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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_LMCOVAR_H</span></div> <div class="line"><a name="l00013"></a><span class="lineno"> 13</span> <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_LMCOVAR_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> Scalar></div> <div class="line"><a name="l00020"></a><span class="lineno"> 20</span> <span class="keywordtype">void</span> covar(</div> <div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  Matrix< Scalar, Dynamic, Dynamic > &r,</div> <div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  <span class="keyword">const</span> VectorXi& ipvt,</div> <div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  Scalar tol = std::sqrt(NumTraits<Scalar>::epsilon()) )</div> <div class="line"><a name="l00024"></a><span class="lineno"> 24</span> {</div> <div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  <span class="keyword">using</span> std::abs;</div> <div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  <span class="keyword">typedef</span> DenseIndex Index;</div> <div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  <span class="comment">/* Local variables */</span></div> <div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  Index i, j, k, l, ii, jj;</div> <div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  <span class="keywordtype">bool</span> sing;</div> <div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  Scalar temp;</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">/* Function Body */</span></div> <div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  <span class="keyword">const</span> Index n = r.cols();</div> <div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="keyword">const</span> Scalar tolr = tol * abs(r(0,0));</div> <div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  Matrix< Scalar, Dynamic, 1 > wa(n);</div> <div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  eigen_assert(ipvt.size()==n);</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">/* form the inverse of r in the full upper triangle of r. */</span></div> <div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  l = -1;</div> <div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="keywordflow">for</span> (k = 0; k < n; ++k)</div> <div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="keywordflow">if</span> (abs(r(k,k)) > tolr) {</div> <div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  r(k,k) = 1. / r(k,k);</div> <div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="keywordflow">for</span> (j = 0; j <= k-1; ++j) {</div> <div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  temp = r(k,k) * r(j,k);</div> <div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  r(j,k) = 0.;</div> <div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  r.col(k).head(j+1) -= r.col(j).head(j+1) * temp;</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>  l = k;</div> <div class="line"><a name="l00049"></a><span class="lineno"> 49</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">/* form the full upper triangle of the inverse of (r transpose)*r */</span></div> <div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  <span class="comment">/* in the full upper triangle of r. */</span></div> <div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  <span class="keywordflow">for</span> (k = 0; k <= l; ++k) {</div> <div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  <span class="keywordflow">for</span> (j = 0; j <= k-1; ++j)</div> <div class="line"><a name="l00055"></a><span class="lineno"> 55</span>  r.col(j).head(j+1) += r.col(k).head(j+1) * r(j,k);</div> <div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  r.col(k).head(k+1) *= r(k,k);</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> </div> <div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="comment">/* form the full lower triangle of the covariance matrix */</span></div> <div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  <span class="comment">/* in the strict lower triangle of r and in wa. */</span></div> <div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="keywordflow">for</span> (j = 0; j < n; ++j) {</div> <div class="line"><a name="l00062"></a><span class="lineno"> 62</span>  jj = ipvt[j];</div> <div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  sing = j > l;</div> <div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="keywordflow">for</span> (i = 0; i <= j; ++i) {</div> <div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keywordflow">if</span> (sing)</div> <div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  r(i,j) = 0.;</div> <div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  ii = ipvt[i];</div> <div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  <span class="keywordflow">if</span> (ii > jj)</div> <div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  r(ii,jj) = r(i,j);</div> <div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  <span class="keywordflow">if</span> (ii < jj)</div> <div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  r(jj,ii) = r(i,j);</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>  wa[jj] = r(j,j);</div> <div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  }</div> <div class="line"><a name="l00075"></a><span class="lineno"> 75</span> </div> <div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="comment">/* symmetrize the covariance matrix in r. */</span></div> <div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  r.topLeftCorner(n,n).template triangularView<StrictlyUpper>() = r.topLeftCorner(n,n).transpose();</div> <div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  r.diagonal() = wa;</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">// end namespace internal</span></div> <div class="line"><a name="l00082"></a><span class="lineno"> 82</span> </div> <div class="line"><a name="l00083"></a><span class="lineno"> 83</span> } <span class="comment">// end namespace Eigen</span></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="preprocessor">#endif // 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