[136] | 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) 2008-2010 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_INVERSE_H
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| 11 | #define EIGEN_INVERSE_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 | /**********************************
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| 18 | *** General case implementation ***
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| 19 | **********************************/
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| 20 |
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| 21 | template<typename MatrixType, typename ResultType, int Size = MatrixType::RowsAtCompileTime>
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| 22 | struct compute_inverse
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| 23 | {
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| 24 | static inline void run(const MatrixType& matrix, ResultType& result)
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| 25 | {
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| 26 | result = matrix.partialPivLu().inverse();
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| 27 | }
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| 28 | };
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| 29 |
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| 30 | template<typename MatrixType, typename ResultType, int Size = MatrixType::RowsAtCompileTime>
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| 31 | struct compute_inverse_and_det_with_check { /* nothing! general case not supported. */ };
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| 32 |
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| 33 | /****************************
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| 34 | *** Size 1 implementation ***
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| 35 | ****************************/
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| 36 |
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| 37 | template<typename MatrixType, typename ResultType>
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| 38 | struct compute_inverse<MatrixType, ResultType, 1>
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| 39 | {
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| 40 | static inline void run(const MatrixType& matrix, ResultType& result)
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| 41 | {
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| 42 | typedef typename MatrixType::Scalar Scalar;
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| 43 | result.coeffRef(0,0) = Scalar(1) / matrix.coeff(0,0);
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| 44 | }
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| 45 | };
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| 46 |
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| 47 | template<typename MatrixType, typename ResultType>
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| 48 | struct compute_inverse_and_det_with_check<MatrixType, ResultType, 1>
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| 49 | {
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| 50 | static inline void run(
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| 51 | const MatrixType& matrix,
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| 52 | const typename MatrixType::RealScalar& absDeterminantThreshold,
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| 53 | ResultType& result,
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| 54 | typename ResultType::Scalar& determinant,
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| 55 | bool& invertible
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| 56 | )
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| 57 | {
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| 58 | using std::abs;
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| 59 | determinant = matrix.coeff(0,0);
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| 60 | invertible = abs(determinant) > absDeterminantThreshold;
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| 61 | if(invertible) result.coeffRef(0,0) = typename ResultType::Scalar(1) / determinant;
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| 62 | }
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| 63 | };
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| 64 |
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| 65 | /****************************
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| 66 | *** Size 2 implementation ***
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| 67 | ****************************/
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| 68 |
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| 69 | template<typename MatrixType, typename ResultType>
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| 70 | inline void compute_inverse_size2_helper(
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| 71 | const MatrixType& matrix, const typename ResultType::Scalar& invdet,
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| 72 | ResultType& result)
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| 73 | {
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| 74 | result.coeffRef(0,0) = matrix.coeff(1,1) * invdet;
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| 75 | result.coeffRef(1,0) = -matrix.coeff(1,0) * invdet;
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| 76 | result.coeffRef(0,1) = -matrix.coeff(0,1) * invdet;
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| 77 | result.coeffRef(1,1) = matrix.coeff(0,0) * invdet;
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| 78 | }
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| 79 |
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| 80 | template<typename MatrixType, typename ResultType>
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| 81 | struct compute_inverse<MatrixType, ResultType, 2>
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| 82 | {
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| 83 | static inline void run(const MatrixType& matrix, ResultType& result)
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| 84 | {
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| 85 | typedef typename ResultType::Scalar Scalar;
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| 86 | const Scalar invdet = typename MatrixType::Scalar(1) / matrix.determinant();
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| 87 | compute_inverse_size2_helper(matrix, invdet, result);
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| 88 | }
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| 89 | };
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| 90 |
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| 91 | template<typename MatrixType, typename ResultType>
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| 92 | struct compute_inverse_and_det_with_check<MatrixType, ResultType, 2>
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| 93 | {
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| 94 | static inline void run(
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| 95 | const MatrixType& matrix,
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| 96 | const typename MatrixType::RealScalar& absDeterminantThreshold,
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| 97 | ResultType& inverse,
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| 98 | typename ResultType::Scalar& determinant,
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| 99 | bool& invertible
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| 100 | )
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| 101 | {
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| 102 | using std::abs;
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| 103 | typedef typename ResultType::Scalar Scalar;
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| 104 | determinant = matrix.determinant();
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| 105 | invertible = abs(determinant) > absDeterminantThreshold;
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| 106 | if(!invertible) return;
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| 107 | const Scalar invdet = Scalar(1) / determinant;
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| 108 | compute_inverse_size2_helper(matrix, invdet, inverse);
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| 109 | }
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| 110 | };
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| 111 |
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| 112 | /****************************
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| 113 | *** Size 3 implementation ***
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| 114 | ****************************/
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| 115 |
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| 116 | template<typename MatrixType, int i, int j>
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| 117 | inline typename MatrixType::Scalar cofactor_3x3(const MatrixType& m)
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| 118 | {
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| 119 | enum {
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| 120 | i1 = (i+1) % 3,
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| 121 | i2 = (i+2) % 3,
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| 122 | j1 = (j+1) % 3,
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| 123 | j2 = (j+2) % 3
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| 124 | };
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| 125 | return m.coeff(i1, j1) * m.coeff(i2, j2)
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| 126 | - m.coeff(i1, j2) * m.coeff(i2, j1);
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| 127 | }
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| 128 |
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| 129 | template<typename MatrixType, typename ResultType>
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| 130 | inline void compute_inverse_size3_helper(
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| 131 | const MatrixType& matrix,
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| 132 | const typename ResultType::Scalar& invdet,
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| 133 | const Matrix<typename ResultType::Scalar,3,1>& cofactors_col0,
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| 134 | ResultType& result)
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| 135 | {
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| 136 | result.row(0) = cofactors_col0 * invdet;
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| 137 | result.coeffRef(1,0) = cofactor_3x3<MatrixType,0,1>(matrix) * invdet;
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| 138 | result.coeffRef(1,1) = cofactor_3x3<MatrixType,1,1>(matrix) * invdet;
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| 139 | result.coeffRef(1,2) = cofactor_3x3<MatrixType,2,1>(matrix) * invdet;
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| 140 | result.coeffRef(2,0) = cofactor_3x3<MatrixType,0,2>(matrix) * invdet;
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| 141 | result.coeffRef(2,1) = cofactor_3x3<MatrixType,1,2>(matrix) * invdet;
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| 142 | result.coeffRef(2,2) = cofactor_3x3<MatrixType,2,2>(matrix) * invdet;
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| 143 | }
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| 144 |
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| 145 | template<typename MatrixType, typename ResultType>
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| 146 | struct compute_inverse<MatrixType, ResultType, 3>
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| 147 | {
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| 148 | static inline void run(const MatrixType& matrix, ResultType& result)
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| 149 | {
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| 150 | typedef typename ResultType::Scalar Scalar;
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| 151 | Matrix<typename MatrixType::Scalar,3,1> cofactors_col0;
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| 152 | cofactors_col0.coeffRef(0) = cofactor_3x3<MatrixType,0,0>(matrix);
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| 153 | cofactors_col0.coeffRef(1) = cofactor_3x3<MatrixType,1,0>(matrix);
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| 154 | cofactors_col0.coeffRef(2) = cofactor_3x3<MatrixType,2,0>(matrix);
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| 155 | const Scalar det = (cofactors_col0.cwiseProduct(matrix.col(0))).sum();
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| 156 | const Scalar invdet = Scalar(1) / det;
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| 157 | compute_inverse_size3_helper(matrix, invdet, cofactors_col0, result);
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| 158 | }
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| 159 | };
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| 160 |
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| 161 | template<typename MatrixType, typename ResultType>
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| 162 | struct compute_inverse_and_det_with_check<MatrixType, ResultType, 3>
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| 163 | {
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| 164 | static inline void run(
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| 165 | const MatrixType& matrix,
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| 166 | const typename MatrixType::RealScalar& absDeterminantThreshold,
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| 167 | ResultType& inverse,
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| 168 | typename ResultType::Scalar& determinant,
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| 169 | bool& invertible
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| 170 | )
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| 171 | {
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| 172 | using std::abs;
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| 173 | typedef typename ResultType::Scalar Scalar;
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| 174 | Matrix<Scalar,3,1> cofactors_col0;
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| 175 | cofactors_col0.coeffRef(0) = cofactor_3x3<MatrixType,0,0>(matrix);
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| 176 | cofactors_col0.coeffRef(1) = cofactor_3x3<MatrixType,1,0>(matrix);
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| 177 | cofactors_col0.coeffRef(2) = cofactor_3x3<MatrixType,2,0>(matrix);
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| 178 | determinant = (cofactors_col0.cwiseProduct(matrix.col(0))).sum();
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| 179 | invertible = abs(determinant) > absDeterminantThreshold;
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| 180 | if(!invertible) return;
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| 181 | const Scalar invdet = Scalar(1) / determinant;
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| 182 | compute_inverse_size3_helper(matrix, invdet, cofactors_col0, inverse);
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| 183 | }
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| 184 | };
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| 185 |
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| 186 | /****************************
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| 187 | *** Size 4 implementation ***
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| 188 | ****************************/
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| 189 |
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| 190 | template<typename Derived>
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| 191 | inline const typename Derived::Scalar general_det3_helper
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| 192 | (const MatrixBase<Derived>& matrix, int i1, int i2, int i3, int j1, int j2, int j3)
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| 193 | {
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| 194 | return matrix.coeff(i1,j1)
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| 195 | * (matrix.coeff(i2,j2) * matrix.coeff(i3,j3) - matrix.coeff(i2,j3) * matrix.coeff(i3,j2));
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| 196 | }
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| 197 |
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| 198 | template<typename MatrixType, int i, int j>
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| 199 | inline typename MatrixType::Scalar cofactor_4x4(const MatrixType& matrix)
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| 200 | {
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| 201 | enum {
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| 202 | i1 = (i+1) % 4,
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| 203 | i2 = (i+2) % 4,
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| 204 | i3 = (i+3) % 4,
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| 205 | j1 = (j+1) % 4,
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| 206 | j2 = (j+2) % 4,
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| 207 | j3 = (j+3) % 4
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| 208 | };
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| 209 | return general_det3_helper(matrix, i1, i2, i3, j1, j2, j3)
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| 210 | + general_det3_helper(matrix, i2, i3, i1, j1, j2, j3)
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| 211 | + general_det3_helper(matrix, i3, i1, i2, j1, j2, j3);
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| 212 | }
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| 213 |
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| 214 | template<int Arch, typename Scalar, typename MatrixType, typename ResultType>
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| 215 | struct compute_inverse_size4
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| 216 | {
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| 217 | static void run(const MatrixType& matrix, ResultType& result)
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| 218 | {
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| 219 | result.coeffRef(0,0) = cofactor_4x4<MatrixType,0,0>(matrix);
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| 220 | result.coeffRef(1,0) = -cofactor_4x4<MatrixType,0,1>(matrix);
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| 221 | result.coeffRef(2,0) = cofactor_4x4<MatrixType,0,2>(matrix);
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| 222 | result.coeffRef(3,0) = -cofactor_4x4<MatrixType,0,3>(matrix);
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| 223 | result.coeffRef(0,2) = cofactor_4x4<MatrixType,2,0>(matrix);
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| 224 | result.coeffRef(1,2) = -cofactor_4x4<MatrixType,2,1>(matrix);
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| 225 | result.coeffRef(2,2) = cofactor_4x4<MatrixType,2,2>(matrix);
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| 226 | result.coeffRef(3,2) = -cofactor_4x4<MatrixType,2,3>(matrix);
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| 227 | result.coeffRef(0,1) = -cofactor_4x4<MatrixType,1,0>(matrix);
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| 228 | result.coeffRef(1,1) = cofactor_4x4<MatrixType,1,1>(matrix);
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| 229 | result.coeffRef(2,1) = -cofactor_4x4<MatrixType,1,2>(matrix);
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| 230 | result.coeffRef(3,1) = cofactor_4x4<MatrixType,1,3>(matrix);
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| 231 | result.coeffRef(0,3) = -cofactor_4x4<MatrixType,3,0>(matrix);
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| 232 | result.coeffRef(1,3) = cofactor_4x4<MatrixType,3,1>(matrix);
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| 233 | result.coeffRef(2,3) = -cofactor_4x4<MatrixType,3,2>(matrix);
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| 234 | result.coeffRef(3,3) = cofactor_4x4<MatrixType,3,3>(matrix);
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| 235 | result /= (matrix.col(0).cwiseProduct(result.row(0).transpose())).sum();
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| 236 | }
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| 237 | };
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| 238 |
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| 239 | template<typename MatrixType, typename ResultType>
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| 240 | struct compute_inverse<MatrixType, ResultType, 4>
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| 241 | : compute_inverse_size4<Architecture::Target, typename MatrixType::Scalar,
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| 242 | MatrixType, ResultType>
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| 243 | {
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| 244 | };
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| 245 |
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| 246 | template<typename MatrixType, typename ResultType>
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| 247 | struct compute_inverse_and_det_with_check<MatrixType, ResultType, 4>
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| 248 | {
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| 249 | static inline void run(
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| 250 | const MatrixType& matrix,
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| 251 | const typename MatrixType::RealScalar& absDeterminantThreshold,
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| 252 | ResultType& inverse,
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| 253 | typename ResultType::Scalar& determinant,
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| 254 | bool& invertible
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| 255 | )
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| 256 | {
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| 257 | using std::abs;
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| 258 | determinant = matrix.determinant();
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| 259 | invertible = abs(determinant) > absDeterminantThreshold;
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| 260 | if(invertible) compute_inverse<MatrixType, ResultType>::run(matrix, inverse);
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| 261 | }
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| 262 | };
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| 263 |
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| 264 | /*************************
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| 265 | *** MatrixBase methods ***
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| 266 | *************************/
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| 267 |
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| 268 | template<typename MatrixType>
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| 269 | struct traits<inverse_impl<MatrixType> >
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| 270 | {
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| 271 | typedef typename MatrixType::PlainObject ReturnType;
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| 272 | };
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| 273 |
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| 274 | template<typename MatrixType>
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| 275 | struct inverse_impl : public ReturnByValue<inverse_impl<MatrixType> >
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| 276 | {
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| 277 | typedef typename MatrixType::Index Index;
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| 278 | typedef typename internal::eval<MatrixType>::type MatrixTypeNested;
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| 279 | typedef typename remove_all<MatrixTypeNested>::type MatrixTypeNestedCleaned;
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| 280 | MatrixTypeNested m_matrix;
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| 281 |
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| 282 | inverse_impl(const MatrixType& matrix)
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| 283 | : m_matrix(matrix)
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| 284 | {}
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| 285 |
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| 286 | inline Index rows() const { return m_matrix.rows(); }
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| 287 | inline Index cols() const { return m_matrix.cols(); }
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| 288 |
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| 289 | template<typename Dest> inline void evalTo(Dest& dst) const
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| 290 | {
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| 291 | const int Size = EIGEN_PLAIN_ENUM_MIN(MatrixType::ColsAtCompileTime,Dest::ColsAtCompileTime);
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| 292 | EIGEN_ONLY_USED_FOR_DEBUG(Size);
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| 293 | eigen_assert(( (Size<=1) || (Size>4) || (extract_data(m_matrix)!=0 && extract_data(m_matrix)!=extract_data(dst)))
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| 294 | && "Aliasing problem detected in inverse(), you need to do inverse().eval() here.");
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| 295 |
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| 296 | compute_inverse<MatrixTypeNestedCleaned, Dest>::run(m_matrix, dst);
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| 297 | }
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| 298 | };
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| 299 |
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| 300 | } // end namespace internal
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| 301 |
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| 302 | /** \lu_module
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| 303 | *
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| 304 | * \returns the matrix inverse of this matrix.
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| 305 | *
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| 306 | * For small fixed sizes up to 4x4, this method uses cofactors.
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| 307 | * In the general case, this method uses class PartialPivLU.
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| 308 | *
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| 309 | * \note This matrix must be invertible, otherwise the result is undefined. If you need an
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| 310 | * invertibility check, do the following:
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| 311 | * \li for fixed sizes up to 4x4, use computeInverseAndDetWithCheck().
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| 312 | * \li for the general case, use class FullPivLU.
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| 313 | *
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| 314 | * Example: \include MatrixBase_inverse.cpp
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| 315 | * Output: \verbinclude MatrixBase_inverse.out
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| 316 | *
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| 317 | * \sa computeInverseAndDetWithCheck()
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| 318 | */
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| 319 | template<typename Derived>
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| 320 | inline const internal::inverse_impl<Derived> MatrixBase<Derived>::inverse() const
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| 321 | {
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| 322 | EIGEN_STATIC_ASSERT(!NumTraits<Scalar>::IsInteger,THIS_FUNCTION_IS_NOT_FOR_INTEGER_NUMERIC_TYPES)
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| 323 | eigen_assert(rows() == cols());
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| 324 | return internal::inverse_impl<Derived>(derived());
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| 325 | }
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| 326 |
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| 327 | /** \lu_module
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| 328 | *
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| 329 | * Computation of matrix inverse and determinant, with invertibility check.
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| 330 | *
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| 331 | * This is only for fixed-size square matrices of size up to 4x4.
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| 332 | *
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| 333 | * \param inverse Reference to the matrix in which to store the inverse.
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| 334 | * \param determinant Reference to the variable in which to store the determinant.
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| 335 | * \param invertible Reference to the bool variable in which to store whether the matrix is invertible.
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| 336 | * \param absDeterminantThreshold Optional parameter controlling the invertibility check.
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| 337 | * The matrix will be declared invertible if the absolute value of its
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| 338 | * determinant is greater than this threshold.
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| 339 | *
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| 340 | * Example: \include MatrixBase_computeInverseAndDetWithCheck.cpp
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| 341 | * Output: \verbinclude MatrixBase_computeInverseAndDetWithCheck.out
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| 342 | *
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| 343 | * \sa inverse(), computeInverseWithCheck()
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| 344 | */
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| 345 | template<typename Derived>
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| 346 | template<typename ResultType>
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| 347 | inline void MatrixBase<Derived>::computeInverseAndDetWithCheck(
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| 348 | ResultType& inverse,
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| 349 | typename ResultType::Scalar& determinant,
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| 350 | bool& invertible,
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| 351 | const RealScalar& absDeterminantThreshold
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| 352 | ) const
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| 353 | {
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| 354 | // i'd love to put some static assertions there, but SFINAE means that they have no effect...
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| 355 | eigen_assert(rows() == cols());
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| 356 | // for 2x2, it's worth giving a chance to avoid evaluating.
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| 357 | // for larger sizes, evaluating has negligible cost and limits code size.
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| 358 | typedef typename internal::conditional<
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| 359 | RowsAtCompileTime == 2,
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| 360 | typename internal::remove_all<typename internal::nested<Derived, 2>::type>::type,
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| 361 | PlainObject
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| 362 | >::type MatrixType;
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| 363 | internal::compute_inverse_and_det_with_check<MatrixType, ResultType>::run
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| 364 | (derived(), absDeterminantThreshold, inverse, determinant, invertible);
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| 365 | }
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| 366 |
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| 367 | /** \lu_module
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| 368 | *
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| 369 | * Computation of matrix inverse, with invertibility check.
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| 370 | *
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| 371 | * This is only for fixed-size square matrices of size up to 4x4.
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| 372 | *
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| 373 | * \param inverse Reference to the matrix in which to store the inverse.
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| 374 | * \param invertible Reference to the bool variable in which to store whether the matrix is invertible.
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| 375 | * \param absDeterminantThreshold Optional parameter controlling the invertibility check.
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| 376 | * The matrix will be declared invertible if the absolute value of its
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| 377 | * determinant is greater than this threshold.
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| 378 | *
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| 379 | * Example: \include MatrixBase_computeInverseWithCheck.cpp
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| 380 | * Output: \verbinclude MatrixBase_computeInverseWithCheck.out
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| 381 | *
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| 382 | * \sa inverse(), computeInverseAndDetWithCheck()
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| 383 | */
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| 384 | template<typename Derived>
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| 385 | template<typename ResultType>
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| 386 | inline void MatrixBase<Derived>::computeInverseWithCheck(
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| 387 | ResultType& inverse,
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| 388 | bool& invertible,
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| 389 | const RealScalar& absDeterminantThreshold
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| 390 | ) const
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| 391 | {
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| 392 | RealScalar determinant;
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| 393 | // i'd love to put some static assertions there, but SFINAE means that they have no effect...
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| 394 | eigen_assert(rows() == cols());
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| 395 | computeInverseAndDetWithCheck(inverse,determinant,invertible,absDeterminantThreshold);
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| 396 | }
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| 397 |
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| 398 | } // end namespace Eigen
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| 399 |
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| 400 | #endif // EIGEN_INVERSE_H
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