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<h1>Determinant.h</h1> </div>
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<a href="_determinant_8h.html">Go to the documentation of this file.</a><div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">// This file is part of Eigen, a lightweight C++ template library</span>
<a name="l00002"></a>00002 <span class="comment">// for linear algebra.</span>
<a name="l00003"></a>00003 <span class="comment">//</span>
<a name="l00004"></a>00004 <span class="comment">// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com></span>
<a name="l00005"></a>00005 <span class="comment">//</span>
<a name="l00006"></a>00006 <span class="comment">// Eigen is free software; you can redistribute it and/or</span>
<a name="l00007"></a>00007 <span class="comment">// modify it under the terms of the GNU Lesser General Public</span>
<a name="l00008"></a>00008 <span class="comment">// License as published by the Free Software Foundation; either</span>
<a name="l00009"></a>00009 <span class="comment">// version 3 of the License, or (at your option) any later version.</span>
<a name="l00010"></a>00010 <span class="comment">//</span>
<a name="l00011"></a>00011 <span class="comment">// Alternatively, you can redistribute it and/or</span>
<a name="l00012"></a>00012 <span class="comment">// modify it under the terms of the GNU General Public License as</span>
<a name="l00013"></a>00013 <span class="comment">// published by the Free Software Foundation; either version 2 of</span>
<a name="l00014"></a>00014 <span class="comment">// the License, or (at your option) any later version.</span>
<a name="l00015"></a>00015 <span class="comment">//</span>
<a name="l00016"></a>00016 <span class="comment">// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY</span>
<a name="l00017"></a>00017 <span class="comment">// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS</span>
<a name="l00018"></a>00018 <span class="comment">// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the</span>
<a name="l00019"></a>00019 <span class="comment">// GNU General Public License for more details.</span>
<a name="l00020"></a>00020 <span class="comment">//</span>
<a name="l00021"></a>00021 <span class="comment">// You should have received a copy of the GNU Lesser General Public</span>
<a name="l00022"></a>00022 <span class="comment">// License and a copy of the GNU General Public License along with</span>
<a name="l00023"></a>00023 <span class="comment">// Eigen. If not, see <http://www.gnu.org/licenses/>.</span>
<a name="l00024"></a>00024
<a name="l00025"></a>00025 <span class="preprocessor">#ifndef EIGEN_DETERMINANT_H</span>
<a name="l00026"></a>00026 <span class="preprocessor"></span><span class="preprocessor">#define EIGEN_DETERMINANT_H</span>
<a name="l00027"></a>00027 <span class="preprocessor"></span>
<a name="l00028"></a>00028 <span class="keyword">namespace </span>internal {
<a name="l00029"></a>00029
<a name="l00030"></a>00030 <span class="keyword">template</span><<span class="keyword">typename</span> Derived>
<a name="l00031"></a>00031 <span class="keyword">inline</span> <span class="keyword">const</span> <span class="keyword">typename</span> Derived::Scalar <a class="code" href="namespaceinternal.html#af90d28e6e10ff1c6f78c8b83d040dc42">bruteforce_det3_helper</a>
<a name="l00032"></a><a class="code" href="namespaceinternal.html#af90d28e6e10ff1c6f78c8b83d040dc42">00032</a> (<span class="keyword">const</span> <a class="code" href="class_matrix_base.html" title="Base class for all dense matrices, vectors, and expressions.">MatrixBase<Derived></a>& matrix, <span class="keywordtype">int</span> a, <span class="keywordtype">int</span> b, <span class="keywordtype">int</span> c)
<a name="l00033"></a>00033 {
<a name="l00034"></a>00034 <span class="keywordflow">return</span> matrix.coeff(0,a)
<a name="l00035"></a>00035 * (matrix.coeff(1,b) * matrix.coeff(2,c) - matrix.coeff(1,c) * matrix.coeff(2,b));
<a name="l00036"></a>00036 }
<a name="l00037"></a>00037
<a name="l00038"></a>00038 <span class="keyword">template</span><<span class="keyword">typename</span> Derived>
<a name="l00039"></a>00039 <span class="keyword">const</span> <span class="keyword">typename</span> Derived::Scalar <a class="code" href="namespaceinternal.html#a841ed4f1c3eb9771462e34d769bdc3d7">bruteforce_det4_helper</a>
<a name="l00040"></a><a class="code" href="namespaceinternal.html#a841ed4f1c3eb9771462e34d769bdc3d7">00040</a> (<span class="keyword">const</span> <a class="code" href="class_matrix_base.html" title="Base class for all dense matrices, vectors, and expressions.">MatrixBase<Derived></a>& matrix, <span class="keywordtype">int</span> j, <span class="keywordtype">int</span> k, <span class="keywordtype">int</span> m, <span class="keywordtype">int</span> n)
<a name="l00041"></a>00041 {
<a name="l00042"></a>00042 <span class="keywordflow">return</span> (matrix.coeff(j,0) * matrix.coeff(k,1) - matrix.coeff(k,0) * matrix.coeff(j,1))
<a name="l00043"></a>00043 * (matrix.coeff(m,2) * matrix.coeff(n,3) - matrix.coeff(n,2) * matrix.coeff(m,3));
<a name="l00044"></a>00044 }
<a name="l00045"></a>00045
<a name="l00046"></a>00046 <span class="keyword">template</span><<span class="keyword">typename</span> Derived,
<a name="l00047"></a>00047 <span class="keywordtype">int</span> DeterminantType = Derived::RowsAtCompileTime
<a name="l00048"></a><a class="code" href="structinternal_1_1determinant__impl.html">00048</a> > <span class="keyword">struct </span><a class="code" href="structinternal_1_1determinant__impl.html">determinant_impl</a>
<a name="l00049"></a>00049 {
<a name="l00050"></a><a class="code" href="structinternal_1_1determinant__impl.html#a74bf7cb6abed0da62e4e01db37062c51">00050</a> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keyword">typename</span> traits<Derived>::Scalar <a class="code" href="structinternal_1_1determinant__impl.html#a74bf7cb6abed0da62e4e01db37062c51">run</a>(<span class="keyword">const</span> Derived& m)
<a name="l00051"></a>00051 {
<a name="l00052"></a>00052 <span class="keywordflow">if</span>(Derived::ColsAtCompileTime==<a class="code" href="_constants_8h.html#adc9da5be31bdce40c25a92c27999c0e3" title="This value means that a quantity is not known at compile-time, and that instead the value is stored i...">Dynamic</a> && m.rows()==0)
<a name="l00053"></a>00053 <span class="keywordflow">return</span> <span class="keyword">typename</span> traits<Derived>::Scalar(1);
<a name="l00054"></a>00054 <span class="keywordflow">return</span> m.partialPivLu().determinant();
<a name="l00055"></a>00055 }
<a name="l00056"></a>00056 };
<a name="l00057"></a>00057
<a name="l00058"></a><a class="code" href="structinternal_1_1determinant__impl_3_01_derived_00_011_01_4.html">00058</a> <span class="keyword">template</span><<span class="keyword">typename</span> Derived> <span class="keyword">struct </span><a class="code" href="structinternal_1_1determinant__impl.html">determinant_impl</a><Derived, 1>
<a name="l00059"></a>00059 {
<a name="l00060"></a><a class="code" href="structinternal_1_1determinant__impl_3_01_derived_00_011_01_4.html#aa59df74f4b39836015b90b4ad7128115">00060</a> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keyword">typename</span> traits<Derived>::Scalar <a class="code" href="structinternal_1_1determinant__impl.html#a74bf7cb6abed0da62e4e01db37062c51">run</a>(<span class="keyword">const</span> Derived& m)
<a name="l00061"></a>00061 {
<a name="l00062"></a>00062 <span class="keywordflow">return</span> m.coeff(0,0);
<a name="l00063"></a>00063 }
<a name="l00064"></a>00064 };
<a name="l00065"></a>00065
<a name="l00066"></a><a class="code" href="structinternal_1_1determinant__impl_3_01_derived_00_012_01_4.html">00066</a> <span class="keyword">template</span><<span class="keyword">typename</span> Derived> <span class="keyword">struct </span><a class="code" href="structinternal_1_1determinant__impl.html">determinant_impl</a><Derived, 2>
<a name="l00067"></a>00067 {
<a name="l00068"></a><a class="code" href="structinternal_1_1determinant__impl_3_01_derived_00_012_01_4.html#aae5913a6b6155f5424a1ec4d7c06c931">00068</a> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keyword">typename</span> traits<Derived>::Scalar <a class="code" href="structinternal_1_1determinant__impl.html#a74bf7cb6abed0da62e4e01db37062c51">run</a>(<span class="keyword">const</span> Derived& m)
<a name="l00069"></a>00069 {
<a name="l00070"></a>00070 <span class="keywordflow">return</span> m.coeff(0,0) * m.coeff(1,1) - m.coeff(1,0) * m.coeff(0,1);
<a name="l00071"></a>00071 }
<a name="l00072"></a>00072 };
<a name="l00073"></a>00073
<a name="l00074"></a><a class="code" href="structinternal_1_1determinant__impl_3_01_derived_00_013_01_4.html">00074</a> <span class="keyword">template</span><<span class="keyword">typename</span> Derived> <span class="keyword">struct </span><a class="code" href="structinternal_1_1determinant__impl.html">determinant_impl</a><Derived, 3>
<a name="l00075"></a>00075 {
<a name="l00076"></a><a class="code" href="structinternal_1_1determinant__impl_3_01_derived_00_013_01_4.html#a4de29b1be7701167af838bfce235a68c">00076</a> <span class="keyword">static</span> <span class="keyword">inline</span> <span class="keyword">typename</span> traits<Derived>::Scalar <a class="code" href="structinternal_1_1determinant__impl.html#a74bf7cb6abed0da62e4e01db37062c51">run</a>(<span class="keyword">const</span> Derived& m)
<a name="l00077"></a>00077 {
<a name="l00078"></a>00078 <span class="keywordflow">return</span> <a class="code" href="namespaceinternal.html#af90d28e6e10ff1c6f78c8b83d040dc42">bruteforce_det3_helper</a>(m,0,1,2)
<a name="l00079"></a>00079 - <a class="code" href="namespaceinternal.html#af90d28e6e10ff1c6f78c8b83d040dc42">bruteforce_det3_helper</a>(m,1,0,2)
<a name="l00080"></a>00080 + <a class="code" href="namespaceinternal.html#af90d28e6e10ff1c6f78c8b83d040dc42">bruteforce_det3_helper</a>(m,2,0,1);
<a name="l00081"></a>00081 }
<a name="l00082"></a>00082 };
<a name="l00083"></a>00083
<a name="l00084"></a><a class="code" href="structinternal_1_1determinant__impl_3_01_derived_00_014_01_4.html">00084</a> <span class="keyword">template</span><<span class="keyword">typename</span> Derived> <span class="keyword">struct </span><a class="code" href="structinternal_1_1determinant__impl.html">determinant_impl</a><Derived, 4>
<a name="l00085"></a>00085 {
<a name="l00086"></a><a class="code" href="structinternal_1_1determinant__impl_3_01_derived_00_014_01_4.html#aa1cb2a3afc3d244621976a51b95f7f0c">00086</a> <span class="keyword">static</span> <span class="keyword">typename</span> traits<Derived>::Scalar <a class="code" href="structinternal_1_1determinant__impl.html#a74bf7cb6abed0da62e4e01db37062c51">run</a>(<span class="keyword">const</span> Derived& m)
<a name="l00087"></a>00087 {
<a name="l00088"></a>00088 <span class="comment">// trick by Martin Costabel to compute 4x4 det with only 30 muls</span>
<a name="l00089"></a>00089 <span class="keywordflow">return</span> <a class="code" href="namespaceinternal.html#a841ed4f1c3eb9771462e34d769bdc3d7">bruteforce_det4_helper</a>(m,0,1,2,3)
<a name="l00090"></a>00090 - <a class="code" href="namespaceinternal.html#a841ed4f1c3eb9771462e34d769bdc3d7">bruteforce_det4_helper</a>(m,0,2,1,3)
<a name="l00091"></a>00091 + <a class="code" href="namespaceinternal.html#a841ed4f1c3eb9771462e34d769bdc3d7">bruteforce_det4_helper</a>(m,0,3,1,2)
<a name="l00092"></a>00092 + <a class="code" href="namespaceinternal.html#a841ed4f1c3eb9771462e34d769bdc3d7">bruteforce_det4_helper</a>(m,1,2,0,3)
<a name="l00093"></a>00093 - <a class="code" href="namespaceinternal.html#a841ed4f1c3eb9771462e34d769bdc3d7">bruteforce_det4_helper</a>(m,1,3,0,2)
<a name="l00094"></a>00094 + <a class="code" href="namespaceinternal.html#a841ed4f1c3eb9771462e34d769bdc3d7">bruteforce_det4_helper</a>(m,2,3,0,1);
<a name="l00095"></a>00095 }
<a name="l00096"></a>00096 };
<a name="l00097"></a>00097
<a name="l00098"></a>00098 } <span class="comment">// end namespace internal</span>
<a name="l00099"></a>00099 <span class="comment"></span>
<a name="l00100"></a>00100 <span class="comment">/** \lu_module</span>
<a name="l00101"></a>00101 <span class="comment"> *</span>
<a name="l00102"></a>00102 <span class="comment"> * \returns the determinant of this matrix</span>
<a name="l00103"></a>00103 <span class="comment"> */</span>
<a name="l00104"></a>00104 <span class="keyword">template</span><<span class="keyword">typename</span> Derived>
<a name="l00105"></a><a class="code" href="class_matrix_base.html#a39c5a3827e58c369981cac7056d72f7b">00105</a> <span class="keyword">inline</span> <span class="keyword">typename</span> internal::traits<Derived>::Scalar <a class="code" href="class_matrix_base.html#a39c5a3827e58c369981cac7056d72f7b">MatrixBase<Derived>::determinant</a>()<span class="keyword"> const</span>
<a name="l00106"></a>00106 <span class="keyword"></span>{
<a name="l00107"></a>00107 assert(rows() == cols());
<a name="l00108"></a>00108 <span class="keyword">typedef</span> <span class="keyword">typename</span> <a class="code" href="structinternal_1_1nested.html">internal::nested<Derived,Base::RowsAtCompileTime>::type</a> Nested;
<a name="l00109"></a>00109 <span class="keywordflow">return</span> <a class="code" href="structinternal_1_1determinant__impl.html">internal::determinant_impl<typename internal::remove_all<Nested>::type</a>>::run(derived());
<a name="l00110"></a>00110 }
<a name="l00111"></a>00111
<a name="l00112"></a>00112 <span class="preprocessor">#endif // EIGEN_DETERMINANT_H</span>
</pre></div></div>
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