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 Eigen  3.3.71
Determinant.h
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
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_eval<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
Eigen
Namespace containing all symbols from the Eigen library.
Definition: Core:309
Eigen::MatrixBase::determinant
Scalar determinant() const
Definition: Determinant.h:92
Eigen::Dynamic
const int Dynamic
Definition: Constants.h:21