType &A)</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span> {</div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  <span class="keyword">const</span> RealScalar b[] = {17643225600., 8821612800., 2075673600., 302702400., 30270240.,</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  2162160., 110880., 3960., 90., 1.};</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  MatrixType A2 = A * A;</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  MatrixType A4 = A2 * A2;</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  MatrixType A6 = A4 * A2;</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  m_tmp1.noalias() = A6 * A2;</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  m_tmp2 = b[9]*m_tmp1 + b[7]*A6 + b[5]*A4 + b[3]*A2 + b[1]*m_Id;</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  m_U.noalias() = A * m_tmp2;</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  m_V = b[8]*m_tmp1 + b[6]*A6 + b[4]*A4 + b[2]*A2 + b[0]*m_Id;</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span> }</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span> </div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span> EIGEN_STRONG_INLINE <span class="keywordtype">void</span> MatrixExponential<MatrixType>::pade13(<span class="keyword">const</span> MatrixType &A)</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span> {</div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  <span class="keyword">const</span> RealScalar b[] = {64764752532480000., 32382376266240000., 7771770303897600.,</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  1187353796428800., 129060195264000., 10559470521600., 670442572800.,</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  33522128640., 1323241920., 40840800., 960960., 16380., 182., 1.};</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  MatrixType A2 = A * A;</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  MatrixType A4 = A2 * A2;</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  m_tmp1.noalias() = A4 * A2;</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  m_V = b[13]*m_tmp1 + b[11]*A4 + b[9]*A2; <span class="comment">// used for temporary storage</span></div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  m_tmp2.noalias() = m_tmp1 * m_V;</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  m_tmp2 += b[7]*m_tmp1 + b[5]*A4 + b[3]*A2 + b[1]*m_Id;</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  m_U.noalias() = A * m_tmp2;</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  m_tmp2 = b[12]*m_tmp1 + b[10]*A4 + b[8]*A2;</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  m_V.noalias() = m_tmp1 * m_tmp2;</div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  m_V += b[6]*m_tmp1 + b[4]*A4 + b[2]*A2 + b[0]*m_Id;</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span> }</div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span> </div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span> <span class="preprocessor">#if LDBL_MANT_DIG > 64</span></div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span> <span class="preprocessor"></span><span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span> EIGEN_STRONG_INLINE <span class="keywordtype">void</span> MatrixExponential<MatrixType>::pade17(<span class="keyword">const</span> MatrixType &A)</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span> {</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  <span class="keyword">const</span> RealScalar b[] = {830034394580628357120000.L, 415017197290314178560000.L,</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  100610229646136770560000.L, 15720348382208870400000.L,</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  1774878043152614400000.L, 153822763739893248000.L, 10608466464820224000.L,</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  595373117923584000.L, 27563570274240000.L, 1060137318240000.L,</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  33924394183680.L, 899510451840.L, 19554575040.L, 341863200.L, 4651200.L,</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  46512.L, 306.L, 1.L};</div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  MatrixType A2 = A * A;</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  MatrixType A4 = A2 * A2;</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  MatrixType A6 = A4 * A2;</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  m_tmp1.noalias() = A4 * A4;</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  m_V = b[17]*m_tmp1 + b[15]*A6 + b[13]*A4 + b[11]*A2; <span class="comment">// used for temporary storage</span></div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  m_tmp2.noalias() = m_tmp1 * m_V;</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  m_tmp2 += b[9]*m_tmp1 + b[7]*A6 + b[5]*A4 + b[3]*A2 + b[1]*m_Id;</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  m_U.noalias() = A * m_tmp2;</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  m_tmp2 = b[16]*m_tmp1 + b[14]*A6 + b[12]*A4 + b[10]*A2;</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  m_V.noalias() = m_tmp1 * m_tmp2;</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  m_V += b[8]*m_tmp1 + b[6]*A6 + b[4]*A4 + b[2]*A2 + b[0]*m_Id;</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span> }</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span> <span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span> <span class="keywordtype">void</span> MatrixExponential<MatrixType>::computeUV(<span class="keywordtype">float</span>)</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span> {</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <span class="keyword">using</span> std::frexp;</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  <span class="keyword">using</span> std::pow;</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="keywordflow">if</span> (m_l1norm < 4.258730016922831e-001) {</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  pade3(m_M);</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (m_l1norm < 1.880152677804762e+000) {</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  pade5(m_M);</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <span class="keyword">const</span> <span class="keywordtype">float</span> maxnorm = 3.925724783138660f;</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  frexp(m_l1norm / maxnorm, &m_squarings);</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  <span class="keywordflow">if</span> (m_squarings < 0) m_squarings = 0;</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  MatrixType A = m_M / pow(Scalar(2), m_squarings);</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  pade7(A);</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  }</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span> }</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span> </div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span> <span class="keywordtype">void</span> MatrixExponential<MatrixType>::computeUV(<span class="keywordtype">double</span>)</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span> {</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  <span class="keyword">using</span> std::frexp;</div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  <span class="keyword">using</span> std::pow;</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  <span class="keywordflow">if</span> (m_l1norm < 1.495585217958292e-002) {</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  pade3(m_M);</div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (m_l1norm < 2.539398330063230e-001) {</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  pade5(m_M);</div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (m_l1norm < 9.504178996162932e-001) {</div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  pade7(m_M);</div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (m_l1norm < 2.097847961257068e+000) {</div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  pade9(m_M);</div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  <span class="keyword">const</span> <span class="keywordtype">double</span> maxnorm = 5.371920351148152;</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  frexp(m_l1norm / maxnorm, &m_squarings);</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  <span class="keywordflow">if</span> (m_squarings < 0) m_squarings = 0;</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  MatrixType A = m_M / pow(Scalar(2), m_squarings);</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  pade13(A);</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  }</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span> }</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span> </div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span> <span class="keyword">template</span> <<span class="keyword">typename</span> MatrixType></div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span> <span class="keywordtype">void</span> MatrixExponential<MatrixType>::computeUV(<span class="keywordtype">long</span> <span class="keywordtype">double</span>)</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span> {</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  <span class="keyword">using</span> std::frexp;</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  <span class="keyword">using</span> std::pow;</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span> <span class="preprocessor">#if LDBL_MANT_DIG == 53 // double precision</span></div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span> <span class="preprocessor"></span> computeUV(<span class="keywordtype">double</span>());</div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span> <span class="preprocessor">#elif LDBL_MANT_DIG <= 64 // extended precision</span></div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span> <span class="preprocessor"></span> <span class="keywordflow">if</span> (m_l1norm < 4.1968497232266989671e-003L) {</div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  pade3(m_M);</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (m_l1norm < 1.1848116734693823091e-001L) {</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  pade5(m_M);</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (m_l1norm < 5.5170388480686700274e-001L) {</div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  pade7(m_M);</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (m_l1norm < 1.3759868875587845383e+000L) {</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  pade9(m_M);</div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  <span class="keyword">const</span> <span class="keywordtype">long</span> <span class="keywordtype">double</span> maxnorm = 4.0246098906697353063L;</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  frexp(m_l1norm / maxnorm, &m_squarings);</div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  <span class="keywordflow">if</span> (m_squarings < 0) m_squarings = 0;</div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  MatrixType A = m_M / pow(Scalar(2), m_squarings);</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  pade13(A);</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>  }</div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span> <span class="preprocessor">#elif LDBL_MANT_DIG <= 106 // double-double</span></div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span> <span class="preprocessor"></span> <span class="keywordflow">if</span> (m_l1norm < 3.2787892205607026992947488108213e-005L) {</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  pade3(m_M);</div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (m_l1norm < 6.4467025060072760084130906076332e-003L) {</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  pade5(m_M);</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (m_l1norm < 6.8988028496595374751374122881143e-002L) {</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  pade7(m_M);</div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (m_l1norm < 2.7339737518502231741495857201670e-001L) {</div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  pade9(m_M);</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (m_l1norm < 1.3203382096514474905666448850278e+000L) {</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  pade13(m_M);</div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  <span class="keyword">const</span> <span class="keywordtype">long</span> <span class="keywordtype">double</span> maxnorm = 3.2579440895405400856599663723517L;</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  frexp(m_l1norm / maxnorm, &m_squarings);</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  <span class="keywordflow">if</span> (m_squarings < 0) m_squarings = 0;</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  MatrixType A = m_M / pow(Scalar(2), m_squarings);</div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  pade17(A);</div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  }</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span> <span class="preprocessor">#elif LDBL_MANT_DIG <= 112 // quadruple precison</span></div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span> <span class="preprocessor"></span> <span class="keywordflow">if</span> (m_l1norm < 1.639394610288918690547467954466970e-005L) {</div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  pade3(m_M);</div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (m_l1norm < 4.253237712165275566025884344433009e-003L) {</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>  pade5(m_M);</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (m_l1norm < 5.125804063165764409885122032933142e-002L) {</div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  pade7(m_M);</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (m_l1norm < 2.170000765161155195453205651889853e-001L) {</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  pade9(m_M);</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (m_l1norm < 1.125358383453143065081397882891878e+000L) {</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  pade13(m_M);</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  <span class="keyword">const</span> <span class="keywordtype">long</span> <span class="keywordtype">double</span> maxnorm = 2.884233277829519311757165057717815L;</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  frexp(m_l1norm / maxnorm, &m_squarings);</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  <span class="keywordflow">if</span> (m_squarings < 0) m_squarings = 0;</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  MatrixType A = m_M / pow(Scalar(2), m_squarings);</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  pade17(A);</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  }</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span> <span class="preprocessor">#else</span></div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span> <span class="preprocessor"></span> <span class="comment">// this case should be handled in compute()</span></div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  eigen_assert(<span class="keyword">false</span> && <span class="stringliteral">"Bug in MatrixExponential"</span>); </div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span> <span class="preprocessor">#endif // LDBL_MANT_DIG</span></div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span> <span class="preprocessor"></span>}</div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span> </div>
<div class="line"><a name="l00400"></a><span class="lineno"><a class="line" href="structEigen_1_1MatrixExponentialReturnValue.html"> 400</a></span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived> <span class="keyword">struct </span><a class="code" href="structEigen_1_1MatrixExponentialReturnValue.html">MatrixExponentialReturnValue</a></div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span> : <span class="keyword">public</span> ReturnByValue<MatrixExponentialReturnValue<Derived> ></div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span> {</div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::Index Index;</div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00410"></a><span class="lineno"><a class="line" href="structEigen_1_1MatrixExponentialReturnValue.html#a7a10d88cebec216ce8dad9fc4926845f"> 410</a></span>  <a class="code" href="structEigen_1_1MatrixExponentialReturnValue.html#a7a10d88cebec216ce8dad9fc4926845f">MatrixExponentialReturnValue</a>(<span class="keyword">const</span> Derived& src) : m_src(src) { }</div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span> </div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  <span class="keyword">template</span> <<span class="keyword">typename</span> ResultType></div>
<div class="line"><a name="l00418"></a><span class="lineno"><a class="line" href="structEigen_1_1MatrixExponentialReturnValue.html#a4f4ce27ebcf7fe1e0078d20d0393c766"> 418</a></span>  <span class="keyword">inline</span> <span class="keywordtype">void</span> <a class="code" href="structEigen_1_1MatrixExponentialReturnValue.html#a4f4ce27ebcf7fe1e0078d20d0393c766">evalTo</a>(ResultType& result)<span class="keyword"> const</span></div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  <span class="keyword">const</span> <span class="keyword">typename</span> Derived::PlainObject srcEvaluated = m_src.eval();</div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  <a class="code" href="classEigen_1_1MatrixExponential.html">MatrixExponential<typename Derived::PlainObject></a> me(srcEvaluated);</div>
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span>  me.<a class="code" href="classEigen_1_1MatrixExponential.html#a37407499d669c7dd9af708e7dd6f9217">compute</a>(result);</div>
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span>  }</div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span> </div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  Index rows()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_src.rows(); }</div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  Index cols()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> m_src.cols(); }</div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span> </div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  <span class="keyword">const</span> Derived& m_src;</div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  <span class="keyword">private</span>:</div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  <a class="code" href="structEigen_1_1MatrixExponentialReturnValue.html#a7a10d88cebec216ce8dad9fc4926845f">MatrixExponentialReturnValue</a>& operator=(<span class="keyword">const</span> <a class="code" href="structEigen_1_1MatrixExponentialReturnValue.html#a7a10d88cebec216ce8dad9fc4926845f">MatrixExponentialReturnValue</a>&);</div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span> };</div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span> </div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span> <span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span> <span class="keyword">struct </span>traits<MatrixExponentialReturnValue<Derived> ></div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span> {</div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Derived::PlainObject ReturnType;</div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span> };</div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span> }</div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span> </div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Derived></div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span> <span class="keyword">const</span> MatrixExponentialReturnValue<Derived> MatrixBase<Derived>::exp()<span class="keyword"> const</span></div>
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  eigen_assert(rows() == cols());</div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  <span class="keywordflow">return</span> MatrixExponentialReturnValue<Derived>(derived());</div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span> }</div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span> </div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span> </div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span> <span class="preprocessor">#endif // EIGEN_MATRIX_EXPONENTIAL</span></div>
<div class="ttc" id="structEigen_1_1MatrixExponentialReturnValue_html_a4f4ce27ebcf7fe1e0078d20d0393c766"><div class="ttname"><a href="structEigen_1_1MatrixExponentialReturnValue.html#a4f4ce27ebcf7fe1e0078d20d0393c766">Eigen::MatrixExponentialReturnValue::evalTo</a></div><div class="ttdeci">void evalTo(ResultType &result) const </div><div class="ttdoc">Compute the matrix exponential. </div><div class="ttdef"><b>Definition:</b> MatrixExponential.h:418</div></div>
<div class="ttc" id="classEigen_1_1MatrixExponential_html"><div class="ttname"><a href="classEigen_1_1MatrixExponential.html">Eigen::MatrixExponential</a></div><div class="ttdoc">Class for computing the matrix exponential. </div><div class="ttdef"><b>Definition:</b> MatrixExponential.h:24</div></div>
<div class="ttc" id="classEigen_1_1MatrixExponential_html_a37407499d669c7dd9af708e7dd6f9217"><div class="ttname"><a href="classEigen_1_1MatrixExponential.html#a37407499d669c7dd9af708e7dd6f9217">Eigen::MatrixExponential::compute</a></div><div class="ttdeci">void compute(ResultType &result)</div><div class="ttdoc">Computes the matrix exponential. </div><div class="ttdef"><b>Definition:</b> MatrixExponential.h:178</div></div>
<div class="ttc" id="classEigen_1_1StdStemFunctions_html"><div class="ttname"><a href="classEigen_1_1StdStemFunctions.html">Eigen::StdStemFunctions</a></div><div class="ttdoc">Stem functions corresponding to standard mathematical functions. </div><div class="ttdef"><b>Definition:</b> StemFunction.h:19</div></div>
<div class="ttc" id="classEigen_1_1MatrixExponential_html_ab95539bf1dcb956849da615f292aa6b1"><div class="ttname"><a href="classEigen_1_1MatrixExponential.html#ab95539bf1dcb956849da615f292aa6b1">Eigen::MatrixExponential::MatrixExponential</a></div><div class="ttdeci">MatrixExponential(const MatrixType &M)</div><div class="ttdoc">Constructor. </div><div class="ttdef"><b>Definition:</b> MatrixExponential.h:163</div></div>
<div class="ttc" id="structEigen_1_1MatrixExponentialReturnValue_html"><div class="ttname"><a href="structEigen_1_1MatrixExponentialReturnValue.html">Eigen::MatrixExponentialReturnValue</a></div><div class="ttdoc">Proxy for the matrix exponential of some matrix (expression). </div><div class="ttdef"><b>Definition:</b> MatrixExponential.h:400</div></div>
<div class="ttc" id="structEigen_1_1MatrixExponentialReturnValue_html_a7a10d88cebec216ce8dad9fc4926845f"><div class="ttname"><a href="structEigen_1_1MatrixExponentialReturnValue.html#a7a10d88cebec216ce8dad9fc4926845f">Eigen::MatrixExponentialReturnValue::MatrixExponentialReturnValue</a></div><div class="ttdeci">MatrixExponentialReturnValue(const Derived &src)</div><div class="ttdoc">Constructor. </div><div class="ttdef"><b>Definition:</b> MatrixExponential.h:410</div></div>
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