Determinant.h (3439B)
1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com> 5 // 6 // This Source Code Form is subject to the terms of the Mozilla 7 // Public License v. 2.0. If a copy of the MPL was not distributed 8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 9 10 #ifndef EIGEN_DETERMINANT_H 11 #define EIGEN_DETERMINANT_H 12 13 namespace Eigen { 14 15 namespace internal { 16 17 template<typename Derived> 18 EIGEN_DEVICE_FUNC 19 inline const typename Derived::Scalar bruteforce_det3_helper 20 (const MatrixBase<Derived>& matrix, int a, int b, int c) 21 { 22 return matrix.coeff(0,a) 23 * (matrix.coeff(1,b) * matrix.coeff(2,c) - matrix.coeff(1,c) * matrix.coeff(2,b)); 24 } 25 26 template<typename Derived, 27 int DeterminantType = Derived::RowsAtCompileTime 28 > struct determinant_impl 29 { 30 static inline typename traits<Derived>::Scalar run(const Derived& m) 31 { 32 if(Derived::ColsAtCompileTime==Dynamic && m.rows()==0) 33 return typename traits<Derived>::Scalar(1); 34 return m.partialPivLu().determinant(); 35 } 36 }; 37 38 template<typename Derived> struct determinant_impl<Derived, 1> 39 { 40 static inline EIGEN_DEVICE_FUNC 41 typename traits<Derived>::Scalar run(const Derived& m) 42 { 43 return m.coeff(0,0); 44 } 45 }; 46 47 template<typename Derived> struct determinant_impl<Derived, 2> 48 { 49 static inline EIGEN_DEVICE_FUNC 50 typename traits<Derived>::Scalar run(const Derived& m) 51 { 52 return m.coeff(0,0) * m.coeff(1,1) - m.coeff(1,0) * m.coeff(0,1); 53 } 54 }; 55 56 template<typename Derived> struct determinant_impl<Derived, 3> 57 { 58 static inline EIGEN_DEVICE_FUNC 59 typename traits<Derived>::Scalar run(const Derived& m) 60 { 61 return bruteforce_det3_helper(m,0,1,2) 62 - bruteforce_det3_helper(m,1,0,2) 63 + bruteforce_det3_helper(m,2,0,1); 64 } 65 }; 66 67 template<typename Derived> struct determinant_impl<Derived, 4> 68 { 69 typedef typename traits<Derived>::Scalar Scalar; 70 static EIGEN_DEVICE_FUNC 71 Scalar run(const Derived& m) 72 { 73 Scalar d2_01 = det2(m, 0, 1); 74 Scalar d2_02 = det2(m, 0, 2); 75 Scalar d2_03 = det2(m, 0, 3); 76 Scalar d2_12 = det2(m, 1, 2); 77 Scalar d2_13 = det2(m, 1, 3); 78 Scalar d2_23 = det2(m, 2, 3); 79 Scalar d3_0 = det3(m, 1,d2_23, 2,d2_13, 3,d2_12); 80 Scalar d3_1 = det3(m, 0,d2_23, 2,d2_03, 3,d2_02); 81 Scalar d3_2 = det3(m, 0,d2_13, 1,d2_03, 3,d2_01); 82 Scalar d3_3 = det3(m, 0,d2_12, 1,d2_02, 2,d2_01); 83 return internal::pmadd(-m(0,3),d3_0, m(1,3)*d3_1) + 84 internal::pmadd(-m(2,3),d3_2, m(3,3)*d3_3); 85 } 86 protected: 87 static EIGEN_DEVICE_FUNC 88 Scalar det2(const Derived& m, Index i0, Index i1) 89 { 90 return m(i0,0) * m(i1,1) - m(i1,0) * m(i0,1); 91 } 92 93 static EIGEN_DEVICE_FUNC 94 Scalar det3(const Derived& m, Index i0, const Scalar& d0, Index i1, const Scalar& d1, Index i2, const Scalar& d2) 95 { 96 return internal::pmadd(m(i0,2), d0, internal::pmadd(-m(i1,2), d1, m(i2,2)*d2)); 97 } 98 }; 99 100 } // end namespace internal 101 102 /** \lu_module 103 * 104 * \returns the determinant of this matrix 105 */ 106 template<typename Derived> 107 EIGEN_DEVICE_FUNC 108 inline typename internal::traits<Derived>::Scalar MatrixBase<Derived>::determinant() const 109 { 110 eigen_assert(rows() == cols()); 111 typedef typename internal::nested_eval<Derived,Base::RowsAtCompileTime>::type Nested; 112 return internal::determinant_impl<typename internal::remove_all<Nested>::type>::run(derived()); 113 } 114 115 } // end namespace Eigen 116 117 #endif // EIGEN_DETERMINANT_H