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>
bruteforce_det3_helper(const MatrixBase<Derived> & matrix,int a,int b,int c)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>
bruteforce_det4_helper(const MatrixBase<Derived> & matrix,int j,int k,int m,int n)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 {
rundeterminant_impl37 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 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
102