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<div class="title">BiCGSTAB.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 Désiré Nuentsa-Wakam <desire.nuentsa_wakam@inria.fr></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_BICGSTAB_H</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_BICGSTAB_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="l00028"></a><span class="lineno"> 28</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="l00029"></a><span class="lineno"> 29</span> <span class="keywordtype">bool</span> bicgstab(<span class="keyword">const</span> MatrixType& mat, <span class="keyword">const</span> Rhs& rhs, Dest& x,</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  <span class="keyword">const</span> Preconditioner& precond, <span class="keywordtype">int</span>& iters,</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <span class="keyword">typename</span> Dest::RealScalar& tol_error)</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span> {</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Dest::RealScalar RealScalar;</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Dest::Scalar Scalar;</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="keyword">typedef</span> Matrix<Scalar,Dynamic,1> VectorType;</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  RealScalar tol = tol_error;</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="keywordtype">int</span> maxIters = iters;</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>  <span class="keywordtype">int</span> n = mat.cols();</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  x = precond.solve(x);</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  VectorType r = rhs - mat * x;</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  VectorType r0 = r;</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  </div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  RealScalar r0_sqnorm = r0.squaredNorm();</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  RealScalar rhs_sqnorm = rhs.squaredNorm();</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="keywordflow">if</span>(rhs_sqnorm == 0)</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>  x.setZero();</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  }</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  Scalar rho = 1;</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  Scalar alpha = 1;</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  Scalar w = 1;</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>  VectorType v = VectorType::Zero(n), p = VectorType::Zero(n);</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  VectorType y(n), z(n);</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  VectorType kt(n), ks(n);</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span> </div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  VectorType s(n), t(n);</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span> </div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  RealScalar tol2 = tol*tol;</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="keywordtype">int</span> i = 0;</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keywordtype">int</span> restarts = 0;</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>  <span class="keywordflow">while</span> ( r.squaredNorm()/rhs_sqnorm > tol2 && i<maxIters )</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  {</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  Scalar rho_old = rho;</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>  rho = r0.dot(r);</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="keywordflow">if</span> (internal::isMuchSmallerThan(rho,r0_sqnorm))</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  {</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="comment">// The new residual vector became too orthogonal to the arbitrarily choosen direction r0</span></div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="comment">// Let's restart with a new r0:</span></div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  r0 = r;</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  rho = r0_sqnorm = r.squaredNorm();</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="keywordflow">if</span>(restarts++ == 0)</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  i = 0;</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  }</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  Scalar beta = (rho/rho_old) * (alpha / w);</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  p = r + beta * (p - w * v);</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  </div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  y = precond.solve(p);</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  </div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  v.noalias() = mat * y;</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span> </div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  alpha = rho / r0.dot(v);</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  s = r - alpha * v;</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span> </div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  z = precond.solve(s);</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  t.noalias() = mat * z;</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>  RealScalar tmp = t.squaredNorm();</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  <span class="keywordflow">if</span>(tmp>RealScalar(0))</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  w = t.dot(s) / tmp;</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  w = Scalar(0);</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  x += alpha * y + w * z;</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  r = s - w * t;</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  ++i;</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>  tol_error = sqrt(r.squaredNorm()/rhs_sqnorm);</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  iters = i;</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="keywordflow">return</span> <span class="keyword">true</span>; </div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span> }</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span> </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="keyword">template</span>< <span class="keyword">typename</span> _MatrixType,</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="keyword">typename</span> _Preconditioner = DiagonalPreconditioner<typename _MatrixType::Scalar> ></div>
<div class="line"><a name="l00112"></a><span class="lineno"><a class="line" href="classEigen_1_1BiCGSTAB.html"> 112</a></span> <span class="keyword">class </span><a class="code" href="classEigen_1_1BiCGSTAB.html">BiCGSTAB</a>;</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="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span> </div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span> <span class="keyword">template</span>< <span class="keyword">typename</span> _MatrixType, <span class="keyword">typename</span> _Preconditioner></div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span> <span class="keyword">struct </span>traits<<a class="code" href="classEigen_1_1BiCGSTAB.html">BiCGSTAB</a><_MatrixType,_Preconditioner> ></div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span> {</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  <span class="keyword">typedef</span> _MatrixType MatrixType;</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  <span class="keyword">typedef</span> _Preconditioner Preconditioner;</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="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="l00171"></a><span class="lineno"> 171</span> <span class="keyword">template</span>< <span class="keyword">typename</span> _MatrixType, <span class="keyword">typename</span> _Preconditioner></div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span> <span class="keyword">class </span>BiCGSTAB : <span class="keyword">public</span> IterativeSolverBase<BiCGSTAB<_MatrixType,_Preconditioner> ></div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span> {</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <span class="keyword">typedef</span> IterativeSolverBase<BiCGSTAB> Base;</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  <span class="keyword">using</span> Base::mp_matrix;</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <span class="keyword">using</span> Base::m_error;</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <span class="keyword">using</span> Base::m_iterations;</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <span class="keyword">using</span> Base::m_info;</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  <span class="keyword">using</span> Base::m_isInitialized;</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span> <span class="keyword">public</span>:</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  <span class="keyword">typedef</span> _MatrixType MatrixType;</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  <span class="keyword">typedef</span> _Preconditioner Preconditioner;</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span> </div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span> <span class="keyword">public</span>:</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span> </div>
<div class="line"><a name="l00190"></a><span class="lineno"><a class="line" href="classEigen_1_1BiCGSTAB.html#abda58f5b65579cb046bcb158cc356013"> 190</a></span>  <a class="code" href="classEigen_1_1BiCGSTAB.html#abda58f5b65579cb046bcb158cc356013">BiCGSTAB</a>() : <a class="code" href="classEigen_1_1IterativeSolverBase.html">Base</a>() {}</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span> </div>
<div class="line"><a name="l00202"></a><span class="lineno"><a class="line" href="classEigen_1_1BiCGSTAB.html#abf2413ba65486c26becf303054d6ec12"> 202</a></span>  <a class="code" href="classEigen_1_1BiCGSTAB.html#abf2413ba65486c26becf303054d6ec12">BiCGSTAB</a>(<span class="keyword">const</span> MatrixType& A) : <a class="code" href="classEigen_1_1IterativeSolverBase.html">Base</a>(A) {}</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span> </div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  ~<a class="code" href="classEigen_1_1BiCGSTAB.html">BiCGSTAB</a>() {}</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  </div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs,<span class="keyword">typename</span> Guess></div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="keyword">inline</span> <span class="keyword">const</span> internal::solve_retval_with_guess<BiCGSTAB, Rhs, Guess></div>
<div class="line"><a name="l00213"></a><span class="lineno"><a class="line" href="classEigen_1_1BiCGSTAB.html#ac6991ac0f70dd889f55ebc0f287c04f2"> 213</a></span>  <a class="code" href="classEigen_1_1BiCGSTAB.html#ac6991ac0f70dd889f55ebc0f287c04f2">solveWithGuess</a>(<span class="keyword">const</span> <a class="code" href="classEigen_1_1MatrixBase.html">MatrixBase<Rhs></a>& b, <span class="keyword">const</span> Guess& x0)<span class="keyword"> const</span></div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"BiCGSTAB is not initialized."</span>);</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  eigen_assert(Base::rows()==b.rows()</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  && <span class="stringliteral">"BiCGSTAB::solve(): invalid number of rows of the right hand side matrix b"</span>);</div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>  <span class="keywordflow">return</span> internal::solve_retval_with_guess</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <<a class="code" href="classEigen_1_1BiCGSTAB.html#abda58f5b65579cb046bcb158cc356013">BiCGSTAB</a>, Rhs, Guess>(*<span class="keyword">this</span>, b.derived(), x0);</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  }</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  </div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs,<span class="keyword">typename</span> Dest></div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</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="l00225"></a><span class="lineno"> 225</span> <span class="keyword"> </span>{ </div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  <span class="keywordtype">bool</span> failed = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>  <span class="keywordflow">for</span>(<span class="keywordtype">int</span> j=0; j<b.cols(); ++j)</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  {</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  m_iterations = <a class="code" href="classEigen_1_1IterativeSolverBase.html#a9c020a2e26d3081eeff611b802962530">Base::maxIterations</a>();</div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  m_error = Base::m_tolerance;</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  </div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <span class="keyword">typename</span> Dest::ColXpr xj(x,j);</div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  <span class="keywordflow">if</span>(!internal::bicgstab(*mp_matrix, b.col(j), xj, Base::m_preconditioner, m_iterations, m_error))</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  failed = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  }</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  m_info = failed ? <a class="code" href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037ba710fff14e8fc77846d4b75d8f4cc2d5c">NumericalIssue</a></div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  : m_error <= Base::m_tolerance ? <a class="code" href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c">Success</a></div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  : <a class="code" href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037ba4ff235bd185f3c5fceeec8d6540eb847">NoConvergence</a>;</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  }</div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span> </div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs,<span class="keyword">typename</span> Dest></div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</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="l00245"></a><span class="lineno"> 245</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span> <span class="comment">// x.setZero();</span></div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  x = b;</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  _solveWithGuess(b,x);</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  }</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span> </div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span> <span class="keyword">protected</span>:</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span> </div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span> };</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span> </div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span> </div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span> <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span> </div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  <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="l00259"></a><span class="lineno"> 259</span> <span class="keyword">struct </span>solve_retval<BiCGSTAB<_MatrixType, _Preconditioner>, Rhs></div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  : solve_retval_base<BiCGSTAB<_MatrixType, _Preconditioner>, Rhs></div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span> {</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  <span class="keyword">typedef</span> BiCGSTAB<_MatrixType, _Preconditioner> Dec;</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)</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>  template<typename Dest> <span class="keywordtype">void</span> evalTo(Dest& dst)<span class="keyword"> const</span></div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  dec()._solve(rhs(),dst);</div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  }</div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span> };</div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span> </div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span> } <span class="comment">// end namespace internal</span></div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span> </div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span> } <span class="comment">// end namespace Eigen</span></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="preprocessor">#endif // EIGEN_BICGSTAB_H</span></div>
<div class="ttc" id="classEigen_1_1BiCGSTAB_html_ac6991ac0f70dd889f55ebc0f287c04f2"><div class="ttname"><a href="classEigen_1_1BiCGSTAB.html#ac6991ac0f70dd889f55ebc0f287c04f2">Eigen::BiCGSTAB::solveWithGuess</a></div><div class="ttdeci">const internal::solve_retval_with_guess< BiCGSTAB, Rhs, Guess > solveWithGuess(const MatrixBase< Rhs > &b, const Guess &x0) const </div><div class="ttdef"><b>Definition:</b> BiCGSTAB.h:213</div></div>
<div class="ttc" id="group__enums_html_gga51bc1ac16f26ebe51eae1abb77bd037ba710fff14e8fc77846d4b75d8f4cc2d5c"><div class="ttname"><a href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037ba710fff14e8fc77846d4b75d8f4cc2d5c">Eigen::NumericalIssue</a></div><div class="ttdef"><b>Definition:</b> Constants.h:378</div></div>
<div class="ttc" id="classEigen_1_1BiCGSTAB_html_abda58f5b65579cb046bcb158cc356013"><div class="ttname"><a href="classEigen_1_1BiCGSTAB.html#abda58f5b65579cb046bcb158cc356013">Eigen::BiCGSTAB::BiCGSTAB</a></div><div class="ttdeci">BiCGSTAB()</div><div class="ttdef"><b>Definition:</b> BiCGSTAB.h:190</div></div>
<div class="ttc" id="classEigen_1_1BiCGSTAB_html_abf2413ba65486c26becf303054d6ec12"><div class="ttname"><a href="classEigen_1_1BiCGSTAB.html#abf2413ba65486c26becf303054d6ec12">Eigen::BiCGSTAB::BiCGSTAB</a></div><div class="ttdeci">BiCGSTAB(const MatrixType &A)</div><div class="ttdef"><b>Definition:</b> BiCGSTAB.h:202</div></div>
<div class="ttc" id="group__enums_html_gga51bc1ac16f26ebe51eae1abb77bd037ba4ff235bd185f3c5fceeec8d6540eb847"><div class="ttname"><a href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037ba4ff235bd185f3c5fceeec8d6540eb847">Eigen::NoConvergence</a></div><div class="ttdef"><b>Definition:</b> Constants.h:380</div></div>
<div class="ttc" id="group__enums_html_gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c"><div class="ttname"><a href="group__enums.html#gga51bc1ac16f26ebe51eae1abb77bd037bafdfbdf3247bd36a1f17270d5cec74c9c">Eigen::Success</a></div><div class="ttdef"><b>Definition:</b> Constants.h:376</div></div>
<div class="ttc" id="classEigen_1_1BiCGSTAB_html"><div class="ttname"><a href="classEigen_1_1BiCGSTAB.html">Eigen::BiCGSTAB</a></div><div class="ttdoc">A bi conjugate gradient stabilized solver for sparse square problems. </div><div class="ttdef"><b>Definition:</b> BiCGSTAB.h:112</div></div>
<div class="ttc" id="classEigen_1_1IterativeSolverBase_html"><div class="ttname"><a href="classEigen_1_1IterativeSolverBase.html">Eigen::IterativeSolverBase</a></div><div class="ttdoc">Base class for linear iterative solvers. </div><div class="ttdef"><b>Definition:</b> IterativeSolverBase.h:21</div></div>
<div class="ttc" id="classEigen_1_1MatrixBase_html"><div class="ttname"><a href="classEigen_1_1MatrixBase.html">Eigen::MatrixBase</a></div><div class="ttdoc">Base class for all dense matrices, vectors, and expressions. </div><div class="ttdef"><b>Definition:</b> MatrixBase.h:48</div></div>
<div class="ttc" id="classEigen_1_1IterativeSolverBase_html_a9c020a2e26d3081eeff611b802962530"><div class="ttname"><a href="classEigen_1_1IterativeSolverBase.html#a9c020a2e26d3081eeff611b802962530">Eigen::IterativeSolverBase::maxIterations</a></div><div class="ttdeci">int maxIterations() const </div><div class="ttdef"><b>Definition:</b> IterativeSolverBase.h:136</div></div>
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