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