[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) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
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| 5 | // Copyright (C) 2009-2011 Gael Guennebaud <gael.guennebaud@inria.fr>
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| 6 | //
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| 7 | // This Source Code Form is subject to the terms of the Mozilla
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| 8 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 9 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 10 |
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| 11 | #ifndef EIGEN_PERMUTATIONMATRIX_H
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| 12 | #define EIGEN_PERMUTATIONMATRIX_H
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| 13 |
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| 14 | namespace Eigen {
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| 15 |
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| 16 | template<int RowCol,typename IndicesType,typename MatrixType, typename StorageKind> class PermutedImpl;
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| 17 |
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| 18 | /** \class PermutationBase
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| 19 | * \ingroup Core_Module
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| 20 | *
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| 21 | * \brief Base class for permutations
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| 22 | *
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| 23 | * \param Derived the derived class
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| 24 | *
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| 25 | * This class is the base class for all expressions representing a permutation matrix,
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| 26 | * internally stored as a vector of integers.
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| 27 | * The convention followed here is that if \f$ \sigma \f$ is a permutation, the corresponding permutation matrix
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| 28 | * \f$ P_\sigma \f$ is such that if \f$ (e_1,\ldots,e_p) \f$ is the canonical basis, we have:
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| 29 | * \f[ P_\sigma(e_i) = e_{\sigma(i)}. \f]
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| 30 | * This convention ensures that for any two permutations \f$ \sigma, \tau \f$, we have:
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| 31 | * \f[ P_{\sigma\circ\tau} = P_\sigma P_\tau. \f]
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| 32 | *
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| 33 | * Permutation matrices are square and invertible.
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| 34 | *
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| 35 | * Notice that in addition to the member functions and operators listed here, there also are non-member
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| 36 | * operator* to multiply any kind of permutation object with any kind of matrix expression (MatrixBase)
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| 37 | * on either side.
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| 38 | *
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| 39 | * \sa class PermutationMatrix, class PermutationWrapper
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| 40 | */
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| 41 |
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| 42 | namespace internal {
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| 43 |
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| 44 | template<typename PermutationType, typename MatrixType, int Side, bool Transposed=false>
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| 45 | struct permut_matrix_product_retval;
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| 46 | template<typename PermutationType, typename MatrixType, int Side, bool Transposed=false>
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| 47 | struct permut_sparsematrix_product_retval;
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| 48 | enum PermPermProduct_t {PermPermProduct};
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| 49 |
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| 50 | } // end namespace internal
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| 51 |
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| 52 | template<typename Derived>
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| 53 | class PermutationBase : public EigenBase<Derived>
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| 54 | {
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| 55 | typedef internal::traits<Derived> Traits;
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| 56 | typedef EigenBase<Derived> Base;
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| 57 | public:
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| 58 |
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| 59 | #ifndef EIGEN_PARSED_BY_DOXYGEN
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| 60 | typedef typename Traits::IndicesType IndicesType;
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| 61 | enum {
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| 62 | Flags = Traits::Flags,
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| 63 | CoeffReadCost = Traits::CoeffReadCost,
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| 64 | RowsAtCompileTime = Traits::RowsAtCompileTime,
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| 65 | ColsAtCompileTime = Traits::ColsAtCompileTime,
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| 66 | MaxRowsAtCompileTime = Traits::MaxRowsAtCompileTime,
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| 67 | MaxColsAtCompileTime = Traits::MaxColsAtCompileTime
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| 68 | };
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| 69 | typedef typename Traits::Scalar Scalar;
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| 70 | typedef typename Traits::Index Index;
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| 71 | typedef Matrix<Scalar,RowsAtCompileTime,ColsAtCompileTime,0,MaxRowsAtCompileTime,MaxColsAtCompileTime>
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| 72 | DenseMatrixType;
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| 73 | typedef PermutationMatrix<IndicesType::SizeAtCompileTime,IndicesType::MaxSizeAtCompileTime,Index>
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| 74 | PlainPermutationType;
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| 75 | using Base::derived;
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| 76 | #endif
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| 77 |
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| 78 | /** Copies the other permutation into *this */
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| 79 | template<typename OtherDerived>
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| 80 | Derived& operator=(const PermutationBase<OtherDerived>& other)
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| 81 | {
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| 82 | indices() = other.indices();
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| 83 | return derived();
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| 84 | }
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| 85 |
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| 86 | /** Assignment from the Transpositions \a tr */
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| 87 | template<typename OtherDerived>
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| 88 | Derived& operator=(const TranspositionsBase<OtherDerived>& tr)
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| 89 | {
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| 90 | setIdentity(tr.size());
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| 91 | for(Index k=size()-1; k>=0; --k)
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| 92 | applyTranspositionOnTheRight(k,tr.coeff(k));
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| 93 | return derived();
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| 94 | }
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| 95 |
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| 96 | #ifndef EIGEN_PARSED_BY_DOXYGEN
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| 97 | /** This is a special case of the templated operator=. Its purpose is to
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| 98 | * prevent a default operator= from hiding the templated operator=.
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| 99 | */
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| 100 | Derived& operator=(const PermutationBase& other)
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| 101 | {
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| 102 | indices() = other.indices();
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| 103 | return derived();
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| 104 | }
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| 105 | #endif
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| 106 |
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| 107 | /** \returns the number of rows */
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| 108 | inline Index rows() const { return Index(indices().size()); }
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| 109 |
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| 110 | /** \returns the number of columns */
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| 111 | inline Index cols() const { return Index(indices().size()); }
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| 112 |
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| 113 | /** \returns the size of a side of the respective square matrix, i.e., the number of indices */
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| 114 | inline Index size() const { return Index(indices().size()); }
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| 115 |
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| 116 | #ifndef EIGEN_PARSED_BY_DOXYGEN
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| 117 | template<typename DenseDerived>
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| 118 | void evalTo(MatrixBase<DenseDerived>& other) const
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| 119 | {
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| 120 | other.setZero();
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| 121 | for (int i=0; i<rows();++i)
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| 122 | other.coeffRef(indices().coeff(i),i) = typename DenseDerived::Scalar(1);
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| 123 | }
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| 124 | #endif
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| 125 |
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| 126 | /** \returns a Matrix object initialized from this permutation matrix. Notice that it
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| 127 | * is inefficient to return this Matrix object by value. For efficiency, favor using
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| 128 | * the Matrix constructor taking EigenBase objects.
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| 129 | */
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| 130 | DenseMatrixType toDenseMatrix() const
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| 131 | {
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| 132 | return derived();
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| 133 | }
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| 134 |
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| 135 | /** const version of indices(). */
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| 136 | const IndicesType& indices() const { return derived().indices(); }
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| 137 | /** \returns a reference to the stored array representing the permutation. */
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| 138 | IndicesType& indices() { return derived().indices(); }
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| 139 |
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| 140 | /** Resizes to given size.
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| 141 | */
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| 142 | inline void resize(Index newSize)
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| 143 | {
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| 144 | indices().resize(newSize);
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| 145 | }
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| 146 |
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| 147 | /** Sets *this to be the identity permutation matrix */
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| 148 | void setIdentity()
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| 149 | {
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| 150 | for(Index i = 0; i < size(); ++i)
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| 151 | indices().coeffRef(i) = i;
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| 152 | }
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| 153 |
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| 154 | /** Sets *this to be the identity permutation matrix of given size.
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| 155 | */
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| 156 | void setIdentity(Index newSize)
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| 157 | {
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| 158 | resize(newSize);
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| 159 | setIdentity();
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| 160 | }
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| 161 |
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| 162 | /** Multiplies *this by the transposition \f$(ij)\f$ on the left.
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| 163 | *
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| 164 | * \returns a reference to *this.
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| 165 | *
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| 166 | * \warning This is much slower than applyTranspositionOnTheRight(int,int):
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| 167 | * this has linear complexity and requires a lot of branching.
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| 168 | *
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| 169 | * \sa applyTranspositionOnTheRight(int,int)
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| 170 | */
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| 171 | Derived& applyTranspositionOnTheLeft(Index i, Index j)
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| 172 | {
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| 173 | eigen_assert(i>=0 && j>=0 && i<size() && j<size());
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| 174 | for(Index k = 0; k < size(); ++k)
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| 175 | {
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| 176 | if(indices().coeff(k) == i) indices().coeffRef(k) = j;
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| 177 | else if(indices().coeff(k) == j) indices().coeffRef(k) = i;
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| 178 | }
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| 179 | return derived();
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| 180 | }
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| 181 |
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| 182 | /** Multiplies *this by the transposition \f$(ij)\f$ on the right.
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| 183 | *
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| 184 | * \returns a reference to *this.
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| 185 | *
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| 186 | * This is a fast operation, it only consists in swapping two indices.
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| 187 | *
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| 188 | * \sa applyTranspositionOnTheLeft(int,int)
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| 189 | */
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| 190 | Derived& applyTranspositionOnTheRight(Index i, Index j)
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| 191 | {
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| 192 | eigen_assert(i>=0 && j>=0 && i<size() && j<size());
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| 193 | std::swap(indices().coeffRef(i), indices().coeffRef(j));
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| 194 | return derived();
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| 195 | }
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| 196 |
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| 197 | /** \returns the inverse permutation matrix.
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| 198 | *
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| 199 | * \note \note_try_to_help_rvo
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| 200 | */
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| 201 | inline Transpose<PermutationBase> inverse() const
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| 202 | { return derived(); }
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| 203 | /** \returns the tranpose permutation matrix.
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| 204 | *
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| 205 | * \note \note_try_to_help_rvo
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| 206 | */
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| 207 | inline Transpose<PermutationBase> transpose() const
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| 208 | { return derived(); }
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| 209 |
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| 210 | /**** multiplication helpers to hopefully get RVO ****/
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| 211 |
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| 212 |
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| 213 | #ifndef EIGEN_PARSED_BY_DOXYGEN
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| 214 | protected:
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| 215 | template<typename OtherDerived>
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| 216 | void assignTranspose(const PermutationBase<OtherDerived>& other)
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| 217 | {
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| 218 | for (int i=0; i<rows();++i) indices().coeffRef(other.indices().coeff(i)) = i;
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| 219 | }
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| 220 | template<typename Lhs,typename Rhs>
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| 221 | void assignProduct(const Lhs& lhs, const Rhs& rhs)
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| 222 | {
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| 223 | eigen_assert(lhs.cols() == rhs.rows());
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| 224 | for (int i=0; i<rows();++i) indices().coeffRef(i) = lhs.indices().coeff(rhs.indices().coeff(i));
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| 225 | }
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| 226 | #endif
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| 227 |
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| 228 | public:
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| 229 |
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| 230 | /** \returns the product permutation matrix.
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| 231 | *
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| 232 | * \note \note_try_to_help_rvo
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| 233 | */
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| 234 | template<typename Other>
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| 235 | inline PlainPermutationType operator*(const PermutationBase<Other>& other) const
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| 236 | { return PlainPermutationType(internal::PermPermProduct, derived(), other.derived()); }
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| 237 |
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| 238 | /** \returns the product of a permutation with another inverse permutation.
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| 239 | *
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| 240 | * \note \note_try_to_help_rvo
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| 241 | */
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| 242 | template<typename Other>
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| 243 | inline PlainPermutationType operator*(const Transpose<PermutationBase<Other> >& other) const
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| 244 | { return PlainPermutationType(internal::PermPermProduct, *this, other.eval()); }
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| 245 |
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| 246 | /** \returns the product of an inverse permutation with another permutation.
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| 247 | *
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| 248 | * \note \note_try_to_help_rvo
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| 249 | */
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| 250 | template<typename Other> friend
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| 251 | inline PlainPermutationType operator*(const Transpose<PermutationBase<Other> >& other, const PermutationBase& perm)
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| 252 | { return PlainPermutationType(internal::PermPermProduct, other.eval(), perm); }
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| 253 |
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| 254 | /** \returns the determinant of the permutation matrix, which is either 1 or -1 depending on the parity of the permutation.
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| 255 | *
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| 256 | * This function is O(\c n) procedure allocating a buffer of \c n booleans.
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| 257 | */
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| 258 | Index determinant() const
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| 259 | {
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| 260 | Index res = 1;
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| 261 | Index n = size();
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| 262 | Matrix<bool,RowsAtCompileTime,1,0,MaxRowsAtCompileTime> mask(n);
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| 263 | mask.fill(false);
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| 264 | Index r = 0;
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| 265 | while(r < n)
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| 266 | {
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| 267 | // search for the next seed
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| 268 | while(r<n && mask[r]) r++;
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| 269 | if(r>=n)
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| 270 | break;
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| 271 | // we got one, let's follow it until we are back to the seed
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| 272 | Index k0 = r++;
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| 273 | mask.coeffRef(k0) = true;
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| 274 | for(Index k=indices().coeff(k0); k!=k0; k=indices().coeff(k))
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| 275 | {
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| 276 | mask.coeffRef(k) = true;
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| 277 | res = -res;
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| 278 | }
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| 279 | }
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| 280 | return res;
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| 281 | }
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| 282 |
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| 283 | protected:
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| 284 |
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| 285 | };
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| 286 |
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| 287 | /** \class PermutationMatrix
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| 288 | * \ingroup Core_Module
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| 289 | *
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| 290 | * \brief Permutation matrix
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| 291 | *
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| 292 | * \param SizeAtCompileTime the number of rows/cols, or Dynamic
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| 293 | * \param MaxSizeAtCompileTime the maximum number of rows/cols, or Dynamic. This optional parameter defaults to SizeAtCompileTime. Most of the time, you should not have to specify it.
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| 294 | * \param IndexType the interger type of the indices
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| 295 | *
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| 296 | * This class represents a permutation matrix, internally stored as a vector of integers.
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| 297 | *
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| 298 | * \sa class PermutationBase, class PermutationWrapper, class DiagonalMatrix
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| 299 | */
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| 300 |
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| 301 | namespace internal {
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| 302 | template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType>
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| 303 | struct traits<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType> >
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| 304 | : traits<Matrix<IndexType,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
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| 305 | {
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| 306 | typedef IndexType Index;
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| 307 | typedef Matrix<IndexType, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1> IndicesType;
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| 308 | };
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| 309 | }
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| 310 |
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| 311 | template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType>
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| 312 | class PermutationMatrix : public PermutationBase<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType> >
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| 313 | {
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| 314 | typedef PermutationBase<PermutationMatrix> Base;
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| 315 | typedef internal::traits<PermutationMatrix> Traits;
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| 316 | public:
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| 317 |
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| 318 | #ifndef EIGEN_PARSED_BY_DOXYGEN
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| 319 | typedef typename Traits::IndicesType IndicesType;
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| 320 | #endif
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| 321 |
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| 322 | inline PermutationMatrix()
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| 323 | {}
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| 324 |
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| 325 | /** Constructs an uninitialized permutation matrix of given size.
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| 326 | */
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| 327 | inline PermutationMatrix(int size) : m_indices(size)
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| 328 | {}
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| 329 |
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| 330 | /** Copy constructor. */
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| 331 | template<typename OtherDerived>
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| 332 | inline PermutationMatrix(const PermutationBase<OtherDerived>& other)
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| 333 | : m_indices(other.indices()) {}
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| 334 |
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| 335 | #ifndef EIGEN_PARSED_BY_DOXYGEN
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| 336 | /** Standard copy constructor. Defined only to prevent a default copy constructor
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| 337 | * from hiding the other templated constructor */
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| 338 | inline PermutationMatrix(const PermutationMatrix& other) : m_indices(other.indices()) {}
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| 339 | #endif
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| 340 |
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| 341 | /** Generic constructor from expression of the indices. The indices
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| 342 | * array has the meaning that the permutations sends each integer i to indices[i].
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| 343 | *
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| 344 | * \warning It is your responsibility to check that the indices array that you passes actually
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| 345 | * describes a permutation, i.e., each value between 0 and n-1 occurs exactly once, where n is the
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| 346 | * array's size.
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| 347 | */
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| 348 | template<typename Other>
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| 349 | explicit inline PermutationMatrix(const MatrixBase<Other>& a_indices) : m_indices(a_indices)
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| 350 | {}
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| 351 |
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| 352 | /** Convert the Transpositions \a tr to a permutation matrix */
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| 353 | template<typename Other>
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| 354 | explicit PermutationMatrix(const TranspositionsBase<Other>& tr)
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| 355 | : m_indices(tr.size())
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| 356 | {
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| 357 | *this = tr;
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| 358 | }
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| 359 |
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| 360 | /** Copies the other permutation into *this */
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| 361 | template<typename Other>
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| 362 | PermutationMatrix& operator=(const PermutationBase<Other>& other)
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| 363 | {
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| 364 | m_indices = other.indices();
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| 365 | return *this;
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| 366 | }
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| 367 |
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| 368 | /** Assignment from the Transpositions \a tr */
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| 369 | template<typename Other>
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| 370 | PermutationMatrix& operator=(const TranspositionsBase<Other>& tr)
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| 371 | {
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| 372 | return Base::operator=(tr.derived());
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| 373 | }
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| 374 |
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| 375 | #ifndef EIGEN_PARSED_BY_DOXYGEN
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| 376 | /** This is a special case of the templated operator=. Its purpose is to
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| 377 | * prevent a default operator= from hiding the templated operator=.
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| 378 | */
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| 379 | PermutationMatrix& operator=(const PermutationMatrix& other)
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| 380 | {
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| 381 | m_indices = other.m_indices;
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| 382 | return *this;
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| 383 | }
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| 384 | #endif
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| 385 |
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| 386 | /** const version of indices(). */
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| 387 | const IndicesType& indices() const { return m_indices; }
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| 388 | /** \returns a reference to the stored array representing the permutation. */
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| 389 | IndicesType& indices() { return m_indices; }
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| 390 |
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| 391 |
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| 392 | /**** multiplication helpers to hopefully get RVO ****/
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| 393 |
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| 394 | #ifndef EIGEN_PARSED_BY_DOXYGEN
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| 395 | template<typename Other>
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| 396 | PermutationMatrix(const Transpose<PermutationBase<Other> >& other)
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| 397 | : m_indices(other.nestedPermutation().size())
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| 398 | {
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| 399 | for (int i=0; i<m_indices.size();++i) m_indices.coeffRef(other.nestedPermutation().indices().coeff(i)) = i;
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| 400 | }
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| 401 | template<typename Lhs,typename Rhs>
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| 402 | PermutationMatrix(internal::PermPermProduct_t, const Lhs& lhs, const Rhs& rhs)
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| 403 | : m_indices(lhs.indices().size())
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| 404 | {
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| 405 | Base::assignProduct(lhs,rhs);
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| 406 | }
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| 407 | #endif
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| 408 |
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| 409 | protected:
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| 410 |
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| 411 | IndicesType m_indices;
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| 412 | };
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| 413 |
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| 414 |
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| 415 | namespace internal {
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| 416 | template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType, int _PacketAccess>
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| 417 | struct traits<Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType>,_PacketAccess> >
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| 418 | : traits<Matrix<IndexType,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
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| 419 | {
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| 420 | typedef IndexType Index;
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| 421 | typedef Map<const Matrix<IndexType, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1>, _PacketAccess> IndicesType;
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| 422 | };
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| 423 | }
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| 424 |
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| 425 | template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType, int _PacketAccess>
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| 426 | class Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType>,_PacketAccess>
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| 427 | : public PermutationBase<Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType>,_PacketAccess> >
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| 428 | {
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| 429 | typedef PermutationBase<Map> Base;
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| 430 | typedef internal::traits<Map> Traits;
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| 431 | public:
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| 432 |
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| 433 | #ifndef EIGEN_PARSED_BY_DOXYGEN
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| 434 | typedef typename Traits::IndicesType IndicesType;
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| 435 | typedef typename IndicesType::Scalar Index;
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| 436 | #endif
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| 437 |
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| 438 | inline Map(const Index* indicesPtr)
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| 439 | : m_indices(indicesPtr)
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| 440 | {}
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| 441 |
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| 442 | inline Map(const Index* indicesPtr, Index size)
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| 443 | : m_indices(indicesPtr,size)
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| 444 | {}
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| 445 |
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| 446 | /** Copies the other permutation into *this */
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| 447 | template<typename Other>
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| 448 | Map& operator=(const PermutationBase<Other>& other)
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| 449 | { return Base::operator=(other.derived()); }
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| 450 |
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| 451 | /** Assignment from the Transpositions \a tr */
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| 452 | template<typename Other>
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| 453 | Map& operator=(const TranspositionsBase<Other>& tr)
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| 454 | { return Base::operator=(tr.derived()); }
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| 455 |
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| 456 | #ifndef EIGEN_PARSED_BY_DOXYGEN
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| 457 | /** This is a special case of the templated operator=. Its purpose is to
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| 458 | * prevent a default operator= from hiding the templated operator=.
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| 459 | */
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| 460 | Map& operator=(const Map& other)
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| 461 | {
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| 462 | m_indices = other.m_indices;
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| 463 | return *this;
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| 464 | }
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| 465 | #endif
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| 466 |
|
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| 467 | /** const version of indices(). */
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| 468 | const IndicesType& indices() const { return m_indices; }
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| 469 | /** \returns a reference to the stored array representing the permutation. */
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| 470 | IndicesType& indices() { return m_indices; }
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| 471 |
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| 472 | protected:
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| 473 |
|
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| 474 | IndicesType m_indices;
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| 475 | };
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| 476 |
|
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| 477 | /** \class PermutationWrapper
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| 478 | * \ingroup Core_Module
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| 479 | *
|
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| 480 | * \brief Class to view a vector of integers as a permutation matrix
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| 481 | *
|
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| 482 | * \param _IndicesType the type of the vector of integer (can be any compatible expression)
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| 483 | *
|
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| 484 | * This class allows to view any vector expression of integers as a permutation matrix.
|
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| 485 | *
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| 486 | * \sa class PermutationBase, class PermutationMatrix
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| 487 | */
|
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| 488 |
|
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| 489 | struct PermutationStorage {};
|
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| 490 |
|
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| 491 | template<typename _IndicesType> class TranspositionsWrapper;
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| 492 | namespace internal {
|
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| 493 | template<typename _IndicesType>
|
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| 494 | struct traits<PermutationWrapper<_IndicesType> >
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| 495 | {
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| 496 | typedef PermutationStorage StorageKind;
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| 497 | typedef typename _IndicesType::Scalar Scalar;
|
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| 498 | typedef typename _IndicesType::Scalar Index;
|
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| 499 | typedef _IndicesType IndicesType;
|
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| 500 | enum {
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| 501 | RowsAtCompileTime = _IndicesType::SizeAtCompileTime,
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| 502 | ColsAtCompileTime = _IndicesType::SizeAtCompileTime,
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| 503 | MaxRowsAtCompileTime = IndicesType::MaxRowsAtCompileTime,
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| 504 | MaxColsAtCompileTime = IndicesType::MaxColsAtCompileTime,
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| 505 | Flags = 0,
|
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| 506 | CoeffReadCost = _IndicesType::CoeffReadCost
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| 507 | };
|
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| 508 | };
|
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| 509 | }
|
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| 510 |
|
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| 511 | template<typename _IndicesType>
|
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| 512 | class PermutationWrapper : public PermutationBase<PermutationWrapper<_IndicesType> >
|
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| 513 | {
|
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| 514 | typedef PermutationBase<PermutationWrapper> Base;
|
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| 515 | typedef internal::traits<PermutationWrapper> Traits;
|
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| 516 | public:
|
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| 517 |
|
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| 518 | #ifndef EIGEN_PARSED_BY_DOXYGEN
|
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| 519 | typedef typename Traits::IndicesType IndicesType;
|
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| 520 | #endif
|
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| 521 |
|
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| 522 | inline PermutationWrapper(const IndicesType& a_indices)
|
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| 523 | : m_indices(a_indices)
|
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| 524 | {}
|
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| 525 |
|
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| 526 | /** const version of indices(). */
|
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| 527 | const typename internal::remove_all<typename IndicesType::Nested>::type&
|
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| 528 | indices() const { return m_indices; }
|
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| 529 |
|
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| 530 | protected:
|
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| 531 |
|
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| 532 | typename IndicesType::Nested m_indices;
|
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| 533 | };
|
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| 534 |
|
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| 535 | /** \returns the matrix with the permutation applied to the columns.
|
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| 536 | */
|
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| 537 | template<typename Derived, typename PermutationDerived>
|
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| 538 | inline const internal::permut_matrix_product_retval<PermutationDerived, Derived, OnTheRight>
|
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| 539 | operator*(const MatrixBase<Derived>& matrix,
|
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| 540 | const PermutationBase<PermutationDerived> &permutation)
|
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| 541 | {
|
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| 542 | return internal::permut_matrix_product_retval
|
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| 543 | <PermutationDerived, Derived, OnTheRight>
|
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| 544 | (permutation.derived(), matrix.derived());
|
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| 545 | }
|
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| 546 |
|
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| 547 | /** \returns the matrix with the permutation applied to the rows.
|
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| 548 | */
|
---|
| 549 | template<typename Derived, typename PermutationDerived>
|
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| 550 | inline const internal::permut_matrix_product_retval
|
---|
| 551 | <PermutationDerived, Derived, OnTheLeft>
|
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| 552 | operator*(const PermutationBase<PermutationDerived> &permutation,
|
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| 553 | const MatrixBase<Derived>& matrix)
|
---|
| 554 | {
|
---|
| 555 | return internal::permut_matrix_product_retval
|
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| 556 | <PermutationDerived, Derived, OnTheLeft>
|
---|
| 557 | (permutation.derived(), matrix.derived());
|
---|
| 558 | }
|
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| 559 |
|
---|
| 560 | namespace internal {
|
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| 561 |
|
---|
| 562 | template<typename PermutationType, typename MatrixType, int Side, bool Transposed>
|
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| 563 | struct traits<permut_matrix_product_retval<PermutationType, MatrixType, Side, Transposed> >
|
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| 564 | {
|
---|
| 565 | typedef typename MatrixType::PlainObject ReturnType;
|
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| 566 | };
|
---|
| 567 |
|
---|
| 568 | template<typename PermutationType, typename MatrixType, int Side, bool Transposed>
|
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| 569 | struct permut_matrix_product_retval
|
---|
| 570 | : public ReturnByValue<permut_matrix_product_retval<PermutationType, MatrixType, Side, Transposed> >
|
---|
| 571 | {
|
---|
| 572 | typedef typename remove_all<typename MatrixType::Nested>::type MatrixTypeNestedCleaned;
|
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| 573 | typedef typename MatrixType::Index Index;
|
---|
| 574 |
|
---|
| 575 | permut_matrix_product_retval(const PermutationType& perm, const MatrixType& matrix)
|
---|
| 576 | : m_permutation(perm), m_matrix(matrix)
|
---|
| 577 | {}
|
---|
| 578 |
|
---|
| 579 | inline Index rows() const { return m_matrix.rows(); }
|
---|
| 580 | inline Index cols() const { return m_matrix.cols(); }
|
---|
| 581 |
|
---|
| 582 | template<typename Dest> inline void evalTo(Dest& dst) const
|
---|
| 583 | {
|
---|
| 584 | const Index n = Side==OnTheLeft ? rows() : cols();
|
---|
| 585 | // FIXME we need an is_same for expression that is not sensitive to constness. For instance
|
---|
| 586 | // is_same_xpr<Block<const Matrix>, Block<Matrix> >::value should be true.
|
---|
| 587 | const typename Dest::Scalar *dst_data = internal::extract_data(dst);
|
---|
| 588 | if( is_same<MatrixTypeNestedCleaned,Dest>::value
|
---|
| 589 | && blas_traits<MatrixTypeNestedCleaned>::HasUsableDirectAccess
|
---|
| 590 | && blas_traits<Dest>::HasUsableDirectAccess
|
---|
| 591 | && dst_data!=0 && dst_data == extract_data(m_matrix))
|
---|
| 592 | {
|
---|
| 593 | // apply the permutation inplace
|
---|
| 594 | Matrix<bool,PermutationType::RowsAtCompileTime,1,0,PermutationType::MaxRowsAtCompileTime> mask(m_permutation.size());
|
---|
| 595 | mask.fill(false);
|
---|
| 596 | Index r = 0;
|
---|
| 597 | while(r < m_permutation.size())
|
---|
| 598 | {
|
---|
| 599 | // search for the next seed
|
---|
| 600 | while(r<m_permutation.size() && mask[r]) r++;
|
---|
| 601 | if(r>=m_permutation.size())
|
---|
| 602 | break;
|
---|
| 603 | // we got one, let's follow it until we are back to the seed
|
---|
| 604 | Index k0 = r++;
|
---|
| 605 | Index kPrev = k0;
|
---|
| 606 | mask.coeffRef(k0) = true;
|
---|
| 607 | for(Index k=m_permutation.indices().coeff(k0); k!=k0; k=m_permutation.indices().coeff(k))
|
---|
| 608 | {
|
---|
| 609 | Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>(dst, k)
|
---|
| 610 | .swap(Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>
|
---|
| 611 | (dst,((Side==OnTheLeft) ^ Transposed) ? k0 : kPrev));
|
---|
| 612 |
|
---|
| 613 | mask.coeffRef(k) = true;
|
---|
| 614 | kPrev = k;
|
---|
| 615 | }
|
---|
| 616 | }
|
---|
| 617 | }
|
---|
| 618 | else
|
---|
| 619 | {
|
---|
| 620 | for(int i = 0; i < n; ++i)
|
---|
| 621 | {
|
---|
| 622 | Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>
|
---|
| 623 | (dst, ((Side==OnTheLeft) ^ Transposed) ? m_permutation.indices().coeff(i) : i)
|
---|
| 624 |
|
---|
| 625 | =
|
---|
| 626 |
|
---|
| 627 | Block<const MatrixTypeNestedCleaned,Side==OnTheLeft ? 1 : MatrixType::RowsAtCompileTime,Side==OnTheRight ? 1 : MatrixType::ColsAtCompileTime>
|
---|
| 628 | (m_matrix, ((Side==OnTheRight) ^ Transposed) ? m_permutation.indices().coeff(i) : i);
|
---|
| 629 | }
|
---|
| 630 | }
|
---|
| 631 | }
|
---|
| 632 |
|
---|
| 633 | protected:
|
---|
| 634 | const PermutationType& m_permutation;
|
---|
| 635 | typename MatrixType::Nested m_matrix;
|
---|
| 636 | };
|
---|
| 637 |
|
---|
| 638 | /* Template partial specialization for transposed/inverse permutations */
|
---|
| 639 |
|
---|
| 640 | template<typename Derived>
|
---|
| 641 | struct traits<Transpose<PermutationBase<Derived> > >
|
---|
| 642 | : traits<Derived>
|
---|
| 643 | {};
|
---|
| 644 |
|
---|
| 645 | } // end namespace internal
|
---|
| 646 |
|
---|
| 647 | template<typename Derived>
|
---|
| 648 | class Transpose<PermutationBase<Derived> >
|
---|
| 649 | : public EigenBase<Transpose<PermutationBase<Derived> > >
|
---|
| 650 | {
|
---|
| 651 | typedef Derived PermutationType;
|
---|
| 652 | typedef typename PermutationType::IndicesType IndicesType;
|
---|
| 653 | typedef typename PermutationType::PlainPermutationType PlainPermutationType;
|
---|
| 654 | public:
|
---|
| 655 |
|
---|
| 656 | #ifndef EIGEN_PARSED_BY_DOXYGEN
|
---|
| 657 | typedef internal::traits<PermutationType> Traits;
|
---|
| 658 | typedef typename Derived::DenseMatrixType DenseMatrixType;
|
---|
| 659 | enum {
|
---|
| 660 | Flags = Traits::Flags,
|
---|
| 661 | CoeffReadCost = Traits::CoeffReadCost,
|
---|
| 662 | RowsAtCompileTime = Traits::RowsAtCompileTime,
|
---|
| 663 | ColsAtCompileTime = Traits::ColsAtCompileTime,
|
---|
| 664 | MaxRowsAtCompileTime = Traits::MaxRowsAtCompileTime,
|
---|
| 665 | MaxColsAtCompileTime = Traits::MaxColsAtCompileTime
|
---|
| 666 | };
|
---|
| 667 | typedef typename Traits::Scalar Scalar;
|
---|
| 668 | #endif
|
---|
| 669 |
|
---|
| 670 | Transpose(const PermutationType& p) : m_permutation(p) {}
|
---|
| 671 |
|
---|
| 672 | inline int rows() const { return m_permutation.rows(); }
|
---|
| 673 | inline int cols() const { return m_permutation.cols(); }
|
---|
| 674 |
|
---|
| 675 | #ifndef EIGEN_PARSED_BY_DOXYGEN
|
---|
| 676 | template<typename DenseDerived>
|
---|
| 677 | void evalTo(MatrixBase<DenseDerived>& other) const
|
---|
| 678 | {
|
---|
| 679 | other.setZero();
|
---|
| 680 | for (int i=0; i<rows();++i)
|
---|
| 681 | other.coeffRef(i, m_permutation.indices().coeff(i)) = typename DenseDerived::Scalar(1);
|
---|
| 682 | }
|
---|
| 683 | #endif
|
---|
| 684 |
|
---|
| 685 | /** \return the equivalent permutation matrix */
|
---|
| 686 | PlainPermutationType eval() const { return *this; }
|
---|
| 687 |
|
---|
| 688 | DenseMatrixType toDenseMatrix() const { return *this; }
|
---|
| 689 |
|
---|
| 690 | /** \returns the matrix with the inverse permutation applied to the columns.
|
---|
| 691 | */
|
---|
| 692 | template<typename OtherDerived> friend
|
---|
| 693 | inline const internal::permut_matrix_product_retval<PermutationType, OtherDerived, OnTheRight, true>
|
---|
| 694 | operator*(const MatrixBase<OtherDerived>& matrix, const Transpose& trPerm)
|
---|
| 695 | {
|
---|
| 696 | return internal::permut_matrix_product_retval<PermutationType, OtherDerived, OnTheRight, true>(trPerm.m_permutation, matrix.derived());
|
---|
| 697 | }
|
---|
| 698 |
|
---|
| 699 | /** \returns the matrix with the inverse permutation applied to the rows.
|
---|
| 700 | */
|
---|
| 701 | template<typename OtherDerived>
|
---|
| 702 | inline const internal::permut_matrix_product_retval<PermutationType, OtherDerived, OnTheLeft, true>
|
---|
| 703 | operator*(const MatrixBase<OtherDerived>& matrix) const
|
---|
| 704 | {
|
---|
| 705 | return internal::permut_matrix_product_retval<PermutationType, OtherDerived, OnTheLeft, true>(m_permutation, matrix.derived());
|
---|
| 706 | }
|
---|
| 707 |
|
---|
| 708 | const PermutationType& nestedPermutation() const { return m_permutation; }
|
---|
| 709 |
|
---|
| 710 | protected:
|
---|
| 711 | const PermutationType& m_permutation;
|
---|
| 712 | };
|
---|
| 713 |
|
---|
| 714 | template<typename Derived>
|
---|
| 715 | const PermutationWrapper<const Derived> MatrixBase<Derived>::asPermutation() const
|
---|
| 716 | {
|
---|
| 717 | return derived();
|
---|
| 718 | }
|
---|
| 719 |
|
---|
| 720 | } // end namespace Eigen
|
---|
| 721 |
|
---|
| 722 | #endif // EIGEN_PERMUTATIONMATRIX_H
|
---|