| Brian Silverman | 72890c2 | 2015-09-19 14:37:37 -0400 | [diff] [blame^] | 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 | inline const typename Derived::Scalar bruteforce_det3_helper |
| 19 | (const MatrixBase<Derived>& matrix, int a, int b, int c) |
| 20 | { |
| 21 | return matrix.coeff(0,a) |
| 22 | * (matrix.coeff(1,b) * matrix.coeff(2,c) - matrix.coeff(1,c) * matrix.coeff(2,b)); |
| 23 | } |
| 24 | |
| 25 | template<typename Derived> |
| 26 | const typename Derived::Scalar bruteforce_det4_helper |
| 27 | (const MatrixBase<Derived>& matrix, int j, int k, int m, int n) |
| 28 | { |
| 29 | return (matrix.coeff(j,0) * matrix.coeff(k,1) - matrix.coeff(k,0) * matrix.coeff(j,1)) |
| 30 | * (matrix.coeff(m,2) * matrix.coeff(n,3) - matrix.coeff(n,2) * matrix.coeff(m,3)); |
| 31 | } |
| 32 | |
| 33 | template<typename Derived, |
| 34 | int DeterminantType = Derived::RowsAtCompileTime |
| 35 | > struct determinant_impl |
| 36 | { |
| 37 | static inline typename traits<Derived>::Scalar run(const Derived& m) |
| 38 | { |
| 39 | if(Derived::ColsAtCompileTime==Dynamic && m.rows()==0) |
| 40 | return typename traits<Derived>::Scalar(1); |
| 41 | return m.partialPivLu().determinant(); |
| 42 | } |
| 43 | }; |
| 44 | |
| 45 | template<typename Derived> struct determinant_impl<Derived, 1> |
| 46 | { |
| 47 | static inline typename traits<Derived>::Scalar run(const Derived& m) |
| 48 | { |
| 49 | return m.coeff(0,0); |
| 50 | } |
| 51 | }; |
| 52 | |
| 53 | template<typename Derived> struct determinant_impl<Derived, 2> |
| 54 | { |
| 55 | static inline typename traits<Derived>::Scalar run(const Derived& m) |
| 56 | { |
| 57 | return m.coeff(0,0) * m.coeff(1,1) - m.coeff(1,0) * m.coeff(0,1); |
| 58 | } |
| 59 | }; |
| 60 | |
| 61 | template<typename Derived> struct determinant_impl<Derived, 3> |
| 62 | { |
| 63 | static inline typename traits<Derived>::Scalar run(const Derived& m) |
| 64 | { |
| 65 | return bruteforce_det3_helper(m,0,1,2) |
| 66 | - bruteforce_det3_helper(m,1,0,2) |
| 67 | + bruteforce_det3_helper(m,2,0,1); |
| 68 | } |
| 69 | }; |
| 70 | |
| 71 | template<typename Derived> struct determinant_impl<Derived, 4> |
| 72 | { |
| 73 | static typename traits<Derived>::Scalar run(const Derived& m) |
| 74 | { |
| 75 | // trick by Martin Costabel to compute 4x4 det with only 30 muls |
| 76 | return bruteforce_det4_helper(m,0,1,2,3) |
| 77 | - bruteforce_det4_helper(m,0,2,1,3) |
| 78 | + bruteforce_det4_helper(m,0,3,1,2) |
| 79 | + bruteforce_det4_helper(m,1,2,0,3) |
| 80 | - bruteforce_det4_helper(m,1,3,0,2) |
| 81 | + bruteforce_det4_helper(m,2,3,0,1); |
| 82 | } |
| 83 | }; |
| 84 | |
| 85 | } // end namespace internal |
| 86 | |
| 87 | /** \lu_module |
| 88 | * |
| 89 | * \returns the determinant of this matrix |
| 90 | */ |
| 91 | template<typename Derived> |
| 92 | inline typename internal::traits<Derived>::Scalar MatrixBase<Derived>::determinant() const |
| 93 | { |
| 94 | eigen_assert(rows() == cols()); |
| 95 | typedef typename internal::nested<Derived,Base::RowsAtCompileTime>::type Nested; |
| 96 | return internal::determinant_impl<typename internal::remove_all<Nested>::type>::run(derived()); |
| 97 | } |
| 98 | |
| 99 | } // end namespace Eigen |
| 100 | |
| 101 | #endif // EIGEN_DETERMINANT_H |