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
13namespace Eigen {
14
15namespace internal {
16
17template<typename Derived>
18inline 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
25template<typename Derived>
26const 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
33template<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
45template<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
53template<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
61template<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
71template<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  */
91template<typename Derived>
92inline 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
102