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Eigen  3.4.0
 
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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
13namespace Eigen {
14
15namespace internal {
16
17template<typename Derived>
18EIGEN_DEVICE_FUNC
19inline const typename Derived::Scalar bruteforce_det3_helper
20(const MatrixBase<Derived>& matrix, int a, int b, int c)
21{
22 return matrix.coeff(0,a)
23 * (matrix.coeff(1,b) * matrix.coeff(2,c) - matrix.coeff(1,c) * matrix.coeff(2,b));
24}
25
26template<typename Derived,
27 int DeterminantType = Derived::RowsAtCompileTime
28> struct determinant_impl
29{
30 static inline typename traits<Derived>::Scalar run(const Derived& m)
31 {
32 if(Derived::ColsAtCompileTime==Dynamic && m.rows()==0)
33 return typename traits<Derived>::Scalar(1);
34 return m.partialPivLu().determinant();
35 }
36};
37
38template<typename Derived> struct determinant_impl<Derived, 1>
39{
40 static inline EIGEN_DEVICE_FUNC
41 typename traits<Derived>::Scalar run(const Derived& m)
42 {
43 return m.coeff(0,0);
44 }
45};
46
47template<typename Derived> struct determinant_impl<Derived, 2>
48{
49 static inline EIGEN_DEVICE_FUNC
50 typename traits<Derived>::Scalar run(const Derived& m)
51 {
52 return m.coeff(0,0) * m.coeff(1,1) - m.coeff(1,0) * m.coeff(0,1);
53 }
54};
55
56template<typename Derived> struct determinant_impl<Derived, 3>
57{
58 static inline EIGEN_DEVICE_FUNC
59 typename traits<Derived>::Scalar run(const Derived& m)
60 {
61 return bruteforce_det3_helper(m,0,1,2)
62 - bruteforce_det3_helper(m,1,0,2)
63 + bruteforce_det3_helper(m,2,0,1);
64 }
65};
66
67template<typename Derived> struct determinant_impl<Derived, 4>
68{
69 typedef typename traits<Derived>::Scalar Scalar;
70 static EIGEN_DEVICE_FUNC
71 Scalar run(const Derived& m)
72 {
73 Scalar d2_01 = det2(m, 0, 1);
74 Scalar d2_02 = det2(m, 0, 2);
75 Scalar d2_03 = det2(m, 0, 3);
76 Scalar d2_12 = det2(m, 1, 2);
77 Scalar d2_13 = det2(m, 1, 3);
78 Scalar d2_23 = det2(m, 2, 3);
79 Scalar d3_0 = det3(m, 1,d2_23, 2,d2_13, 3,d2_12);
80 Scalar d3_1 = det3(m, 0,d2_23, 2,d2_03, 3,d2_02);
81 Scalar d3_2 = det3(m, 0,d2_13, 1,d2_03, 3,d2_01);
82 Scalar d3_3 = det3(m, 0,d2_12, 1,d2_02, 2,d2_01);
83 return internal::pmadd(-m(0,3),d3_0, m(1,3)*d3_1) +
84 internal::pmadd(-m(2,3),d3_2, m(3,3)*d3_3);
85 }
86protected:
87 static EIGEN_DEVICE_FUNC
88 Scalar det2(const Derived& m, Index i0, Index i1)
89 {
90 return m(i0,0) * m(i1,1) - m(i1,0) * m(i0,1);
91 }
92
93 static EIGEN_DEVICE_FUNC
94 Scalar det3(const Derived& m, Index i0, const Scalar& d0, Index i1, const Scalar& d1, Index i2, const Scalar& d2)
95 {
96 return internal::pmadd(m(i0,2), d0, internal::pmadd(-m(i1,2), d1, m(i2,2)*d2));
97 }
98};
99
100} // end namespace internal
101
106template<typename Derived>
107EIGEN_DEVICE_FUNC
108inline typename internal::traits<Derived>::Scalar MatrixBase<Derived>::determinant() const
109{
110 eigen_assert(rows() == cols());
111 typedef typename internal::nested_eval<Derived,Base::RowsAtCompileTime>::type Nested;
112 return internal::determinant_impl<typename internal::remove_all<Nested>::type>::run(derived());
113}
114
115} // end namespace Eigen
116
117#endif // EIGEN_DETERMINANT_H
Base class for all dense matrices, vectors, and expressions.
Definition: MatrixBase.h:50
Namespace containing all symbols from the Eigen library.
Definition: Core:141
EIGEN_DEFAULT_DENSE_INDEX_TYPE Index
The Index type as used for the API.
Definition: Meta.h:74
const int Dynamic
Definition: Constants.h:22