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{ </div> <div class="line"><a name="l00002"></a><span class="lineno"> 2</span> </div> <div class="line"><a name="l00003"></a><span class="lineno"> 3</span> <span class="keyword">namespace </span>internal {</div> <div class="line"><a name="l00004"></a><span class="lineno"> 4</span> </div> <div class="line"><a name="l00005"></a><span class="lineno"> 5</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Scalar></div> <div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="keywordtype">void</span> lmpar(</div> <div class="line"><a name="l00007"></a><span class="lineno"> 7</span>  Matrix< Scalar, Dynamic, Dynamic > &r,</div> <div class="line"><a name="l00008"></a><span class="lineno"> 8</span>  <span class="keyword">const</span> VectorXi &ipvt,</div> <div class="line"><a name="l00009"></a><span class="lineno"> 9</span>  <span class="keyword">const</span> Matrix< Scalar, Dynamic, 1 > &diag,</div> <div class="line"><a name="l00010"></a><span class="lineno"> 10</span>  <span class="keyword">const</span> Matrix< Scalar, Dynamic, 1 > &qtb,</div> <div class="line"><a name="l00011"></a><span class="lineno"> 11</span>  Scalar delta,</div> <div class="line"><a name="l00012"></a><span class="lineno"> 12</span>  Scalar &par,</div> <div class="line"><a name="l00013"></a><span class="lineno"> 13</span>  Matrix< Scalar, Dynamic, 1 > &x)</div> <div class="line"><a name="l00014"></a><span class="lineno"> 14</span> {</div> <div class="line"><a name="l00015"></a><span class="lineno"> 15</span>  <span class="keyword">using</span> std::abs;</div> <div class="line"><a name="l00016"></a><span class="lineno"> 16</span>  <span class="keyword">using</span> std::sqrt;</div> <div class="line"><a name="l00017"></a><span class="lineno"> 17</span>  <span class="keyword">typedef</span> DenseIndex Index;</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="comment">/* Local variables */</span></div> <div class="line"><a name="l00020"></a><span class="lineno"> 20</span>  Index i, j, l;</div> <div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  Scalar fp;</div> <div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  Scalar parc, parl;</div> <div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  Index iter;</div> <div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  Scalar temp, paru;</div> <div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  Scalar gnorm;</div> <div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  Scalar dxnorm;</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="comment">/* Function Body */</span></div> <div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  <span class="keyword">const</span> Scalar dwarf = (std::numeric_limits<Scalar>::min)();</div> <div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <span class="keyword">const</span> Index n = r.cols();</div> <div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  eigen_assert(n==diag.size());</div> <div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  eigen_assert(n==qtb.size());</div> <div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  eigen_assert(n==x.size());</div> <div class="line"><a name="l00035"></a><span class="lineno"> 35</span> </div> <div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  Matrix< Scalar, Dynamic, 1 > wa1, wa2;</div> <div class="line"><a name="l00037"></a><span class="lineno"> 37</span> </div> <div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <span class="comment">/* compute and store in x the gauss-newton direction. if the */</span></div> <div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="comment">/* jacobian is rank-deficient, obtain a least squares solution. */</span></div> <div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  Index nsing = n-1;</div> <div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  wa1 = qtb;</div> <div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="keywordflow">for</span> (j = 0; j < n; ++j) {</div> <div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="keywordflow">if</span> (r(j,j) == 0. && nsing == n-1)</div> <div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  nsing = j - 1;</div> <div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keywordflow">if</span> (nsing < n-1)</div> <div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  wa1[j] = 0.;</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="keywordflow">for</span> (j = nsing; j>=0; --j) {</div> <div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  wa1[j] /= r(j,j);</div> <div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  temp = wa1[j];</div> <div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="keywordflow">for</span> (i = 0; i < j ; ++i)</div> <div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  wa1[i] -= r(i,j) * temp;</div> <div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  }</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>  <span class="keywordflow">for</span> (j = 0; j < n; ++j)</div> <div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  x[ipvt[j]] = wa1[j];</div> <div class="line"><a name="l00057"></a><span class="lineno"> 57</span> </div> <div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="comment">/* initialize the iteration counter. */</span></div> <div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="comment">/* evaluate the function at the origin, and test */</span></div> <div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="comment">/* for acceptance of the gauss-newton direction. */</span></div> <div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  iter = 0;</div> <div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  wa2 = diag.cwiseProduct(x);</div> <div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  dxnorm = wa2.blueNorm();</div> <div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  fp = dxnorm - delta;</div> <div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keywordflow">if</span> (fp <= Scalar(0.1) * delta) {</div> <div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  par = 0;</div> <div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keywordflow">return</span>;</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> </div> <div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="comment">/* if the jacobian is not rank deficient, the newton */</span></div> <div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="comment">/* step provides a lower bound, parl, for the zero of */</span></div> <div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  <span class="comment">/* the function. otherwise set this bound to zero. */</span></div> <div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  parl = 0.;</div> <div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="keywordflow">if</span> (nsing >= n-1) {</div> <div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keywordflow">for</span> (j = 0; j < n; ++j) {</div> <div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  l = ipvt[j];</div> <div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  wa1[j] = diag[l] * (wa2[l] / dxnorm);</div> <div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  }</div> <div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="comment">// it's actually a triangularView.solveInplace(), though in a weird</span></div> <div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  <span class="comment">// way:</span></div> <div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  <span class="keywordflow">for</span> (j = 0; j < n; ++j) {</div> <div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  Scalar sum = 0.;</div> <div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  <span class="keywordflow">for</span> (i = 0; i < j; ++i)</div> <div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  sum += r(i,j) * wa1[i];</div> <div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  wa1[j] = (wa1[j] - sum) / r(j,j);</div> <div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  }</div> <div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  temp = wa1.blueNorm();</div> <div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  parl = fp / delta / temp / temp;</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> </div> <div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="comment">/* calculate an upper bound, paru, for the zero of the function. */</span></div> <div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="keywordflow">for</span> (j = 0; j < n; ++j)</div> <div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  wa1[j] = r.col(j).head(j+1).dot(qtb.head(j+1)) / diag[ipvt[j]];</div> <div class="line"><a name="l00094"></a><span class="lineno"> 94</span> </div> <div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  gnorm = wa1.stableNorm();</div> <div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  paru = gnorm / delta;</div> <div class="line"><a name="l00097"></a><span class="lineno"> 97</span>  <span class="keywordflow">if</span> (paru == 0.)</div> <div class="line"><a name="l00098"></a><span class="lineno"> 98</span>  paru = dwarf / (std::min)(delta,Scalar(0.1));</div> <div class="line"><a name="l00099"></a><span class="lineno"> 99</span> </div> <div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="comment">/* if the input par lies outside of the interval (parl,paru), */</span></div> <div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  <span class="comment">/* set par to the closer endpoint. */</span></div> <div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  par = (std::max)(par,parl);</div> <div class="line"><a name="l00103"></a><span class="lineno"> 103</span>  par = (std::min)(par,paru);</div> <div class="line"><a name="l00104"></a><span class="lineno"> 104</span>  <span class="keywordflow">if</span> (par == 0.)</div> <div class="line"><a name="l00105"></a><span class="lineno"> 105</span>  par = gnorm / dxnorm;</div> <div class="line"><a name="l00106"></a><span class="lineno"> 106</span> </div> <div class="line"><a name="l00107"></a><span class="lineno"> 107</span>  <span class="comment">/* beginning of an iteration. */</span></div> <div class="line"><a name="l00108"></a><span class="lineno"> 108</span>  <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div> <div class="line"><a name="l00109"></a><span class="lineno"> 109</span>  ++iter;</div> <div class="line"><a name="l00110"></a><span class="lineno"> 110</span> </div> <div class="line"><a name="l00111"></a><span class="lineno"> 111</span>  <span class="comment">/* evaluate the function at the current value of par. */</span></div> <div class="line"><a name="l00112"></a><span class="lineno"> 112</span>  <span class="keywordflow">if</span> (par == 0.)</div> <div class="line"><a name="l00113"></a><span class="lineno"> 113</span>  par = (std::max)(dwarf,Scalar(.001) * paru); <span class="comment">/* Computing MAX */</span></div> <div class="line"><a name="l00114"></a><span class="lineno"> 114</span>  wa1 = sqrt(par)* diag;</div> <div class="line"><a name="l00115"></a><span class="lineno"> 115</span> </div> <div class="line"><a name="l00116"></a><span class="lineno"> 116</span>  Matrix< Scalar, Dynamic, 1 > sdiag(n);</div> <div class="line"><a name="l00117"></a><span class="lineno"> 117</span>  qrsolv<Scalar>(r, ipvt, wa1, qtb, x, sdiag);</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>  wa2 = diag.cwiseProduct(x);</div> <div class="line"><a name="l00120"></a><span class="lineno"> 120</span>  dxnorm = wa2.blueNorm();</div> <div class="line"><a name="l00121"></a><span class="lineno"> 121</span>  temp = fp;</div> <div class="line"><a name="l00122"></a><span class="lineno"> 122</span>  fp = dxnorm - delta;</div> <div class="line"><a name="l00123"></a><span class="lineno"> 123</span> </div> <div class="line"><a name="l00124"></a><span class="lineno"> 124</span>  <span class="comment">/* if the function is small enough, accept the current value */</span></div> <div class="line"><a name="l00125"></a><span class="lineno"> 125</span>  <span class="comment">/* of par. also test for the exceptional cases where parl */</span></div> <div class="line"><a name="l00126"></a><span class="lineno"> 126</span>  <span class="comment">/* is zero or the number of iterations has reached 10. */</span></div> <div class="line"><a name="l00127"></a><span class="lineno"> 127</span>  <span class="keywordflow">if</span> (abs(fp) <= Scalar(0.1) * delta || (parl == 0. && fp <= temp && temp < 0.) || iter == 10)</div> <div class="line"><a name="l00128"></a><span class="lineno"> 128</span>  <span class="keywordflow">break</span>;</div> <div class="line"><a name="l00129"></a><span class="lineno"> 129</span> </div> <div class="line"><a name="l00130"></a><span class="lineno"> 130</span>  <span class="comment">/* compute the newton correction. */</span></div> <div class="line"><a name="l00131"></a><span class="lineno"> 131</span>  <span class="keywordflow">for</span> (j = 0; j < n; ++j) {</div> <div class="line"><a name="l00132"></a><span class="lineno"> 132</span>  l = ipvt[j];</div> <div class="line"><a name="l00133"></a><span class="lineno"> 133</span>  wa1[j] = diag[l] * (wa2[l] / dxnorm);</div> <div class="line"><a name="l00134"></a><span class="lineno"> 134</span>  }</div> <div class="line"><a name="l00135"></a><span class="lineno"> 135</span>  <span class="keywordflow">for</span> (j = 0; j < n; ++j) {</div> <div class="line"><a name="l00136"></a><span class="lineno"> 136</span>  wa1[j] /= sdiag[j];</div> <div class="line"><a name="l00137"></a><span class="lineno"> 137</span>  temp = wa1[j];</div> <div class="line"><a name="l00138"></a><span class="lineno"> 138</span>  <span class="keywordflow">for</span> (i = j+1; i < n; ++i)</div> <div class="line"><a name="l00139"></a><span class="lineno"> 139</span>  wa1[i] -= r(i,j) * temp;</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>  temp = wa1.blueNorm();</div> <div class="line"><a name="l00142"></a><span class="lineno"> 142</span>  parc = fp / delta / temp / temp;</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">/* depending on the sign of the function, update parl or paru. */</span></div> <div class="line"><a name="l00145"></a><span class="lineno"> 145</span>  <span class="keywordflow">if</span> (fp > 0.)</div> <div class="line"><a name="l00146"></a><span class="lineno"> 146</span>  parl = (std::max)(parl,par);</div> <div class="line"><a name="l00147"></a><span class="lineno"> 147</span>  <span class="keywordflow">if</span> (fp < 0.)</div> <div class="line"><a name="l00148"></a><span class="lineno"> 148</span>  paru = (std::min)(paru,par);</div> <div class="line"><a name="l00149"></a><span class="lineno"> 149</span> </div> <div class="line"><a name="l00150"></a><span class="lineno"> 150</span>  <span class="comment">/* compute an improved estimate for par. */</span></div> <div class="line"><a name="l00151"></a><span class="lineno"> 151</span>  <span class="comment">/* Computing MAX */</span></div> <div class="line"><a name="l00152"></a><span class="lineno"> 152</span>  par = (std::max)(parl,par+parc);</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>  <span class="comment">/* end of an iteration. */</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> </div> <div class="line"><a name="l00157"></a><span class="lineno"> 157</span>  <span class="comment">/* termination. */</span></div> <div class="line"><a name="l00158"></a><span class="lineno"> 158</span>  <span class="keywordflow">if</span> (iter == 0)</div> <div class="line"><a name="l00159"></a><span class="lineno"> 159</span>  par = 0.;</div> <div class="line"><a name="l00160"></a><span class="lineno"> 160</span>  <span class="keywordflow">return</span>;</div> <div class="line"><a name="l00161"></a><span class="lineno"> 161</span> }</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> <span class="keyword">template</span> <<span class="keyword">typename</span> Scalar></div> <div class="line"><a name="l00164"></a><span class="lineno"> 164</span> <span class="keywordtype">void</span> lmpar2(</div> <div class="line"><a name="l00165"></a><span class="lineno"> 165</span>  <span class="keyword">const</span> ColPivHouseholderQR<Matrix< Scalar, Dynamic, Dynamic> > &qr,</div> <div class="line"><a name="l00166"></a><span class="lineno"> 166</span>  <span class="keyword">const</span> Matrix< Scalar, Dynamic, 1 > &diag,</div> <div class="line"><a name="l00167"></a><span class="lineno"> 167</span>  <span class="keyword">const</span> Matrix< Scalar, Dynamic, 1 > &qtb,</div> <div class="line"><a name="l00168"></a><span class="lineno"> 168</span>  Scalar delta,</div> <div class="line"><a name="l00169"></a><span class="lineno"> 169</span>  Scalar &par,</div> <div class="line"><a name="l00170"></a><span class="lineno"> 170</span>  Matrix< Scalar, Dynamic, 1 > &x)</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> {</div> <div class="line"><a name="l00173"></a><span class="lineno"> 173</span>  <span class="keyword">using</span> std::sqrt;</div> <div class="line"><a name="l00174"></a><span class="lineno"> 174</span>  <span class="keyword">using</span> std::abs;</div> <div class="line"><a name="l00175"></a><span class="lineno"> 175</span>  <span class="keyword">typedef</span> DenseIndex Index;</div> <div class="line"><a name="l00176"></a><span class="lineno"> 176</span> </div> <div class="line"><a name="l00177"></a><span class="lineno"> 177</span>  <span class="comment">/* Local variables */</span></div> <div class="line"><a name="l00178"></a><span class="lineno"> 178</span>  Index j;</div> <div class="line"><a name="l00179"></a><span class="lineno"> 179</span>  Scalar fp;</div> <div class="line"><a name="l00180"></a><span class="lineno"> 180</span>  Scalar parc, parl;</div> <div class="line"><a name="l00181"></a><span class="lineno"> 181</span>  Index iter;</div> <div class="line"><a name="l00182"></a><span class="lineno"> 182</span>  Scalar temp, paru;</div> <div class="line"><a name="l00183"></a><span class="lineno"> 183</span>  Scalar gnorm;</div> <div class="line"><a name="l00184"></a><span class="lineno"> 184</span>  Scalar dxnorm;</div> <div class="line"><a name="l00185"></a><span class="lineno"> 185</span> </div> <div class="line"><a name="l00186"></a><span class="lineno"> 186</span> </div> <div class="line"><a name="l00187"></a><span class="lineno"> 187</span>  <span class="comment">/* Function Body */</span></div> <div class="line"><a name="l00188"></a><span class="lineno"> 188</span>  <span class="keyword">const</span> Scalar dwarf = (std::numeric_limits<Scalar>::min)();</div> <div class="line"><a name="l00189"></a><span class="lineno"> 189</span>  <span class="keyword">const</span> Index n = qr.matrixQR().cols();</div> <div class="line"><a name="l00190"></a><span class="lineno"> 190</span>  eigen_assert(n==diag.size());</div> <div class="line"><a name="l00191"></a><span class="lineno"> 191</span>  eigen_assert(n==qtb.size());</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>  Matrix< Scalar, Dynamic, 1 > wa1, wa2;</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>  <span class="comment">/* compute and store in x the gauss-newton direction. if the */</span></div> <div class="line"><a name="l00196"></a><span class="lineno"> 196</span>  <span class="comment">/* jacobian is rank-deficient, obtain a least squares solution. */</span></div> <div class="line"><a name="l00197"></a><span class="lineno"> 197</span> </div> <div class="line"><a name="l00198"></a><span class="lineno"> 198</span> <span class="comment">// const Index rank = qr.nonzeroPivots(); // exactly double(0.)</span></div> <div class="line"><a name="l00199"></a><span class="lineno"> 199</span>  <span class="keyword">const</span> Index rank = qr.rank(); <span class="comment">// use a threshold</span></div> <div class="line"><a name="l00200"></a><span class="lineno"> 200</span>  wa1 = qtb;</div> <div class="line"><a name="l00201"></a><span class="lineno"> 201</span>  wa1.tail(n-rank).setZero();</div> <div class="line"><a name="l00202"></a><span class="lineno"> 202</span>  qr.matrixQR().topLeftCorner(rank, rank).template triangularView<Upper>().solveInPlace(wa1.head(rank));</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>  x = qr.colsPermutation()*wa1;</div> <div class="line"><a name="l00205"></a><span class="lineno"> 205</span> </div> <div class="line"><a name="l00206"></a><span class="lineno"> 206</span>  <span class="comment">/* initialize the iteration counter. */</span></div> <div class="line"><a name="l00207"></a><span class="lineno"> 207</span>  <span class="comment">/* evaluate the function at the origin, and test */</span></div> <div class="line"><a name="l00208"></a><span class="lineno"> 208</span>  <span class="comment">/* for acceptance of the gauss-newton direction. */</span></div> <div class="line"><a name="l00209"></a><span class="lineno"> 209</span>  iter = 0;</div> <div class="line"><a name="l00210"></a><span class="lineno"> 210</span>  wa2 = diag.cwiseProduct(x);</div> <div class="line"><a name="l00211"></a><span class="lineno"> 211</span>  dxnorm = wa2.blueNorm();</div> <div class="line"><a name="l00212"></a><span class="lineno"> 212</span>  fp = dxnorm - delta;</div> <div class="line"><a name="l00213"></a><span class="lineno"> 213</span>  <span class="keywordflow">if</span> (fp <= Scalar(0.1) * delta) {</div> <div class="line"><a name="l00214"></a><span class="lineno"> 214</span>  par = 0;</div> <div class="line"><a name="l00215"></a><span class="lineno"> 215</span>  <span class="keywordflow">return</span>;</div> <div class="line"><a name="l00216"></a><span class="lineno"> 216</span>  }</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>  <span class="comment">/* if the jacobian is not rank deficient, the newton */</span></div> <div class="line"><a name="l00219"></a><span class="lineno"> 219</span>  <span class="comment">/* step provides a lower bound, parl, for the zero of */</span></div> <div class="line"><a name="l00220"></a><span class="lineno"> 220</span>  <span class="comment">/* the function. otherwise set this bound to zero. */</span></div> <div class="line"><a name="l00221"></a><span class="lineno"> 221</span>  parl = 0.;</div> <div class="line"><a name="l00222"></a><span class="lineno"> 222</span>  <span class="keywordflow">if</span> (rank==n) {</div> <div class="line"><a name="l00223"></a><span class="lineno"> 223</span>  wa1 = qr.colsPermutation().inverse() * diag.cwiseProduct(wa2)/dxnorm;</div> <div class="line"><a name="l00224"></a><span class="lineno"> 224</span>  qr.matrixQR().topLeftCorner(n, n).transpose().template triangularView<Lower>().solveInPlace(wa1);</div> <div class="line"><a name="l00225"></a><span class="lineno"> 225</span>  temp = wa1.blueNorm();</div> <div class="line"><a name="l00226"></a><span class="lineno"> 226</span>  parl = fp / delta / temp / temp;</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> </div> <div class="line"><a name="l00229"></a><span class="lineno"> 229</span>  <span class="comment">/* calculate an upper bound, paru, for the zero of the function. */</span></div> <div class="line"><a name="l00230"></a><span class="lineno"> 230</span>  <span class="keywordflow">for</span> (j = 0; j < n; ++j)</div> <div class="line"><a name="l00231"></a><span class="lineno"> 231</span>  wa1[j] = qr.matrixQR().col(j).head(j+1).dot(qtb.head(j+1)) / diag[qr.colsPermutation().indices()(j)];</div> <div class="line"><a name="l00232"></a><span class="lineno"> 232</span> </div> <div class="line"><a name="l00233"></a><span class="lineno"> 233</span>  gnorm = wa1.stableNorm();</div> <div class="line"><a name="l00234"></a><span class="lineno"> 234</span>  paru = gnorm / delta;</div> <div class="line"><a name="l00235"></a><span class="lineno"> 235</span>  <span class="keywordflow">if</span> (paru == 0.)</div> <div class="line"><a name="l00236"></a><span class="lineno"> 236</span>  paru = dwarf / (std::min)(delta,Scalar(0.1));</div> <div class="line"><a name="l00237"></a><span class="lineno"> 237</span> </div> <div class="line"><a name="l00238"></a><span class="lineno"> 238</span>  <span class="comment">/* if the input par lies outside of the interval (parl,paru), */</span></div> <div class="line"><a name="l00239"></a><span class="lineno"> 239</span>  <span class="comment">/* set par to the closer endpoint. */</span></div> <div class="line"><a name="l00240"></a><span class="lineno"> 240</span>  par = (std::max)(par,parl);</div> <div class="line"><a name="l00241"></a><span class="lineno"> 241</span>  par = (std::min)(par,paru);</div> <div class="line"><a name="l00242"></a><span class="lineno"> 242</span>  <span class="keywordflow">if</span> (par == 0.)</div> <div class="line"><a name="l00243"></a><span class="lineno"> 243</span>  par = gnorm / dxnorm;</div> <div class="line"><a name="l00244"></a><span class="lineno"> 244</span> </div> <div class="line"><a name="l00245"></a><span class="lineno"> 245</span>  <span class="comment">/* beginning of an iteration. */</span></div> <div class="line"><a name="l00246"></a><span class="lineno"> 246</span>  Matrix< Scalar, Dynamic, Dynamic > s = qr.matrixQR();</div> <div class="line"><a name="l00247"></a><span class="lineno"> 247</span>  <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div> <div class="line"><a name="l00248"></a><span class="lineno"> 248</span>  ++iter;</div> <div class="line"><a name="l00249"></a><span class="lineno"> 249</span> </div> <div class="line"><a name="l00250"></a><span class="lineno"> 250</span>  <span class="comment">/* evaluate the function at the current value of par. */</span></div> <div class="line"><a name="l00251"></a><span class="lineno"> 251</span>  <span class="keywordflow">if</span> (par == 0.)</div> <div class="line"><a name="l00252"></a><span class="lineno"> 252</span>  par = (std::max)(dwarf,Scalar(.001) * paru); <span class="comment">/* Computing MAX */</span></div> <div class="line"><a name="l00253"></a><span class="lineno"> 253</span>  wa1 = sqrt(par)* diag;</div> <div class="line"><a name="l00254"></a><span class="lineno"> 254</span> </div> <div class="line"><a name="l00255"></a><span class="lineno"> 255</span>  Matrix< Scalar, Dynamic, 1 > sdiag(n);</div> <div class="line"><a name="l00256"></a><span class="lineno"> 256</span>  qrsolv<Scalar>(s, qr.colsPermutation().indices(), wa1, qtb, x, sdiag);</div> <div class="line"><a name="l00257"></a><span class="lineno"> 257</span> </div> <div class="line"><a name="l00258"></a><span class="lineno"> 258</span>  wa2 = diag.cwiseProduct(x);</div> <div class="line"><a name="l00259"></a><span class="lineno"> 259</span>  dxnorm = wa2.blueNorm();</div> <div class="line"><a name="l00260"></a><span class="lineno"> 260</span>  temp = fp;</div> <div class="line"><a name="l00261"></a><span class="lineno"> 261</span>  fp = dxnorm - delta;</div> <div class="line"><a name="l00262"></a><span class="lineno"> 262</span> </div> <div class="line"><a name="l00263"></a><span class="lineno"> 263</span>  <span class="comment">/* if the function is small enough, accept the current value */</span></div> <div class="line"><a name="l00264"></a><span class="lineno"> 264</span>  <span class="comment">/* of par. also test for the exceptional cases where parl */</span></div> <div class="line"><a name="l00265"></a><span class="lineno"> 265</span>  <span class="comment">/* is zero or the number of iterations has reached 10. */</span></div> <div class="line"><a name="l00266"></a><span class="lineno"> 266</span>  <span class="keywordflow">if</span> (abs(fp) <= Scalar(0.1) * delta || (parl == 0. && fp <= temp && temp < 0.) || iter == 10)</div> <div class="line"><a name="l00267"></a><span class="lineno"> 267</span>  <span class="keywordflow">break</span>;</div> <div class="line"><a name="l00268"></a><span class="lineno"> 268</span> </div> <div class="line"><a name="l00269"></a><span class="lineno"> 269</span>  <span class="comment">/* compute the newton correction. */</span></div> <div class="line"><a name="l00270"></a><span class="lineno"> 270</span>  wa1 = qr.colsPermutation().inverse() * diag.cwiseProduct(wa2/dxnorm);</div> <div class="line"><a name="l00271"></a><span class="lineno"> 271</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="l00272"></a><span class="lineno"> 272</span>  <span class="comment">// qr.matrixQR().topLeftCorner(n, n).transpose().template triangularView<Lower>().solveInPlace(wa1);</span></div> <div class="line"><a name="l00273"></a><span class="lineno"> 273</span>  <span class="keywordflow">for</span> (j = 0; j < n; ++j) {</div> <div class="line"><a name="l00274"></a><span class="lineno"> 274</span>  wa1[j] /= sdiag[j];</div> <div class="line"><a name="l00275"></a><span class="lineno"> 275</span>  temp = wa1[j];</div> <div class="line"><a name="l00276"></a><span class="lineno"> 276</span>  <span class="keywordflow">for</span> (Index i = j+1; i < n; ++i)</div> <div class="line"><a name="l00277"></a><span class="lineno"> 277</span>  wa1[i] -= s(i,j) * temp;</div> <div class="line"><a name="l00278"></a><span class="lineno"> 278</span>  }</div> <div class="line"><a name="l00279"></a><span class="lineno"> 279</span>  temp = wa1.blueNorm();</div> <div class="line"><a name="l00280"></a><span class="lineno"> 280</span>  parc = fp / delta / temp / temp;</div> <div class="line"><a name="l00281"></a><span class="lineno"> 281</span> </div> <div class="line"><a name="l00282"></a><span class="lineno"> 282</span>  <span class="comment">/* depending on the sign of the function, update parl or paru. */</span></div> <div class="line"><a name="l00283"></a><span class="lineno"> 283</span>  <span class="keywordflow">if</span> (fp > 0.)</div> <div class="line"><a name="l00284"></a><span class="lineno"> 284</span>  parl = (std::max)(parl,par);</div> <div class="line"><a name="l00285"></a><span class="lineno"> 285</span>  <span class="keywordflow">if</span> (fp < 0.)</div> <div class="line"><a name="l00286"></a><span class="lineno"> 286</span>  paru = (std::min)(paru,par);</div> <div class="line"><a name="l00287"></a><span class="lineno"> 287</span> </div> <div class="line"><a name="l00288"></a><span class="lineno"> 288</span>  <span class="comment">/* compute an improved estimate for par. */</span></div> <div class="line"><a name="l00289"></a><span class="lineno"> 289</span>  par = (std::max)(parl,par+parc);</div> <div class="line"><a name="l00290"></a><span class="lineno"> 290</span>  }</div> <div class="line"><a name="l00291"></a><span class="lineno"> 291</span>  <span class="keywordflow">if</span> (iter == 0)</div> <div class="line"><a name="l00292"></a><span class="lineno"> 292</span>  par = 0.;</div> <div class="line"><a name="l00293"></a><span class="lineno"> 293</span>  <span class="keywordflow">return</span>;</div> <div class="line"><a name="l00294"></a><span class="lineno"> 294</span> }</div> <div class="line"><a name="l00295"></a><span class="lineno"> 295</span> </div> <div class="line"><a name="l00296"></a><span class="lineno"> 296</span> } <span class="comment">// end namespace internal</span></div> <div class="line"><a name="l00297"></a><span class="lineno"> 297</span> </div> <div class="line"><a name="l00298"></a><span class="lineno"> 298</span> } <span class="comment">// end namespace Eigen</span></div> </div><!-- fragment --></div><!-- contents --> </div><!-- doc-content --> <!-- start footer part --> <div id="nav-path" class="navpath"><!-- id is needed for treeview function! --> <ul> <li class="navelem"><a class="el" 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