[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) 2010-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
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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_TRANSPOSITIONS_H
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| 11 | #define EIGEN_TRANSPOSITIONS_H
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| 12 |
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| 13 | namespace Eigen {
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| 14 |
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| 15 | /** \class Transpositions
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| 16 | * \ingroup Core_Module
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| 17 | *
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| 18 | * \brief Represents a sequence of transpositions (row/column interchange)
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| 19 | *
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| 20 | * \param SizeAtCompileTime the number of transpositions, or Dynamic
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| 21 | * \param MaxSizeAtCompileTime the maximum number of transpositions, or Dynamic. This optional parameter defaults to SizeAtCompileTime. Most of the time, you should not have to specify it.
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| 22 | *
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| 23 | * This class represents a permutation transformation as a sequence of \em n transpositions
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| 24 | * \f$[T_{n-1} \ldots T_{i} \ldots T_{0}]\f$. It is internally stored as a vector of integers \c indices.
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| 25 | * Each transposition \f$ T_{i} \f$ applied on the left of a matrix (\f$ T_{i} M\f$) interchanges
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| 26 | * the rows \c i and \c indices[i] of the matrix \c M.
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| 27 | * A transposition applied on the right (e.g., \f$ M T_{i}\f$) yields a column interchange.
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| 28 | *
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| 29 | * Compared to the class PermutationMatrix, such a sequence of transpositions is what is
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| 30 | * computed during a decomposition with pivoting, and it is faster when applying the permutation in-place.
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| 31 | *
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| 32 | * To apply a sequence of transpositions to a matrix, simply use the operator * as in the following example:
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| 33 | * \code
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| 34 | * Transpositions tr;
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| 35 | * MatrixXf mat;
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| 36 | * mat = tr * mat;
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| 37 | * \endcode
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| 38 | * In this example, we detect that the matrix appears on both side, and so the transpositions
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| 39 | * are applied in-place without any temporary or extra copy.
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| 40 | *
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| 41 | * \sa class PermutationMatrix
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| 42 | */
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| 43 |
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| 44 | namespace internal {
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| 45 | template<typename TranspositionType, typename MatrixType, int Side, bool Transposed=false> struct transposition_matrix_product_retval;
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| 46 | }
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| 47 |
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| 48 | template<typename Derived>
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| 49 | class TranspositionsBase
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| 50 | {
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| 51 | typedef internal::traits<Derived> Traits;
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| 52 |
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| 53 | public:
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| 54 |
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| 55 | typedef typename Traits::IndicesType IndicesType;
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| 56 | typedef typename IndicesType::Scalar Index;
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| 57 |
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| 58 | Derived& derived() { return *static_cast<Derived*>(this); }
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| 59 | const Derived& derived() const { return *static_cast<const Derived*>(this); }
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| 60 |
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| 61 | /** Copies the \a other transpositions into \c *this */
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| 62 | template<typename OtherDerived>
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| 63 | Derived& operator=(const TranspositionsBase<OtherDerived>& other)
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| 64 | {
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| 65 | indices() = other.indices();
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| 66 | return derived();
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| 67 | }
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| 68 |
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| 69 | #ifndef EIGEN_PARSED_BY_DOXYGEN
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| 70 | /** This is a special case of the templated operator=. Its purpose is to
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| 71 | * prevent a default operator= from hiding the templated operator=.
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| 72 | */
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| 73 | Derived& operator=(const TranspositionsBase& other)
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| 74 | {
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| 75 | indices() = other.indices();
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| 76 | return derived();
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| 77 | }
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| 78 | #endif
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| 79 |
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| 80 | /** \returns the number of transpositions */
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| 81 | inline Index size() const { return indices().size(); }
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| 82 |
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| 83 | /** Direct access to the underlying index vector */
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| 84 | inline const Index& coeff(Index i) const { return indices().coeff(i); }
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| 85 | /** Direct access to the underlying index vector */
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| 86 | inline Index& coeffRef(Index i) { return indices().coeffRef(i); }
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| 87 | /** Direct access to the underlying index vector */
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| 88 | inline const Index& operator()(Index i) const { return indices()(i); }
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| 89 | /** Direct access to the underlying index vector */
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| 90 | inline Index& operator()(Index i) { return indices()(i); }
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| 91 | /** Direct access to the underlying index vector */
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| 92 | inline const Index& operator[](Index i) const { return indices()(i); }
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| 93 | /** Direct access to the underlying index vector */
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| 94 | inline Index& operator[](Index i) { return indices()(i); }
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| 95 |
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| 96 | /** const version of indices(). */
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| 97 | const IndicesType& indices() const { return derived().indices(); }
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| 98 | /** \returns a reference to the stored array representing the transpositions. */
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| 99 | IndicesType& indices() { return derived().indices(); }
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| 100 |
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| 101 | /** Resizes to given size. */
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| 102 | inline void resize(int newSize)
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| 103 | {
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| 104 | indices().resize(newSize);
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| 105 | }
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| 106 |
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| 107 | /** Sets \c *this to represents an identity transformation */
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| 108 | void setIdentity()
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| 109 | {
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| 110 | for(int i = 0; i < indices().size(); ++i)
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| 111 | coeffRef(i) = i;
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| 112 | }
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| 113 |
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| 114 | // FIXME: do we want such methods ?
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| 115 | // might be usefull when the target matrix expression is complex, e.g.:
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| 116 | // object.matrix().block(..,..,..,..) = trans * object.matrix().block(..,..,..,..);
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| 117 | /*
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| 118 | template<typename MatrixType>
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| 119 | void applyForwardToRows(MatrixType& mat) const
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| 120 | {
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| 121 | for(Index k=0 ; k<size() ; ++k)
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| 122 | if(m_indices(k)!=k)
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| 123 | mat.row(k).swap(mat.row(m_indices(k)));
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| 124 | }
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| 125 |
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| 126 | template<typename MatrixType>
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| 127 | void applyBackwardToRows(MatrixType& mat) const
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| 128 | {
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| 129 | for(Index k=size()-1 ; k>=0 ; --k)
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| 130 | if(m_indices(k)!=k)
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| 131 | mat.row(k).swap(mat.row(m_indices(k)));
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| 132 | }
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| 133 | */
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| 134 |
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| 135 | /** \returns the inverse transformation */
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| 136 | inline Transpose<TranspositionsBase> inverse() const
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| 137 | { return Transpose<TranspositionsBase>(derived()); }
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| 138 |
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| 139 | /** \returns the tranpose transformation */
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| 140 | inline Transpose<TranspositionsBase> transpose() const
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| 141 | { return Transpose<TranspositionsBase>(derived()); }
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| 142 |
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| 143 | protected:
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| 144 | };
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| 145 |
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| 146 | namespace internal {
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| 147 | template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType>
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| 148 | struct traits<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,IndexType> >
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| 149 | {
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| 150 | typedef IndexType Index;
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| 151 | typedef Matrix<Index, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1> IndicesType;
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| 152 | };
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| 153 | }
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| 154 |
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| 155 | template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType>
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| 156 | class Transpositions : public TranspositionsBase<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,IndexType> >
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| 157 | {
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| 158 | typedef internal::traits<Transpositions> Traits;
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| 159 | public:
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| 160 |
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| 161 | typedef TranspositionsBase<Transpositions> Base;
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| 162 | typedef typename Traits::IndicesType IndicesType;
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| 163 | typedef typename IndicesType::Scalar Index;
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| 164 |
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| 165 | inline Transpositions() {}
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| 166 |
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| 167 | /** Copy constructor. */
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| 168 | template<typename OtherDerived>
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| 169 | inline Transpositions(const TranspositionsBase<OtherDerived>& other)
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| 170 | : m_indices(other.indices()) {}
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| 171 |
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| 172 | #ifndef EIGEN_PARSED_BY_DOXYGEN
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| 173 | /** Standard copy constructor. Defined only to prevent a default copy constructor
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| 174 | * from hiding the other templated constructor */
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| 175 | inline Transpositions(const Transpositions& other) : m_indices(other.indices()) {}
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| 176 | #endif
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| 177 |
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| 178 | /** Generic constructor from expression of the transposition indices. */
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| 179 | template<typename Other>
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| 180 | explicit inline Transpositions(const MatrixBase<Other>& a_indices) : m_indices(a_indices)
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| 181 | {}
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| 182 |
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| 183 | /** Copies the \a other transpositions into \c *this */
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| 184 | template<typename OtherDerived>
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| 185 | Transpositions& operator=(const TranspositionsBase<OtherDerived>& other)
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| 186 | {
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| 187 | return Base::operator=(other);
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| 188 | }
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| 189 |
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| 190 | #ifndef EIGEN_PARSED_BY_DOXYGEN
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| 191 | /** This is a special case of the templated operator=. Its purpose is to
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| 192 | * prevent a default operator= from hiding the templated operator=.
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| 193 | */
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| 194 | Transpositions& operator=(const Transpositions& other)
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| 195 | {
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| 196 | m_indices = other.m_indices;
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| 197 | return *this;
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| 198 | }
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| 199 | #endif
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| 200 |
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| 201 | /** Constructs an uninitialized permutation matrix of given size.
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| 202 | */
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| 203 | inline Transpositions(Index size) : m_indices(size)
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| 204 | {}
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| 205 |
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| 206 | /** const version of indices(). */
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| 207 | const IndicesType& indices() const { return m_indices; }
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| 208 | /** \returns a reference to the stored array representing the transpositions. */
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| 209 | IndicesType& indices() { return m_indices; }
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| 210 |
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| 211 | protected:
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| 212 |
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| 213 | IndicesType m_indices;
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| 214 | };
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| 215 |
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| 216 |
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| 217 | namespace internal {
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| 218 | template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType, int _PacketAccess>
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| 219 | struct traits<Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,IndexType>,_PacketAccess> >
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| 220 | {
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| 221 | typedef IndexType Index;
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| 222 | typedef Map<const Matrix<Index,SizeAtCompileTime,1,0,MaxSizeAtCompileTime,1>, _PacketAccess> IndicesType;
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| 223 | };
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| 224 | }
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| 225 |
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| 226 | template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType, int PacketAccess>
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| 227 | class Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,IndexType>,PacketAccess>
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| 228 | : public TranspositionsBase<Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,IndexType>,PacketAccess> >
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| 229 | {
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| 230 | typedef internal::traits<Map> Traits;
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| 231 | public:
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| 232 |
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| 233 | typedef TranspositionsBase<Map> Base;
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| 234 | typedef typename Traits::IndicesType IndicesType;
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| 235 | typedef typename IndicesType::Scalar Index;
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| 236 |
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| 237 | inline Map(const Index* indicesPtr)
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| 238 | : m_indices(indicesPtr)
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| 239 | {}
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| 240 |
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| 241 | inline Map(const Index* indicesPtr, Index size)
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| 242 | : m_indices(indicesPtr,size)
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| 243 | {}
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| 244 |
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| 245 | /** Copies the \a other transpositions into \c *this */
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| 246 | template<typename OtherDerived>
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| 247 | Map& operator=(const TranspositionsBase<OtherDerived>& other)
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| 248 | {
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| 249 | return Base::operator=(other);
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| 250 | }
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| 251 |
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| 252 | #ifndef EIGEN_PARSED_BY_DOXYGEN
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| 253 | /** This is a special case of the templated operator=. Its purpose is to
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| 254 | * prevent a default operator= from hiding the templated operator=.
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| 255 | */
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| 256 | Map& operator=(const Map& other)
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| 257 | {
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| 258 | m_indices = other.m_indices;
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| 259 | return *this;
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| 260 | }
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| 261 | #endif
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| 262 |
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| 263 | /** const version of indices(). */
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| 264 | const IndicesType& indices() const { return m_indices; }
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| 265 |
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| 266 | /** \returns a reference to the stored array representing the transpositions. */
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| 267 | IndicesType& indices() { return m_indices; }
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| 268 |
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| 269 | protected:
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| 270 |
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| 271 | IndicesType m_indices;
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| 272 | };
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| 273 |
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| 274 | namespace internal {
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| 275 | template<typename _IndicesType>
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| 276 | struct traits<TranspositionsWrapper<_IndicesType> >
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| 277 | {
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| 278 | typedef typename _IndicesType::Scalar Index;
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| 279 | typedef _IndicesType IndicesType;
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| 280 | };
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| 281 | }
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| 282 |
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| 283 | template<typename _IndicesType>
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| 284 | class TranspositionsWrapper
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| 285 | : public TranspositionsBase<TranspositionsWrapper<_IndicesType> >
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| 286 | {
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| 287 | typedef internal::traits<TranspositionsWrapper> Traits;
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| 288 | public:
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| 289 |
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| 290 | typedef TranspositionsBase<TranspositionsWrapper> Base;
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| 291 | typedef typename Traits::IndicesType IndicesType;
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| 292 | typedef typename IndicesType::Scalar Index;
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| 293 |
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| 294 | inline TranspositionsWrapper(IndicesType& a_indices)
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| 295 | : m_indices(a_indices)
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| 296 | {}
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| 297 |
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| 298 | /** Copies the \a other transpositions into \c *this */
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| 299 | template<typename OtherDerived>
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| 300 | TranspositionsWrapper& operator=(const TranspositionsBase<OtherDerived>& other)
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| 301 | {
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| 302 | return Base::operator=(other);
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| 303 | }
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| 304 |
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| 305 | #ifndef EIGEN_PARSED_BY_DOXYGEN
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| 306 | /** This is a special case of the templated operator=. Its purpose is to
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| 307 | * prevent a default operator= from hiding the templated operator=.
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| 308 | */
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| 309 | TranspositionsWrapper& operator=(const TranspositionsWrapper& other)
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| 310 | {
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| 311 | m_indices = other.m_indices;
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| 312 | return *this;
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| 313 | }
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| 314 | #endif
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| 315 |
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| 316 | /** const version of indices(). */
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| 317 | const IndicesType& indices() const { return m_indices; }
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| 318 |
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| 319 | /** \returns a reference to the stored array representing the transpositions. */
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| 320 | IndicesType& indices() { return m_indices; }
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| 321 |
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| 322 | protected:
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| 323 |
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| 324 | const typename IndicesType::Nested m_indices;
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| 325 | };
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| 326 |
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| 327 | /** \returns the \a matrix with the \a transpositions applied to the columns.
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| 328 | */
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| 329 | template<typename Derived, typename TranspositionsDerived>
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| 330 | inline const internal::transposition_matrix_product_retval<TranspositionsDerived, Derived, OnTheRight>
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| 331 | operator*(const MatrixBase<Derived>& matrix,
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| 332 | const TranspositionsBase<TranspositionsDerived> &transpositions)
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| 333 | {
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| 334 | return internal::transposition_matrix_product_retval
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| 335 | <TranspositionsDerived, Derived, OnTheRight>
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| 336 | (transpositions.derived(), matrix.derived());
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| 337 | }
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| 338 |
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| 339 | /** \returns the \a matrix with the \a transpositions applied to the rows.
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| 340 | */
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| 341 | template<typename Derived, typename TranspositionDerived>
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| 342 | inline const internal::transposition_matrix_product_retval
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| 343 | <TranspositionDerived, Derived, OnTheLeft>
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| 344 | operator*(const TranspositionsBase<TranspositionDerived> &transpositions,
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| 345 | const MatrixBase<Derived>& matrix)
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| 346 | {
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| 347 | return internal::transposition_matrix_product_retval
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| 348 | <TranspositionDerived, Derived, OnTheLeft>
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| 349 | (transpositions.derived(), matrix.derived());
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| 350 | }
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| 351 |
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| 352 | namespace internal {
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| 353 |
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| 354 | template<typename TranspositionType, typename MatrixType, int Side, bool Transposed>
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| 355 | struct traits<transposition_matrix_product_retval<TranspositionType, MatrixType, Side, Transposed> >
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| 356 | {
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| 357 | typedef typename MatrixType::PlainObject ReturnType;
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| 358 | };
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| 359 |
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| 360 | template<typename TranspositionType, typename MatrixType, int Side, bool Transposed>
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| 361 | struct transposition_matrix_product_retval
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| 362 | : public ReturnByValue<transposition_matrix_product_retval<TranspositionType, MatrixType, Side, Transposed> >
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| 363 | {
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| 364 | typedef typename remove_all<typename MatrixType::Nested>::type MatrixTypeNestedCleaned;
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| 365 | typedef typename TranspositionType::Index Index;
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| 366 |
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| 367 | transposition_matrix_product_retval(const TranspositionType& tr, const MatrixType& matrix)
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| 368 | : m_transpositions(tr), m_matrix(matrix)
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| 369 | {}
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| 370 |
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| 371 | inline int rows() const { return m_matrix.rows(); }
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| 372 | inline int cols() const { return m_matrix.cols(); }
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| 373 |
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| 374 | template<typename Dest> inline void evalTo(Dest& dst) const
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| 375 | {
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| 376 | const int size = m_transpositions.size();
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| 377 | Index j = 0;
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| 378 |
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| 379 | const typename Dest::Scalar *dst_data = internal::extract_data(dst);
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| 380 | if(!(is_same<MatrixTypeNestedCleaned,Dest>::value && dst_data!=0 && dst_data == extract_data(m_matrix)))
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| 381 | dst = m_matrix;
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| 382 |
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| 383 | for(int k=(Transposed?size-1:0) ; Transposed?k>=0:k<size ; Transposed?--k:++k)
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| 384 | if((j=m_transpositions.coeff(k))!=k)
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| 385 | {
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| 386 | if(Side==OnTheLeft)
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| 387 | dst.row(k).swap(dst.row(j));
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| 388 | else if(Side==OnTheRight)
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| 389 | dst.col(k).swap(dst.col(j));
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| 390 | }
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| 391 | }
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| 392 |
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| 393 | protected:
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| 394 | const TranspositionType& m_transpositions;
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| 395 | typename MatrixType::Nested m_matrix;
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| 396 | };
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| 397 |
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| 398 | } // end namespace internal
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| 399 |
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| 400 | /* Template partial specialization for transposed/inverse transpositions */
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| 401 |
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| 402 | template<typename TranspositionsDerived>
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| 403 | class Transpose<TranspositionsBase<TranspositionsDerived> >
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| 404 | {
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| 405 | typedef TranspositionsDerived TranspositionType;
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| 406 | typedef typename TranspositionType::IndicesType IndicesType;
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| 407 | public:
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| 408 |
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| 409 | Transpose(const TranspositionType& t) : m_transpositions(t) {}
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| 410 |
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| 411 | inline int size() const { return m_transpositions.size(); }
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| 412 |
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| 413 | /** \returns the \a matrix with the inverse transpositions applied to the columns.
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| 414 | */
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| 415 | template<typename Derived> friend
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| 416 | inline const internal::transposition_matrix_product_retval<TranspositionType, Derived, OnTheRight, true>
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| 417 | operator*(const MatrixBase<Derived>& matrix, const Transpose& trt)
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| 418 | {
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| 419 | return internal::transposition_matrix_product_retval<TranspositionType, Derived, OnTheRight, true>(trt.m_transpositions, matrix.derived());
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| 420 | }
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| 421 |
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| 422 | /** \returns the \a matrix with the inverse transpositions applied to the rows.
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| 423 | */
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| 424 | template<typename Derived>
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| 425 | inline const internal::transposition_matrix_product_retval<TranspositionType, Derived, OnTheLeft, true>
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| 426 | operator*(const MatrixBase<Derived>& matrix) const
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| 427 | {
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| 428 | return internal::transposition_matrix_product_retval<TranspositionType, Derived, OnTheLeft, true>(m_transpositions, matrix.derived());
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| 429 | }
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| 430 |
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| 431 | protected:
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| 432 | const TranspositionType& m_transpositions;
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| 433 | };
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| 434 |
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| 435 | } // end namespace Eigen
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| 436 |
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| 437 | #endif // EIGEN_TRANSPOSITIONS_H
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