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<div class="title">MINRES.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 Giacomo Po <gpo@ucla.edu></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">// Copyright (C) 2011 Gael Guennebaud <gael.guennebaud@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> </div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor">#ifndef EIGEN_MINRES_H_</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_MINRES_H_</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> </div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="keyword">namespace </span>Eigen {</div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span>  </div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span>  <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>  </div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</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="l00030"></a><span class="lineno"> 30</span>  EIGEN_DONT_INLINE</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <span class="keywordtype">void</span> minres(<span class="keyword">const</span> MatrixType& mat, <span class="keyword">const</span> Rhs& rhs, Dest& x,</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  <span class="keyword">const</span> Preconditioner& precond, <span class="keywordtype">int</span>& iters,</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  <span class="keyword">typename</span> Dest::RealScalar& tol_error)</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  {</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Dest::RealScalar RealScalar;</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> Dest::Scalar Scalar;</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <span class="keyword">typedef</span> Matrix<Scalar,Dynamic,1> VectorType;</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span> </div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="comment">// initialize</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> maxIters(iters); <span class="comment">// initialize maxIters to iters</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="keyword">const</span> <span class="keywordtype">int</span> N(mat.cols()); <span class="comment">// the size of the matrix</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="keyword">const</span> RealScalar rhsNorm2(rhs.squaredNorm());</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keyword">const</span> RealScalar threshold2(tol_error*tol_error*rhsNorm2); <span class="comment">// convergence threshold (compared to residualNorm2)</span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  </div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="comment">// Initialize preconditioned Lanczos</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span> <span class="comment">// VectorType v_old(N); // will be initialized inside loop</span></div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  VectorType v( VectorType::Zero(N) ); <span class="comment">//initialize v</span></div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  VectorType v_new(rhs-mat*x); <span class="comment">//initialize v_new</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  RealScalar residualNorm2(v_new.squaredNorm());</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> <span class="comment">// VectorType w(N); // will be initialized inside loop</span></div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  VectorType w_new(precond.solve(v_new)); <span class="comment">// initialize w_new</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span> <span class="comment">// RealScalar beta; // will be initialized inside loop</span></div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  RealScalar beta_new2(v_new.dot(w_new));</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  eigen_assert(beta_new2 >= 0 && <span class="stringliteral">"PRECONDITIONER IS NOT POSITIVE DEFINITE"</span>);</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  RealScalar beta_new(sqrt(beta_new2));</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="keyword">const</span> RealScalar beta_one(beta_new);</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  v_new /= beta_new;</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  w_new /= beta_new;</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="comment">// Initialize other variables</span></div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  RealScalar c(1.0); <span class="comment">// the cosine of the Givens rotation</span></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  RealScalar c_old(1.0);</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  RealScalar s(0.0); <span class="comment">// the sine of the Givens rotation</span></div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  RealScalar s_old(0.0); <span class="comment">// the sine of the Givens rotation</span></div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span> <span class="comment">// VectorType p_oold(N); // will be initialized in loop</span></div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  VectorType p_old(VectorType::Zero(N)); <span class="comment">// initialize p_old=0</span></div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  VectorType p(p_old); <span class="comment">// initialize p=0</span></div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  RealScalar eta(1.0);</div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  </div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  iters = 0; <span class="comment">// reset iters</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="keywordflow">while</span> ( iters < maxIters ){</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>  <span class="comment">// Preconditioned Lanczos</span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="comment">/* Note that there are 4 variants on the Lanczos algorithm. These are</span></div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span> <span class="comment"> * described in Paige, C. C. (1972). Computational variants of</span></div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span> <span class="comment"> * the Lanczos method for the eigenproblem. IMA Journal of Applied</span></div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span> <span class="comment"> * Mathematics, 10(3), 373–381. The current implementation corresponds </span></div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span> <span class="comment"> * to the case A(2,7) in the paper. It also corresponds to </span></div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span> <span class="comment"> * algorithm 6.14 in Y. Saad, Iterative Methods for Sparse Linear</span></div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span> <span class="comment"> * Systems, 2003 p.173. For the preconditioned version see </span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span> <span class="comment"> * A. Greenbaum, Iterative Methods for Solving Linear Systems, SIAM (1987).</span></div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span> <span class="comment"> */</span></div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keyword">const</span> RealScalar beta(beta_new);</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span> <span class="comment">// v_old = v; // update: at first time step, this makes v_old = 0 so value of beta doesn't matter</span></div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keyword">const</span> VectorType v_old(v); <span class="comment">// NOT SURE IF CREATING v_old EVERY ITERATION IS EFFICIENT</span></div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  v = v_new; <span class="comment">// update</span></div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="comment">// w = w_new; // update</span></div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="keyword">const</span> VectorType w(w_new); <span class="comment">// NOT SURE IF CREATING w EVERY ITERATION IS EFFICIENT</span></div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  v_new.noalias() = mat*w - beta*v_old; <span class="comment">// compute v_new</span></div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="keyword">const</span> RealScalar alpha = v_new.dot(w);</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  v_new -= alpha*v; <span class="comment">// overwrite v_new</span></div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  w_new = precond.solve(v_new); <span class="comment">// overwrite w_new</span></div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  beta_new2 = v_new.dot(w_new); <span class="comment">// compute beta_new</span></div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  eigen_assert(beta_new2 >= 0 && <span class="stringliteral">"PRECONDITIONER IS NOT POSITIVE DEFINITE"</span>);</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  beta_new = sqrt(beta_new2); <span class="comment">// compute beta_new</span></div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  v_new /= beta_new; <span class="comment">// overwrite v_new for next iteration</span></div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  w_new /= beta_new; <span class="comment">// overwrite w_new for next iteration</span></div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  </div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  <span class="comment">// Givens rotation</span></div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="keyword">const</span> RealScalar r2 =s*alpha+c*c_old*beta; <span class="comment">// s, s_old, c and c_old are still from previous iteration</span></div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="keyword">const</span> RealScalar r3 =s_old*beta; <span class="comment">// s, s_old, c and c_old are still from previous iteration</span></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="keyword">const</span> RealScalar r1_hat=c*alpha-c_old*s*beta;</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keyword">const</span> RealScalar r1 =sqrt( std::pow(r1_hat,2) + std::pow(beta_new,2) );</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  c_old = c; <span class="comment">// store for next iteration</span></div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  s_old = s; <span class="comment">// store for next iteration</span></div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  c=r1_hat/r1; <span class="comment">// new cosine</span></div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  s=beta_new/r1; <span class="comment">// new sine</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>  <span class="comment">// Update solution</span></div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span> <span class="comment">// p_oold = p_old;</span></div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="keyword">const</span> VectorType p_oold(p_old); <span class="comment">// NOT SURE IF CREATING p_oold EVERY ITERATION IS EFFICIENT</span></div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  p_old = p;</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  p.noalias()=(w-r2*p_old-r3*p_oold) /r1; <span class="comment">// IS NOALIAS REQUIRED?</span></div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  x += beta_one*c*eta*p;</div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  residualNorm2 *= s*s;</div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  </div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  <span class="keywordflow">if</span> ( residualNorm2 < threshold2){</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  <span class="keywordflow">break</span>;</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>  </div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  eta=-s*eta; <span class="comment">// update eta</span></div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  iters++; <span class="comment">// increment iteration number (for output purposes)</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>  tol_error = std::sqrt(residualNorm2 / rhsNorm2); <span class="comment">// return error. Note that this is the estimated error. The real error |Ax-b|/|b| may be slightly larger </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>  </div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  }</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  </div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="keyword">template</span>< <span class="keyword">typename</span> _MatrixType, <span class="keywordtype">int</span> _UpLo=Lower,</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keyword">typename</span> _Preconditioner = IdentityPreconditioner></div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span> <span class="comment">// typename _Preconditioner = IdentityPreconditioner<typename _MatrixType::Scalar> > // preconditioner must be positive definite</span></div>
<div class="line"><a name="l00132"></a><span class="lineno"><a class="line" href="classEigen_1_1MINRES.html"> 132</a></span>  <span class="keyword">class </span><a class="code" href="classEigen_1_1MINRES.html">MINRES</a>;</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  </div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keyword">namespace </span>internal {</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  </div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  <span class="keyword">template</span>< <span class="keyword">typename</span> _MatrixType, <span class="keywordtype">int</span> _UpLo, <span class="keyword">typename</span> _Preconditioner></div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="keyword">struct </span>traits<<a class="code" href="classEigen_1_1MINRES.html">MINRES</a><_MatrixType,_UpLo,_Preconditioner> ></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>  <span class="keyword">typedef</span> _MatrixType MatrixType;</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  <span class="keyword">typedef</span> _Preconditioner Preconditioner;</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>  }</div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  </div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  <span class="keyword">template</span>< <span class="keyword">typename</span> _MatrixType, <span class="keywordtype">int</span> _UpLo, <span class="keyword">typename</span> _Preconditioner></div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>  <span class="keyword">class </span>MINRES : <span class="keyword">public</span> IterativeSolverBase<MINRES<_MatrixType,_UpLo,_Preconditioner> ></div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  {</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  </div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="keyword">typedef</span> IterativeSolverBase<MINRES> Base;</div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="keyword">using</span> Base::mp_matrix;</div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  <span class="keyword">using</span> Base::m_error;</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  <span class="keyword">using</span> Base::m_iterations;</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  <span class="keyword">using</span> Base::m_info;</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>  <span class="keyword">using</span> Base::m_isInitialized;</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <span class="keyword">typedef</span> _MatrixType MatrixType;</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Scalar Scalar;</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::Index Index;</div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> MatrixType::RealScalar RealScalar;</div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  <span class="keyword">typedef</span> _Preconditioner 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">enum</span> {UpLo = _UpLo};</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  </div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="keyword">public</span>:</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  </div>
<div class="line"><a name="l00216"></a><span class="lineno"><a class="line" href="classEigen_1_1MINRES.html#a659d9410353da2cd0805a8d8da66f7ef"> 216</a></span>  <a class="code" href="classEigen_1_1MINRES.html#a659d9410353da2cd0805a8d8da66f7ef">MINRES</a>() : Base() {}</div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  </div>
<div class="line"><a name="l00228"></a><span class="lineno"><a class="line" href="classEigen_1_1MINRES.html#a0044acd402c536a32be6e9575da39141"> 228</a></span>  <a class="code" href="classEigen_1_1MINRES.html#a0044acd402c536a32be6e9575da39141">MINRES</a>(<span class="keyword">const</span> MatrixType& A) : Base(A) {}</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  </div>
<div class="line"><a name="l00231"></a><span class="lineno"><a class="line" href="classEigen_1_1MINRES.html#a0ca81ac3b24c8216b3c526c1e454a40b"> 231</a></span>  <a class="code" href="classEigen_1_1MINRES.html#a0ca81ac3b24c8216b3c526c1e454a40b">~MINRES</a>(){}</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  </div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs,<span class="keyword">typename</span> Guess></div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="keyword">inline</span> <span class="keyword">const</span> internal::solve_retval_with_guess<MINRES, Rhs, Guess></div>
<div class="line"><a name="l00240"></a><span class="lineno"><a class="line" href="classEigen_1_1MINRES.html#a4a42888f2c0db9ad90fc3b718ae582ca"> 240</a></span>  <a class="code" href="classEigen_1_1MINRES.html#a4a42888f2c0db9ad90fc3b718ae582ca">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="l00241"></a><span class="lineno"> 241</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  eigen_assert(m_isInitialized && <span class="stringliteral">"MINRES is not initialized."</span>);</div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  eigen_assert(Base::rows()==b.rows()</div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  && <span class="stringliteral">"MINRES::solve(): invalid number of rows of the right hand side matrix b"</span>);</div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <span class="keywordflow">return</span> internal::solve_retval_with_guess</div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  <<a class="code" href="classEigen_1_1MINRES.html#a659d9410353da2cd0805a8d8da66f7ef">MINRES</a>, Rhs, Guess>(*<span class="keyword">this</span>, b.derived(), x0);</div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  }</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  </div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs,<span class="keyword">typename</span> Dest></div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</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="l00252"></a><span class="lineno"> 252</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  m_iterations = Base::maxIterations();</div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>  m_error = Base::m_tolerance;</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="keywordflow">for</span>(<span class="keywordtype">int</span> j=0; j<b.cols(); ++j)</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>  m_iterations = Base::maxIterations();</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  m_error = Base::m_tolerance;</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  </div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  <span class="keyword">typename</span> Dest::ColXpr xj(x,j);</div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  internal::minres(mp_matrix->template selfadjointView<UpLo>(), b.col(j), xj,</div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  Base::m_preconditioner, m_iterations, m_error);</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>  </div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  m_isInitialized = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  m_info = m_error <= Base::m_tolerance ? Success : NoConvergence;</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="l00271"></a><span class="lineno"> 271</span>  <span class="keyword">template</span><<span class="keyword">typename</span> Rhs,<span class="keyword">typename</span> Dest></div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</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="l00273"></a><span class="lineno"> 273</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  x.setZero();</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  _solveWithGuess(b,x);</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>  </div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  <span class="keyword">protected</span>:</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>  };</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">namespace </span>internal {</div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  </div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  <span class="keyword">template</span><<span class="keyword">typename</span> _MatrixType, <span class="keywordtype">int</span> _UpLo, <span class="keyword">typename</span> _Preconditioner, <span class="keyword">typename</span> Rhs></div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  <span class="keyword">struct </span>solve_retval<MINRES<_MatrixType,_UpLo,_Preconditioner>, Rhs></div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  : solve_retval_base<MINRES<_MatrixType,_UpLo,_Preconditioner>, Rhs></div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  {</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="keyword">typedef</span> MINRES<_MatrixType,_UpLo,_Preconditioner> Dec;</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  EIGEN_MAKE_SOLVE_HELPERS(Dec,Rhs)</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  </div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  template<typename Dest> <span class="keywordtype">void</span> evalTo(Dest& dst)<span class="keyword"> const</span></div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span> <span class="keyword"> </span>{</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  dec()._solve(rhs(),dst);</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  }</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>  };</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>  </div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>  } <span class="comment">// end namespace internal</span></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> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span> </div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span> <span class="preprocessor">#endif // EIGEN_MINRES_H</span></div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span> <span class="preprocessor"></span></div>
<div class="ttc" id="classEigen_1_1MINRES_html_a4a42888f2c0db9ad90fc3b718ae582ca"><div class="ttname"><a href="classEigen_1_1MINRES.html#a4a42888f2c0db9ad90fc3b718ae582ca">Eigen::MINRES::solveWithGuess</a></div><div class="ttdeci">const internal::solve_retval_with_guess< MINRES, Rhs, Guess > solveWithGuess(const MatrixBase< Rhs > &b, const Guess &x0) const </div><div class="ttdef"><b>Definition:</b> MINRES.h:240</div></div>
<div class="ttc" id="classEigen_1_1MINRES_html_a0ca81ac3b24c8216b3c526c1e454a40b"><div class="ttname"><a href="classEigen_1_1MINRES.html#a0ca81ac3b24c8216b3c526c1e454a40b">Eigen::MINRES::~MINRES</a></div><div class="ttdeci">~MINRES()</div><div class="ttdef"><b>Definition:</b> MINRES.h:231</div></div>
<div class="ttc" id="classEigen_1_1MINRES_html"><div class="ttname"><a href="classEigen_1_1MINRES.html">Eigen::MINRES</a></div><div class="ttdoc">A minimal residual solver for sparse symmetric problems. </div><div class="ttdef"><b>Definition:</b> MINRES.h:132</div></div>
<div class="ttc" id="classEigen_1_1MINRES_html_a659d9410353da2cd0805a8d8da66f7ef"><div class="ttname"><a href="classEigen_1_1MINRES.html#a659d9410353da2cd0805a8d8da66f7ef">Eigen::MINRES::MINRES</a></div><div class="ttdeci">MINRES()</div><div class="ttdef"><b>Definition:</b> MINRES.h:216</div></div>
<div class="ttc" id="classEigen_1_1MINRES_html_a0044acd402c536a32be6e9575da39141"><div class="ttname"><a href="classEigen_1_1MINRES.html#a0044acd402c536a32be6e9575da39141">Eigen::MINRES::MINRES</a></div><div class="ttdeci">MINRES(const MatrixType &A)</div><div class="ttdef"><b>Definition:</b> MINRES.h:228</div></div>
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