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<div class="title">GMRES.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) 2011 Gael Guennebaud <gael.guennebaud@inria.fr></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">// Copyright (C) 2012 Kolja Brix <brix@igpm.rwth-aaachen.de></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_GMRES_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_GMRES_H</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="keyword">namespace </span>Eigen { </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>internal {</div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> </div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> <span class="keyword">template</span><<span class="keyword">typename</span> MatrixType, <span class="keyword">typename</span> Rhs, <span class="keyword">typename</span> Dest, <span class="keyword">typename</span> Preconditioner></div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> <span class="keywordtype">bool</span> gmres(<span class="keyword">const</span> MatrixType & mat, <span class="keyword">const</span> Rhs & rhs, Dest & x, <span class="keyword">const</span> Preconditioner & precond,</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="keywordtype">int</span> &iters, <span class="keyword">const</span> <span class="keywordtype">int</span> &restart, <span class="keyword">typename</span> Dest::RealScalar & tol_error) {</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>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> </div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Dest::RealScalar RealScalar;</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Dest::Scalar Scalar;</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="keyword">typedef</span> Matrix < Scalar, Dynamic, 1 > VectorType;</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keyword">typedef</span> Matrix < Scalar, Dynamic, Dynamic > FMatrixType;</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span> </div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  RealScalar tol = tol_error;</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> maxIters = iters;</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  iters = 0;</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span> </div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> m = mat.rows();</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span> </div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  VectorType p0 = rhs - mat*x;</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  VectorType r0 = precond.solve(p0);</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="comment">// RealScalar r0_sqnorm = r0.squaredNorm();</span></div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span> </div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  VectorType w = VectorType::Zero(restart + 1);</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> </div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  FMatrixType H = FMatrixType::Zero(m, restart + 1);</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  VectorType tau = VectorType::Zero(restart + 1);</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  std::vector < JacobiRotation < Scalar > > G(restart);</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> </div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="comment">// generate first Householder vector</span></div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  VectorType e;</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  RealScalar beta;</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  r0.makeHouseholder(e, tau.coeffRef(0), beta);</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  w(0)=(Scalar) beta;</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  H.bottomLeftCorner(m - 1, 1) = e;</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span> </div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> k = 1; k <= restart; ++k) {</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span> </div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  ++iters;</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span> </div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  VectorType v = VectorType::Unit(m, k - 1), workspace(m);</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span> </div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  <span class="comment">// apply Householder reflections H_{1} ... H_{k-1} to v</span></div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = k - 1; i >= 0; --i) {</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  v.tail(m - i).applyHouseholderOnTheLeft(H.col(i).tail(m - i - 1), tau.coeffRef(i), workspace.data());</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  }</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> </div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="comment">// apply matrix M to v: v = mat * v;</span></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  VectorType t=mat*v;</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  v=precond.solve(t);</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span> </div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="comment">// apply Householder reflections H_{k-1} ... H_{1} to v</span></div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < k; ++i) {</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  v.tail(m - i).applyHouseholderOnTheLeft(H.col(i).tail(m - i - 1), tau.coeffRef(i), workspace.data());</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  }</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span> </div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  <span class="keywordflow">if</span> (v.tail(m - k).norm() != 0.0) {</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span> </div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keywordflow">if</span> (k <= restart) {</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span> </div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="comment">// generate new Householder vector</span></div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  VectorType e(m - k - 1);</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  RealScalar beta;</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  v.tail(m - k).makeHouseholder(e, tau.coeffRef(k), beta);</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  H.col(k).tail(m - k - 1) = e;</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span> </div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="comment">// apply Householder reflection H_{k} to v</span></div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  v.tail(m - k).applyHouseholderOnTheLeft(H.col(k).tail(m - k - 1), tau.coeffRef(k), workspace.data());</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span> </div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  }</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  }</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span> </div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="keywordflow">if</span> (k > 1) {</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < k - 1; ++i) {</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="comment">// apply old Givens rotations to v</span></div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  v.applyOnTheLeft(i, i + 1, G[i].adjoint());</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  }</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</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="keywordflow">if</span> (k<m && v(k) != (Scalar) 0) {</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="comment">// determine next Givens rotation</span></div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  G[k - 1].makeGivens(v(k - 1), v(k));</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span> </div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="comment">// apply Givens rotation to v and w</span></div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  v.applyOnTheLeft(k - 1, k, G[k - 1].adjoint());</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  w.applyOnTheLeft(k - 1, k, G[k - 1].adjoint());</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span> </div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  }</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span> </div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="comment">// insert coefficients into upper matrix triangle</span></div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  H.col(k - 1).head(k) = v.head(k);</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span> </div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="keywordtype">bool</span> stop=(k==m || abs(w(k)) < tol || iters == maxIters);</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span> </div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  <span class="keywordflow">if</span> (stop || k == restart) {</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span> </div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="comment">// solve upper triangular system</span></div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  VectorType y = w.head(k);</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  H.topLeftCorner(k, k).template triangularView < Eigen::Upper > ().solveInPlace(y);</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span> </div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <span class="comment">// use Horner-like scheme to calculate solution vector</span></div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  VectorType x_new = y(k - 1) * VectorType::Unit(m, k - 1);</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span> </div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  <span class="comment">// apply Householder reflection H_{k} to x_new</span></div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  x_new.tail(m - k + 1).applyHouseholderOnTheLeft(H.col(k - 1).tail(m - k), tau.coeffRef(k - 1), workspace.data());</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span> </div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = k - 2; i >= 0; --i) {</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  x_new += y(i) * VectorType::Unit(m, i);</div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="comment">// apply Householder reflection H_{i} to x_new</span></div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  x_new.tail(m - i).applyHouseholderOnTheLeft(H.col(i).tail(m - i - 1), tau.coeffRef(i), workspace.data());</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  }</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span> </div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  x += x_new;</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span> </div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  <span class="keywordflow">if</span> (stop) {</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  k=0;</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">// reset data for a restart r0 = rhs - mat * x;</span></div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  VectorType p0=mat*x;</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  VectorType p1=precond.solve(p0);</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  r0 = rhs - p1;</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span> <span class="comment">// r0_sqnorm = r0.squaredNorm();</span></div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  w = VectorType::Zero(restart + 1);</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  H = FMatrixType::Zero(m, restart + 1);</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  tau = VectorType::Zero(restart + 1);</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span> </div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <span class="comment">// generate first Householder vector</span></div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  RealScalar beta;</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  r0.makeHouseholder(e, tau.coeffRef(0), beta);</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  w(0)=(Scalar) beta;</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  H.bottomLeftCorner(m - 1, 1) = e;</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span> </div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  }</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span> </div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  }</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</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>  }</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  </div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="keywordflow">return</span> <span class="keyword">false</span>;</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> }</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</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="l00202"></a><span class="lineno"> 202</span> <span class="keyword">template</span>< <span class="keyword">typename</span> _MatrixType,</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="keyword">typename</span> _Preconditioner = DiagonalPreconditioner<typename _MatrixType::Scalar> ></div>
<div class="line"><a name="l00204"></a><span class="lineno"><a class="line" href="classEigen_1_1GMRES.html"> 204</a></span> <span class="keyword">class </span><a class="code" href="classEigen_1_1GMRES.html">GMRES</a>;</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span> </div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span> </div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span> <span class="keyword">template</span>< <span class="keyword">typename</span> _MatrixType, <span class="keyword">typename</span> _Preconditioner></div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span> <span class="keyword">struct </span>traits<<a class="code" href="classEigen_1_1GMRES.html">GMRES</a><_MatrixType,_Preconditioner> ></div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span> {</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="keyword">typedef</span> _MatrixType MatrixType;</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="keyword">typedef</span> _Preconditioner Preconditioner;</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> }</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span> </div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span> <span class="keyword">template</span>< <span class="keyword">typename</span> _MatrixType, <span class="keyword">typename</span> _Preconditioner></div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span> <span class="keyword">class </span>GMRES : <span class="keyword">public</span> IterativeSolverBase<GMRES<_MatrixType,_Preconditioner> ></div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span> {</div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  <span class="keyword">typedef</span> IterativeSolverBase<GMRES> Base;</div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <span class="keyword">using</span> Base::mp_matrix;</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <span class="keyword">using</span> Base::m_error;</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  <span class="keyword">using</span> Base::m_iterations;</div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  <span class="keyword">using</span> Base::m_info;</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  <span class="keyword">using</span> Base::m_isInitialized;</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>  </div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span> <span class="keyword">private</span>:</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  <span class="keywordtype">int</span> m_restart;</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  </div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span> <span class="keyword">public</span>:</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  <span class="keyword">typedef</span> _MatrixType MatrixType;</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  <span class="keyword">typedef</span> _Preconditioner Preconditioner;</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="keyword">public</span>:</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span> </div>
<div class="line"><a name="l00285"></a><span class="lineno"><a class="line" href="classEigen_1_1GMRES.html#add9a5ff2ad65b482c41d012a0aaa67f2"> 285</a></span>  <a class="code" href="classEigen_1_1GMRES.html#add9a5ff2ad65b482c41d012a0aaa67f2">GMRES</a>() : Base(), m_restart(30) {}</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span> </div>
<div class="line"><a name="l00297"></a><span class="lineno"><a class="line" href="classEigen_1_1GMRES.html#aabc3674283f6f4acbebd68eb72a00e03"> 297</a></span>  <a class="code" href="classEigen_1_1GMRES.html#aabc3674283f6f4acbebd68eb72a00e03">GMRES</a>(<span class="keyword">const</span> MatrixType& A) : Base(A), m_restart(30) {}</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>  ~<a class="code" href="classEigen_1_1GMRES.html">GMRES</a>() {}</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  </div>
<div class="line"><a name="l00303"></a><span class="lineno"><a class="line" href="classEigen_1_1GMRES.html#a577e417ca9e13ffb281283eddb7b72e7"> 303</a></span>  <span class="keywordtype">int</span> <a class="code" href="classEigen_1_1GMRES.html#a577e417ca9e13ffb281283eddb7b72e7">get_restart</a>() { <span class="keywordflow">return</span> m_restart; }</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  </div>
<div class="line"><a name="l00308"></a><span class="lineno"><a class="line" href="classEigen_1_1GMRES.html#a88b3d18c69eccbd4b1c68a5713a05bb3"> 308</a></span>  <span class="keywordtype">void</span> <a class="code" href="classEigen_1_1GMRES.html#a88b3d18c69eccbd4b1c68a5713a05bb3">set_restart</a>(<span class="keyword">const</span> <span class="keywordtype">int</span> restart) { m_restart=restart; }</div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>  </div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs,<span class="keyword">typename</span> Guess></div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  <span class="keyword">inline</span> <span class="keyword">const</span> internal::solve_retval_with_guess<GMRES, Rhs, Guess></div>
<div class="line"><a name="l00317"></a><span class="lineno"><a class="line" href="classEigen_1_1GMRES.html#adc63f61d3b9cadbcbd7841ddae858110"> 317</a></span>  <a class="code" href="classEigen_1_1GMRES.html#adc63f61d3b9cadbcbd7841ddae858110">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="l00318"></a><span class="lineno"> 318</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"GMRES is not initialized."</span>);</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  eigen_assert(Base::rows()==b.rows()</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  && <span class="stringliteral">"GMRES::solve(): invalid number of rows of the right hand side matrix b"</span>);</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <span class="keywordflow">return</span> internal::solve_retval_with_guess</div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>  <<a class="code" href="classEigen_1_1GMRES.html#add9a5ff2ad65b482c41d012a0aaa67f2">GMRES</a>, Rhs, Guess>(*<span class="keyword">this</span>, b.derived(), x0);</div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  }</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  </div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs,<span class="keyword">typename</span> Dest></div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</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="l00329"></a><span class="lineno"> 329</span> <span class="keyword"> </span>{ </div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  <span class="keywordtype">bool</span> failed = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j=0; j<b.cols(); ++j)</div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  {</div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  m_iterations = Base::maxIterations();</div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  m_error = Base::m_tolerance;</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  </div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>  <span class="keyword">typename</span> Dest::ColXpr xj(x,j);</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  <span class="keywordflow">if</span>(!internal::gmres(*mp_matrix, b.col(j), xj, Base::m_preconditioner, m_iterations, m_restart, m_error))</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  failed = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  }</div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>  m_info = failed ? NumericalIssue</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>  : m_error <= Base::m_tolerance ? Success</div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>  : NoConvergence;</div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>  }</div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span> </div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs,<span class="keyword">typename</span> Dest></div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</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="l00349"></a><span class="lineno"> 349</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  x = b;</div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  <span class="keywordflow">if</span>(x.squaredNorm() == 0) <span class="keywordflow">return</span>; <span class="comment">// Check Zero right hand side</span></div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>  _solveWithGuess(b,x);</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> </div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span> <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span> </div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span> };</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> </div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span> </div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</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="l00363"></a><span class="lineno"> 363</span> <span class="keyword">struct </span>solve_retval<GMRES<_MatrixType, _Preconditioner>, Rhs></div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>  : solve_retval_base<GMRES<_MatrixType, _Preconditioner>, Rhs></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>  <span class="keyword">typedef</span> GMRES<_MatrixType, _Preconditioner> Dec;</div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span> </div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>  template<typename Dest> <span class="keywordtype">void</span> evalTo(Dest& dst)<span class="keyword"> const</span></div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  dec()._solve(rhs(),dst);</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> };</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span> </div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span> } <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span> </div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span> </div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span> <span class="preprocessor">#endif // EIGEN_GMRES_H</span></div>
<div class="ttc" id="classEigen_1_1GMRES_html_adc63f61d3b9cadbcbd7841ddae858110"><div class="ttname"><a href="classEigen_1_1GMRES.html#adc63f61d3b9cadbcbd7841ddae858110">Eigen::GMRES::solveWithGuess</a></div><div class="ttdeci">const internal::solve_retval_with_guess< GMRES, Rhs, Guess > solveWithGuess(const MatrixBase< Rhs > &b, const Guess &x0) const </div><div class="ttdef"><b>Definition:</b> GMRES.h:317</div></div>
<div class="ttc" id="classEigen_1_1GMRES_html_add9a5ff2ad65b482c41d012a0aaa67f2"><div class="ttname"><a href="classEigen_1_1GMRES.html#add9a5ff2ad65b482c41d012a0aaa67f2">Eigen::GMRES::GMRES</a></div><div class="ttdeci">GMRES()</div><div class="ttdef"><b>Definition:</b> GMRES.h:285</div></div>
<div class="ttc" id="classEigen_1_1GMRES_html_a88b3d18c69eccbd4b1c68a5713a05bb3"><div class="ttname"><a href="classEigen_1_1GMRES.html#a88b3d18c69eccbd4b1c68a5713a05bb3">Eigen::GMRES::set_restart</a></div><div class="ttdeci">void set_restart(const int restart)</div><div class="ttdef"><b>Definition:</b> GMRES.h:308</div></div>
<div class="ttc" id="classEigen_1_1GMRES_html_aabc3674283f6f4acbebd68eb72a00e03"><div class="ttname"><a href="classEigen_1_1GMRES.html#aabc3674283f6f4acbebd68eb72a00e03">Eigen::GMRES::GMRES</a></div><div class="ttdeci">GMRES(const MatrixType &A)</div><div class="ttdef"><b>Definition:</b> GMRES.h:297</div></div>
<div class="ttc" id="classEigen_1_1GMRES_html"><div class="ttname"><a href="classEigen_1_1GMRES.html">Eigen::GMRES</a></div><div class="ttdoc">A GMRES solver for sparse square problems. </div><div class="ttdef"><b>Definition:</b> GMRES.h:204</div></div>
<div class="ttc" id="classEigen_1_1GMRES_html_a577e417ca9e13ffb281283eddb7b72e7"><div class="ttname"><a href="classEigen_1_1GMRES.html#a577e417ca9e13ffb281283eddb7b72e7">Eigen::GMRES::get_restart</a></div><div class="ttdeci">int get_restart()</div><div class="ttdef"><b>Definition:</b> GMRES.h:303</div></div>
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