<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml"> <head> <meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/> <meta http-equiv="X-UA-Compatible" content="IE=9"/> <meta name="generator" content="Doxygen 1.8.5"/> <title>Eigen-unsupported: HybridNonLinearSolver.h Source File</title> <link href="tabs.css" rel="stylesheet" type="text/css"/> <script type="text/javascript" src="jquery.js"></script> <script type="text/javascript" src="dynsections.js"></script> <link href="navtree.css" rel="stylesheet" type="text/css"/> <script type="text/javascript" src="resize.js"></script> <script type="text/javascript" src="navtree.js"></script> <script type="text/javascript"> $(document).ready(initResizable); $(window).load(resizeHeight); </script> <link href="search/search.css" rel="stylesheet" type="text/css"/> <script type="text/javascript" src="search/search.js"></script> <script type="text/javascript"> $(document).ready(function() { searchBox.OnSelectItem(0); }); </script> <link href="doxygen.css" rel="stylesheet" type="text/css" /> <link href="eigendoxy.css" rel="stylesheet" type="text/css"> <!-- --> <script type="text/javascript" src="eigen_navtree_hacks.js"></script> <!-- <script type="text/javascript"> --> <!-- </script> --> </head> <body> <div id="top"><!-- do not remove this div, it is closed by doxygen! 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If a copy of the MPL was not distributed</span></div> <div class="line"><a name="l00011"></a><span class="lineno"> 11</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="l00012"></a><span class="lineno"> 12</span> </div> <div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor">#ifndef EIGEN_HYBRIDNONLINEARSOLVER_H</span></div> <div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_HYBRIDNONLINEARSOLVER_H</span></div> <div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor"></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>HybridNonLinearSolverSpace { </div> <div class="line"><a name="l00019"></a><span class="lineno"> 19</span>  <span class="keyword">enum</span> Status {</div> <div class="line"><a name="l00020"></a><span class="lineno"> 20</span>  Running = -1,</div> <div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  ImproperInputParameters = 0,</div> <div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  RelativeErrorTooSmall = 1,</div> <div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  TooManyFunctionEvaluation = 2,</div> <div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  TolTooSmall = 3,</div> <div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  NotMakingProgressJacobian = 4,</div> <div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  NotMakingProgressIterations = 5,</div> <div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  UserAsked = 6</div> <div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  };</div> <div class="line"><a name="l00029"></a><span class="lineno"> 29</span> }</div> <div class="line"><a name="l00030"></a><span class="lineno"> 30</span> </div> <div class="line"><a name="l00042"></a><span class="lineno"> 42</span> <span class="keyword">template</span><<span class="keyword">typename</span> FunctorType, <span class="keyword">typename</span> Scalar=<span class="keywordtype">double</span>></div> <div class="line"><a name="l00043"></a><span class="lineno"><a class="line" href="classEigen_1_1HybridNonLinearSolver.html"> 43</a></span> <span class="keyword">class </span><a class="code" href="classEigen_1_1HybridNonLinearSolver.html">HybridNonLinearSolver</a></div> <div class="line"><a name="l00044"></a><span class="lineno"> 44</span> {</div> <div class="line"><a name="l00045"></a><span class="lineno"> 45</span> <span class="keyword">public</span>:</div> <div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="keyword">typedef</span> DenseIndex Index;</div> <div class="line"><a name="l00047"></a><span class="lineno"> 47</span> </div> <div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <a class="code" href="classEigen_1_1HybridNonLinearSolver.html">HybridNonLinearSolver</a>(FunctorType &_functor)</div> <div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  : functor(_functor) { nfev=njev=iter = 0; fnorm= 0.; useExternalScaling=<span class="keyword">false</span>;}</div> <div class="line"><a name="l00050"></a><span class="lineno"> 50</span> </div> <div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="keyword">struct </span>Parameters {</div> <div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  Parameters()</div> <div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  : factor(Scalar(100.))</div> <div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  , maxfev(1000)</div> <div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  , xtol(std::sqrt(NumTraits<Scalar>::epsilon()))</div> <div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  , nb_of_subdiagonals(-1)</div> <div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  , nb_of_superdiagonals(-1)</div> <div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  , epsfcn(Scalar(0.)) {}</div> <div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  Scalar factor;</div> <div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  Index maxfev; <span class="comment">// maximum number of function evaluation</span></div> <div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  Scalar xtol;</div> <div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  Index nb_of_subdiagonals;</div> <div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  Index nb_of_superdiagonals;</div> <div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  Scalar epsfcn;</div> <div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  };</div> <div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="keyword">typedef</span> Matrix< Scalar, Dynamic, 1 > FVectorType;</div> <div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keyword">typedef</span> Matrix< Scalar, Dynamic, Dynamic > JacobianType;</div> <div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="comment">/* TODO: if eigen provides a triangular storage, use it here */</span></div> <div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="keyword">typedef</span> Matrix< Scalar, Dynamic, Dynamic > UpperTriangularType;</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>  HybridNonLinearSolverSpace::Status hybrj1(</div> <div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  FVectorType &x,</div> <div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="keyword">const</span> Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())</div> <div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  );</div> <div class="line"><a name="l00075"></a><span class="lineno"> 75</span> </div> <div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  HybridNonLinearSolverSpace::Status solveInit(FVectorType &x);</div> <div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  HybridNonLinearSolverSpace::Status solveOneStep(FVectorType &x);</div> <div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  HybridNonLinearSolverSpace::Status solve(FVectorType &x);</div> <div class="line"><a name="l00079"></a><span class="lineno"> 79</span> </div> <div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  HybridNonLinearSolverSpace::Status hybrd1(</div> <div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  FVectorType &x,</div> <div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="keyword">const</span> Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon())</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> </div> <div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  HybridNonLinearSolverSpace::Status solveNumericalDiffInit(FVectorType &x);</div> <div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  HybridNonLinearSolverSpace::Status solveNumericalDiffOneStep(FVectorType &x);</div> <div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  HybridNonLinearSolverSpace::Status solveNumericalDiff(FVectorType &x);</div> <div class="line"><a name="l00088"></a><span class="lineno"> 88</span> </div> <div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  <span class="keywordtype">void</span> resetParameters(<span class="keywordtype">void</span>) { parameters = Parameters(); }</div> <div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  Parameters parameters;</div> <div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  FVectorType fvec, qtf, diag;</div> <div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  JacobianType fjac;</div> <div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  UpperTriangularType R;</div> <div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  Index nfev;</div> <div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  Index njev;</div> <div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  Index iter;</div> <div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  Scalar fnorm;</div> <div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keywordtype">bool</span> useExternalScaling; </div> <div class="line"><a name="l00099"></a><span class="lineno"> 99</span> <span class="keyword">private</span>:</div> <div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  FunctorType &functor;</div> <div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  Index n;</div> <div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  Scalar sum;</div> <div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="keywordtype">bool</span> sing;</div> <div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  Scalar temp;</div> <div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  Scalar delta;</div> <div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  <span class="keywordtype">bool</span> jeval;</div> <div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  Index ncsuc;</div> <div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  Scalar ratio;</div> <div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  Scalar pnorm, xnorm, fnorm1;</div> <div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  Index nslow1, nslow2;</div> <div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  Index ncfail;</div> <div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  Scalar actred, prered;</div> <div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  FVectorType wa1, wa2, wa3, wa4;</div> <div class="line"><a name="l00114"></a><span class="lineno"> 114</span> </div> <div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <a class="code" href="classEigen_1_1HybridNonLinearSolver.html">HybridNonLinearSolver</a>& operator=(<span class="keyword">const</span> <a class="code" href="classEigen_1_1HybridNonLinearSolver.html">HybridNonLinearSolver</a>&);</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> </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> </div> <div class="line"><a name="l00120"></a><span class="lineno"> 120</span> <span class="keyword">template</span><<span class="keyword">typename</span> FunctorType, <span class="keyword">typename</span> Scalar></div> <div class="line"><a name="l00121"></a><span class="lineno"> 121</span> HybridNonLinearSolverSpace::Status</div> <div class="line"><a name="l00122"></a><span class="lineno"> 122</span> <a class="code" href="classEigen_1_1HybridNonLinearSolver.html">HybridNonLinearSolver<FunctorType,Scalar>::hybrj1</a>(</div> <div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  FVectorType &x,</div> <div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="keyword">const</span> Scalar tol</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>  n = x.size();</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="comment">/* check the input parameters for errors. */</span></div> <div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keywordflow">if</span> (n <= 0 || tol < 0.)</div> <div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::ImproperInputParameters;</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>  resetParameters();</div> <div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  parameters.maxfev = 100*(n+1);</div> <div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  parameters.xtol = tol;</div> <div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  diag.setConstant(n, 1.);</div> <div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  useExternalScaling = <span class="keyword">true</span>;</div> <div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="keywordflow">return</span> solve(x);</div> <div class="line"><a name="l00139"></a><span class="lineno"> 139</span> }</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> <span class="keyword">template</span><<span class="keyword">typename</span> FunctorType, <span class="keyword">typename</span> Scalar></div> <div class="line"><a name="l00142"></a><span class="lineno"> 142</span> HybridNonLinearSolverSpace::Status</div> <div class="line"><a name="l00143"></a><span class="lineno"> 143</span> HybridNonLinearSolver<FunctorType,Scalar>::solveInit(FVectorType &x)</div> <div class="line"><a name="l00144"></a><span class="lineno"> 144</span> {</div> <div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  n = x.size();</div> <div class="line"><a name="l00146"></a><span class="lineno"> 146</span> </div> <div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  wa1.resize(n); wa2.resize(n); wa3.resize(n); wa4.resize(n);</div> <div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  fvec.resize(n);</div> <div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  qtf.resize(n);</div> <div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  fjac.resize(n, n);</div> <div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <span class="keywordflow">if</span> (!useExternalScaling)</div> <div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  diag.resize(n);</div> <div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  eigen_assert( (!useExternalScaling || diag.size()==n) || <span class="stringliteral">"When useExternalScaling is set, the caller must provide a valid 'diag'"</span>);</div> <div class="line"><a name="l00154"></a><span class="lineno"> 154</span> </div> <div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="comment">/* Function Body */</span></div> <div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  nfev = 0;</div> <div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  njev = 0;</div> <div class="line"><a name="l00158"></a><span class="lineno"> 158</span> </div> <div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  <span class="comment">/* check the input parameters for errors. */</span></div> <div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="keywordflow">if</span> (n <= 0 || parameters.xtol < 0. || parameters.maxfev <= 0 || parameters.factor <= 0. )</div> <div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::ImproperInputParameters;</div> <div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  <span class="keywordflow">if</span> (useExternalScaling)</div> <div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  <span class="keywordflow">for</span> (Index j = 0; j < n; ++j)</div> <div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <span class="keywordflow">if</span> (diag[j] <= 0.)</div> <div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::ImproperInputParameters;</div> <div class="line"><a name="l00166"></a><span class="lineno"> 166</span> </div> <div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  <span class="comment">/* evaluate the function at the starting point */</span></div> <div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  <span class="comment">/* and calculate its norm. */</span></div> <div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  nfev = 1;</div> <div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  <span class="keywordflow">if</span> ( functor(x, fvec) < 0)</div> <div class="line"><a name="l00171"></a><span class="lineno"> 171</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::UserAsked;</div> <div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  fnorm = fvec.stableNorm();</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="comment">/* initialize iteration counter and monitors. */</span></div> <div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  iter = 1;</div> <div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  ncsuc = 0;</div> <div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  ncfail = 0;</div> <div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  nslow1 = 0;</div> <div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  nslow2 = 0;</div> <div class="line"><a name="l00180"></a><span class="lineno"> 180</span> </div> <div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::Running;</div> <div class="line"><a name="l00182"></a><span class="lineno"> 182</span> }</div> <div class="line"><a name="l00183"></a><span class="lineno"> 183</span> </div> <div class="line"><a name="l00184"></a><span class="lineno"> 184</span> <span class="keyword">template</span><<span class="keyword">typename</span> FunctorType, <span class="keyword">typename</span> Scalar></div> <div class="line"><a name="l00185"></a><span class="lineno"> 185</span> HybridNonLinearSolverSpace::Status</div> <div class="line"><a name="l00186"></a><span class="lineno"> 186</span> HybridNonLinearSolver<FunctorType,Scalar>::solveOneStep(FVectorType &x)</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>  <span class="keyword">using</span> std::abs;</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>  eigen_assert(x.size()==n); <span class="comment">// check the caller is not cheating us</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>  Index j;</div> <div class="line"><a name="l00193"></a><span class="lineno"> 193</span>  std::vector<JacobiRotation<Scalar> > v_givens(n), w_givens(n);</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>  jeval = <span class="keyword">true</span>;</div> <div class="line"><a name="l00196"></a><span class="lineno"> 196</span> </div> <div class="line"><a name="l00197"></a><span class="lineno"> 197</span>  <span class="comment">/* calculate the jacobian matrix. */</span></div> <div class="line"><a name="l00198"></a><span class="lineno"> 198</span>  <span class="keywordflow">if</span> ( functor.df(x, fjac) < 0)</div> <div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::UserAsked;</div> <div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  ++njev;</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>  wa2 = fjac.colwise().blueNorm();</div> <div class="line"><a name="l00203"></a><span class="lineno"> 203</span> </div> <div class="line"><a name="l00204"></a><span class="lineno"> 204</span>  <span class="comment">/* on the first iteration and if external scaling is not used, scale according */</span></div> <div class="line"><a name="l00205"></a><span class="lineno"> 205</span>  <span class="comment">/* to the norms of the columns of the initial jacobian. */</span></div> <div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <span class="keywordflow">if</span> (iter == 1) {</div> <div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  <span class="keywordflow">if</span> (!useExternalScaling)</div> <div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <span class="keywordflow">for</span> (j = 0; j < n; ++j)</div> <div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  diag[j] = (wa2[j]==0.) ? 1. : wa2[j];</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="comment">/* on the first iteration, calculate the norm of the scaled x */</span></div> <div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  <span class="comment">/* and initialize the step bound delta. */</span></div> <div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  xnorm = diag.cwiseProduct(x).stableNorm();</div> <div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  delta = parameters.factor * xnorm;</div> <div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="keywordflow">if</span> (delta == 0.)</div> <div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  delta = parameters.factor;</div> <div class="line"><a name="l00217"></a><span class="lineno"> 217</span>  }</div> <div class="line"><a name="l00218"></a><span class="lineno"> 218</span> </div> <div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="comment">/* compute the qr factorization of the jacobian. */</span></div> <div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  HouseholderQR<JacobianType> qrfac(fjac); <span class="comment">// no pivoting:</span></div> <div class="line"><a name="l00221"></a><span class="lineno"> 221</span> </div> <div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <span class="comment">/* copy the triangular factor of the qr factorization into r. */</span></div> <div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  R = qrfac.matrixQR();</div> <div class="line"><a name="l00224"></a><span class="lineno"> 224</span> </div> <div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  <span class="comment">/* accumulate the orthogonal factor in fjac. */</span></div> <div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  fjac = qrfac.householderQ();</div> <div class="line"><a name="l00227"></a><span class="lineno"> 227</span> </div> <div class="line"><a name="l00228"></a><span class="lineno"> 228</span>  <span class="comment">/* form (q transpose)*fvec and store in qtf. */</span></div> <div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  qtf = fjac.transpose() * fvec;</div> <div class="line"><a name="l00230"></a><span class="lineno"> 230</span> </div> <div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  <span class="comment">/* rescale if necessary. */</span></div> <div class="line"><a name="l00232"></a><span class="lineno"> 232</span>  <span class="keywordflow">if</span> (!useExternalScaling)</div> <div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  diag = diag.cwiseMax(wa2);</div> <div class="line"><a name="l00234"></a><span class="lineno"> 234</span> </div> <div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div> <div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  <span class="comment">/* determine the direction p. */</span></div> <div class="line"><a name="l00237"></a><span class="lineno"> 237</span>  internal::dogleg<Scalar>(R, diag, qtf, delta, wa1);</div> <div class="line"><a name="l00238"></a><span class="lineno"> 238</span> </div> <div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="comment">/* store the direction p and x + p. calculate the norm of p. */</span></div> <div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  wa1 = -wa1;</div> <div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  wa2 = x + wa1;</div> <div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  pnorm = diag.cwiseProduct(wa1).stableNorm();</div> <div class="line"><a name="l00243"></a><span class="lineno"> 243</span> </div> <div class="line"><a name="l00244"></a><span class="lineno"> 244</span>  <span class="comment">/* on the first iteration, adjust the initial step bound. */</span></div> <div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <span class="keywordflow">if</span> (iter == 1)</div> <div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  delta = (std::min)(delta,pnorm);</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>  <span class="comment">/* evaluate the function at x + p and calculate its norm. */</span></div> <div class="line"><a name="l00249"></a><span class="lineno"> 249</span>  <span class="keywordflow">if</span> ( functor(wa2, wa4) < 0)</div> <div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::UserAsked;</div> <div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  ++nfev;</div> <div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  fnorm1 = wa4.stableNorm();</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>  <span class="comment">/* compute the scaled actual reduction. */</span></div> <div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  actred = -1.;</div> <div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  <span class="keywordflow">if</span> (fnorm1 < fnorm) <span class="comment">/* Computing 2nd power */</span></div> <div class="line"><a name="l00257"></a><span class="lineno"> 257</span>  actred = 1. - numext::abs2(fnorm1 / fnorm);</div> <div class="line"><a name="l00258"></a><span class="lineno"> 258</span> </div> <div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  <span class="comment">/* compute the scaled predicted reduction. */</span></div> <div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  wa3 = R.template triangularView<Upper>()*wa1 + qtf;</div> <div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  temp = wa3.stableNorm();</div> <div class="line"><a name="l00262"></a><span class="lineno"> 262</span>  prered = 0.;</div> <div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  <span class="keywordflow">if</span> (temp < fnorm) <span class="comment">/* Computing 2nd power */</span></div> <div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  prered = 1. - numext::abs2(temp / fnorm);</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>  <span class="comment">/* compute the ratio of the actual to the predicted reduction. */</span></div> <div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  ratio = 0.;</div> <div class="line"><a name="l00268"></a><span class="lineno"> 268</span>  <span class="keywordflow">if</span> (prered > 0.)</div> <div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  ratio = actred / prered;</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">/* update the step bound. */</span></div> <div class="line"><a name="l00272"></a><span class="lineno"> 272</span>  <span class="keywordflow">if</span> (ratio < Scalar(.1)) {</div> <div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  ncsuc = 0;</div> <div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  ++ncfail;</div> <div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  delta = Scalar(.5) * delta;</div> <div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  } <span class="keywordflow">else</span> {</div> <div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  ncfail = 0;</div> <div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  ++ncsuc;</div> <div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  <span class="keywordflow">if</span> (ratio >= Scalar(.5) || ncsuc > 1)</div> <div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  delta = (std::max)(delta, pnorm / Scalar(.5));</div> <div class="line"><a name="l00281"></a><span class="lineno"> 281</span>  <span class="keywordflow">if</span> (abs(ratio - 1.) <= Scalar(.1)) {</div> <div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  delta = pnorm / Scalar(.5);</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>  }</div> <div class="line"><a name="l00285"></a><span class="lineno"> 285</span> </div> <div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  <span class="comment">/* test for successful iteration. */</span></div> <div class="line"><a name="l00287"></a><span class="lineno"> 287</span>  <span class="keywordflow">if</span> (ratio >= Scalar(1e-4)) {</div> <div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="comment">/* successful iteration. update x, fvec, and their norms. */</span></div> <div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  x = wa2;</div> <div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  wa2 = diag.cwiseProduct(x);</div> <div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  fvec = wa4;</div> <div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  xnorm = wa2.stableNorm();</div> <div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  fnorm = fnorm1;</div> <div class="line"><a name="l00294"></a><span class="lineno"> 294</span>  ++iter;</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">/* determine the progress of the iteration. */</span></div> <div class="line"><a name="l00298"></a><span class="lineno"> 298</span>  ++nslow1;</div> <div class="line"><a name="l00299"></a><span class="lineno"> 299</span>  <span class="keywordflow">if</span> (actred >= Scalar(.001))</div> <div class="line"><a name="l00300"></a><span class="lineno"> 300</span>  nslow1 = 0;</div> <div class="line"><a name="l00301"></a><span class="lineno"> 301</span>  <span class="keywordflow">if</span> (jeval)</div> <div class="line"><a name="l00302"></a><span class="lineno"> 302</span>  ++nslow2;</div> <div class="line"><a name="l00303"></a><span class="lineno"> 303</span>  <span class="keywordflow">if</span> (actred >= Scalar(.1))</div> <div class="line"><a name="l00304"></a><span class="lineno"> 304</span>  nslow2 = 0;</div> <div class="line"><a name="l00305"></a><span class="lineno"> 305</span> </div> <div class="line"><a name="l00306"></a><span class="lineno"> 306</span>  <span class="comment">/* test for convergence. */</span></div> <div class="line"><a name="l00307"></a><span class="lineno"> 307</span>  <span class="keywordflow">if</span> (delta <= parameters.xtol * xnorm || fnorm == 0.)</div> <div class="line"><a name="l00308"></a><span class="lineno"> 308</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::RelativeErrorTooSmall;</div> <div class="line"><a name="l00309"></a><span class="lineno"> 309</span> </div> <div class="line"><a name="l00310"></a><span class="lineno"> 310</span>  <span class="comment">/* tests for termination and stringent tolerances. */</span></div> <div class="line"><a name="l00311"></a><span class="lineno"> 311</span>  <span class="keywordflow">if</span> (nfev >= parameters.maxfev)</div> <div class="line"><a name="l00312"></a><span class="lineno"> 312</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::TooManyFunctionEvaluation;</div> <div class="line"><a name="l00313"></a><span class="lineno"> 313</span>  <span class="keywordflow">if</span> (Scalar(.1) * (std::max)(Scalar(.1) * delta, pnorm) <= NumTraits<Scalar>::epsilon() * xnorm)</div> <div class="line"><a name="l00314"></a><span class="lineno"> 314</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::TolTooSmall;</div> <div class="line"><a name="l00315"></a><span class="lineno"> 315</span>  <span class="keywordflow">if</span> (nslow2 == 5)</div> <div class="line"><a name="l00316"></a><span class="lineno"> 316</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::NotMakingProgressJacobian;</div> <div class="line"><a name="l00317"></a><span class="lineno"> 317</span>  <span class="keywordflow">if</span> (nslow1 == 10)</div> <div class="line"><a name="l00318"></a><span class="lineno"> 318</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::NotMakingProgressIterations;</div> <div class="line"><a name="l00319"></a><span class="lineno"> 319</span> </div> <div class="line"><a name="l00320"></a><span class="lineno"> 320</span>  <span class="comment">/* criterion for recalculating jacobian. */</span></div> <div class="line"><a name="l00321"></a><span class="lineno"> 321</span>  <span class="keywordflow">if</span> (ncfail == 2)</div> <div class="line"><a name="l00322"></a><span class="lineno"> 322</span>  <span class="keywordflow">break</span>; <span class="comment">// leave inner loop and go for the next outer loop iteration</span></div> <div class="line"><a name="l00323"></a><span class="lineno"> 323</span> </div> <div class="line"><a name="l00324"></a><span class="lineno"> 324</span>  <span class="comment">/* calculate the rank one modification to the jacobian */</span></div> <div class="line"><a name="l00325"></a><span class="lineno"> 325</span>  <span class="comment">/* and update qtf if necessary. */</span></div> <div class="line"><a name="l00326"></a><span class="lineno"> 326</span>  wa1 = diag.cwiseProduct( diag.cwiseProduct(wa1)/pnorm );</div> <div class="line"><a name="l00327"></a><span class="lineno"> 327</span>  wa2 = fjac.transpose() * wa4;</div> <div class="line"><a name="l00328"></a><span class="lineno"> 328</span>  <span class="keywordflow">if</span> (ratio >= Scalar(1e-4))</div> <div class="line"><a name="l00329"></a><span class="lineno"> 329</span>  qtf = wa2;</div> <div class="line"><a name="l00330"></a><span class="lineno"> 330</span>  wa2 = (wa2-wa3)/pnorm;</div> <div class="line"><a name="l00331"></a><span class="lineno"> 331</span> </div> <div class="line"><a name="l00332"></a><span class="lineno"> 332</span>  <span class="comment">/* compute the qr factorization of the updated jacobian. */</span></div> <div class="line"><a name="l00333"></a><span class="lineno"> 333</span>  internal::r1updt<Scalar>(R, wa1, v_givens, w_givens, wa2, wa3, &sing);</div> <div class="line"><a name="l00334"></a><span class="lineno"> 334</span>  internal::r1mpyq<Scalar>(n, n, fjac.data(), v_givens, w_givens);</div> <div class="line"><a name="l00335"></a><span class="lineno"> 335</span>  internal::r1mpyq<Scalar>(1, n, qtf.data(), v_givens, w_givens);</div> <div class="line"><a name="l00336"></a><span class="lineno"> 336</span> </div> <div class="line"><a name="l00337"></a><span class="lineno"> 337</span>  jeval = <span class="keyword">false</span>;</div> <div class="line"><a name="l00338"></a><span class="lineno"> 338</span>  }</div> <div class="line"><a name="l00339"></a><span class="lineno"> 339</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::Running;</div> <div class="line"><a name="l00340"></a><span class="lineno"> 340</span> }</div> <div class="line"><a name="l00341"></a><span class="lineno"> 341</span> </div> <div class="line"><a name="l00342"></a><span class="lineno"> 342</span> <span class="keyword">template</span><<span class="keyword">typename</span> FunctorType, <span class="keyword">typename</span> Scalar></div> <div class="line"><a name="l00343"></a><span class="lineno"> 343</span> HybridNonLinearSolverSpace::Status</div> <div class="line"><a name="l00344"></a><span class="lineno"> 344</span> HybridNonLinearSolver<FunctorType,Scalar>::solve(FVectorType &x)</div> <div class="line"><a name="l00345"></a><span class="lineno"> 345</span> {</div> <div class="line"><a name="l00346"></a><span class="lineno"> 346</span>  HybridNonLinearSolverSpace::Status status = solveInit(x);</div> <div class="line"><a name="l00347"></a><span class="lineno"> 347</span>  <span class="keywordflow">if</span> (status==HybridNonLinearSolverSpace::ImproperInputParameters)</div> <div class="line"><a name="l00348"></a><span class="lineno"> 348</span>  <span class="keywordflow">return</span> status;</div> <div class="line"><a name="l00349"></a><span class="lineno"> 349</span>  <span class="keywordflow">while</span> (status==HybridNonLinearSolverSpace::Running)</div> <div class="line"><a name="l00350"></a><span class="lineno"> 350</span>  status = solveOneStep(x);</div> <div class="line"><a name="l00351"></a><span class="lineno"> 351</span>  <span class="keywordflow">return</span> status;</div> <div class="line"><a name="l00352"></a><span class="lineno"> 352</span> }</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> </div> <div class="line"><a name="l00356"></a><span class="lineno"> 356</span> <span class="keyword">template</span><<span class="keyword">typename</span> FunctorType, <span class="keyword">typename</span> Scalar></div> <div class="line"><a name="l00357"></a><span class="lineno"> 357</span> HybridNonLinearSolverSpace::Status</div> <div class="line"><a name="l00358"></a><span class="lineno"> 358</span> HybridNonLinearSolver<FunctorType,Scalar>::hybrd1(</div> <div class="line"><a name="l00359"></a><span class="lineno"> 359</span>  FVectorType &x,</div> <div class="line"><a name="l00360"></a><span class="lineno"> 360</span>  <span class="keyword">const</span> Scalar tol</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> {</div> <div class="line"><a name="l00363"></a><span class="lineno"> 363</span>  n = x.size();</div> <div class="line"><a name="l00364"></a><span class="lineno"> 364</span> </div> <div class="line"><a name="l00365"></a><span class="lineno"> 365</span>  <span class="comment">/* check the input parameters for errors. */</span></div> <div class="line"><a name="l00366"></a><span class="lineno"> 366</span>  <span class="keywordflow">if</span> (n <= 0 || tol < 0.)</div> <div class="line"><a name="l00367"></a><span class="lineno"> 367</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::ImproperInputParameters;</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>  resetParameters();</div> <div class="line"><a name="l00370"></a><span class="lineno"> 370</span>  parameters.maxfev = 200*(n+1);</div> <div class="line"><a name="l00371"></a><span class="lineno"> 371</span>  parameters.xtol = tol;</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>  diag.setConstant(n, 1.);</div> <div class="line"><a name="l00374"></a><span class="lineno"> 374</span>  useExternalScaling = <span class="keyword">true</span>;</div> <div class="line"><a name="l00375"></a><span class="lineno"> 375</span>  <span class="keywordflow">return</span> solveNumericalDiff(x);</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> </div> <div class="line"><a name="l00378"></a><span class="lineno"> 378</span> <span class="keyword">template</span><<span class="keyword">typename</span> FunctorType, <span class="keyword">typename</span> Scalar></div> <div class="line"><a name="l00379"></a><span class="lineno"> 379</span> HybridNonLinearSolverSpace::Status</div> <div class="line"><a name="l00380"></a><span class="lineno"> 380</span> HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffInit(FVectorType &x)</div> <div class="line"><a name="l00381"></a><span class="lineno"> 381</span> {</div> <div class="line"><a name="l00382"></a><span class="lineno"> 382</span>  n = x.size();</div> <div class="line"><a name="l00383"></a><span class="lineno"> 383</span> </div> <div class="line"><a name="l00384"></a><span class="lineno"> 384</span>  <span class="keywordflow">if</span> (parameters.nb_of_subdiagonals<0) parameters.nb_of_subdiagonals= n-1;</div> <div class="line"><a name="l00385"></a><span class="lineno"> 385</span>  <span class="keywordflow">if</span> (parameters.nb_of_superdiagonals<0) parameters.nb_of_superdiagonals= n-1;</div> <div class="line"><a name="l00386"></a><span class="lineno"> 386</span> </div> <div class="line"><a name="l00387"></a><span class="lineno"> 387</span>  wa1.resize(n); wa2.resize(n); wa3.resize(n); wa4.resize(n);</div> <div class="line"><a name="l00388"></a><span class="lineno"> 388</span>  qtf.resize(n);</div> <div class="line"><a name="l00389"></a><span class="lineno"> 389</span>  fjac.resize(n, n);</div> <div class="line"><a name="l00390"></a><span class="lineno"> 390</span>  fvec.resize(n);</div> <div class="line"><a name="l00391"></a><span class="lineno"> 391</span>  <span class="keywordflow">if</span> (!useExternalScaling)</div> <div class="line"><a name="l00392"></a><span class="lineno"> 392</span>  diag.resize(n);</div> <div class="line"><a name="l00393"></a><span class="lineno"> 393</span>  eigen_assert( (!useExternalScaling || diag.size()==n) || <span class="stringliteral">"When useExternalScaling is set, the caller must provide a valid 'diag'"</span>);</div> <div class="line"><a name="l00394"></a><span class="lineno"> 394</span> </div> <div class="line"><a name="l00395"></a><span class="lineno"> 395</span>  <span class="comment">/* Function Body */</span></div> <div class="line"><a name="l00396"></a><span class="lineno"> 396</span>  nfev = 0;</div> <div class="line"><a name="l00397"></a><span class="lineno"> 397</span>  njev = 0;</div> <div class="line"><a name="l00398"></a><span class="lineno"> 398</span> </div> <div class="line"><a name="l00399"></a><span class="lineno"> 399</span>  <span class="comment">/* check the input parameters for errors. */</span></div> <div class="line"><a name="l00400"></a><span class="lineno"> 400</span>  <span class="keywordflow">if</span> (n <= 0 || parameters.xtol < 0. || parameters.maxfev <= 0 || parameters.nb_of_subdiagonals< 0 || parameters.nb_of_superdiagonals< 0 || parameters.factor <= 0. )</div> <div class="line"><a name="l00401"></a><span class="lineno"> 401</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::ImproperInputParameters;</div> <div class="line"><a name="l00402"></a><span class="lineno"> 402</span>  <span class="keywordflow">if</span> (useExternalScaling)</div> <div class="line"><a name="l00403"></a><span class="lineno"> 403</span>  <span class="keywordflow">for</span> (Index j = 0; j < n; ++j)</div> <div class="line"><a name="l00404"></a><span class="lineno"> 404</span>  <span class="keywordflow">if</span> (diag[j] <= 0.)</div> <div class="line"><a name="l00405"></a><span class="lineno"> 405</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::ImproperInputParameters;</div> <div class="line"><a name="l00406"></a><span class="lineno"> 406</span> </div> <div class="line"><a name="l00407"></a><span class="lineno"> 407</span>  <span class="comment">/* evaluate the function at the starting point */</span></div> <div class="line"><a name="l00408"></a><span class="lineno"> 408</span>  <span class="comment">/* and calculate its norm. */</span></div> <div class="line"><a name="l00409"></a><span class="lineno"> 409</span>  nfev = 1;</div> <div class="line"><a name="l00410"></a><span class="lineno"> 410</span>  <span class="keywordflow">if</span> ( functor(x, fvec) < 0)</div> <div class="line"><a name="l00411"></a><span class="lineno"> 411</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::UserAsked;</div> <div class="line"><a name="l00412"></a><span class="lineno"> 412</span>  fnorm = fvec.stableNorm();</div> <div class="line"><a name="l00413"></a><span class="lineno"> 413</span> </div> <div class="line"><a name="l00414"></a><span class="lineno"> 414</span>  <span class="comment">/* initialize iteration counter and monitors. */</span></div> <div class="line"><a name="l00415"></a><span class="lineno"> 415</span>  iter = 1;</div> <div class="line"><a name="l00416"></a><span class="lineno"> 416</span>  ncsuc = 0;</div> <div class="line"><a name="l00417"></a><span class="lineno"> 417</span>  ncfail = 0;</div> <div class="line"><a name="l00418"></a><span class="lineno"> 418</span>  nslow1 = 0;</div> <div class="line"><a name="l00419"></a><span class="lineno"> 419</span>  nslow2 = 0;</div> <div class="line"><a name="l00420"></a><span class="lineno"> 420</span> </div> <div class="line"><a name="l00421"></a><span class="lineno"> 421</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::Running;</div> <div class="line"><a name="l00422"></a><span class="lineno"> 422</span> }</div> <div class="line"><a name="l00423"></a><span class="lineno"> 423</span> </div> <div class="line"><a name="l00424"></a><span class="lineno"> 424</span> <span class="keyword">template</span><<span class="keyword">typename</span> FunctorType, <span class="keyword">typename</span> Scalar></div> <div class="line"><a name="l00425"></a><span class="lineno"> 425</span> HybridNonLinearSolverSpace::Status</div> <div class="line"><a name="l00426"></a><span class="lineno"> 426</span> HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiffOneStep(FVectorType &x)</div> <div class="line"><a name="l00427"></a><span class="lineno"> 427</span> {</div> <div class="line"><a name="l00428"></a><span class="lineno"> 428</span>  <span class="keyword">using</span> std::sqrt;</div> <div class="line"><a name="l00429"></a><span class="lineno"> 429</span>  <span class="keyword">using</span> std::abs;</div> <div class="line"><a name="l00430"></a><span class="lineno"> 430</span>  </div> <div class="line"><a name="l00431"></a><span class="lineno"> 431</span>  assert(x.size()==n); <span class="comment">// check the caller is not cheating us</span></div> <div class="line"><a name="l00432"></a><span class="lineno"> 432</span> </div> <div class="line"><a name="l00433"></a><span class="lineno"> 433</span>  Index j;</div> <div class="line"><a name="l00434"></a><span class="lineno"> 434</span>  std::vector<JacobiRotation<Scalar> > v_givens(n), w_givens(n);</div> <div class="line"><a name="l00435"></a><span class="lineno"> 435</span> </div> <div class="line"><a name="l00436"></a><span class="lineno"> 436</span>  jeval = <span class="keyword">true</span>;</div> <div class="line"><a name="l00437"></a><span class="lineno"> 437</span>  <span class="keywordflow">if</span> (parameters.nb_of_subdiagonals<0) parameters.nb_of_subdiagonals= n-1;</div> <div class="line"><a name="l00438"></a><span class="lineno"> 438</span>  <span class="keywordflow">if</span> (parameters.nb_of_superdiagonals<0) parameters.nb_of_superdiagonals= n-1;</div> <div class="line"><a name="l00439"></a><span class="lineno"> 439</span> </div> <div class="line"><a name="l00440"></a><span class="lineno"> 440</span>  <span class="comment">/* calculate the jacobian matrix. */</span></div> <div class="line"><a name="l00441"></a><span class="lineno"> 441</span>  <span class="keywordflow">if</span> (internal::fdjac1(functor, x, fvec, fjac, parameters.nb_of_subdiagonals, parameters.nb_of_superdiagonals, parameters.epsfcn) <0)</div> <div class="line"><a name="l00442"></a><span class="lineno"> 442</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::UserAsked;</div> <div class="line"><a name="l00443"></a><span class="lineno"> 443</span>  nfev += (std::min)(parameters.nb_of_subdiagonals+parameters.nb_of_superdiagonals+ 1, n);</div> <div class="line"><a name="l00444"></a><span class="lineno"> 444</span> </div> <div class="line"><a name="l00445"></a><span class="lineno"> 445</span>  wa2 = fjac.colwise().blueNorm();</div> <div class="line"><a name="l00446"></a><span class="lineno"> 446</span> </div> <div class="line"><a name="l00447"></a><span class="lineno"> 447</span>  <span class="comment">/* on the first iteration and if external scaling is not used, scale according */</span></div> <div class="line"><a name="l00448"></a><span class="lineno"> 448</span>  <span class="comment">/* to the norms of the columns of the initial jacobian. */</span></div> <div class="line"><a name="l00449"></a><span class="lineno"> 449</span>  <span class="keywordflow">if</span> (iter == 1) {</div> <div class="line"><a name="l00450"></a><span class="lineno"> 450</span>  <span class="keywordflow">if</span> (!useExternalScaling)</div> <div class="line"><a name="l00451"></a><span class="lineno"> 451</span>  <span class="keywordflow">for</span> (j = 0; j < n; ++j)</div> <div class="line"><a name="l00452"></a><span class="lineno"> 452</span>  diag[j] = (wa2[j]==0.) ? 1. : wa2[j];</div> <div class="line"><a name="l00453"></a><span class="lineno"> 453</span> </div> <div class="line"><a name="l00454"></a><span class="lineno"> 454</span>  <span class="comment">/* on the first iteration, calculate the norm of the scaled x */</span></div> <div class="line"><a name="l00455"></a><span class="lineno"> 455</span>  <span class="comment">/* and initialize the step bound delta. */</span></div> <div class="line"><a name="l00456"></a><span class="lineno"> 456</span>  xnorm = diag.cwiseProduct(x).stableNorm();</div> <div class="line"><a name="l00457"></a><span class="lineno"> 457</span>  delta = parameters.factor * xnorm;</div> <div class="line"><a name="l00458"></a><span class="lineno"> 458</span>  <span class="keywordflow">if</span> (delta == 0.)</div> <div class="line"><a name="l00459"></a><span class="lineno"> 459</span>  delta = parameters.factor;</div> <div class="line"><a name="l00460"></a><span class="lineno"> 460</span>  }</div> <div class="line"><a name="l00461"></a><span class="lineno"> 461</span> </div> <div class="line"><a name="l00462"></a><span class="lineno"> 462</span>  <span class="comment">/* compute the qr factorization of the jacobian. */</span></div> <div class="line"><a name="l00463"></a><span class="lineno"> 463</span>  HouseholderQR<JacobianType> qrfac(fjac); <span class="comment">// no pivoting:</span></div> <div class="line"><a name="l00464"></a><span class="lineno"> 464</span> </div> <div class="line"><a name="l00465"></a><span class="lineno"> 465</span>  <span class="comment">/* copy the triangular factor of the qr factorization into r. */</span></div> <div class="line"><a name="l00466"></a><span class="lineno"> 466</span>  R = qrfac.matrixQR();</div> <div class="line"><a name="l00467"></a><span class="lineno"> 467</span> </div> <div class="line"><a name="l00468"></a><span class="lineno"> 468</span>  <span class="comment">/* accumulate the orthogonal factor in fjac. */</span></div> <div class="line"><a name="l00469"></a><span class="lineno"> 469</span>  fjac = qrfac.householderQ();</div> <div class="line"><a name="l00470"></a><span class="lineno"> 470</span> </div> <div class="line"><a name="l00471"></a><span class="lineno"> 471</span>  <span class="comment">/* form (q transpose)*fvec and store in qtf. */</span></div> <div class="line"><a name="l00472"></a><span class="lineno"> 472</span>  qtf = fjac.transpose() * fvec;</div> <div class="line"><a name="l00473"></a><span class="lineno"> 473</span> </div> <div class="line"><a name="l00474"></a><span class="lineno"> 474</span>  <span class="comment">/* rescale if necessary. */</span></div> <div class="line"><a name="l00475"></a><span class="lineno"> 475</span>  <span class="keywordflow">if</span> (!useExternalScaling)</div> <div class="line"><a name="l00476"></a><span class="lineno"> 476</span>  diag = diag.cwiseMax(wa2);</div> <div class="line"><a name="l00477"></a><span class="lineno"> 477</span> </div> <div class="line"><a name="l00478"></a><span class="lineno"> 478</span>  <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div> <div class="line"><a name="l00479"></a><span class="lineno"> 479</span>  <span class="comment">/* determine the direction p. */</span></div> <div class="line"><a name="l00480"></a><span class="lineno"> 480</span>  internal::dogleg<Scalar>(R, diag, qtf, delta, wa1);</div> <div class="line"><a name="l00481"></a><span class="lineno"> 481</span> </div> <div class="line"><a name="l00482"></a><span class="lineno"> 482</span>  <span class="comment">/* store the direction p and x + p. calculate the norm of p. */</span></div> <div class="line"><a name="l00483"></a><span class="lineno"> 483</span>  wa1 = -wa1;</div> <div class="line"><a name="l00484"></a><span class="lineno"> 484</span>  wa2 = x + wa1;</div> <div class="line"><a name="l00485"></a><span class="lineno"> 485</span>  pnorm = diag.cwiseProduct(wa1).stableNorm();</div> <div class="line"><a name="l00486"></a><span class="lineno"> 486</span> </div> <div class="line"><a name="l00487"></a><span class="lineno"> 487</span>  <span class="comment">/* on the first iteration, adjust the initial step bound. */</span></div> <div class="line"><a name="l00488"></a><span class="lineno"> 488</span>  <span class="keywordflow">if</span> (iter == 1)</div> <div class="line"><a name="l00489"></a><span class="lineno"> 489</span>  delta = (std::min)(delta,pnorm);</div> <div class="line"><a name="l00490"></a><span class="lineno"> 490</span> </div> <div class="line"><a name="l00491"></a><span class="lineno"> 491</span>  <span class="comment">/* evaluate the function at x + p and calculate its norm. */</span></div> <div class="line"><a name="l00492"></a><span class="lineno"> 492</span>  <span class="keywordflow">if</span> ( functor(wa2, wa4) < 0)</div> <div class="line"><a name="l00493"></a><span class="lineno"> 493</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::UserAsked;</div> <div class="line"><a name="l00494"></a><span class="lineno"> 494</span>  ++nfev;</div> <div class="line"><a name="l00495"></a><span class="lineno"> 495</span>  fnorm1 = wa4.stableNorm();</div> <div class="line"><a name="l00496"></a><span class="lineno"> 496</span> </div> <div class="line"><a name="l00497"></a><span class="lineno"> 497</span>  <span class="comment">/* compute the scaled actual reduction. */</span></div> <div class="line"><a name="l00498"></a><span class="lineno"> 498</span>  actred = -1.;</div> <div class="line"><a name="l00499"></a><span class="lineno"> 499</span>  <span class="keywordflow">if</span> (fnorm1 < fnorm) <span class="comment">/* Computing 2nd power */</span></div> <div class="line"><a name="l00500"></a><span class="lineno"> 500</span>  actred = 1. - numext::abs2(fnorm1 / fnorm);</div> <div class="line"><a name="l00501"></a><span class="lineno"> 501</span> </div> <div class="line"><a name="l00502"></a><span class="lineno"> 502</span>  <span class="comment">/* compute the scaled predicted reduction. */</span></div> <div class="line"><a name="l00503"></a><span class="lineno"> 503</span>  wa3 = R.template triangularView<Upper>()*wa1 + qtf;</div> <div class="line"><a name="l00504"></a><span class="lineno"> 504</span>  temp = wa3.stableNorm();</div> <div class="line"><a name="l00505"></a><span class="lineno"> 505</span>  prered = 0.;</div> <div class="line"><a name="l00506"></a><span class="lineno"> 506</span>  <span class="keywordflow">if</span> (temp < fnorm) <span class="comment">/* Computing 2nd power */</span></div> <div class="line"><a name="l00507"></a><span class="lineno"> 507</span>  prered = 1. - numext::abs2(temp / fnorm);</div> <div class="line"><a name="l00508"></a><span class="lineno"> 508</span> </div> <div class="line"><a name="l00509"></a><span class="lineno"> 509</span>  <span class="comment">/* compute the ratio of the actual to the predicted reduction. */</span></div> <div class="line"><a name="l00510"></a><span class="lineno"> 510</span>  ratio = 0.;</div> <div class="line"><a name="l00511"></a><span class="lineno"> 511</span>  <span class="keywordflow">if</span> (prered > 0.)</div> <div class="line"><a name="l00512"></a><span class="lineno"> 512</span>  ratio = actred / prered;</div> <div class="line"><a name="l00513"></a><span class="lineno"> 513</span> </div> <div class="line"><a name="l00514"></a><span class="lineno"> 514</span>  <span class="comment">/* update the step bound. */</span></div> <div class="line"><a name="l00515"></a><span class="lineno"> 515</span>  <span class="keywordflow">if</span> (ratio < Scalar(.1)) {</div> <div class="line"><a name="l00516"></a><span class="lineno"> 516</span>  ncsuc = 0;</div> <div class="line"><a name="l00517"></a><span class="lineno"> 517</span>  ++ncfail;</div> <div class="line"><a name="l00518"></a><span class="lineno"> 518</span>  delta = Scalar(.5) * delta;</div> <div class="line"><a name="l00519"></a><span class="lineno"> 519</span>  } <span class="keywordflow">else</span> {</div> <div class="line"><a name="l00520"></a><span class="lineno"> 520</span>  ncfail = 0;</div> <div class="line"><a name="l00521"></a><span class="lineno"> 521</span>  ++ncsuc;</div> <div class="line"><a name="l00522"></a><span class="lineno"> 522</span>  <span class="keywordflow">if</span> (ratio >= Scalar(.5) || ncsuc > 1)</div> <div class="line"><a name="l00523"></a><span class="lineno"> 523</span>  delta = (std::max)(delta, pnorm / Scalar(.5));</div> <div class="line"><a name="l00524"></a><span class="lineno"> 524</span>  <span class="keywordflow">if</span> (abs(ratio - 1.) <= Scalar(.1)) {</div> <div class="line"><a name="l00525"></a><span class="lineno"> 525</span>  delta = pnorm / Scalar(.5);</div> <div class="line"><a name="l00526"></a><span class="lineno"> 526</span>  }</div> <div class="line"><a name="l00527"></a><span class="lineno"> 527</span>  }</div> <div class="line"><a name="l00528"></a><span class="lineno"> 528</span> </div> <div class="line"><a name="l00529"></a><span class="lineno"> 529</span>  <span class="comment">/* test for successful iteration. */</span></div> <div class="line"><a name="l00530"></a><span class="lineno"> 530</span>  <span class="keywordflow">if</span> (ratio >= Scalar(1e-4)) {</div> <div class="line"><a name="l00531"></a><span class="lineno"> 531</span>  <span class="comment">/* successful iteration. update x, fvec, and their norms. */</span></div> <div class="line"><a name="l00532"></a><span class="lineno"> 532</span>  x = wa2;</div> <div class="line"><a name="l00533"></a><span class="lineno"> 533</span>  wa2 = diag.cwiseProduct(x);</div> <div class="line"><a name="l00534"></a><span class="lineno"> 534</span>  fvec = wa4;</div> <div class="line"><a name="l00535"></a><span class="lineno"> 535</span>  xnorm = wa2.stableNorm();</div> <div class="line"><a name="l00536"></a><span class="lineno"> 536</span>  fnorm = fnorm1;</div> <div class="line"><a name="l00537"></a><span class="lineno"> 537</span>  ++iter;</div> <div class="line"><a name="l00538"></a><span class="lineno"> 538</span>  }</div> <div class="line"><a name="l00539"></a><span class="lineno"> 539</span> </div> <div class="line"><a name="l00540"></a><span class="lineno"> 540</span>  <span class="comment">/* determine the progress of the iteration. */</span></div> <div class="line"><a name="l00541"></a><span class="lineno"> 541</span>  ++nslow1;</div> <div class="line"><a name="l00542"></a><span class="lineno"> 542</span>  <span class="keywordflow">if</span> (actred >= Scalar(.001))</div> <div class="line"><a name="l00543"></a><span class="lineno"> 543</span>  nslow1 = 0;</div> <div class="line"><a name="l00544"></a><span class="lineno"> 544</span>  <span class="keywordflow">if</span> (jeval)</div> <div class="line"><a name="l00545"></a><span class="lineno"> 545</span>  ++nslow2;</div> <div class="line"><a name="l00546"></a><span class="lineno"> 546</span>  <span class="keywordflow">if</span> (actred >= Scalar(.1))</div> <div class="line"><a name="l00547"></a><span class="lineno"> 547</span>  nslow2 = 0;</div> <div class="line"><a name="l00548"></a><span class="lineno"> 548</span> </div> <div class="line"><a name="l00549"></a><span class="lineno"> 549</span>  <span class="comment">/* test for convergence. */</span></div> <div class="line"><a name="l00550"></a><span class="lineno"> 550</span>  <span class="keywordflow">if</span> (delta <= parameters.xtol * xnorm || fnorm == 0.)</div> <div class="line"><a name="l00551"></a><span class="lineno"> 551</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::RelativeErrorTooSmall;</div> <div class="line"><a name="l00552"></a><span class="lineno"> 552</span> </div> <div class="line"><a name="l00553"></a><span class="lineno"> 553</span>  <span class="comment">/* tests for termination and stringent tolerances. */</span></div> <div class="line"><a name="l00554"></a><span class="lineno"> 554</span>  <span class="keywordflow">if</span> (nfev >= parameters.maxfev)</div> <div class="line"><a name="l00555"></a><span class="lineno"> 555</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::TooManyFunctionEvaluation;</div> <div class="line"><a name="l00556"></a><span class="lineno"> 556</span>  <span class="keywordflow">if</span> (Scalar(.1) * (std::max)(Scalar(.1) * delta, pnorm) <= NumTraits<Scalar>::epsilon() * xnorm)</div> <div class="line"><a name="l00557"></a><span class="lineno"> 557</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::TolTooSmall;</div> <div class="line"><a name="l00558"></a><span class="lineno"> 558</span>  <span class="keywordflow">if</span> (nslow2 == 5)</div> <div class="line"><a name="l00559"></a><span class="lineno"> 559</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::NotMakingProgressJacobian;</div> <div class="line"><a name="l00560"></a><span class="lineno"> 560</span>  <span class="keywordflow">if</span> (nslow1 == 10)</div> <div class="line"><a name="l00561"></a><span class="lineno"> 561</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::NotMakingProgressIterations;</div> <div class="line"><a name="l00562"></a><span class="lineno"> 562</span> </div> <div class="line"><a name="l00563"></a><span class="lineno"> 563</span>  <span class="comment">/* criterion for recalculating jacobian. */</span></div> <div class="line"><a name="l00564"></a><span class="lineno"> 564</span>  <span class="keywordflow">if</span> (ncfail == 2)</div> <div class="line"><a name="l00565"></a><span class="lineno"> 565</span>  <span class="keywordflow">break</span>; <span class="comment">// leave inner loop and go for the next outer loop iteration</span></div> <div class="line"><a name="l00566"></a><span class="lineno"> 566</span> </div> <div class="line"><a name="l00567"></a><span class="lineno"> 567</span>  <span class="comment">/* calculate the rank one modification to the jacobian */</span></div> <div class="line"><a name="l00568"></a><span class="lineno"> 568</span>  <span class="comment">/* and update qtf if necessary. */</span></div> <div class="line"><a name="l00569"></a><span class="lineno"> 569</span>  wa1 = diag.cwiseProduct( diag.cwiseProduct(wa1)/pnorm );</div> <div class="line"><a name="l00570"></a><span class="lineno"> 570</span>  wa2 = fjac.transpose() * wa4;</div> <div class="line"><a name="l00571"></a><span class="lineno"> 571</span>  <span class="keywordflow">if</span> (ratio >= Scalar(1e-4))</div> <div class="line"><a name="l00572"></a><span class="lineno"> 572</span>  qtf = wa2;</div> <div class="line"><a name="l00573"></a><span class="lineno"> 573</span>  wa2 = (wa2-wa3)/pnorm;</div> <div class="line"><a name="l00574"></a><span class="lineno"> 574</span> </div> <div class="line"><a name="l00575"></a><span class="lineno"> 575</span>  <span class="comment">/* compute the qr factorization of the updated jacobian. */</span></div> <div class="line"><a name="l00576"></a><span class="lineno"> 576</span>  internal::r1updt<Scalar>(R, wa1, v_givens, w_givens, wa2, wa3, &sing);</div> <div class="line"><a name="l00577"></a><span class="lineno"> 577</span>  internal::r1mpyq<Scalar>(n, n, fjac.data(), v_givens, w_givens);</div> <div class="line"><a name="l00578"></a><span class="lineno"> 578</span>  internal::r1mpyq<Scalar>(1, n, qtf.data(), v_givens, w_givens);</div> <div class="line"><a name="l00579"></a><span class="lineno"> 579</span> </div> <div class="line"><a name="l00580"></a><span class="lineno"> 580</span>  jeval = <span class="keyword">false</span>;</div> <div class="line"><a name="l00581"></a><span class="lineno"> 581</span>  }</div> <div class="line"><a name="l00582"></a><span class="lineno"> 582</span>  <span class="keywordflow">return</span> HybridNonLinearSolverSpace::Running;</div> <div class="line"><a name="l00583"></a><span class="lineno"> 583</span> }</div> <div class="line"><a name="l00584"></a><span class="lineno"> 584</span> </div> <div class="line"><a name="l00585"></a><span class="lineno"> 585</span> <span class="keyword">template</span><<span class="keyword">typename</span> FunctorType, <span class="keyword">typename</span> Scalar></div> <div class="line"><a name="l00586"></a><span class="lineno"> 586</span> HybridNonLinearSolverSpace::Status</div> <div class="line"><a name="l00587"></a><span class="lineno"> 587</span> HybridNonLinearSolver<FunctorType,Scalar>::solveNumericalDiff(FVectorType &x)</div> <div class="line"><a name="l00588"></a><span class="lineno"> 588</span> {</div> <div class="line"><a name="l00589"></a><span class="lineno"> 589</span>  HybridNonLinearSolverSpace::Status status = solveNumericalDiffInit(x);</div> <div class="line"><a name="l00590"></a><span class="lineno"> 590</span>  <span class="keywordflow">if</span> (status==HybridNonLinearSolverSpace::ImproperInputParameters)</div> <div class="line"><a name="l00591"></a><span class="lineno"> 591</span>  <span class="keywordflow">return</span> status;</div> <div class="line"><a name="l00592"></a><span class="lineno"> 592</span>  <span class="keywordflow">while</span> (status==HybridNonLinearSolverSpace::Running)</div> <div class="line"><a name="l00593"></a><span class="lineno"> 593</span>  status = solveNumericalDiffOneStep(x);</div> <div class="line"><a name="l00594"></a><span class="lineno"> 594</span>  <span class="keywordflow">return</span> status;</div> <div class="line"><a name="l00595"></a><span class="lineno"> 595</span> }</div> <div class="line"><a name="l00596"></a><span class="lineno"> 596</span> </div> <div class="line"><a name="l00597"></a><span class="lineno"> 597</span> } <span class="comment">// end namespace Eigen</span></div> <div class="line"><a name="l00598"></a><span class="lineno"> 598</span> </div> <div class="line"><a name="l00599"></a><span class="lineno"> 599</span> <span class="preprocessor">#endif // EIGEN_HYBRIDNONLINEARSOLVER_H</span></div> <div class="line"><a name="l00600"></a><span class="lineno"> 600</span> <span class="preprocessor"></span></div> <div class="line"><a name="l00601"></a><span class="lineno"> 601</span> <span class="comment">//vim: ai ts=4 sts=4 et sw=4</span></div> <div class="ttc" id="classEigen_1_1HybridNonLinearSolver_html"><div class="ttname"><a href="classEigen_1_1HybridNonLinearSolver.html">Eigen::HybridNonLinearSolver</a></div><div class="ttdoc">Finds a zero of a system of n nonlinear functions in n variables by a modification of the Powell hybr...</div><div class="ttdef"><b>Definition:</b> HybridNonLinearSolver.h:43</div></div> </div><!-- fragment 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