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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="comment">// TODO : once qrsolv2 is removed, use ColPivHouseholderQR or PermutationMatrix instead of ipvt</span></div> <div class="line"><a name="l00006"></a><span class="lineno"> 6</span> <span class="keyword">template</span> <<span class="keyword">typename</span> Scalar></div> <div class="line"><a name="l00007"></a><span class="lineno"> 7</span> <span class="keywordtype">void</span> qrsolv(</div> <div class="line"><a name="l00008"></a><span class="lineno"> 8</span>  Matrix< Scalar, Dynamic, Dynamic > &s,</div> <div class="line"><a name="l00009"></a><span class="lineno"> 9</span>  <span class="comment">// TODO : use a PermutationMatrix once lmpar is no more:</span></div> <div class="line"><a name="l00010"></a><span class="lineno"> 10</span>  <span class="keyword">const</span> VectorXi &ipvt,</div> <div class="line"><a name="l00011"></a><span class="lineno"> 11</span>  <span class="keyword">const</span> Matrix< Scalar, Dynamic, 1 > &diag,</div> <div class="line"><a name="l00012"></a><span class="lineno"> 12</span>  <span class="keyword">const</span> Matrix< Scalar, Dynamic, 1 > &qtb,</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>  Matrix< Scalar, Dynamic, 1 > &sdiag)</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> {</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, k, l;</div> <div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  Scalar temp;</div> <div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  Index n = s.cols();</div> <div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  Matrix< Scalar, Dynamic, 1 > wa(n);</div> <div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  JacobiRotation<Scalar> givens;</div> <div class="line"><a name="l00025"></a><span class="lineno"> 25</span> </div> <div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  <span class="comment">/* Function Body */</span></div> <div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  <span class="comment">// the following will only change the lower triangular part of s, including</span></div> <div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  <span class="comment">// the diagonal, though the diagonal is restored afterward</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>  <span class="comment">/* copy r and (q transpose)*b to preserve input and initialize s. */</span></div> <div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <span class="comment">/* in particular, save the diagonal elements of r in x. */</span></div> <div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  x = s.diagonal();</div> <div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  wa = qtb;</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>  s.topLeftCorner(n,n).template triangularView<StrictlyLower>() = s.topLeftCorner(n,n).transpose();</div> <div class="line"><a name="l00036"></a><span class="lineno"> 36</span> </div> <div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="comment">/* eliminate the diagonal matrix d using a givens rotation. */</span></div> <div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <span class="keywordflow">for</span> (j = 0; j < n; ++j) {</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">/* prepare the row of d to be eliminated, locating the */</span></div> <div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="comment">/* diagonal element using p from the qr factorization. */</span></div> <div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  l = ipvt[j];</div> <div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="keywordflow">if</span> (diag[l] == 0.)</div> <div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  <span class="keywordflow">break</span>;</div> <div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  sdiag.tail(n-j).setZero();</div> <div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  sdiag[j] = diag[l];</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">/* the transformations to eliminate the row of d */</span></div> <div class="line"><a name="l00049"></a><span class="lineno"> 49</span>  <span class="comment">/* modify only a single element of (q transpose)*b */</span></div> <div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="comment">/* beyond the first n, which is initially zero. */</span></div> <div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  Scalar qtbpj = 0.;</div> <div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="keywordflow">for</span> (k = j; k < n; ++k) {</div> <div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="comment">/* determine a givens rotation which eliminates the */</span></div> <div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="comment">/* appropriate element in the current row of d. */</span></div> <div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  givens.makeGivens(-s(k,k), sdiag[k]);</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 the modified diagonal element of r and */</span></div> <div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="comment">/* the modified element of ((q transpose)*b,0). */</span></div> <div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  s(k,k) = givens.c() * s(k,k) + givens.s() * sdiag[k];</div> <div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  temp = givens.c() * wa[k] + givens.s() * qtbpj;</div> <div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  qtbpj = -givens.s() * wa[k] + givens.c() * qtbpj;</div> <div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  wa[k] = temp;</div> <div class="line"><a name="l00063"></a><span class="lineno"> 63</span> </div> <div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="comment">/* accumulate the tranformation in the row of s. */</span></div> <div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keywordflow">for</span> (i = k+1; i<n; ++i) {</div> <div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  temp = givens.c() * s(i,k) + givens.s() * sdiag[i];</div> <div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  sdiag[i] = -givens.s() * s(i,k) + givens.c() * sdiag[i];</div> <div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  s(i,k) = temp;</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>  }</div> <div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  }</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">/* solve the triangular system for z. if the system is */</span></div> <div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="comment">/* singular, then obtain a least squares solution. */</span></div> <div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  Index nsing;</div> <div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordflow">for</span>(nsing=0; nsing<n && sdiag[nsing]!=0; nsing++) {}</div> <div class="line"><a name="l00077"></a><span class="lineno"> 77</span> </div> <div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  wa.tail(n-nsing).setZero();</div> <div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  s.topLeftCorner(nsing, nsing).transpose().template triangularView<Upper>().solveInPlace(wa.head(nsing));</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">// restore</span></div> <div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  sdiag = s.diagonal();</div> <div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  s.diagonal() = x;</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">/* permute the components of z back to components of x. */</span></div> <div class="line"><a name="l00086"></a><span class="lineno"> 86</span>  <span class="keywordflow">for</span> (j = 0; j < n; ++j) x[ipvt[j]] = wa[j];</div> <div class="line"><a name="l00087"></a><span class="lineno"> 87</span> }</div> <div class="line"><a name="l00088"></a><span class="lineno"> 88</span> </div> <div class="line"><a name="l00089"></a><span class="lineno"> 89</span> } <span class="comment">// end namespace internal</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">// end namespace Eigen</span></div> </div><!-- fragment --></div><!-- contents --> </div><!-- doc-content --> <!-- start footer part --> <div 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