Michael Ernst Peter / Eigen

src/LU/Determinant.h@0:13a5d365ba16, 2016-10-13 (annotated)

Committer:
ykuroda
Date:
Thu Oct 13 04:07:23 2016 +0000
Revision:
0:13a5d365ba16
First commint, Eigne Matrix Class Library

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ykuroda 0:13a5d365ba16 1 // This file is part of Eigen, a lightweight C++ template library
ykuroda 0:13a5d365ba16 2 // for linear algebra.
ykuroda 0:13a5d365ba16 3 //
ykuroda 0:13a5d365ba16 4 // Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
ykuroda 0:13a5d365ba16 5 //
ykuroda 0:13a5d365ba16 6 // This Source Code Form is subject to the terms of the Mozilla
ykuroda 0:13a5d365ba16 7 // Public License v. 2.0. If a copy of the MPL was not distributed
ykuroda 0:13a5d365ba16 8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
ykuroda 0:13a5d365ba16 9
ykuroda 0:13a5d365ba16 10 #ifndef EIGEN_DETERMINANT_H
ykuroda 0:13a5d365ba16 11 #define EIGEN_DETERMINANT_H
ykuroda 0:13a5d365ba16 12
ykuroda 0:13a5d365ba16 13 namespace Eigen {
ykuroda 0:13a5d365ba16 14
ykuroda 0:13a5d365ba16 15 namespace internal {
ykuroda 0:13a5d365ba16 16
ykuroda 0:13a5d365ba16 17 template<typename Derived>
ykuroda 0:13a5d365ba16 18 inline const typename Derived::Scalar bruteforce_det3_helper
ykuroda 0:13a5d365ba16 19 (const MatrixBase<Derived>& matrix, int a, int b, int c)
ykuroda 0:13a5d365ba16 20 {
ykuroda 0:13a5d365ba16 21 return matrix.coeff(0,a)
ykuroda 0:13a5d365ba16 22 * (matrix.coeff(1,b) * matrix.coeff(2,c) - matrix.coeff(1,c) * matrix.coeff(2,b));
ykuroda 0:13a5d365ba16 23 }
ykuroda 0:13a5d365ba16 24
ykuroda 0:13a5d365ba16 25 template<typename Derived>
ykuroda 0:13a5d365ba16 26 const typename Derived::Scalar bruteforce_det4_helper
ykuroda 0:13a5d365ba16 27 (const MatrixBase<Derived>& matrix, int j, int k, int m, int n)
ykuroda 0:13a5d365ba16 28 {
ykuroda 0:13a5d365ba16 29 return (matrix.coeff(j,0) * matrix.coeff(k,1) - matrix.coeff(k,0) * matrix.coeff(j,1))
ykuroda 0:13a5d365ba16 30 * (matrix.coeff(m,2) * matrix.coeff(n,3) - matrix.coeff(n,2) * matrix.coeff(m,3));
ykuroda 0:13a5d365ba16 31 }
ykuroda 0:13a5d365ba16 32
ykuroda 0:13a5d365ba16 33 template<typename Derived,
ykuroda 0:13a5d365ba16 34 int DeterminantType = Derived::RowsAtCompileTime
ykuroda 0:13a5d365ba16 35 > struct determinant_impl
ykuroda 0:13a5d365ba16 36 {
ykuroda 0:13a5d365ba16 37 static inline typename traits<Derived>::Scalar run(const Derived& m)
ykuroda 0:13a5d365ba16 38 {
ykuroda 0:13a5d365ba16 39 if(Derived::ColsAtCompileTime==Dynamic && m.rows()==0)
ykuroda 0:13a5d365ba16 40 return typename traits<Derived>::Scalar(1);
ykuroda 0:13a5d365ba16 41 return m.partialPivLu().determinant();
ykuroda 0:13a5d365ba16 42 }
ykuroda 0:13a5d365ba16 43 };
ykuroda 0:13a5d365ba16 44
ykuroda 0:13a5d365ba16 45 template<typename Derived> struct determinant_impl<Derived, 1>
ykuroda 0:13a5d365ba16 46 {
ykuroda 0:13a5d365ba16 47 static inline typename traits<Derived>::Scalar run(const Derived& m)
ykuroda 0:13a5d365ba16 48 {
ykuroda 0:13a5d365ba16 49 return m.coeff(0,0);
ykuroda 0:13a5d365ba16 50 }
ykuroda 0:13a5d365ba16 51 };
ykuroda 0:13a5d365ba16 52
ykuroda 0:13a5d365ba16 53 template<typename Derived> struct determinant_impl<Derived, 2>
ykuroda 0:13a5d365ba16 54 {
ykuroda 0:13a5d365ba16 55 static inline typename traits<Derived>::Scalar run(const Derived& m)
ykuroda 0:13a5d365ba16 56 {
ykuroda 0:13a5d365ba16 57 return m.coeff(0,0) * m.coeff(1,1) - m.coeff(1,0) * m.coeff(0,1);
ykuroda 0:13a5d365ba16 58 }
ykuroda 0:13a5d365ba16 59 };
ykuroda 0:13a5d365ba16 60
ykuroda 0:13a5d365ba16 61 template<typename Derived> struct determinant_impl<Derived, 3>
ykuroda 0:13a5d365ba16 62 {
ykuroda 0:13a5d365ba16 63 static inline typename traits<Derived>::Scalar run(const Derived& m)
ykuroda 0:13a5d365ba16 64 {
ykuroda 0:13a5d365ba16 65 return bruteforce_det3_helper(m,0,1,2)
ykuroda 0:13a5d365ba16 66 - bruteforce_det3_helper(m,1,0,2)
ykuroda 0:13a5d365ba16 67 + bruteforce_det3_helper(m,2,0,1);
ykuroda 0:13a5d365ba16 68 }
ykuroda 0:13a5d365ba16 69 };
ykuroda 0:13a5d365ba16 70
ykuroda 0:13a5d365ba16 71 template<typename Derived> struct determinant_impl<Derived, 4>
ykuroda 0:13a5d365ba16 72 {
ykuroda 0:13a5d365ba16 73 static typename traits<Derived>::Scalar run(const Derived& m)
ykuroda 0:13a5d365ba16 74 {
ykuroda 0:13a5d365ba16 75 // trick by Martin Costabel to compute 4x4 det with only 30 muls
ykuroda 0:13a5d365ba16 76 return bruteforce_det4_helper(m,0,1,2,3)
ykuroda 0:13a5d365ba16 77 - bruteforce_det4_helper(m,0,2,1,3)
ykuroda 0:13a5d365ba16 78 + bruteforce_det4_helper(m,0,3,1,2)
ykuroda 0:13a5d365ba16 79 + bruteforce_det4_helper(m,1,2,0,3)
ykuroda 0:13a5d365ba16 80 - bruteforce_det4_helper(m,1,3,0,2)
ykuroda 0:13a5d365ba16 81 + bruteforce_det4_helper(m,2,3,0,1);
ykuroda 0:13a5d365ba16 82 }
ykuroda 0:13a5d365ba16 83 };
ykuroda 0:13a5d365ba16 84
ykuroda 0:13a5d365ba16 85 } // end namespace internal
ykuroda 0:13a5d365ba16 86
ykuroda 0:13a5d365ba16 87 /** \lu_module
ykuroda 0:13a5d365ba16 88 *
ykuroda 0:13a5d365ba16 89 * \returns the determinant of this matrix
ykuroda 0:13a5d365ba16 90 */
ykuroda 0:13a5d365ba16 91 template<typename Derived>
ykuroda 0:13a5d365ba16 92 inline typename internal::traits<Derived>::Scalar MatrixBase<Derived>::determinant() const
ykuroda 0:13a5d365ba16 93 {
ykuroda 0:13a5d365ba16 94 eigen_assert(rows() == cols());
ykuroda 0:13a5d365ba16 95 typedef typename internal::nested<Derived,Base::RowsAtCompileTime>::type Nested;
ykuroda 0:13a5d365ba16 96 return internal::determinant_impl<typename internal::remove_all<Nested>::type>::run(derived());
ykuroda 0:13a5d365ba16 97 }
ykuroda 0:13a5d365ba16 98
ykuroda 0:13a5d365ba16 99 } // end namespace Eigen
ykuroda 0:13a5d365ba16 100
ykuroda 0:13a5d365ba16 101 #endif // EIGEN_DETERMINANT_H