123 lines
4.0 KiB
C++
123 lines
4.0 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra. Eigen itself is part of the KDE project.
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//
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// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
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//
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// Eigen is free software; you can redistribute it and/or
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// modify it under the terms of the GNU Lesser General Public
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// License as published by the Free Software Foundation; either
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// version 3 of the License, or (at your option) any later version.
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//
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// Alternatively, you can redistribute it and/or
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// modify it under the terms of the GNU General Public License as
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// published by the Free Software Foundation; either version 2 of
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// the License, or (at your option) any later version.
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//
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// Eigen is distributed in the hope that it will be useful, but WITHOUT ANY
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// WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
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// FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License or the
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// GNU General Public License for more details.
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//
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// You should have received a copy of the GNU Lesser General Public
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// License and a copy of the GNU General Public License along with
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// Eigen. If not, see <http://www.gnu.org/licenses/>.
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#ifndef EIGEN_DETERMINANT_H
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#define EIGEN_DETERMINANT_H
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template<typename Derived>
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inline const typename Derived::Scalar ei_bruteforce_det3_helper
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(const MatrixBase<Derived>& matrix, int a, int b, int c)
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{
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return matrix.coeff(0,a)
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* (matrix.coeff(1,b) * matrix.coeff(2,c) - matrix.coeff(1,c) * matrix.coeff(2,b));
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}
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template<typename Derived>
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const typename Derived::Scalar ei_bruteforce_det4_helper
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(const MatrixBase<Derived>& matrix, int j, int k, int m, int n)
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{
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return (matrix.coeff(j,0) * matrix.coeff(k,1) - matrix.coeff(k,0) * matrix.coeff(j,1))
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* (matrix.coeff(m,2) * matrix.coeff(n,3) - matrix.coeff(n,2) * matrix.coeff(m,3));
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}
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const int TriangularDeterminant = 0;
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template<typename Derived,
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int DeterminantType =
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(Derived::Flags & (UpperTriangularBit | LowerTriangularBit))
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? TriangularDeterminant : Derived::RowsAtCompileTime
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> struct ei_determinant_impl
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{
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static inline typename ei_traits<Derived>::Scalar run(const Derived& m)
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{
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return m.lu().determinant();
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}
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};
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template<typename Derived> struct ei_determinant_impl<Derived, TriangularDeterminant>
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{
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static inline typename ei_traits<Derived>::Scalar run(const Derived& m)
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{
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if (Derived::Flags & UnitDiagBit)
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return 1;
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else if (Derived::Flags & ZeroDiagBit)
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return 0;
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else
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return m.diagonal().redux(ei_scalar_product_op<typename ei_traits<Derived>::Scalar>());
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}
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};
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template<typename Derived> struct ei_determinant_impl<Derived, 1>
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{
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static inline typename ei_traits<Derived>::Scalar run(const Derived& m)
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{
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return m.coeff(0,0);
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}
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};
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template<typename Derived> struct ei_determinant_impl<Derived, 2>
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{
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static inline typename ei_traits<Derived>::Scalar run(const Derived& m)
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{
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return m.coeff(0,0) * m.coeff(1,1) - m.coeff(1,0) * m.coeff(0,1);
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}
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};
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template<typename Derived> struct ei_determinant_impl<Derived, 3>
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{
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static typename ei_traits<Derived>::Scalar run(const Derived& m)
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{
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return ei_bruteforce_det3_helper(m,0,1,2)
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- ei_bruteforce_det3_helper(m,1,0,2)
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+ ei_bruteforce_det3_helper(m,2,0,1);
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}
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};
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template<typename Derived> struct ei_determinant_impl<Derived, 4>
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{
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static typename ei_traits<Derived>::Scalar run(const Derived& m)
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{
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// trick by Martin Costabel to compute 4x4 det with only 30 muls
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return ei_bruteforce_det4_helper(m,0,1,2,3)
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- ei_bruteforce_det4_helper(m,0,2,1,3)
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+ ei_bruteforce_det4_helper(m,0,3,1,2)
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+ ei_bruteforce_det4_helper(m,1,2,0,3)
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- ei_bruteforce_det4_helper(m,1,3,0,2)
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+ ei_bruteforce_det4_helper(m,2,3,0,1);
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}
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};
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/** \lu_module
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*
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* \returns the determinant of this matrix
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*/
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template<typename Derived>
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inline typename ei_traits<Derived>::Scalar MatrixBase<Derived>::determinant() const
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{
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assert(rows() == cols());
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return ei_determinant_impl<Derived>::run(derived());
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}
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#endif // EIGEN_DETERMINANT_H
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