1 | // This file is part of Eigen, a lightweight C++ template library
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2 | // for linear algebra.
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3 | //
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4 | // Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
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5 | //
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6 | // This Source Code Form is subject to the terms of the Mozilla
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7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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9 |
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10 | #ifndef EIGEN_DETERMINANT_H
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11 | #define EIGEN_DETERMINANT_H
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12 |
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13 | namespace Eigen {
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14 |
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15 | namespace internal {
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16 |
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17 | template<typename Derived>
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18 | inline const typename Derived::Scalar bruteforce_det3_helper
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19 | (const MatrixBase<Derived>& matrix, int a, int b, int c)
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20 | {
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21 | return matrix.coeff(0,a)
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22 | * (matrix.coeff(1,b) * matrix.coeff(2,c) - matrix.coeff(1,c) * matrix.coeff(2,b));
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23 | }
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24 |
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25 | template<typename Derived>
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26 | const typename Derived::Scalar bruteforce_det4_helper
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27 | (const MatrixBase<Derived>& matrix, int j, int k, int m, int n)
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28 | {
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29 | return (matrix.coeff(j,0) * matrix.coeff(k,1) - matrix.coeff(k,0) * matrix.coeff(j,1))
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30 | * (matrix.coeff(m,2) * matrix.coeff(n,3) - matrix.coeff(n,2) * matrix.coeff(m,3));
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31 | }
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32 |
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33 | template<typename Derived,
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34 | int DeterminantType = Derived::RowsAtCompileTime
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35 | > struct determinant_impl
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36 | {
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37 | static inline typename traits<Derived>::Scalar run(const Derived& m)
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38 | {
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39 | if(Derived::ColsAtCompileTime==Dynamic && m.rows()==0)
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40 | return typename traits<Derived>::Scalar(1);
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41 | return m.partialPivLu().determinant();
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42 | }
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43 | };
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44 |
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45 | template<typename Derived> struct determinant_impl<Derived, 1>
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46 | {
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47 | static inline typename traits<Derived>::Scalar run(const Derived& m)
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48 | {
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49 | return m.coeff(0,0);
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50 | }
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51 | };
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52 |
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53 | template<typename Derived> struct determinant_impl<Derived, 2>
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54 | {
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55 | static inline typename traits<Derived>::Scalar run(const Derived& m)
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56 | {
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57 | return m.coeff(0,0) * m.coeff(1,1) - m.coeff(1,0) * m.coeff(0,1);
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58 | }
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59 | };
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60 |
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61 | template<typename Derived> struct determinant_impl<Derived, 3>
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62 | {
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63 | static inline typename traits<Derived>::Scalar run(const Derived& m)
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64 | {
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65 | return bruteforce_det3_helper(m,0,1,2)
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66 | - bruteforce_det3_helper(m,1,0,2)
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67 | + bruteforce_det3_helper(m,2,0,1);
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68 | }
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69 | };
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70 |
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71 | template<typename Derived> struct determinant_impl<Derived, 4>
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72 | {
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73 | static typename traits<Derived>::Scalar run(const Derived& m)
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74 | {
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75 | // trick by Martin Costabel to compute 4x4 det with only 30 muls
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76 | return bruteforce_det4_helper(m,0,1,2,3)
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77 | - bruteforce_det4_helper(m,0,2,1,3)
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78 | + bruteforce_det4_helper(m,0,3,1,2)
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79 | + bruteforce_det4_helper(m,1,2,0,3)
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80 | - bruteforce_det4_helper(m,1,3,0,2)
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81 | + bruteforce_det4_helper(m,2,3,0,1);
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82 | }
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83 | };
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84 |
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85 | } // end namespace internal
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86 |
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87 | /** \lu_module
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88 | *
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89 | * \returns the determinant of this matrix
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90 | */
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91 | template<typename Derived>
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92 | inline typename internal::traits<Derived>::Scalar MatrixBase<Derived>::determinant() const
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93 | {
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94 | eigen_assert(rows() == cols());
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95 | typedef typename internal::nested<Derived,Base::RowsAtCompileTime>::type Nested;
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96 | return internal::determinant_impl<typename internal::remove_all<Nested>::type>::run(derived());
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97 | }
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98 |
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99 | } // end namespace Eigen
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100 |
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101 | #endif // EIGEN_DETERMINANT_H
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