vcglib: Determinant.h Source File

00001 // This file is part of Eigen, a lightweight C++ template library
00002 // for linear algebra. Eigen itself is part of the KDE project.
00003 //
00004 // Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
00005 //
00006 // Eigen is free software; you can redistribute it and/or
00007 // modify it under the terms of the GNU Lesser General Public
00008 // License as published by the Free Software Foundation; either
00009 // version 3 of the License, or (at your option) any later version.
00010 //
00011 // Alternatively, you can redistribute it and/or
00012 // modify it under the terms of the GNU General Public License as
00013 // published by the Free Software Foundation; either version 2 of
00014 // the License, or (at your option) any later version.
00015 //
00016 // Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
00017 // WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
00018 // FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
00019 // GNU General Public License for more details.
00020 //
00021 // You should have received a copy of the GNU Lesser General Public
00022 // License and a copy of the GNU General Public License along with
00023 // Eigen. If not, see <http://www.gnu.org/licenses/>.
00024 
00025 #ifndef EIGEN_DETERMINANT_H
00026 #define EIGEN_DETERMINANT_H
00027 
00028 template<typename Derived>
00029 inline const typename Derived::Scalar ei_bruteforce_det3_helper
00030 (const MatrixBase<Derived>& matrix, int a, int b, int c)
00031 {
00032   return matrix.coeff(0,a)
00033          * (matrix.coeff(1,b) * matrix.coeff(2,c) - matrix.coeff(1,c) * matrix.coeff(2,b));
00034 }
00035 
00036 template<typename Derived>
00037 const typename Derived::Scalar ei_bruteforce_det4_helper
00038 (const MatrixBase<Derived>& matrix, int j, int k, int m, int n)
00039 {
00040   return (matrix.coeff(j,0) * matrix.coeff(k,1) - matrix.coeff(k,0) * matrix.coeff(j,1))
00041        * (matrix.coeff(m,2) * matrix.coeff(n,3) - matrix.coeff(n,2) * matrix.coeff(m,3));
00042 }
00043 
00044 const int TriangularDeterminant = 0;
00045 
00046 template<typename Derived,
00047          int DeterminantType =
00048            (Derived::Flags & (UpperTriangularBit | LowerTriangularBit))
00049            ? TriangularDeterminant : Derived::RowsAtCompileTime
00050 > struct ei_determinant_impl
00051 {
00052   static inline typename ei_traits<Derived>::Scalar run(const Derived& m)
00053   {
00054     return m.lu().determinant();
00055   }
00056 };
00057 
00058 template<typename Derived> struct ei_determinant_impl<Derived, TriangularDeterminant>
00059 {
00060   static inline typename ei_traits<Derived>::Scalar run(const Derived& m)
00061   {
00062     if (Derived::Flags & UnitDiagBit)
00063       return 1;
00064     else if (Derived::Flags & ZeroDiagBit)
00065       return 0;
00066     else
00067       return m.diagonal().redux(ei_scalar_product_op<typename ei_traits<Derived>::Scalar>());
00068   }
00069 };
00070 
00071 template<typename Derived> struct ei_determinant_impl<Derived, 1>
00072 {
00073   static inline typename ei_traits<Derived>::Scalar run(const Derived& m)
00074   {
00075     return m.coeff(0,0);
00076   }
00077 };
00078 
00079 template<typename Derived> struct ei_determinant_impl<Derived, 2>
00080 {
00081   static inline typename ei_traits<Derived>::Scalar run(const Derived& m)
00082   {
00083     return m.coeff(0,0) * m.coeff(1,1) - m.coeff(1,0) * m.coeff(0,1);
00084   }
00085 };
00086 
00087 template<typename Derived> struct ei_determinant_impl<Derived, 3>
00088 {
00089   static typename ei_traits<Derived>::Scalar run(const Derived& m)
00090   {
00091     return ei_bruteforce_det3_helper(m,0,1,2)
00092           - ei_bruteforce_det3_helper(m,1,0,2)
00093           + ei_bruteforce_det3_helper(m,2,0,1);
00094   }
00095 };
00096 
00097 template<typename Derived> struct ei_determinant_impl<Derived, 4>
00098 {
00099   static typename ei_traits<Derived>::Scalar run(const Derived& m)
00100   {
00101     // trick by Martin Costabel to compute 4x4 det with only 30 muls
00102     return ei_bruteforce_det4_helper(m,0,1,2,3)
00103           - ei_bruteforce_det4_helper(m,0,2,1,3)
00104           + ei_bruteforce_det4_helper(m,0,3,1,2)
00105           + ei_bruteforce_det4_helper(m,1,2,0,3)
00106           - ei_bruteforce_det4_helper(m,1,3,0,2)
00107           + ei_bruteforce_det4_helper(m,2,3,0,1);
00108   }
00109 };
00110 
00115 template<typename Derived>
00116 inline typename ei_traits<Derived>::Scalar MatrixBase<Derived>::determinant() const
00117 {
00118   assert(rows() == cols());
00119   return ei_determinant_impl<Derived>::run(derived());
00120 }
00121 
00122 #endif // EIGEN_DETERMINANT_H