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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">// This code initially comes from MINPACK whose original authors are:</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="comment">// Copyright Jorge More - Argonne National Laboratory</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="comment">// Copyright Burt Garbow - Argonne National Laboratory</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="comment">// Copyright Ken Hillstrom - Argonne National Laboratory</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span> <span class="comment">//</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// This Source Code Form is subject to the terms of the Minpack license</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span> <span class="comment">// (a BSD-like license) described in the campaigned CopyrightMINPACK.txt file.</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span> </div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span> <span class="preprocessor">#ifndef EIGEN_LMPAR_H</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_LMPAR_H</span></div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="preprocessor"></span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="keyword">namespace </span>Eigen {</div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span> </div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="keyword">namespace </span>internal {</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> QRSolver, <span class="keyword">typename</span> VectorType></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>  <span class="keywordtype">void</span> lmpar2(</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  <span class="keyword">const</span> QRSolver &qr,</div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  <span class="keyword">const</span> VectorType &diag,</div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  <span class="keyword">const</span> VectorType &qtb,</div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  <span class="keyword">typename</span> VectorType::Scalar m_delta,</div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  <span class="keyword">typename</span> VectorType::Scalar &par,</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  VectorType &x)</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span> </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>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  <span class="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> QRSolver::MatrixType MatrixType;</div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> QRSolver::Scalar Scalar;</div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  <span class="keyword">typedef</span> <span class="keyword">typename</span> QRSolver::Index Index;</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span> </div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="comment">/* Local variables */</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  Index j;</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  Scalar fp;</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  Scalar parc, parl;</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  Index iter;</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  Scalar temp, paru;</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  Scalar gnorm;</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  Scalar dxnorm;</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  </div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="comment">// Make a copy of the triangular factor. </span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="comment">// This copy is modified during call the qrsolv</span></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  MatrixType s;</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  s = qr.matrixR();</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span> </div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="comment">/* Function Body */</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="keyword">const</span> Scalar dwarf = (std::numeric_limits<Scalar>::min)();</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="keyword">const</span> Index n = qr.matrixR().cols();</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  eigen_assert(n==diag.size());</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  eigen_assert(n==qtb.size());</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span> </div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  VectorType wa1, wa2;</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span> </div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="comment">/* compute and store in x the gauss-newton direction. if the */</span></div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="comment">/* jacobian is rank-deficient, obtain a least squares solution. */</span></div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span> </div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="comment">// const Index rank = qr.nonzeroPivots(); // exactly double(0.)</span></div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="keyword">const</span> Index rank = qr.rank(); <span class="comment">// use a threshold</span></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  wa1 = qtb;</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  wa1.tail(n-rank).setZero();</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="comment">//FIXME There is no solve in place for sparse triangularView</span></div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  wa1.head(rank) = s.topLeftCorner(rank,rank).template triangularView<Upper>().solve(qtb.head(rank));</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>  x = qr.colsPermutation()*wa1;</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span> </div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="comment">/* initialize the iteration counter. */</span></div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="comment">/* evaluate the function at the origin, and test */</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="comment">/* for acceptance of the gauss-newton direction. */</span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  iter = 0;</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  wa2 = diag.cwiseProduct(x);</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  dxnorm = wa2.blueNorm();</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  fp = dxnorm - m_delta;</div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordflow">if</span> (fp <= Scalar(0.1) * m_delta) {</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  par = 0;</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="keywordflow">return</span>;</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> </div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="comment">/* if the jacobian is not rank deficient, the newton */</span></div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  <span class="comment">/* step provides a lower bound, parl, for the zero of */</span></div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="comment">/* the function. otherwise set this bound to zero. */</span></div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  parl = 0.;</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  <span class="keywordflow">if</span> (rank==n) {</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  wa1 = qr.colsPermutation().inverse() * diag.cwiseProduct(wa2)/dxnorm;</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  s.topLeftCorner(n,n).transpose().template triangularView<Lower>().solveInPlace(wa1);</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  temp = wa1.blueNorm();</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  parl = fp / m_delta / temp / temp;</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>  }</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span> </div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="comment">/* calculate an upper bound, paru, for the zero of the function. */</span></div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  <span class="keywordflow">for</span> (j = 0; j < n; ++j)</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  wa1[j] = s.col(j).head(j+1).dot(qtb.head(j+1)) / diag[qr.colsPermutation().indices()(j)];</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span> </div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  gnorm = wa1.stableNorm();</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  paru = gnorm / m_delta;</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  <span class="keywordflow">if</span> (paru == 0.)</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>  paru = dwarf / (std::min)(m_delta,Scalar(0.1));</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span> </div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="comment">/* if the input par lies outside of the interval (parl,paru), */</span></div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  <span class="comment">/* set par to the closer endpoint. */</span></div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  par = (std::max)(par,parl);</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  par = (std::min)(par,paru);</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  <span class="keywordflow">if</span> (par == 0.)</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>  par = gnorm / dxnorm;</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span> </div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="comment">/* beginning of an iteration. */</span></div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>  ++iter;</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span> </div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="comment">/* evaluate the function at the current value of par. */</span></div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  <span class="keywordflow">if</span> (par == 0.)</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  par = (std::max)(dwarf,Scalar(.001) * paru); <span class="comment">/* Computing MAX */</span></div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>  wa1 = sqrt(par)* diag;</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>  VectorType sdiag(n);</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>  lmqrsolv(s, qr.colsPermutation(), wa1, qtb, x, sdiag);</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>  wa2 = diag.cwiseProduct(x);</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  dxnorm = wa2.blueNorm();</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  temp = fp;</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>  fp = dxnorm - m_delta;</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span> </div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="comment">/* if the function is small enough, accept the current value */</span></div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="comment">/* of par. also test for the exceptional cases where parl */</span></div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="comment">/* is zero or the number of iterations has reached 10. */</span></div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keywordflow">if</span> (abs(fp) <= Scalar(0.1) * m_delta || (parl == 0. && fp <= temp && temp < 0.) || iter == 10)</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>  <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span> </div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="comment">/* compute the newton correction. */</span></div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  wa1 = qr.colsPermutation().inverse() * diag.cwiseProduct(wa2/dxnorm);</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  <span class="comment">// we could almost use this here, but the diagonal is outside qr, in sdiag[]</span></div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  <span class="keywordflow">for</span> (j = 0; j < n; ++j) {</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  wa1[j] /= sdiag[j];</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  temp = wa1[j];</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  <span class="keywordflow">for</span> (Index i = j+1; i < n; ++i)</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  wa1[i] -= s.coeff(i,j) * temp;</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>  temp = wa1.blueNorm();</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>  parc = fp / m_delta / temp / temp;</div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span> </div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>  <span class="comment">/* depending on the sign of the function, update parl or paru. */</span></div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>  <span class="keywordflow">if</span> (fp > 0.)</div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  parl = (std::max)(parl,par);</div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  <span class="keywordflow">if</span> (fp < 0.)</div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  paru = (std::min)(paru,par);</div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span> </div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>  <span class="comment">/* compute an improved estimate for par. */</span></div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  par = (std::max)(parl,par+parc);</div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  }</div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  <span class="keywordflow">if</span> (iter == 0)</div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>  par = 0.;</div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>  <span class="keywordflow">return</span>;</div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>  }</div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span> } <span class="comment">// end namespace internal</span></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> } <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span> </div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span> <span class="preprocessor">#endif // EIGEN_LMPAR_H</span></div>
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