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<div class="title">dogleg.h</div> </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="keyword">namespace </span>Eigen { </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> dogleg(</div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span>  <span class="keyword">const</span> Matrix< Scalar, Dynamic, Dynamic > &qrfac,</div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span>  <span class="keyword">const</span> Matrix< Scalar, Dynamic, 1 > &diag,</div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span>  <span class="keyword">const</span> Matrix< Scalar, Dynamic, 1 > &qtb,</div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span>  Scalar delta,</div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span>  Matrix< Scalar, Dynamic, 1 > &x)</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="keyword">using</span> std::abs;</div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span>  <span class="keyword">using</span> std::sqrt;</div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span>  </div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span>  <span class="keyword">typedef</span> DenseIndex Index;</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="comment">/* Local variables */</span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>  Index i, j;</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>  Scalar sum, temp, alpha, bnorm;</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  Scalar gnorm, qnorm;</div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  Scalar sgnorm;</div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span> </div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  <span class="comment">/* Function Body */</span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  <span class="keyword">const</span> Scalar epsmch = NumTraits<Scalar>::epsilon();</div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  <span class="keyword">const</span> Index n = qrfac.cols();</div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  eigen_assert(n==qtb.size());</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  eigen_assert(n==x.size());</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  eigen_assert(n==diag.size());</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  Matrix< Scalar, Dynamic, 1 > wa1(n), wa2(n);</div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span> </div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  <span class="comment">/* first, calculate the gauss-newton direction. */</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  <span class="keywordflow">for</span> (j = n-1; j >=0; --j) {</div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  temp = qrfac(j,j);</div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="keywordflow">if</span> (temp == 0.) {</div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  temp = epsmch * qrfac.col(j).head(j+1).maxCoeff();</div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="keywordflow">if</span> (temp == 0.)</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  temp = epsmch;</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="keywordflow">if</span> (j==n-1)</div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  x[j] = qtb[j] / temp;</div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="keywordflow">else</span></div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  x[j] = (qtb[j] - qrfac.row(j).tail(n-j-1).dot(x.tail(n-j-1))) / temp;</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> </div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  <span class="comment">/* test whether the gauss-newton direction is acceptable. */</span></div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  qnorm = diag.cwiseProduct(x).stableNorm();</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  <span class="keywordflow">if</span> (qnorm <= delta)</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="keywordflow">return</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="comment">// TODO : this path is not tested by Eigen unit tests</span></div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span> </div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="comment">/* the gauss-newton direction is not acceptable. */</span></div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="comment">/* next, calculate the scaled gradient direction. */</span></div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span> </div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  wa1.fill(0.);</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>  <span class="keywordflow">for</span> (j = 0; j < n; ++j) {</div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  wa1.tail(n-j) += qrfac.row(j).tail(n-j) * qtb[j];</div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  wa1[j] /= diag[j];</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  }</div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span> </div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  <span class="comment">/* calculate the norm of the scaled gradient and test for */</span></div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="comment">/* the special case in which the scaled gradient is zero. */</span></div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  gnorm = wa1.stableNorm();</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  sgnorm = 0.;</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  alpha = delta / qnorm;</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="keywordflow">if</span> (gnorm == 0.)</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keywordflow">goto</span> algo_end;</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">/* calculate the point along the scaled gradient */</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="comment">/* at which the quadratic is minimized. */</span></div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  wa1.array() /= (diag*gnorm).array();</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  <span class="comment">// TODO : once unit tests cover this part,:</span></div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="comment">// wa2 = qrfac.template triangularView<Upper>() * wa1;</span></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>  sum = 0.;</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="keywordflow">for</span> (i = j; i < n; ++i) {</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  sum += qrfac(j,i) * wa1[i];</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>  wa2[j] = sum;</div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  }</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  temp = wa2.stableNorm();</div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  sgnorm = gnorm / temp / temp;</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>  <span class="comment">/* test whether the scaled gradient direction is acceptable. */</span></div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  alpha = 0.;</div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>  <span class="keywordflow">if</span> (sgnorm >= delta)</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="keywordflow">goto</span> algo_end;</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="comment">/* the scaled gradient direction is not acceptable. */</span></div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>  <span class="comment">/* finally, calculate the point along the dogleg */</span></div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  <span class="comment">/* at which the quadratic is minimized. */</span></div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  bnorm = qtb.stableNorm();</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  temp = bnorm / gnorm * (bnorm / qnorm) * (sgnorm / delta);</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>  temp = temp - delta / qnorm * numext::abs2(sgnorm / delta) + sqrt(numext::abs2(temp - delta / qnorm) + (1.-numext::abs2(delta / qnorm)) * (1.-numext::abs2(sgnorm / delta)));</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>  alpha = delta / qnorm * (1. - numext::abs2(sgnorm / delta)) / temp;</div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> algo_end:</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">/* form appropriate convex combination of the gauss-newton */</span></div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>  <span class="comment">/* direction and the scaled gradient direction. */</span></div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>  temp = (1.-alpha) * (std::min)(sgnorm,delta);</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>  x = temp * wa1 + alpha * x;</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span> }</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span> </div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span> } <span class="comment">// end namespace internal</span></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">// end namespace Eigen</span></div>
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