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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) 2009 Thomas Capricelli <orzel@freehackers.org></span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// This code initially comes from MINPACK whose original authors are:</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">// Copyright Jorge More - Argonne National Laboratory</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">// Copyright Burt Garbow - Argonne National Laboratory</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// Copyright Ken Hillstrom - Argonne National Laboratory</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">//</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> <span class="comment">// This Source Code Form is subject to the terms of the Minpack license</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// (a BSD-like license) described in the campaigned CopyrightMINPACK.txt file.</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> </div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor">#ifndef EIGEN_LMONESTEP_H</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_LMONESTEP_H</span></div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="keyword">namespace </span>Eigen {</div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span> </div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span> <span class="keyword">template</span><<span class="keyword">typename</span> FunctorType></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span> LevenbergMarquardtSpace::Status</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span> LevenbergMarquardt<FunctorType>::minimizeOneStep(FVectorType &x)</div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span> {</div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  RealScalar temp, temp1,temp2; </div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  RealScalar ratio; </div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  RealScalar pnorm, xnorm, fnorm1, actred, dirder, prered;</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  eigen_assert(x.size()==n); <span class="comment">// check the caller is not cheating us</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>  temp = 0.0; xnorm = 0.0;</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <span class="comment">/* calculate the jacobian matrix. */</span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  Index df_ret = m_functor.df(x, m_fjac);</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  <span class="keywordflow">if</span> (df_ret<0)</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::UserAsked;</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="keywordflow">if</span> (df_ret>0)</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="comment">// numerical diff, we evaluated the function df_ret times</span></div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  m_nfev += df_ret;</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <span class="keywordflow">else</span> m_njev++;</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">/* compute the qr factorization of the jacobian. */</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < x.size(); ++j)</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  m_wa2(j) = m_fjac.col(j).blueNorm();</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  QRSolver qrfac(m_fjac);</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keywordflow">if</span>(qrfac.info() != Success) {</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  m_info = NumericalIssue;</div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::ImproperInputParameters;</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>  <span class="comment">// Make a copy of the first factor with the associated permutation</span></div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  m_rfactor = qrfac.matrixR();</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  m_permutation = (qrfac.colsPermutation());</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span> </div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="comment">/* on the first iteration and if external scaling is not used, scale according */</span></div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="comment">/* to the norms of the columns of the initial jacobian. */</span></div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keywordflow">if</span> (m_iter == 1) {</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  <span class="keywordflow">if</span> (!m_useExternalScaling)</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="keywordflow">for</span> (Index j = 0; j < n; ++j)</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  m_diag[j] = (m_wa2[j]==0.)? 1. : m_wa2[j];</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span> </div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="comment">/* on the first iteration, calculate the norm of the scaled x */</span></div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="comment">/* and initialize the step bound m_delta. */</span></div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  xnorm = m_diag.cwiseProduct(x).stableNorm();</div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  m_delta = m_factor * xnorm;</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="keywordflow">if</span> (m_delta == 0.)</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  m_delta = m_factor;</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> </div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="comment">/* form (q transpose)*m_fvec and store the first n components in */</span></div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="comment">/* m_qtf. */</span></div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  m_wa4 = m_fvec;</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  m_wa4 = qrfac.matrixQ().adjoint() * m_fvec; </div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  m_qtf = m_wa4.head(n);</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">/* compute the norm of the scaled gradient. */</span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  m_gnorm = 0.;</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keywordflow">if</span> (m_fnorm != 0.)</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordflow">for</span> (Index j = 0; j < n; ++j)</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="keywordflow">if</span> (m_wa2[m_permutation.indices()[j]] != 0.)</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  m_gnorm = (std::max)(m_gnorm, abs( m_rfactor.col(j).head(j+1).dot(m_qtf.head(j+1)/m_fnorm) / m_wa2[m_permutation.indices()[j]]));</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>  <span class="comment">/* test for convergence of the gradient norm. */</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="keywordflow">if</span> (m_gnorm <= m_gtol) {</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  m_info = Success;</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::CosinusTooSmall;</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> </div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="comment">/* rescale if necessary. */</span></div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keywordflow">if</span> (!m_useExternalScaling)</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  m_diag = m_diag.cwiseMax(m_wa2);</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span> </div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  <span class="keywordflow">do</span> {</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="comment">/* determine the levenberg-marquardt parameter. */</span></div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  internal::lmpar2(qrfac, m_diag, m_qtf, m_delta, m_par, m_wa1);</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span> </div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="comment">/* store the direction p and x + p. calculate the norm of p. */</span></div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  m_wa1 = -m_wa1;</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  m_wa2 = x + m_wa1;</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  pnorm = m_diag.cwiseProduct(m_wa1).stableNorm();</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">/* on the first iteration, adjust the initial step bound. */</span></div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="keywordflow">if</span> (m_iter == 1)</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  m_delta = (std::min)(m_delta,pnorm);</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span> </div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  <span class="comment">/* evaluate the function at x + p and calculate its norm. */</span></div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="keywordflow">if</span> ( m_functor(m_wa2, m_wa4) < 0)</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::UserAsked;</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  ++m_nfev;</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  fnorm1 = m_wa4.stableNorm();</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">/* compute the scaled actual reduction. */</span></div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  actred = -1.;</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="keywordflow">if</span> (Scalar(.1) * fnorm1 < m_fnorm)</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  actred = 1. - numext::abs2(fnorm1 / m_fnorm);</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span> </div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  <span class="comment">/* compute the scaled predicted reduction and */</span></div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  <span class="comment">/* the scaled directional derivative. */</span></div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  m_wa3 = m_rfactor.template triangularView<Upper>() * (m_permutation.inverse() *m_wa1);</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  temp1 = numext::abs2(m_wa3.stableNorm() / m_fnorm);</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  temp2 = numext::abs2(sqrt(m_par) * pnorm / m_fnorm);</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>  prered = temp1 + temp2 / Scalar(.5);</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  dirder = -(temp1 + temp2);</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span> </div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  <span class="comment">/* compute the ratio of the actual to the predicted */</span></div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  <span class="comment">/* reduction. */</span></div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  ratio = 0.;</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="keywordflow">if</span> (prered != 0.)</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  ratio = actred / prered;</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>  <span class="comment">/* update the step bound. */</span></div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="keywordflow">if</span> (ratio <= Scalar(.25)) {</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="keywordflow">if</span> (actred >= 0.)</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  temp = RealScalar(.5);</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  <span class="keywordflow">if</span> (actred < 0.)</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  temp = RealScalar(.5) * dirder / (dirder + RealScalar(.5) * actred);</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keywordflow">if</span> (RealScalar(.1) * fnorm1 >= m_fnorm || temp < RealScalar(.1))</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  temp = Scalar(.1);</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  <span class="comment">/* Computing MIN */</span></div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  m_delta = temp * (std::min)(m_delta, pnorm / RealScalar(.1));</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  m_par /= temp;</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  } <span class="keywordflow">else</span> <span class="keywordflow">if</span> (!(m_par != 0. && ratio < RealScalar(.75))) {</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>  m_delta = pnorm / RealScalar(.5);</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  m_par = RealScalar(.5) * m_par;</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>  <span class="comment">/* test for successful iteration. */</span></div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="keywordflow">if</span> (ratio >= RealScalar(1e-4)) {</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="comment">/* successful iteration. update x, m_fvec, and their norms. */</span></div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  x = m_wa2;</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  m_wa2 = m_diag.cwiseProduct(x);</div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  m_fvec = m_wa4;</div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  xnorm = m_wa2.stableNorm();</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  m_fnorm = fnorm1;</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  ++m_iter;</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  }</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span> </div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  <span class="comment">/* tests for convergence. */</span></div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>  <span class="keywordflow">if</span> (abs(actred) <= m_ftol && prered <= m_ftol && Scalar(.5) * ratio <= 1. && m_delta <= m_xtol * xnorm)</div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  {</div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  m_info = Success;</div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::RelativeErrorAndReductionTooSmall;</div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  }</div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>  <span class="keywordflow">if</span> (abs(actred) <= m_ftol && prered <= m_ftol && Scalar(.5) * ratio <= 1.) </div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>  {</div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>  m_info = Success;</div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::RelativeReductionTooSmall;</div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  }</div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <span class="keywordflow">if</span> (m_delta <= m_xtol * xnorm)</div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  {</div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  m_info = Success;</div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::RelativeErrorTooSmall;</div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  }</div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span> </div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>  <span class="comment">/* tests for termination and stringent tolerances. */</span></div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <span class="keywordflow">if</span> (m_nfev >= m_maxfev) </div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  {</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  m_info = NoConvergence;</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::TooManyFunctionEvaluation;</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  }</div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  <span class="keywordflow">if</span> (abs(actred) <= NumTraits<Scalar>::epsilon() && prered <= NumTraits<Scalar>::epsilon() && Scalar(.5) * ratio <= 1.)</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  {</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  m_info = Success;</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::FtolTooSmall;</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>  <span class="keywordflow">if</span> (m_delta <= NumTraits<Scalar>::epsilon() * xnorm) </div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  {</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>  m_info = Success;</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::XtolTooSmall;</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="keywordflow">if</span> (m_gnorm <= NumTraits<Scalar>::epsilon())</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>  m_info = Success;</div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::GtolTooSmall;</div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>  }</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span> </div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>  } <span class="keywordflow">while</span> (ratio < Scalar(1e-4));</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span> </div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="keywordflow">return</span> LevenbergMarquardtSpace::Running;</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span> }</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span> </div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  </div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span> </div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span> <span class="preprocessor">#endif // EIGEN_LMONESTEP_H</span></div>
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