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<div class="title">DGMRES.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) 2012 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</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="l00008"></a><span class="lineno"> 8</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="l00009"></a><span class="lineno"> 9</span> </div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="preprocessor">#ifndef EIGEN_DGMRES_H</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_DGMRES_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor">#include <Eigen/Eigenvalues></span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> </div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="keyword">namespace </span>Eigen { </div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span>  </div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="keyword">template</span>< <span class="keyword">typename</span> _MatrixType,</div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span>  <span class="keyword">typename</span> _Preconditioner = DiagonalPreconditioner<typename _MatrixType::Scalar> ></div>
<div class="line"><a name="l00019"></a><span class="lineno"><a class="line" href="classEigen_1_1DGMRES.html"> 19</a></span> <span class="keyword">class </span><a class="code" href="classEigen_1_1DGMRES.html">DGMRES</a>;</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> </div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</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, <span class="keyword">typename</span> _Preconditioner></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span> <span class="keyword">struct </span>traits<<a class="code" href="classEigen_1_1DGMRES.html">DGMRES</a><_MatrixType,_Preconditioner> ></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">typedef</span> _MatrixType MatrixType;</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  <span class="keyword">typedef</span> _Preconditioner Preconditioner;</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span> };</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span> </div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span> <span class="keyword">template</span> <<span class="keyword">typename</span> VectorType, <span class="keyword">typename</span> IndexType></div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> <span class="keywordtype">void</span> sortWithPermutation (VectorType& vec, IndexType& perm, <span class="keyword">typename</span> IndexType::Scalar& ncut)</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span> {</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  eigen_assert(vec.size() == perm.size());</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> IndexType::Scalar Index; </div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> VectorType::Scalar Scalar; </div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keywordtype">bool</span> flag; </div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keywordflow">for</span> (Index k = 0; k < ncut; k++)</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  {</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  flag = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="keywordflow">for</span> (Index j = 0; j < vec.size()-1; j++)</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  {</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="keywordflow">if</span> ( vec(perm(j)) < vec(perm(j+1)) )</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  {</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  std::swap(perm(j),perm(j+1)); </div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  flag = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  }</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keywordflow">if</span> (!flag) <span class="keywordflow">break</span>; <span class="comment">// The vector is in sorted order</span></div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  }</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  }</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> }</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> </div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> }</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> <span class="keyword">template</span>< <span class="keyword">typename</span> _MatrixType, <span class="keyword">typename</span> _Preconditioner></div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span> <span class="keyword">class </span>DGMRES : <span class="keyword">public</span> IterativeSolverBase<DGMRES<_MatrixType,_Preconditioner> ></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span> {</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keyword">typedef</span> IterativeSolverBase<DGMRES> Base;</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="keyword">using</span> Base::mp_matrix;</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="keyword">using</span> Base::m_error;</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keyword">using</span> Base::m_iterations;</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="keyword">using</span> Base::m_info;</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="keyword">using</span> Base::m_isInitialized;</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keyword">using</span> Base::m_tolerance; </div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="keyword">typedef</span> _MatrixType MatrixType;</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="keyword">typedef</span> _Preconditioner Preconditioner;</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  <span class="keyword">typedef</span> Matrix<Scalar,Dynamic,Dynamic> DenseMatrix; </div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="keyword">typedef</span> Matrix<RealScalar,Dynamic,Dynamic> DenseRealMatrix; </div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="keyword">typedef</span> Matrix<Scalar,Dynamic,1> DenseVector;</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="keyword">typedef</span> Matrix<RealScalar,Dynamic,1> DenseRealVector; </div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keyword">typedef</span> Matrix<std::complex<RealScalar>, Dynamic, 1> ComplexVector;</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  </div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  </div>
<div class="line"><a name="l00124"></a><span class="lineno"><a class="line" href="classEigen_1_1DGMRES.html#acebe7001a430de6ff6059e42a2c3d7e1"> 124</a></span>  <a class="code" href="classEigen_1_1DGMRES.html#acebe7001a430de6ff6059e42a2c3d7e1">DGMRES</a>() : Base(),m_restart(30),m_neig(0),m_r(0),m_maxNeig(5),m_isDeflAllocated(false),m_isDeflInitialized(false) {}</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span> </div>
<div class="line"><a name="l00136"></a><span class="lineno"><a class="line" href="classEigen_1_1DGMRES.html#a13ee3911a809ab56f9d207f4201134ad"> 136</a></span>  <a class="code" href="classEigen_1_1DGMRES.html#a13ee3911a809ab56f9d207f4201134ad">DGMRES</a>(<span class="keyword">const</span> MatrixType& A) : Base(A),m_restart(30),m_neig(0),m_r(0),m_maxNeig(5),m_isDeflAllocated(false),m_isDeflInitialized(false)</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  {}</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span> </div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  ~<a class="code" href="classEigen_1_1DGMRES.html">DGMRES</a>() {}</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  </div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs,<span class="keyword">typename</span> Guess></div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  <span class="keyword">inline</span> <span class="keyword">const</span> internal::solve_retval_with_guess<DGMRES, Rhs, Guess></div>
<div class="line"><a name="l00148"></a><span class="lineno"><a class="line" href="classEigen_1_1DGMRES.html#a3ceaab72040862ca224adc3984eed08c"> 148</a></span>  <a class="code" href="classEigen_1_1DGMRES.html#a3ceaab72040862ca224adc3984eed08c">solveWithGuess</a>(<span class="keyword">const</span> MatrixBase<Rhs>& b, <span class="keyword">const</span> Guess& x0)<span class="keyword"> const</span></div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"DGMRES is not initialized."</span>);</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  eigen_assert(Base::rows()==b.rows()</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  && <span class="stringliteral">"DGMRES::solve(): invalid number of rows of the right hand side matrix b"</span>);</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  <span class="keywordflow">return</span> internal::solve_retval_with_guess</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <<a class="code" href="classEigen_1_1DGMRES.html#acebe7001a430de6ff6059e42a2c3d7e1">DGMRES</a>, Rhs, Guess>(*<span class="keyword">this</span>, b.derived(), x0);</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  }</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  </div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs,<span class="keyword">typename</span> Dest></div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  <span class="keywordtype">void</span> _solveWithGuess(<span class="keyword">const</span> Rhs& b, Dest& x)<span class="keyword"> const</span></div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span> <span class="keyword"> </span>{ </div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <span class="keywordtype">bool</span> failed = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j=0; j<b.cols(); ++j)</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  {</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  m_iterations = Base::maxIterations();</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  m_error = Base::m_tolerance;</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  </div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  <span class="keyword">typename</span> Dest::ColXpr xj(x,j);</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  <a class="code" href="classEigen_1_1DGMRES.html#ac77967ca048597f4b4cba3a6bf00b0a4">dgmres</a>(*mp_matrix, b.col(j), xj, Base::m_preconditioner);</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  }</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  m_info = failed ? NumericalIssue</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  : m_error <= Base::m_tolerance ? Success</div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  : NoConvergence;</div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  m_isInitialized = <span class="keyword">true</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="l00177"></a><span class="lineno"> 177</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs,<span class="keyword">typename</span> Dest></div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <span class="keywordtype">void</span> _solve(<span class="keyword">const</span> Rhs& b, Dest& x)<span class="keyword"> const</span></div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  x = b;</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  _solveWithGuess(b,x);</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  }</div>
<div class="line"><a name="l00186"></a><span class="lineno"><a class="line" href="classEigen_1_1DGMRES.html#ae246359e104d63520158c26329caac80"> 186</a></span>  <span class="keywordtype">int</span> <a class="code" href="classEigen_1_1DGMRES.html#ae246359e104d63520158c26329caac80">restart</a>() { <span class="keywordflow">return</span> m_restart; }</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  </div>
<div class="line"><a name="l00191"></a><span class="lineno"><a class="line" href="classEigen_1_1DGMRES.html#a88b3d18c69eccbd4b1c68a5713a05bb3"> 191</a></span>  <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1DGMRES.html#a88b3d18c69eccbd4b1c68a5713a05bb3">set_restart</a>(<span class="keyword">const</span> <span class="keywordtype">int</span> <a class="code" href="classEigen_1_1DGMRES.html#ae246359e104d63520158c26329caac80">restart</a>) { m_restart=<a class="code" href="classEigen_1_1DGMRES.html#ae246359e104d63520158c26329caac80">restart</a>; }</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  </div>
<div class="line"><a name="l00196"></a><span class="lineno"><a class="line" href="classEigen_1_1DGMRES.html#a16852b8c7e2b1a8154937d392d342051"> 196</a></span>  <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1DGMRES.html#a16852b8c7e2b1a8154937d392d342051">setEigenv</a>(<span class="keyword">const</span> <span class="keywordtype">int</span> neig) </div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  {</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  m_neig = neig;</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="keywordflow">if</span> (neig+1 > m_maxNeig) m_maxNeig = neig+1; <span class="comment">// To allow for complex conjugates</span></div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  }</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  </div>
<div class="line"><a name="l00205"></a><span class="lineno"><a class="line" href="classEigen_1_1DGMRES.html#a62f9d64844caff6007cabecc997fbad1"> 205</a></span>  <span class="keywordtype">int</span> <a class="code" href="classEigen_1_1DGMRES.html#a62f9d64844caff6007cabecc997fbad1">deflSize</a>() {<span class="keywordflow">return</span> m_r; }</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  </div>
<div class="line"><a name="l00210"></a><span class="lineno"><a class="line" href="classEigen_1_1DGMRES.html#afed207f423f44020219ac444b982dcf9"> 210</a></span>  <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1DGMRES.html#afed207f423f44020219ac444b982dcf9">setMaxEigenv</a>(<span class="keyword">const</span> <span class="keywordtype">int</span> maxNeig) { m_maxNeig = maxNeig; }</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  </div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="comment">// DGMRES algorithm </span></div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs, <span class="keyword">typename</span> Dest></div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1DGMRES.html#ac77967ca048597f4b4cba3a6bf00b0a4">dgmres</a>(<span class="keyword">const</span> MatrixType& mat,<span class="keyword">const</span> Rhs& rhs, Dest& x, <span class="keyword">const</span> Preconditioner& precond) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  <span class="comment">// Perform one cycle of GMRES</span></div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Dest></div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="keywordtype">int</span> <a class="code" href="classEigen_1_1DGMRES.html#ad56b61782bcd392b88b807c9e6099e02">dgmresCycle</a>(<span class="keyword">const</span> MatrixType& mat, <span class="keyword">const</span> Preconditioner& precond, Dest& x, DenseVector& r0, RealScalar& beta, <span class="keyword">const</span> RealScalar& normRhs, <span class="keywordtype">int</span>& nbIts) <span class="keyword">const</span>; </div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="comment">// Compute data to use for deflation </span></div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="keywordtype">int</span> dgmresComputeDeflationData(<span class="keyword">const</span> MatrixType& mat, <span class="keyword">const</span> Preconditioner& precond, <span class="keyword">const</span> Index& it, Index& neig) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  <span class="comment">// Apply deflation to a vector</span></div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <span class="keyword">template</span><<span class="keyword">typename</span> RhsType, <span class="keyword">typename</span> DestType></div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <span class="keywordtype">int</span> dgmresApplyDeflation(<span class="keyword">const</span> RhsType& In, DestType& Out) <span class="keyword">const</span>; </div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  ComplexVector schurValues(<span class="keyword">const</span> ComplexSchur<DenseMatrix>& schurofH) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  ComplexVector schurValues(<span class="keyword">const</span> RealSchur<DenseMatrix>& schurofH) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <span class="comment">// Init data for deflation</span></div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="keywordtype">void</span> dgmresInitDeflation(Index& rows) <span class="keyword">const</span>; </div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  <span class="keyword">mutable</span> DenseMatrix m_V; <span class="comment">// Krylov basis vectors</span></div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  <span class="keyword">mutable</span> DenseMatrix m_H; <span class="comment">// Hessenberg matrix </span></div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  <span class="keyword">mutable</span> DenseMatrix m_Hes; <span class="comment">// Initial hessenberg matrix wihout Givens rotations applied</span></div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  <span class="keyword">mutable</span> Index m_restart; <span class="comment">// Maximum size of the Krylov subspace</span></div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <span class="keyword">mutable</span> DenseMatrix m_U; <span class="comment">// Vectors that form the basis of the invariant subspace </span></div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="keyword">mutable</span> DenseMatrix m_MU; <span class="comment">// matrix operator applied to m_U (for next cycles)</span></div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  <span class="keyword">mutable</span> DenseMatrix m_T; <span class="comment">/* T=U^T*M^{-1}*A*U */</span></div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keyword">mutable</span> PartialPivLU<DenseMatrix> m_luT; <span class="comment">// LU factorization of m_T</span></div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="keyword">mutable</span> <span class="keywordtype">int</span> m_neig; <span class="comment">//Number of eigenvalues to extract at each restart</span></div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  <span class="keyword">mutable</span> <span class="keywordtype">int</span> m_r; <span class="comment">// Current number of deflated eigenvalues, size of m_U</span></div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="keyword">mutable</span> <span class="keywordtype">int</span> m_maxNeig; <span class="comment">// Maximum number of eigenvalues to deflate</span></div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="keyword">mutable</span> RealScalar m_lambdaN; <span class="comment">//Modulus of the largest eigenvalue of A</span></div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  <span class="keyword">mutable</span> <span class="keywordtype">bool</span> m_isDeflAllocated;</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  <span class="keyword">mutable</span> <span class="keywordtype">bool</span> m_isDeflInitialized;</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  </div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="comment">//Adaptive strategy </span></div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  <span class="keyword">mutable</span> RealScalar m_smv; <span class="comment">// Smaller multiple of the remaining number of steps allowed</span></div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <span class="keyword">mutable</span> <span class="keywordtype">bool</span> m_force; <span class="comment">// Force the use of deflation at each restart</span></div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  </div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span> }; </div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span> <span class="keyword">template</span>< <span class="keyword">typename</span> _MatrixType, <span class="keyword">typename</span> _Preconditioner></div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span> <span class="keyword">template</span><<span class="keyword">typename</span> Rhs, <span class="keyword">typename</span> Dest></div>
<div class="line"><a name="l00256"></a><span class="lineno"><a class="line" href="classEigen_1_1DGMRES.html#ac77967ca048597f4b4cba3a6bf00b0a4"> 256</a></span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1DGMRES.html#ac77967ca048597f4b4cba3a6bf00b0a4">DGMRES<_MatrixType, _Preconditioner>::dgmres</a>(<span class="keyword">const</span> MatrixType& mat,<span class="keyword">const</span> Rhs& rhs, Dest& x,</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  <span class="keyword">const</span> Preconditioner& precond)<span class="keyword"> const</span></div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <span class="comment">//Initialization</span></div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  <span class="keywordtype">int</span> n = mat.rows(); </div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  DenseVector r0(n); </div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  <span class="keywordtype">int</span> nbIts = 0; </div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  m_H.resize(m_restart+1, m_restart);</div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  m_Hes.resize(m_restart, m_restart);</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  m_V.resize(n,m_restart+1);</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <span class="comment">//Initial residual vector and intial norm</span></div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  x = precond.solve(x);</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  r0 = rhs - mat * x; </div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  RealScalar beta = r0.norm(); </div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  RealScalar normRhs = rhs.norm();</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  m_error = beta/normRhs; </div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="keywordflow">if</span>(m_error < m_tolerance)</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  m_info = Success; </div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  m_info = NoConvergence;</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  </div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="comment">// Iterative process</span></div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  <span class="keywordflow">while</span> (nbIts < m_iterations && m_info == NoConvergence)</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  {</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  dgmresCycle(mat, precond, x, r0, beta, normRhs, nbIts); </div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  </div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  <span class="comment">// Compute the new residual vector for the restart </span></div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  <span class="keywordflow">if</span> (nbIts < m_iterations && m_info == NoConvergence)</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  r0 = rhs - mat * x; </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> } </div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span> </div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span> <span class="keyword">template</span>< <span class="keyword">typename</span> _MatrixType, <span class="keyword">typename</span> _Preconditioner></div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span> <span class="keyword">template</span><<span class="keyword">typename</span> Dest></div>
<div class="line"><a name="l00300"></a><span class="lineno"><a class="line" href="classEigen_1_1DGMRES.html#ad56b61782bcd392b88b807c9e6099e02"> 300</a></span> <span class="keywordtype">int</span> <a class="code" href="classEigen_1_1DGMRES.html#ad56b61782bcd392b88b807c9e6099e02">DGMRES<_MatrixType, _Preconditioner>::dgmresCycle</a>(<span class="keyword">const</span> MatrixType& mat, <span class="keyword">const</span> Preconditioner& precond, Dest& x, DenseVector& r0, RealScalar& beta, <span class="keyword">const</span> RealScalar& normRhs, <span class="keywordtype">int</span>& nbIts)<span class="keyword"> const</span></div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  <span class="comment">//Initialization </span></div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  DenseVector g(m_restart+1); <span class="comment">// Right hand side of the least square problem</span></div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  g.setZero(); </div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>  g(0) = Scalar(beta); </div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  m_V.col(0) = r0/beta; </div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  m_info = NoConvergence; </div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  std::vector<JacobiRotation<Scalar> >gr(m_restart); <span class="comment">// Givens rotations</span></div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  <span class="keywordtype">int</span> it = 0; <span class="comment">// Number of inner iterations </span></div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <span class="keywordtype">int</span> n = mat.rows();</div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  DenseVector tv1(n), tv2(n); <span class="comment">//Temporary vectors</span></div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <span class="keywordflow">while</span> (m_info == NoConvergence && it < m_restart && nbIts < m_iterations)</div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  { </div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <span class="comment">// Apply preconditioner(s) at right</span></div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  <span class="keywordflow">if</span> (m_isDeflInitialized )</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  {</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  dgmresApplyDeflation(m_V.col(it), tv1); <span class="comment">// Deflation</span></div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  tv2 = precond.solve(tv1); </div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  }</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  <span class="keywordflow">else</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>  tv2 = precond.solve(m_V.col(it)); <span class="comment">// User's selected preconditioner</span></div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  }</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  tv1 = mat * tv2; </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="comment">// Orthogonalize it with the previous basis in the basis using modified Gram-Schmidt</span></div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  Scalar coef; </div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i <= it; ++i)</div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  { </div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  coef = tv1.dot(m_V.col(i));</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  tv1 = tv1 - coef * m_V.col(i); </div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  m_H(i,it) = coef; </div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  m_Hes(i,it) = coef; </div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  }</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  <span class="comment">// Normalize the vector </span></div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  coef = tv1.norm(); </div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  m_V.col(it+1) = tv1/coef;</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  m_H(it+1, it) = coef;</div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span> <span class="comment">// m_Hes(it+1,it) = coef; </span></div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  </div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  <span class="comment">// FIXME Check for happy breakdown </span></div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  </div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  <span class="comment">// Update Hessenberg matrix with Givens rotations</span></div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 1; i <= it; ++i) </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>  m_H.col(it).applyOnTheLeft(i-1,i,gr[i-1].adjoint());</div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  }</div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  <span class="comment">// Compute the new plane rotation </span></div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  gr[it].makeGivens(m_H(it, it), m_H(it+1,it)); </div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  <span class="comment">// Apply the new rotation</span></div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  m_H.col(it).applyOnTheLeft(it,it+1,gr[it].adjoint());</div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  g.applyOnTheLeft(it,it+1, gr[it].adjoint()); </div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>  </div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>  beta = std::abs(g(it+1));</div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>  m_error = beta/normRhs; </div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>  std::cerr << nbIts << <span class="stringliteral">" Relative Residual Norm "</span> << m_error << std::endl;</div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>  it++; nbIts++; </div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>  </div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  <span class="keywordflow">if</span> (m_error < m_tolerance)</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  {</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>  <span class="comment">// The method has converged</span></div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>  m_info = Success;</div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  }</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  }</div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  </div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  <span class="comment">// Compute the new coefficients by solving the least square problem</span></div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span> <span class="comment">// it++;</span></div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  <span class="comment">//FIXME Check first if the matrix is singular ... zero diagonal</span></div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  DenseVector nrs(m_restart); </div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  nrs = m_H.topLeftCorner(it,it).template triangularView<Upper>().solve(g.head(it)); </div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>  </div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>  <span class="comment">// Form the new solution</span></div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  <span class="keywordflow">if</span> (m_isDeflInitialized)</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  {</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>  tv1 = m_V.leftCols(it) * nrs; </div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>  dgmresApplyDeflation(tv1, tv2); </div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>  x = x + precond.solve(tv2);</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>  }</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>  x = x + precond.solve(m_V.leftCols(it) * nrs); </div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  </div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>  <span class="comment">// Go for a new cycle and compute data for deflation</span></div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  <span class="keywordflow">if</span>(nbIts < m_iterations && m_info == NoConvergence && m_neig > 0 && (m_r+m_neig) < m_maxNeig)</div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  dgmresComputeDeflationData(mat, precond, it, m_neig); </div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>  <span class="keywordflow">return</span> 0; </div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  </div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span> }</div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span> </div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span> </div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span> <span class="keyword">template</span>< <span class="keyword">typename</span> _MatrixType, <span class="keyword">typename</span> _Preconditioner></div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span> <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1DGMRES.html">DGMRES<_MatrixType, _Preconditioner>::dgmresInitDeflation</a>(Index& rows)<span class="keyword"> const</span></div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>  m_U.resize(rows, m_maxNeig);</div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  m_MU.resize(rows, m_maxNeig); </div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  m_T.resize(m_maxNeig, m_maxNeig);</div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  m_lambdaN = 0.0; </div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>  m_isDeflAllocated = <span class="keyword">true</span>; </div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span> }</div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span> </div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span> <span class="keyword">template</span>< <span class="keyword">typename</span> _MatrixType, <span class="keyword">typename</span> _Preconditioner></div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span> <span class="keyword">inline</span> <span class="keyword">typename</span> DGMRES<_MatrixType, _Preconditioner>::ComplexVector DGMRES<_MatrixType, _Preconditioner>::schurValues(<span class="keyword">const</span> ComplexSchur<DenseMatrix>& schurofH)<span class="keyword"> const</span></div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  <span class="keywordflow">return</span> schurofH.matrixT().diagonal();</div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span> }</div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span> </div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span> <span class="keyword">template</span>< <span class="keyword">typename</span> _MatrixType, <span class="keyword">typename</span> _Preconditioner></div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span> <span class="keyword">inline</span> <span class="keyword">typename</span> DGMRES<_MatrixType, _Preconditioner>::ComplexVector DGMRES<_MatrixType, _Preconditioner>::schurValues(<span class="keyword">const</span> RealSchur<DenseMatrix>& schurofH)<span class="keyword"> const</span></div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  <span class="keyword">const</span> DenseMatrix& T = schurofH.matrixT();</div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  Index it = T.rows();</div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>  ComplexVector eig(it);</div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  Index j = 0;</div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  <span class="keywordflow">while</span> (j < it-1)</div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  {</div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  <span class="keywordflow">if</span> (T(j+1,j) ==Scalar(0))</div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  {</div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  eig(j) = std::complex<RealScalar>(T(j,j),RealScalar(0)); </div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>  j++; </div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  }</div>
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span>  <span class="keywordflow">else</span></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>  eig(j) = std::complex<RealScalar>(T(j,j),T(j+1,j)); </div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>  eig(j+1) = std::complex<RealScalar>(T(j,j+1),T(j+1,j+1));</div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>  j++;</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>  }</div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  <span class="keywordflow">if</span> (j < it-1) eig(j) = std::complex<RealScalar>(T(j,j),RealScalar(0));</div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  <span class="keywordflow">return</span> eig;</div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span> }</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> <span class="keyword">template</span>< <span class="keyword">typename</span> _MatrixType, <span class="keyword">typename</span> _Preconditioner></div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span> <span class="keywordtype">int</span> DGMRES<_MatrixType, _Preconditioner>::dgmresComputeDeflationData(<span class="keyword">const</span> MatrixType& mat, <span class="keyword">const</span> Preconditioner& precond, <span class="keyword">const</span> Index& it, Index& neig)<span class="keyword"> const</span></div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  <span class="comment">// First, find the Schur form of the Hessenberg matrix H</span></div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  <span class="keyword">typename</span> internal::conditional<NumTraits<Scalar>::IsComplex, ComplexSchur<DenseMatrix>, RealSchur<DenseMatrix> >::type schurofH; </div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  <span class="keywordtype">bool</span> computeU = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>  DenseMatrix matrixQ(it,it); </div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  matrixQ.setIdentity();</div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  schurofH.computeFromHessenberg(m_Hes.topLeftCorner(it,it), matrixQ, computeU); </div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  </div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span>  ComplexVector eig(it);</div>
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span>  Matrix<Index,Dynamic,1>perm(it); </div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  eig = this->schurValues(schurofH);</div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span>  </div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  <span class="comment">// Reorder the absolute values of Schur values</span></div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  DenseRealVector modulEig(it); </div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j=0; j<it; ++j) modulEig(j) = std::abs(eig(j)); </div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  perm.setLinSpaced(it,0,it-1);</div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  internal::sortWithPermutation(modulEig, perm, neig);</div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  </div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>  <span class="keywordflow">if</span> (!m_lambdaN)</div>
<div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  {</div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  m_lambdaN = (std::max)(modulEig.maxCoeff(), m_lambdaN);</div>
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  }</div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  <span class="comment">//Count the real number of extracted eigenvalues (with complex conjugates)</span></div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  <span class="keywordtype">int</span> nbrEig = 0; </div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  <span class="keywordflow">while</span> (nbrEig < neig)</div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  {</div>
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span>  <span class="keywordflow">if</span>(eig(perm(it-nbrEig-1)).imag() == RealScalar(0)) nbrEig++; </div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  <span class="keywordflow">else</span> nbrEig += 2; </div>
<div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  }</div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span>  <span class="comment">// Extract the Schur vectors corresponding to the smallest Ritz values</span></div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  DenseMatrix Sr(it, nbrEig); </div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  Sr.setZero();</div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < nbrEig; j++)</div>
<div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  {</div>
<div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  Sr.col(j) = schurofH.matrixU().col(perm(it-j-1));</div>
<div class="line"><a name="l00470"></a><span class="lineno"> 470</span>  }</div>
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span>  </div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  <span class="comment">// Form the Schur vectors of the initial matrix using the Krylov basis</span></div>
<div class="line"><a name="l00473"></a><span class="lineno"> 473</span>  DenseMatrix X; </div>
<div class="line"><a name="l00474"></a><span class="lineno"> 474</span>  X = m_V.leftCols(it) * Sr;</div>
<div class="line"><a name="l00475"></a><span class="lineno"> 475</span>  <span class="keywordflow">if</span> (m_r)</div>
<div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  {</div>
<div class="line"><a name="l00477"></a><span class="lineno"> 477</span>  <span class="comment">// Orthogonalize X against m_U using modified Gram-Schmidt</span></div>
<div class="line"><a name="l00478"></a><span class="lineno"> 478</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < nbrEig; j++)</div>
<div class="line"><a name="l00479"></a><span class="lineno"> 479</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k =0; k < m_r; k++)</div>
<div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  X.col(j) = X.col(j) - (m_U.col(k).dot(X.col(j)))*m_U.col(k); </div>
<div class="line"><a name="l00481"></a><span class="lineno"> 481</span>  }</div>
<div class="line"><a name="l00482"></a><span class="lineno"> 482</span>  </div>
<div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  <span class="comment">// Compute m_MX = A * M^-1 * X</span></div>
<div class="line"><a name="l00484"></a><span class="lineno"> 484</span>  Index m = m_V.rows();</div>
<div class="line"><a name="l00485"></a><span class="lineno"> 485</span>  <span class="keywordflow">if</span> (!m_isDeflAllocated) </div>
<div class="line"><a name="l00486"></a><span class="lineno"> 486</span>  dgmresInitDeflation(m); </div>
<div class="line"><a name="l00487"></a><span class="lineno"> 487</span>  DenseMatrix MX(m, nbrEig);</div>
<div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  DenseVector tv1(m);</div>
<div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < nbrEig; j++)</div>
<div class="line"><a name="l00490"></a><span class="lineno"> 490</span>  {</div>
<div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  tv1 = mat * X.col(j);</div>
<div class="line"><a name="l00492"></a><span class="lineno"> 492</span>  MX.col(j) = precond.solve(tv1);</div>
<div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  }</div>
<div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  </div>
<div class="line"><a name="l00495"></a><span class="lineno"> 495</span>  <span class="comment">//Update m_T = [U'MU U'MX; X'MU X'MX]</span></div>
<div class="line"><a name="l00496"></a><span class="lineno"> 496</span>  m_T.block(m_r, m_r, nbrEig, nbrEig) = X.transpose() * MX; </div>
<div class="line"><a name="l00497"></a><span class="lineno"> 497</span>  <span class="keywordflow">if</span>(m_r)</div>
<div class="line"><a name="l00498"></a><span class="lineno"> 498</span>  {</div>
<div class="line"><a name="l00499"></a><span class="lineno"> 499</span>  m_T.block(0, m_r, m_r, nbrEig) = m_U.leftCols(m_r).transpose() * MX; </div>
<div class="line"><a name="l00500"></a><span class="lineno"> 500</span>  m_T.block(m_r, 0, nbrEig, m_r) = X.transpose() * m_MU.leftCols(m_r);</div>
<div class="line"><a name="l00501"></a><span class="lineno"> 501</span>  }</div>
<div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  </div>
<div class="line"><a name="l00503"></a><span class="lineno"> 503</span>  <span class="comment">// Save X into m_U and m_MX in m_MU</span></div>
<div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < nbrEig; j++) m_U.col(m_r+j) = X.col(j);</div>
<div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < nbrEig; j++) m_MU.col(m_r+j) = MX.col(j);</div>
<div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  <span class="comment">// Increase the size of the invariant subspace</span></div>
<div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  m_r += nbrEig; </div>
<div class="line"><a name="l00508"></a><span class="lineno"> 508</span>  </div>
<div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  <span class="comment">// Factorize m_T into m_luT</span></div>
<div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  m_luT.compute(m_T.topLeftCorner(m_r, m_r));</div>
<div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  </div>
<div class="line"><a name="l00512"></a><span class="lineno"> 512</span>  <span class="comment">//FIXME CHeck if the factorization was correctly done (nonsingular matrix)</span></div>
<div class="line"><a name="l00513"></a><span class="lineno"> 513</span>  m_isDeflInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  <span class="keywordflow">return</span> 0; </div>
<div class="line"><a name="l00515"></a><span class="lineno"> 515</span> }</div>
<div class="line"><a name="l00516"></a><span class="lineno"> 516</span> <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType, <span class="keyword">typename</span> _Preconditioner></div>
<div class="line"><a name="l00517"></a><span class="lineno"> 517</span> <span class="keyword">template</span><<span class="keyword">typename</span> RhsType, <span class="keyword">typename</span> DestType></div>
<div class="line"><a name="l00518"></a><span class="lineno"> 518</span> <span class="keywordtype">int</span> DGMRES<_MatrixType, _Preconditioner>::dgmresApplyDeflation(<span class="keyword">const</span> RhsType &x, DestType &y)<span class="keyword"> const</span></div>
<div class="line"><a name="l00519"></a><span class="lineno"> 519</span> <span class="keyword"></span>{</div>
<div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  DenseVector x1 = m_U.leftCols(m_r).transpose() * x; </div>
<div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  y = x + m_U.leftCols(m_r) * ( m_lambdaN * m_luT.solve(x1) - x1);</div>
<div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  <span class="keywordflow">return</span> 0; </div>
<div class="line"><a name="l00523"></a><span class="lineno"> 523</span> }</div>
<div class="line"><a name="l00524"></a><span class="lineno"> 524</span> </div>
<div class="line"><a name="l00525"></a><span class="lineno"> 525</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00526"></a><span class="lineno"> 526</span> </div>
<div class="line"><a name="l00527"></a><span class="lineno"> 527</span>  <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType, <span class="keyword">typename</span> _Preconditioner, <span class="keyword">typename</span> Rhs></div>
<div class="line"><a name="l00528"></a><span class="lineno"> 528</span> <span class="keyword">struct </span>solve_retval<DGMRES<_MatrixType, _Preconditioner>, Rhs></div>
<div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  : solve_retval_base<DGMRES<_MatrixType, _Preconditioner>, Rhs></div>
<div class="line"><a name="l00530"></a><span class="lineno"> 530</span> {</div>
<div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  <span class="keyword">typedef</span> DGMRES<_MatrixType, _Preconditioner> Dec;</div>
<div class="line"><a name="l00532"></a><span class="lineno"> 532</span>  EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)</div>
<div class="line"><a name="l00533"></a><span class="lineno"> 533</span> </div>
<div class="line"><a name="l00534"></a><span class="lineno"> 534</span>  template<typename Dest> <span class="keywordtype">void</span> evalTo(Dest& dst)<span class="keyword"> const</span></div>
<div class="line"><a name="l00535"></a><span class="lineno"> 535</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00536"></a><span class="lineno"> 536</span>  dec()._solve(rhs(),dst);</div>
<div class="line"><a name="l00537"></a><span class="lineno"> 537</span>  }</div>
<div class="line"><a name="l00538"></a><span class="lineno"> 538</span> };</div>
<div class="line"><a name="l00539"></a><span class="lineno"> 539</span> } <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00540"></a><span class="lineno"> 540</span> </div>
<div class="line"><a name="l00541"></a><span class="lineno"> 541</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00542"></a><span class="lineno"> 542</span> <span class="preprocessor">#endif </span></div>
<div class="ttc" id="classEigen_1_1DGMRES_html_a16852b8c7e2b1a8154937d392d342051"><div class="ttname"><a href="classEigen_1_1DGMRES.html#a16852b8c7e2b1a8154937d392d342051">Eigen::DGMRES::setEigenv</a></div><div class="ttdeci">void setEigenv(const int neig)</div><div class="ttdef"><b>Definition:</b> DGMRES.h:196</div></div>
<div class="ttc" id="classEigen_1_1DGMRES_html"><div class="ttname"><a href="classEigen_1_1DGMRES.html">Eigen::DGMRES</a></div><div class="ttdoc">A Restarted GMRES with deflation. This class implements a modification of the GMRES solver for sparse...</div><div class="ttdef"><b>Definition:</b> DGMRES.h:19</div></div>
<div class="ttc" id="classEigen_1_1DGMRES_html_ae246359e104d63520158c26329caac80"><div class="ttname"><a href="classEigen_1_1DGMRES.html#ae246359e104d63520158c26329caac80">Eigen::DGMRES::restart</a></div><div class="ttdeci">int restart()</div><div class="ttdef"><b>Definition:</b> DGMRES.h:186</div></div>
<div class="ttc" id="classEigen_1_1DGMRES_html_ad56b61782bcd392b88b807c9e6099e02"><div class="ttname"><a href="classEigen_1_1DGMRES.html#ad56b61782bcd392b88b807c9e6099e02">Eigen::DGMRES::dgmresCycle</a></div><div class="ttdeci">int dgmresCycle(const MatrixType &mat, const Preconditioner &precond, Dest &x, DenseVector &r0, RealScalar &beta, const RealScalar &normRhs, int &nbIts) const </div><div class="ttdoc">Perform one restart cycle of DGMRES. </div><div class="ttdef"><b>Definition:</b> DGMRES.h:300</div></div>
<div class="ttc" id="classEigen_1_1DGMRES_html_afed207f423f44020219ac444b982dcf9"><div class="ttname"><a href="classEigen_1_1DGMRES.html#afed207f423f44020219ac444b982dcf9">Eigen::DGMRES::setMaxEigenv</a></div><div class="ttdeci">void setMaxEigenv(const int maxNeig)</div><div class="ttdef"><b>Definition:</b> DGMRES.h:210</div></div>
<div class="ttc" id="classEigen_1_1DGMRES_html_acebe7001a430de6ff6059e42a2c3d7e1"><div class="ttname"><a href="classEigen_1_1DGMRES.html#acebe7001a430de6ff6059e42a2c3d7e1">Eigen::DGMRES::DGMRES</a></div><div class="ttdeci">DGMRES()</div><div class="ttdef"><b>Definition:</b> DGMRES.h:124</div></div>
<div class="ttc" id="classEigen_1_1DGMRES_html_a3ceaab72040862ca224adc3984eed08c"><div class="ttname"><a href="classEigen_1_1DGMRES.html#a3ceaab72040862ca224adc3984eed08c">Eigen::DGMRES::solveWithGuess</a></div><div class="ttdeci">const internal::solve_retval_with_guess< DGMRES, Rhs, Guess > solveWithGuess(const MatrixBase< Rhs > &b, const Guess &x0) const </div><div class="ttdef"><b>Definition:</b> DGMRES.h:148</div></div>
<div class="ttc" id="classEigen_1_1DGMRES_html_a62f9d64844caff6007cabecc997fbad1"><div class="ttname"><a href="classEigen_1_1DGMRES.html#a62f9d64844caff6007cabecc997fbad1">Eigen::DGMRES::deflSize</a></div><div class="ttdeci">int deflSize()</div><div class="ttdef"><b>Definition:</b> DGMRES.h:205</div></div>
<div class="ttc" id="classEigen_1_1DGMRES_html_a88b3d18c69eccbd4b1c68a5713a05bb3"><div class="ttname"><a href="classEigen_1_1DGMRES.html#a88b3d18c69eccbd4b1c68a5713a05bb3">Eigen::DGMRES::set_restart</a></div><div class="ttdeci">void set_restart(const int restart)</div><div class="ttdef"><b>Definition:</b> DGMRES.h:191</div></div>
<div class="ttc" id="classEigen_1_1DGMRES_html_ac77967ca048597f4b4cba3a6bf00b0a4"><div class="ttname"><a href="classEigen_1_1DGMRES.html#ac77967ca048597f4b4cba3a6bf00b0a4">Eigen::DGMRES::dgmres</a></div><div class="ttdeci">void dgmres(const MatrixType &mat, const Rhs &rhs, Dest &x, const Preconditioner &precond) const </div><div class="ttdoc">Perform several cycles of restarted GMRES with modified Gram Schmidt,. </div><div class="ttdef"><b>Definition:</b> DGMRES.h:256</div></div>
<div class="ttc" id="classEigen_1_1DGMRES_html_a13ee3911a809ab56f9d207f4201134ad"><div class="ttname"><a href="classEigen_1_1DGMRES.html#a13ee3911a809ab56f9d207f4201134ad">Eigen::DGMRES::DGMRES</a></div><div class="ttdeci">DGMRES(const MatrixType &A)</div><div class="ttdef"><b>Definition:</b> DGMRES.h:136</div></div>
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