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<div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// This file is part of Eigen, a lightweight C++ template library</span></div>
<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// for linear algebra.</span></div>
<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">//</span></div>
<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com></span></div>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">// This Source Code Form is subject to the terms of the Mozilla</span></div>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">// Public License v. 2.0. If a copy of the MPL was not distributed</span></div>
<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.</span></div>
<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span> </div>
<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="preprocessor">#ifndef EIGEN_DETERMINANT_H</span></div>
<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="preprocessor">#define EIGEN_DETERMINANT_H</span></div>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span> </div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span><span class="preprocessor">#include "./InternalHeaderCheck.h"</span></div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span> </div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceEigen.html">Eigen</a> { </div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span> </div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="keyword">namespace </span>internal {</div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span> </div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span>EIGEN_DEVICE_FUNC</div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="keyword">inline</span> <span class="keyword">const</span> <span class="keyword">typename</span> Derived::Scalar bruteforce_det3_helper</div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span>(<span class="keyword">const</span> MatrixBase<Derived>& matrix, <span class="keywordtype">int</span> a, <span class="keywordtype">int</span> b, <span class="keywordtype">int</span> c)</div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span>{</div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span> <span class="keywordflow">return</span> matrix.coeff(0,a)</div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span> * (matrix.coeff(1,b) * matrix.coeff(2,c) - matrix.coeff(1,c) * matrix.coeff(2,b));</div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span>}</div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span> </div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived,</div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span> <span class="keywordtype">int</span> DeterminantType = Derived::RowsAtCompileTime</div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span>> <span class="keyword">struct </span>determinant_impl</div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span>{</div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keyword">typename</span> traits<Derived>::Scalar run(<span class="keyword">const</span> Derived& m)</div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span> {</div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span> <span class="keywordflow">if</span>(Derived::ColsAtCompileTime==<a class="code hl_variable" href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Dynamic</a> && m.rows()==0)</div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span> <span class="keywordflow">return</span> <span class="keyword">typename</span> traits<Derived>::Scalar(1);</div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span> <span class="keywordflow">return</span> m.partialPivLu().determinant();</div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span> }</div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span>};</div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span> </div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived> <span class="keyword">struct </span>determinant_impl<Derived, 1></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span>{</div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span> <span class="keyword">static</span> <span class="keyword">inline</span> EIGEN_DEVICE_FUNC</div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span> <span class="keyword">typename</span> traits<Derived>::Scalar run(<span class="keyword">const</span> Derived& m)</div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span> {</div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span> <span class="keywordflow">return</span> m.coeff(0,0);</div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span> }</div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span>};</div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> </div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived> <span class="keyword">struct </span>determinant_impl<Derived, 2></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span>{</div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span> <span class="keyword">static</span> <span class="keyword">inline</span> EIGEN_DEVICE_FUNC</div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span> <span class="keyword">typename</span> traits<Derived>::Scalar run(<span class="keyword">const</span> Derived& m)</div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span> {</div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> <span class="keywordflow">return</span> m.coeff(0,0) * m.coeff(1,1) - m.coeff(1,0) * m.coeff(0,1);</div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span> }</div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span>};</div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span> </div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived> <span class="keyword">struct </span>determinant_impl<Derived, 3></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span>{</div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span> <span class="keyword">static</span> <span class="keyword">inline</span> EIGEN_DEVICE_FUNC</div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span> <span class="keyword">typename</span> traits<Derived>::Scalar run(<span class="keyword">const</span> Derived& m)</div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span> {</div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span> <span class="keywordflow">return</span> bruteforce_det3_helper(m,0,1,2)</div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span> - bruteforce_det3_helper(m,1,0,2)</div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span> + bruteforce_det3_helper(m,2,0,1);</div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span> }</div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span>};</div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span> </div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived> <span class="keyword">struct </span>determinant_impl<Derived, 4></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span>{</div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> traits<Derived>::Scalar Scalar;</div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span> <span class="keyword">static</span> EIGEN_DEVICE_FUNC</div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span> Scalar run(<span class="keyword">const</span> Derived& m)</div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span> {</div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> Scalar d2_01 = det2(m, 0, 1);</div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span> Scalar d2_02 = det2(m, 0, 2);</div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span> Scalar d2_03 = det2(m, 0, 3);</div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span> Scalar d2_12 = det2(m, 1, 2);</div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> Scalar d2_13 = det2(m, 1, 3);</div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> Scalar d2_23 = det2(m, 2, 3);</div>
<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"> 81</span> Scalar d3_0 = det3(m, 1,d2_23, 2,d2_13, 3,d2_12);</div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> Scalar d3_1 = det3(m, 0,d2_23, 2,d2_03, 3,d2_02);</div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> Scalar d3_2 = det3(m, 0,d2_13, 1,d2_03, 3,d2_01);</div>
<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> Scalar d3_3 = det3(m, 0,d2_12, 1,d2_02, 2,d2_01);</div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span> <span class="keywordflow">return</span> internal::pmadd(<span class="keyword">static_cast<</span>Scalar<span class="keyword">></span>(-m(0,3)),d3_0, <span class="keyword">static_cast<</span>Scalar<span class="keyword">></span>(m(1,3)*d3_1)) +</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> internal::pmadd(<span class="keyword">static_cast<</span>Scalar<span class="keyword">></span>(-m(2,3)),d3_2, <span class="keyword">static_cast<</span>Scalar<span class="keyword">></span>(m(3,3)*d3_3));</div>
<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span> }</div>
<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span><span class="keyword">protected</span>:</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> <span class="keyword">static</span> EIGEN_DEVICE_FUNC</div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> Scalar det2(<span class="keyword">const</span> Derived& m, <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i0, <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i1)</div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span> {</div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span> <span class="keywordflow">return</span> m(i0,0) * m(i1,1) - m(i1,0) * m(i0,1);</div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span> }</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> </div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> <span class="keyword">static</span> EIGEN_DEVICE_FUNC</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> Scalar det3(<span class="keyword">const</span> Derived& m, <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i0, <span class="keyword">const</span> Scalar& d0, <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i1, <span class="keyword">const</span> Scalar& d1, <a class="code hl_typedef" href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Index</a> i2, <span class="keyword">const</span> Scalar& d2)</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> {</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> <span class="keywordflow">return</span> internal::pmadd(m(i0,2), d0, internal::pmadd(<span class="keyword">static_cast<</span>Scalar<span class="keyword">></span>(-m(i1,2)), d1, <span class="keyword">static_cast<</span>Scalar<span class="keyword">></span>(m(i2,2)*d2)));</div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span> }</div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span>};</div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> </div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span>} <span class="comment">// end namespace internal</span></div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> </div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span><span class="keyword">template</span><<span class="keyword">typename</span> Derived></div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span>EIGEN_DEVICE_FUNC</div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"><a class="line" href="classEigen_1_1MatrixBase.html#a7ad8f77004bb956b603bb43fd2e3c061"> 110</a></span><span class="keyword">inline</span> <span class="keyword">typename</span> internal::traits<Derived>::Scalar <a class="code hl_class" href="classEigen_1_1MatrixBase.html">MatrixBase<Derived>::determinant</a>()<span class="keyword"> const</span></div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span><span class="keyword"></span>{</div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> eigen_assert(rows() == cols());</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <span class="keyword">typedef</span> <span class="keyword">typename</span> internal::nested_eval<Derived,Base::RowsAtCompileTime>::type Nested;</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="keywordflow">return</span> internal::determinant_impl<internal::remove_all_t<Nested>>::run(derived());</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span>}</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> </div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span>} <span class="comment">// end namespace Eigen</span></div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> </div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span><span class="preprocessor">#endif </span><span class="comment">// EIGEN_DETERMINANT_H</span></div>
<div class="ttc" id="aclassEigen_1_1MatrixBase_html"><div class="ttname"><a href="classEigen_1_1MatrixBase.html">Eigen::MatrixBase</a></div><div class="ttdoc">Base class for all dense matrices, vectors, and expressions.</div><div class="ttdef"><b>Definition</b> MatrixBase.h:52</div></div>
<div class="ttc" id="anamespaceEigen_html"><div class="ttname"><a href="namespaceEigen.html">Eigen</a></div><div class="ttdoc">Namespace containing all symbols from the Eigen library.</div><div class="ttdef"><b>Definition</b> Core:139</div></div>
<div class="ttc" id="anamespaceEigen_html_a62e77e0933482dafde8fe197d9a2cfde"><div class="ttname"><a href="namespaceEigen.html#a62e77e0933482dafde8fe197d9a2cfde">Eigen::Index</a></div><div class="ttdeci">EIGEN_DEFAULT_DENSE_INDEX_TYPE Index</div><div class="ttdoc">The Index type as used for the API.</div><div class="ttdef"><b>Definition</b> Meta.h:82</div></div>
<div class="ttc" id="anamespaceEigen_html_ad81fa7195215a0ce30017dfac309f0b2"><div class="ttname"><a href="namespaceEigen.html#ad81fa7195215a0ce30017dfac309f0b2">Eigen::Dynamic</a></div><div class="ttdeci">const int Dynamic</div><div class="ttdef"><b>Definition</b> Constants.h:24</div></div>
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