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<div class="title">r1updt.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> r1updt(</div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span>  Matrix< Scalar, Dynamic, Dynamic > &s,</div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span>  <span class="keyword">const</span> Matrix< Scalar, Dynamic, 1> &u,</div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span>  std::vector<JacobiRotation<Scalar> > &v_givens,</div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span>  std::vector<JacobiRotation<Scalar> > &w_givens,</div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span>  Matrix< Scalar, Dynamic, 1> &v,</div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span>  Matrix< Scalar, Dynamic, 1> &w,</div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span>  <span class="keywordtype">bool</span> *sing)</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">typedef</span> DenseIndex Index;</div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span>  <span class="keyword">const</span> JacobiRotation<Scalar> IdentityRotation = JacobiRotation<Scalar>(1,0);</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>  <span class="keyword">const</span> Index m = s.rows();</div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>  <span class="keyword">const</span> Index n = s.cols();</div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  Index i, j=1;</div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  Scalar temp;</div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  JacobiRotation<Scalar> givens;</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="comment">// r1updt had a broader usecase, but we dont use it here. And, more</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  <span class="comment">// importantly, we can not test it.</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  eigen_assert(m==n);</div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  eigen_assert(u.size()==m);</div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  eigen_assert(v.size()==n);</div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  eigen_assert(w.size()==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">/* move the nontrivial part of the last column of s into w. */</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>  w[n-1] = s(n-1,n-1);</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">/* rotate the vector v into a multiple of the n-th unit vector */</span></div>
<div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="comment">/* in such a way that a spike is introduced into w. */</span></div>
<div class="line"><a name="l00037"></a><span class="lineno"> 37</span>  <span class="keywordflow">for</span> (j=n-2; j>=0; --j) {</div>
<div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  w[j] = 0.;</div>
<div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="keywordflow">if</span> (v[j] != 0.) {</div>
<div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  <span class="comment">/* determine a givens rotation which eliminates the */</span></div>
<div class="line"><a name="l00041"></a><span class="lineno"> 41</span>  <span class="comment">/* j-th element of v. */</span></div>
<div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  givens.makeGivens(-v[n-1], v[j]);</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">/* apply the transformation to v and store the information */</span></div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="comment">/* necessary to recover the givens rotation. */</span></div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  v[n-1] = givens.s() * v[j] + givens.c() * v[n-1];</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  v_givens[j] = givens;</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">/* apply the transformation to s and extend the spike in w. */</span></div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="keywordflow">for</span> (i = j; i < m; ++i) {</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  temp = givens.c() * s(j,i) - givens.s() * w[i];</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  w[i] = givens.s() * s(j,i) + givens.c() * w[i];</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  s(j,i) = temp;</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">else</span></div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  v_givens[j] = IdentityRotation;</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">/* add the spike from the rank 1 update to w. */</span></div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  w += v[n-1] * u;</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">/* eliminate the spike. */</span></div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  *sing = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="keywordflow">for</span> (j = 0; j < n-1; ++j) {</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  <span class="keywordflow">if</span> (w[j] != 0.) {</div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  <span class="comment">/* determine a givens rotation which eliminates the */</span></div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  <span class="comment">/* j-th element of the spike. */</span></div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  givens.makeGivens(-s(j,j), w[j]);</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">/* apply the transformation to s and reduce the spike in w. */</span></div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="keywordflow">for</span> (i = j; i < m; ++i) {</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  temp = givens.c() * s(j,i) + givens.s() * w[i];</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  w[i] = -givens.s() * s(j,i) + givens.c() * w[i];</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  s(j,i) = temp;</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> </div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  <span class="comment">/* store the information necessary to recover the */</span></div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  <span class="comment">/* givens rotation. */</span></div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  w_givens[j] = givens;</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  } <span class="keywordflow">else</span></div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  v_givens[j] = IdentityRotation;</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">/* test for zero diagonal elements in the output s. */</span></div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="keywordflow">if</span> (s(j,j) == 0.) {</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  *sing = <span class="keyword">true</span>;</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>  }</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>  <span class="comment">/* move w back into the last column of the output s. */</span></div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>  s(n-1,n-1) = w[n-1];</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="keywordflow">if</span> (s(j,j) == 0.) {</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>  *sing = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>  }</div>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>  <span class="keywordflow">return</span>;</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> </div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span> } <span class="comment">// end namespace internal</span></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">// end namespace Eigen</span></div>
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