Eigen/src/Core/PermutationMatrix.h - mirror - Git at Google

 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
 // Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
 // Copyright (C) 2009-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

 #ifndef EIGEN_PERMUTATIONMATRIX_H
 #define EIGEN_PERMUTATIONMATRIX_H

 // IWYU pragma: private
 #include "./InternalHeaderCheck.h"

 namespace Eigen {

 namespace internal {

 enum PermPermProduct_t { PermPermProduct };

 }  // end namespace internal

 /** \class PermutationBase
  * \ingroup Core_Module
  *
  * \brief Base class for permutations
  *
  * \tparam Derived the derived class
  *
  * This class is the base class for all expressions representing a permutation matrix,
  * internally stored as a vector of integers.
  * The convention followed here is that if \f$ \sigma \f$ is a permutation, the corresponding permutation matrix
  * \f$ P_\sigma \f$ is such that if \f$ (e_1,\ldots,e_p) \f$ is the canonical basis, we have:
  *  \f[ P_\sigma(e_i) = e_{\sigma(i)}. \f]
  * This convention ensures that for any two permutations \f$ \sigma, \tau \f$, we have:
  *  \f[ P_{\sigma\circ\tau} = P_\sigma P_\tau. \f]
  *
  * Permutation matrices are square and invertible.
  *
  * Notice that in addition to the member functions and operators listed here, there also are non-member
  * operator* to multiply any kind of permutation object with any kind of matrix expression (MatrixBase)
  * on either side.
  *
  * \sa class PermutationMatrix, class PermutationWrapper
  */
 template <typename Derived>
 class PermutationBase : public EigenBase<Derived> {
   typedef internal::traits<Derived> Traits;
   typedef EigenBase<Derived> Base;

  public:
 #ifndef EIGEN_PARSED_BY_DOXYGEN
   typedef typename Traits::IndicesType IndicesType;
   enum {
     Flags = Traits::Flags,
     RowsAtCompileTime = Traits::RowsAtCompileTime,
     ColsAtCompileTime = Traits::ColsAtCompileTime,
     MaxRowsAtCompileTime = Traits::MaxRowsAtCompileTime,
     MaxColsAtCompileTime = Traits::MaxColsAtCompileTime
   };
   typedef typename Traits::StorageIndex StorageIndex;
   typedef Matrix<StorageIndex, RowsAtCompileTime, ColsAtCompileTime, 0, MaxRowsAtCompileTime, MaxColsAtCompileTime>
       DenseMatrixType;
   typedef PermutationMatrix<IndicesType::SizeAtCompileTime, IndicesType::MaxSizeAtCompileTime, StorageIndex>
       PlainPermutationType;
   typedef PlainPermutationType PlainObject;
   using Base::derived;
   typedef Inverse<Derived> InverseReturnType;
   typedef void Scalar;
 #endif

   /** Copies the other permutation into *this */
   template <typename OtherDerived>
   Derived& operator=(const PermutationBase<OtherDerived>& other) {
     indices() = other.indices();
     return derived();
   }

   /** Assignment from the Transpositions \a tr */
   template <typename OtherDerived>
   Derived& operator=(const TranspositionsBase<OtherDerived>& tr) {
     setIdentity(tr.size());
     for (Index k = size() - 1; k >= 0; --k) applyTranspositionOnTheRight(k, tr.coeff(k));
     return derived();
   }

   /** \returns the number of rows */
   inline EIGEN_DEVICE_FUNC Index rows() const { return Index(indices().size()); }

   /** \returns the number of columns */
   inline EIGEN_DEVICE_FUNC Index cols() const { return Index(indices().size()); }

   /** \returns the size of a side of the respective square matrix, i.e., the number of indices */
   inline EIGEN_DEVICE_FUNC Index size() const { return Index(indices().size()); }

 #ifndef EIGEN_PARSED_BY_DOXYGEN
   template <typename DenseDerived>
   void evalTo(MatrixBase<DenseDerived>& other) const {
     other.setZero();
     for (Index i = 0; i < rows(); ++i) other.coeffRef(indices().coeff(i), i) = typename DenseDerived::Scalar(1);
   }
 #endif

   /** \returns a Matrix object initialized from this permutation matrix. Notice that it
    * is inefficient to return this Matrix object by value. For efficiency, favor using
    * the Matrix constructor taking EigenBase objects.
    */
   DenseMatrixType toDenseMatrix() const { return derived(); }

   /** const version of indices(). */
   const IndicesType& indices() const { return derived().indices(); }
   /** \returns a reference to the stored array representing the permutation. */
   IndicesType& indices() { return derived().indices(); }

   /** Resizes to given size.
    */
   inline void resize(Index newSize) { indices().resize(newSize); }

   /** Sets *this to be the identity permutation matrix */
   void setIdentity() {
     StorageIndex n = StorageIndex(size());
     for (StorageIndex i = 0; i < n; ++i) indices().coeffRef(i) = i;
   }

   /** Sets *this to be the identity permutation matrix of given size.
    */
   void setIdentity(Index newSize) {
     resize(newSize);
     setIdentity();
   }

   /** Multiplies *this by the transposition \f$(ij)\f$ on the left.
    *
    * \returns a reference to *this.
    *
    * \warning This is much slower than applyTranspositionOnTheRight(Index,Index):
    * this has linear complexity and requires a lot of branching.
    *
    * \sa applyTranspositionOnTheRight(Index,Index)
    */
   Derived& applyTranspositionOnTheLeft(Index i, Index j) {
     eigen_assert(i >= 0 && j >= 0 && i < size() && j < size());
     for (Index k = 0; k < size(); ++k) {
       if (indices().coeff(k) == i)
         indices().coeffRef(k) = StorageIndex(j);
       else if (indices().coeff(k) == j)
         indices().coeffRef(k) = StorageIndex(i);
     }
     return derived();
   }

   /** Multiplies *this by the transposition \f$(ij)\f$ on the right.
    *
    * \returns a reference to *this.
    *
    * This is a fast operation, it only consists in swapping two indices.
    *
    * \sa applyTranspositionOnTheLeft(Index,Index)
    */
   Derived& applyTranspositionOnTheRight(Index i, Index j) {
     eigen_assert(i >= 0 && j >= 0 && i < size() && j < size());
     std::swap(indices().coeffRef(i), indices().coeffRef(j));
     return derived();
   }

   /** \returns the inverse permutation matrix.
    *
    * \note \blank \note_try_to_help_rvo
    */
   inline InverseReturnType inverse() const { return InverseReturnType(derived()); }
   /** \returns the tranpose permutation matrix.
    *
    * \note \blank \note_try_to_help_rvo
    */
   inline InverseReturnType transpose() const { return InverseReturnType(derived()); }

   /**** multiplication helpers to hopefully get RVO ****/

 #ifndef EIGEN_PARSED_BY_DOXYGEN
  protected:
   template <typename OtherDerived>
   void assignTranspose(const PermutationBase<OtherDerived>& other) {
     for (Index i = 0; i < rows(); ++i) indices().coeffRef(other.indices().coeff(i)) = i;
   }
   template <typename Lhs, typename Rhs>
   void assignProduct(const Lhs& lhs, const Rhs& rhs) {
     eigen_assert(lhs.cols() == rhs.rows());
     for (Index i = 0; i < rows(); ++i) indices().coeffRef(i) = lhs.indices().coeff(rhs.indices().coeff(i));
   }
 #endif

  public:
   /** \returns the product permutation matrix.
    *
    * \note \blank \note_try_to_help_rvo
    */
   template <typename Other>
   inline PlainPermutationType operator*(const PermutationBase<Other>& other) const {
     return PlainPermutationType(internal::PermPermProduct, derived(), other.derived());
   }

   /** \returns the product of a permutation with another inverse permutation.
    *
    * \note \blank \note_try_to_help_rvo
    */
   template <typename Other>
   inline PlainPermutationType operator*(const InverseImpl<Other, PermutationStorage>& other) const {
     return PlainPermutationType(internal::PermPermProduct, *this, other.eval());
   }

   /** \returns the product of an inverse permutation with another permutation.
    *
    * \note \blank \note_try_to_help_rvo
    */
   template <typename Other>
   friend inline PlainPermutationType operator*(const InverseImpl<Other, PermutationStorage>& other,
                                                const PermutationBase& perm) {
     return PlainPermutationType(internal::PermPermProduct, other.eval(), perm);
   }

   /** \returns the determinant of the permutation matrix, which is either 1 or -1 depending on the parity of the
    * permutation.
    *
    * This function is O(\c n) procedure allocating a buffer of \c n booleans.
    */
   Index determinant() const {
     Index res = 1;
     Index n = size();
     Matrix<bool, RowsAtCompileTime, 1, 0, MaxRowsAtCompileTime> mask(n);
     mask.fill(false);
     Index r = 0;
     while (r < n) {
       // search for the next seed
       while (r < n && mask[r]) r++;
       if (r >= n) break;
       // we got one, let's follow it until we are back to the seed
       Index k0 = r++;
       mask.coeffRef(k0) = true;
       for (Index k = indices().coeff(k0); k != k0; k = indices().coeff(k)) {
         mask.coeffRef(k) = true;
         res = -res;
       }
     }
     return res;
   }

  protected:
 };

 namespace internal {
 template <int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_>
 struct traits<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_> >
     : traits<
           Matrix<StorageIndex_, SizeAtCompileTime, SizeAtCompileTime, 0, MaxSizeAtCompileTime, MaxSizeAtCompileTime> > {
   typedef PermutationStorage StorageKind;
   typedef Matrix<StorageIndex_, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1> IndicesType;
   typedef StorageIndex_ StorageIndex;
   typedef void Scalar;
 };
 }  // namespace internal

 /** \class PermutationMatrix
  * \ingroup Core_Module
  *
  * \brief Permutation matrix
  *
  * \tparam SizeAtCompileTime the number of rows/cols, or Dynamic
  * \tparam 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. \tparam StorageIndex_ the integer type of the
  * indices
  *
  * This class represents a permutation matrix, internally stored as a vector of integers.
  *
  * \sa class PermutationBase, class PermutationWrapper, class DiagonalMatrix
  */
 template <int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_>
 class PermutationMatrix
     : public PermutationBase<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_> > {
   typedef PermutationBase<PermutationMatrix> Base;
   typedef internal::traits<PermutationMatrix> Traits;

  public:
   typedef const PermutationMatrix& Nested;

 #ifndef EIGEN_PARSED_BY_DOXYGEN
   typedef typename Traits::IndicesType IndicesType;
   typedef typename Traits::StorageIndex StorageIndex;
 #endif

   inline PermutationMatrix() {}

   /** Constructs an uninitialized permutation matrix of given size.
    */
   explicit inline PermutationMatrix(Index size) : m_indices(size) {
     eigen_internal_assert(size <= NumTraits<StorageIndex>::highest());
   }

   /** Copy constructor. */
   template <typename OtherDerived>
   inline PermutationMatrix(const PermutationBase<OtherDerived>& other) : m_indices(other.indices()) {}

   /** Generic constructor from expression of the indices. The indices
    * array has the meaning that the permutations sends each integer i to indices[i].
    *
    * \warning It is your responsibility to check that the indices array that you passes actually
    * describes a permutation, i.e., each value between 0 and n-1 occurs exactly once, where n is the
    * array's size.
    */
   template <typename Other>
   explicit inline PermutationMatrix(const MatrixBase<Other>& indices) : m_indices(indices) {}

   /** Convert the Transpositions \a tr to a permutation matrix */
   template <typename Other>
   explicit PermutationMatrix(const TranspositionsBase<Other>& tr) : m_indices(tr.size()) {
     *this = tr;
   }

   /** Copies the other permutation into *this */
   template <typename Other>
   PermutationMatrix& operator=(const PermutationBase<Other>& other) {
     m_indices = other.indices();
     return *this;
   }

   /** Assignment from the Transpositions \a tr */
   template <typename Other>
   PermutationMatrix& operator=(const TranspositionsBase<Other>& tr) {
     return Base::operator=(tr.derived());
   }

   /** const version of indices(). */
   const IndicesType& indices() const { return m_indices; }
   /** \returns a reference to the stored array representing the permutation. */
   IndicesType& indices() { return m_indices; }

   /**** multiplication helpers to hopefully get RVO ****/

 #ifndef EIGEN_PARSED_BY_DOXYGEN
   template <typename Other>
   PermutationMatrix(const InverseImpl<Other, PermutationStorage>& other)
       : m_indices(other.derived().nestedExpression().size()) {
     eigen_internal_assert(m_indices.size() <= NumTraits<StorageIndex>::highest());
     StorageIndex end = StorageIndex(m_indices.size());
     for (StorageIndex i = 0; i < end; ++i)
       m_indices.coeffRef(other.derived().nestedExpression().indices().coeff(i)) = i;
   }
   template <typename Lhs, typename Rhs>
   PermutationMatrix(internal::PermPermProduct_t, const Lhs& lhs, const Rhs& rhs) : m_indices(lhs.indices().size()) {
     Base::assignProduct(lhs, rhs);
   }
 #endif

  protected:
   IndicesType m_indices;
 };

 namespace internal {
 template <int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_, int PacketAccess_>
 struct traits<Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_>, PacketAccess_> >
     : traits<
           Matrix<StorageIndex_, SizeAtCompileTime, SizeAtCompileTime, 0, MaxSizeAtCompileTime, MaxSizeAtCompileTime> > {
   typedef PermutationStorage StorageKind;
   typedef Map<const Matrix<StorageIndex_, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1>, PacketAccess_> IndicesType;
   typedef StorageIndex_ StorageIndex;
   typedef void Scalar;
 };
 }  // namespace internal

 template <int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_, int PacketAccess_>
 class Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_>, PacketAccess_>
     : public PermutationBase<
           Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_>, PacketAccess_> > {
   typedef PermutationBase<Map> Base;
   typedef internal::traits<Map> Traits;

  public:
 #ifndef EIGEN_PARSED_BY_DOXYGEN
   typedef typename Traits::IndicesType IndicesType;
   typedef typename IndicesType::Scalar StorageIndex;
 #endif

   inline Map(const StorageIndex* indicesPtr) : m_indices(indicesPtr) {}

   inline Map(const StorageIndex* indicesPtr, Index size) : m_indices(indicesPtr, size) {}

   /** Copies the other permutation into *this */
   template <typename Other>
   Map& operator=(const PermutationBase<Other>& other) {
     return Base::operator=(other.derived());
   }

   /** Assignment from the Transpositions \a tr */
   template <typename Other>
   Map& operator=(const TranspositionsBase<Other>& tr) {
     return Base::operator=(tr.derived());
   }

 #ifndef EIGEN_PARSED_BY_DOXYGEN
   /** This is a special case of the templated operator=. Its purpose is to
    * prevent a default operator= from hiding the templated operator=.
    */
   Map& operator=(const Map& other) {
     m_indices = other.m_indices;
     return *this;
   }
 #endif

   /** const version of indices(). */
   const IndicesType& indices() const { return m_indices; }
   /** \returns a reference to the stored array representing the permutation. */
   IndicesType& indices() { return m_indices; }

  protected:
   IndicesType m_indices;
 };

 template <typename IndicesType_>
 class TranspositionsWrapper;
 namespace internal {
 template <typename IndicesType_>
 struct traits<PermutationWrapper<IndicesType_> > {
   typedef PermutationStorage StorageKind;
   typedef void Scalar;
   typedef typename IndicesType_::Scalar StorageIndex;
   typedef IndicesType_ IndicesType;
   enum {
     RowsAtCompileTime = IndicesType_::SizeAtCompileTime,
     ColsAtCompileTime = IndicesType_::SizeAtCompileTime,
     MaxRowsAtCompileTime = IndicesType::MaxSizeAtCompileTime,
     MaxColsAtCompileTime = IndicesType::MaxSizeAtCompileTime,
     Flags = 0
   };
 };
 }  // namespace internal

 /** \class PermutationWrapper
  * \ingroup Core_Module
  *
  * \brief Class to view a vector of integers as a permutation matrix
  *
  * \tparam IndicesType_ the type of the vector of integer (can be any compatible expression)
  *
  * This class allows to view any vector expression of integers as a permutation matrix.
  *
  * \sa class PermutationBase, class PermutationMatrix
  */
 template <typename IndicesType_>
 class PermutationWrapper : public PermutationBase<PermutationWrapper<IndicesType_> > {
   typedef PermutationBase<PermutationWrapper> Base;
   typedef internal::traits<PermutationWrapper> Traits;

  public:
 #ifndef EIGEN_PARSED_BY_DOXYGEN
   typedef typename Traits::IndicesType IndicesType;
 #endif

   inline PermutationWrapper(const IndicesType& indices) : m_indices(indices) {}

   /** const version of indices(). */
   const internal::remove_all_t<typename IndicesType::Nested>& indices() const { return m_indices; }

  protected:
   typename IndicesType::Nested m_indices;
 };

 /** \returns the matrix with the permutation applied to the columns.
  */
 template <typename MatrixDerived, typename PermutationDerived>
 EIGEN_DEVICE_FUNC const Product<MatrixDerived, PermutationDerived, AliasFreeProduct> operator*(
     const MatrixBase<MatrixDerived>& matrix, const PermutationBase<PermutationDerived>& permutation) {
   return Product<MatrixDerived, PermutationDerived, AliasFreeProduct>(matrix.derived(), permutation.derived());
 }

 /** \returns the matrix with the permutation applied to the rows.
  */
 template <typename PermutationDerived, typename MatrixDerived>
 EIGEN_DEVICE_FUNC const Product<PermutationDerived, MatrixDerived, AliasFreeProduct> operator*(
     const PermutationBase<PermutationDerived>& permutation, const MatrixBase<MatrixDerived>& matrix) {
   return Product<PermutationDerived, MatrixDerived, AliasFreeProduct>(permutation.derived(), matrix.derived());
 }

 template <typename PermutationType>
 class InverseImpl<PermutationType, PermutationStorage> : public EigenBase<Inverse<PermutationType> > {
   typedef typename PermutationType::PlainPermutationType PlainPermutationType;
   typedef internal::traits<PermutationType> PermTraits;

  protected:
   InverseImpl() {}

  public:
   typedef Inverse<PermutationType> InverseType;
   using EigenBase<Inverse<PermutationType> >::derived;

 #ifndef EIGEN_PARSED_BY_DOXYGEN
   typedef typename PermutationType::DenseMatrixType DenseMatrixType;
   enum {
     RowsAtCompileTime = PermTraits::RowsAtCompileTime,
     ColsAtCompileTime = PermTraits::ColsAtCompileTime,
     MaxRowsAtCompileTime = PermTraits::MaxRowsAtCompileTime,
     MaxColsAtCompileTime = PermTraits::MaxColsAtCompileTime
   };
 #endif

 #ifndef EIGEN_PARSED_BY_DOXYGEN
   template <typename DenseDerived>
   void evalTo(MatrixBase<DenseDerived>& other) const {
     other.setZero();
     for (Index i = 0; i < derived().rows(); ++i)
       other.coeffRef(i, derived().nestedExpression().indices().coeff(i)) = typename DenseDerived::Scalar(1);
   }
 #endif

   /** \return the equivalent permutation matrix */
   PlainPermutationType eval() const { return derived(); }

   DenseMatrixType toDenseMatrix() const { return derived(); }

   /** \returns the matrix with the inverse permutation applied to the columns.
    */
   template <typename OtherDerived>
   friend const Product<OtherDerived, InverseType, AliasFreeProduct> operator*(const MatrixBase<OtherDerived>& matrix,
                                                                               const InverseType& trPerm) {
     return Product<OtherDerived, InverseType, AliasFreeProduct>(matrix.derived(), trPerm.derived());
   }

   /** \returns the matrix with the inverse permutation applied to the rows.
    */
   template <typename OtherDerived>
   const Product<InverseType, OtherDerived, AliasFreeProduct> operator*(const MatrixBase<OtherDerived>& matrix) const {
     return Product<InverseType, OtherDerived, AliasFreeProduct>(derived(), matrix.derived());
   }
 };

 template <typename Derived>
 const PermutationWrapper<const Derived> MatrixBase<Derived>::asPermutation() const {
   return derived();
 }

 namespace internal {

 template <>
 struct AssignmentKind<DenseShape, PermutationShape> {
   typedef EigenBase2EigenBase Kind;
 };

 }  // end namespace internal

 }  // end namespace Eigen

 #endif  // EIGEN_PERMUTATIONMATRIX_H
	// This file is part of Eigen, a lightweight C++ template library
	// for linear algebra.
	//
	// Copyright (C) 2009 Benoit Jacob <jacob.benoit.1@gmail.com>
	// Copyright (C) 2009-2015 Gael Guennebaud <gael.guennebaud@inria.fr>
	//
	// This Source Code Form is subject to the terms of the Mozilla
	// Public License v. 2.0. If a copy of the MPL was not distributed
	// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

	#ifndef EIGEN_PERMUTATIONMATRIX_H
	#define EIGEN_PERMUTATIONMATRIX_H

	// IWYU pragma: private
	#include "./InternalHeaderCheck.h"

	namespace Eigen {

	namespace internal {

	enum PermPermProduct_t { PermPermProduct };

	} // end namespace internal

	/** \class PermutationBase
	* \ingroup Core_Module
	*
	* \brief Base class for permutations
	*
	* \tparam Derived the derived class
	*
	* This class is the base class for all expressions representing a permutation matrix,
	* internally stored as a vector of integers.
	* The convention followed here is that if \f$ \sigma \f$ is a permutation, the corresponding permutation matrix
	* \f$ P_\sigma \f$ is such that if \f$ (e_1,\ldots,e_p) \f$ is the canonical basis, we have:
	* \f[ P_\sigma(e_i) = e_{\sigma(i)}. \f]
	* This convention ensures that for any two permutations \f$ \sigma, \tau \f$, we have:
	* \f[ P_{\sigma\circ\tau} = P_\sigma P_\tau. \f]
	*
	* Permutation matrices are square and invertible.
	*
	* Notice that in addition to the member functions and operators listed here, there also are non-member
	* operator* to multiply any kind of permutation object with any kind of matrix expression (MatrixBase)
	* on either side.
	*
	* \sa class PermutationMatrix, class PermutationWrapper
	*/
	template <typename Derived>
	class PermutationBase : public EigenBase<Derived> {
	typedef internal::traits<Derived> Traits;
	typedef EigenBase<Derived> Base;

	public:
	#ifndef EIGEN_PARSED_BY_DOXYGEN
	typedef typename Traits::IndicesType IndicesType;
	enum {
	Flags = Traits::Flags,
	RowsAtCompileTime = Traits::RowsAtCompileTime,
	ColsAtCompileTime = Traits::ColsAtCompileTime,
	MaxRowsAtCompileTime = Traits::MaxRowsAtCompileTime,
	MaxColsAtCompileTime = Traits::MaxColsAtCompileTime
	};
	typedef typename Traits::StorageIndex StorageIndex;
	typedef Matrix<StorageIndex, RowsAtCompileTime, ColsAtCompileTime, 0, MaxRowsAtCompileTime, MaxColsAtCompileTime>
	DenseMatrixType;
	typedef PermutationMatrix<IndicesType::SizeAtCompileTime, IndicesType::MaxSizeAtCompileTime, StorageIndex>
	PlainPermutationType;
	typedef PlainPermutationType PlainObject;
	using Base::derived;
	typedef Inverse<Derived> InverseReturnType;
	typedef void Scalar;
	#endif

	/** Copies the other permutation into this /
	template <typename OtherDerived>
	Derived& operator=(const PermutationBase<OtherDerived>& other) {
	indices() = other.indices();
	return derived();
	}

	/** Assignment from the Transpositions \a tr */
	template <typename OtherDerived>
	Derived& operator=(const TranspositionsBase<OtherDerived>& tr) {
	setIdentity(tr.size());
	for (Index k = size() - 1; k >= 0; --k) applyTranspositionOnTheRight(k, tr.coeff(k));
	return derived();
	}

	/** \returns the number of rows */
	inline EIGEN_DEVICE_FUNC Index rows() const { return Index(indices().size()); }

	/** \returns the number of columns */
	inline EIGEN_DEVICE_FUNC Index cols() const { return Index(indices().size()); }

	/** \returns the size of a side of the respective square matrix, i.e., the number of indices */
	inline EIGEN_DEVICE_FUNC Index size() const { return Index(indices().size()); }

	#ifndef EIGEN_PARSED_BY_DOXYGEN
	template <typename DenseDerived>
	void evalTo(MatrixBase<DenseDerived>& other) const {
	other.setZero();
	for (Index i = 0; i < rows(); ++i) other.coeffRef(indices().coeff(i), i) = typename DenseDerived::Scalar(1);
	}
	#endif

	/** \returns a Matrix object initialized from this permutation matrix. Notice that it
	* is inefficient to return this Matrix object by value. For efficiency, favor using
	* the Matrix constructor taking EigenBase objects.
	*/
	DenseMatrixType toDenseMatrix() const { return derived(); }

	/** const version of indices(). */
	const IndicesType& indices() const { return derived().indices(); }
	/** \returns a reference to the stored array representing the permutation. */
	IndicesType& indices() { return derived().indices(); }

	/** Resizes to given size.
	*/
	inline void resize(Index newSize) { indices().resize(newSize); }

	/** Sets this to be the identity permutation matrix /
	void setIdentity() {
	StorageIndex n = StorageIndex(size());
	for (StorageIndex i = 0; i < n; ++i) indices().coeffRef(i) = i;
	}

	/** Sets *this to be the identity permutation matrix of given size.
	*/
	void setIdentity(Index newSize) {
	resize(newSize);
	setIdentity();
	}

	/** Multiplies *this by the transposition \f$(ij)\f$ on the left.
	*
	* \returns a reference to *this.
	*
	* \warning This is much slower than applyTranspositionOnTheRight(Index,Index):
	* this has linear complexity and requires a lot of branching.
	*
	* \sa applyTranspositionOnTheRight(Index,Index)
	*/
	Derived& applyTranspositionOnTheLeft(Index i, Index j) {
	eigen_assert(i >= 0 && j >= 0 && i < size() && j < size());
	for (Index k = 0; k < size(); ++k) {
	if (indices().coeff(k) == i)
	indices().coeffRef(k) = StorageIndex(j);
	else if (indices().coeff(k) == j)
	indices().coeffRef(k) = StorageIndex(i);
	}
	return derived();
	}

	/** Multiplies *this by the transposition \f$(ij)\f$ on the right.
	*
	* \returns a reference to *this.
	*
	* This is a fast operation, it only consists in swapping two indices.
	*
	* \sa applyTranspositionOnTheLeft(Index,Index)
	*/
	Derived& applyTranspositionOnTheRight(Index i, Index j) {
	eigen_assert(i >= 0 && j >= 0 && i < size() && j < size());
	std::swap(indices().coeffRef(i), indices().coeffRef(j));
	return derived();
	}

	/** \returns the inverse permutation matrix.
	*
	* \note \blank \note_try_to_help_rvo
	*/
	inline InverseReturnType inverse() const { return InverseReturnType(derived()); }
	/** \returns the tranpose permutation matrix.
	*
	* \note \blank \note_try_to_help_rvo
	*/
	inline InverseReturnType transpose() const { return InverseReturnType(derived()); }

	/** multiplication helpers to hopefully get RVO **/

	#ifndef EIGEN_PARSED_BY_DOXYGEN
	protected:
	template <typename OtherDerived>
	void assignTranspose(const PermutationBase<OtherDerived>& other) {
	for (Index i = 0; i < rows(); ++i) indices().coeffRef(other.indices().coeff(i)) = i;
	}
	template <typename Lhs, typename Rhs>
	void assignProduct(const Lhs& lhs, const Rhs& rhs) {
	eigen_assert(lhs.cols() == rhs.rows());
	for (Index i = 0; i < rows(); ++i) indices().coeffRef(i) = lhs.indices().coeff(rhs.indices().coeff(i));
	}
	#endif

	public:
	/** \returns the product permutation matrix.
	*
	* \note \blank \note_try_to_help_rvo
	*/
	template <typename Other>
	inline PlainPermutationType operator*(const PermutationBase<Other>& other) const {
	return PlainPermutationType(internal::PermPermProduct, derived(), other.derived());
	}

	/** \returns the product of a permutation with another inverse permutation.
	*
	* \note \blank \note_try_to_help_rvo
	*/
	template <typename Other>
	inline PlainPermutationType operator*(const InverseImpl<Other, PermutationStorage>& other) const {
	return PlainPermutationType(internal::PermPermProduct, *this, other.eval());
	}

	/** \returns the product of an inverse permutation with another permutation.
	*
	* \note \blank \note_try_to_help_rvo
	*/
	template <typename Other>
	friend inline PlainPermutationType operator*(const InverseImpl<Other, PermutationStorage>& other,
	const PermutationBase& perm) {
	return PlainPermutationType(internal::PermPermProduct, other.eval(), perm);
	}

	/** \returns the determinant of the permutation matrix, which is either 1 or -1 depending on the parity of the
	* permutation.
	*
	* This function is O(\c n) procedure allocating a buffer of \c n booleans.
	*/
	Index determinant() const {
	Index res = 1;
	Index n = size();
	Matrix<bool, RowsAtCompileTime, 1, 0, MaxRowsAtCompileTime> mask(n);
	mask.fill(false);
	Index r = 0;
	while (r < n) {
	// search for the next seed
	while (r < n && mask[r]) r++;
	if (r >= n) break;
	// we got one, let's follow it until we are back to the seed
	Index k0 = r++;
	mask.coeffRef(k0) = true;
	for (Index k = indices().coeff(k0); k != k0; k = indices().coeff(k)) {
	mask.coeffRef(k) = true;
	res = -res;
	}
	}
	return res;
	}

	protected:
	};

	namespace internal {
	template <int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_>
	struct traits<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_> >
	: traits<
	Matrix<StorageIndex_, SizeAtCompileTime, SizeAtCompileTime, 0, MaxSizeAtCompileTime, MaxSizeAtCompileTime> > {
	typedef PermutationStorage StorageKind;
	typedef Matrix<StorageIndex_, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1> IndicesType;
	typedef StorageIndex_ StorageIndex;
	typedef void Scalar;
	};
	} // namespace internal

	/** \class PermutationMatrix
	* \ingroup Core_Module
	*
	* \brief Permutation matrix
	*
	* \tparam SizeAtCompileTime the number of rows/cols, or Dynamic
	* \tparam 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. \tparam StorageIndex_ the integer type of the
	* indices
	*
	* This class represents a permutation matrix, internally stored as a vector of integers.
	*
	* \sa class PermutationBase, class PermutationWrapper, class DiagonalMatrix
	*/
	template <int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_>
	class PermutationMatrix
	: public PermutationBase<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_> > {
	typedef PermutationBase<PermutationMatrix> Base;
	typedef internal::traits<PermutationMatrix> Traits;

	public:
	typedef const PermutationMatrix& Nested;

	#ifndef EIGEN_PARSED_BY_DOXYGEN
	typedef typename Traits::IndicesType IndicesType;
	typedef typename Traits::StorageIndex StorageIndex;
	#endif

	inline PermutationMatrix() {}

	/** Constructs an uninitialized permutation matrix of given size.
	*/
	explicit inline PermutationMatrix(Index size) : m_indices(size) {
	eigen_internal_assert(size <= NumTraits<StorageIndex>::highest());
	}

	/** Copy constructor. */
	template <typename OtherDerived>
	inline PermutationMatrix(const PermutationBase<OtherDerived>& other) : m_indices(other.indices()) {}

	/** Generic constructor from expression of the indices. The indices
	* array has the meaning that the permutations sends each integer i to indices[i].
	*
	* \warning It is your responsibility to check that the indices array that you passes actually
	* describes a permutation, i.e., each value between 0 and n-1 occurs exactly once, where n is the
	* array's size.
	*/
	template <typename Other>
	explicit inline PermutationMatrix(const MatrixBase<Other>& indices) : m_indices(indices) {}

	/** Convert the Transpositions \a tr to a permutation matrix */
	template <typename Other>
	explicit PermutationMatrix(const TranspositionsBase<Other>& tr) : m_indices(tr.size()) {
	*this = tr;
	}

	/** Copies the other permutation into this /
	template <typename Other>
	PermutationMatrix& operator=(const PermutationBase<Other>& other) {
	m_indices = other.indices();
	return *this;
	}

	/** Assignment from the Transpositions \a tr */
	template <typename Other>
	PermutationMatrix& operator=(const TranspositionsBase<Other>& tr) {
	return Base::operator=(tr.derived());
	}

	/** const version of indices(). */
	const IndicesType& indices() const { return m_indices; }
	/** \returns a reference to the stored array representing the permutation. */
	IndicesType& indices() { return m_indices; }

	/** multiplication helpers to hopefully get RVO **/

	#ifndef EIGEN_PARSED_BY_DOXYGEN
	template <typename Other>
	PermutationMatrix(const InverseImpl<Other, PermutationStorage>& other)
	: m_indices(other.derived().nestedExpression().size()) {
	eigen_internal_assert(m_indices.size() <= NumTraits<StorageIndex>::highest());
	StorageIndex end = StorageIndex(m_indices.size());
	for (StorageIndex i = 0; i < end; ++i)
	m_indices.coeffRef(other.derived().nestedExpression().indices().coeff(i)) = i;
	}
	template <typename Lhs, typename Rhs>
	PermutationMatrix(internal::PermPermProduct_t, const Lhs& lhs, const Rhs& rhs) : m_indices(lhs.indices().size()) {
	Base::assignProduct(lhs, rhs);
	}
	#endif

	protected:
	IndicesType m_indices;
	};

	namespace internal {
	template <int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_, int PacketAccess_>
	struct traits<Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_>, PacketAccess_> >
	: traits<
	Matrix<StorageIndex_, SizeAtCompileTime, SizeAtCompileTime, 0, MaxSizeAtCompileTime, MaxSizeAtCompileTime> > {
	typedef PermutationStorage StorageKind;
	typedef Map<const Matrix<StorageIndex_, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1>, PacketAccess_> IndicesType;
	typedef StorageIndex_ StorageIndex;
	typedef void Scalar;
	};
	} // namespace internal

	template <int SizeAtCompileTime, int MaxSizeAtCompileTime, typename StorageIndex_, int PacketAccess_>
	class Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_>, PacketAccess_>
	: public PermutationBase<
	Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_>, PacketAccess_> > {
	typedef PermutationBase<Map> Base;
	typedef internal::traits<Map> Traits;

	public:
	#ifndef EIGEN_PARSED_BY_DOXYGEN
	typedef typename Traits::IndicesType IndicesType;
	typedef typename IndicesType::Scalar StorageIndex;
	#endif

	inline Map(const StorageIndex* indicesPtr) : m_indices(indicesPtr) {}

	inline Map(const StorageIndex* indicesPtr, Index size) : m_indices(indicesPtr, size) {}

	/** Copies the other permutation into this /
	template <typename Other>
	Map& operator=(const PermutationBase<Other>& other) {
	return Base::operator=(other.derived());
	}

	/** Assignment from the Transpositions \a tr */
	template <typename Other>
	Map& operator=(const TranspositionsBase<Other>& tr) {
	return Base::operator=(tr.derived());
	}

	#ifndef EIGEN_PARSED_BY_DOXYGEN
	/** This is a special case of the templated operator=. Its purpose is to
	* prevent a default operator= from hiding the templated operator=.
	*/
	Map& operator=(const Map& other) {
	m_indices = other.m_indices;
	return *this;
	}
	#endif

	/** const version of indices(). */
	const IndicesType& indices() const { return m_indices; }
	/** \returns a reference to the stored array representing the permutation. */
	IndicesType& indices() { return m_indices; }

	protected:
	IndicesType m_indices;
	};

	template <typename IndicesType_>
	class TranspositionsWrapper;
	namespace internal {
	template <typename IndicesType_>
	struct traits<PermutationWrapper<IndicesType_> > {
	typedef PermutationStorage StorageKind;
	typedef void Scalar;
	typedef typename IndicesType_::Scalar StorageIndex;
	typedef IndicesType_ IndicesType;
	enum {
	RowsAtCompileTime = IndicesType_::SizeAtCompileTime,
	ColsAtCompileTime = IndicesType_::SizeAtCompileTime,
	MaxRowsAtCompileTime = IndicesType::MaxSizeAtCompileTime,
	MaxColsAtCompileTime = IndicesType::MaxSizeAtCompileTime,
	Flags = 0
	};
	};
	} // namespace internal

	/** \class PermutationWrapper
	* \ingroup Core_Module
	*
	* \brief Class to view a vector of integers as a permutation matrix
	*
	* \tparam IndicesType_ the type of the vector of integer (can be any compatible expression)
	*
	* This class allows to view any vector expression of integers as a permutation matrix.
	*
	* \sa class PermutationBase, class PermutationMatrix
	*/
	template <typename IndicesType_>
	class PermutationWrapper : public PermutationBase<PermutationWrapper<IndicesType_> > {
	typedef PermutationBase<PermutationWrapper> Base;
	typedef internal::traits<PermutationWrapper> Traits;

	public:
	#ifndef EIGEN_PARSED_BY_DOXYGEN
	typedef typename Traits::IndicesType IndicesType;
	#endif

	inline PermutationWrapper(const IndicesType& indices) : m_indices(indices) {}

	/** const version of indices(). */
	const internal::remove_all_t<typename IndicesType::Nested>& indices() const { return m_indices; }

	protected:
	typename IndicesType::Nested m_indices;
	};

	/** \returns the matrix with the permutation applied to the columns.
	*/
	template <typename MatrixDerived, typename PermutationDerived>
	EIGEN_DEVICE_FUNC const Product<MatrixDerived, PermutationDerived, AliasFreeProduct> operator*(
	const MatrixBase<MatrixDerived>& matrix, const PermutationBase<PermutationDerived>& permutation) {
	return Product<MatrixDerived, PermutationDerived, AliasFreeProduct>(matrix.derived(), permutation.derived());
	}

	/** \returns the matrix with the permutation applied to the rows.
	*/
	template <typename PermutationDerived, typename MatrixDerived>
	EIGEN_DEVICE_FUNC const Product<PermutationDerived, MatrixDerived, AliasFreeProduct> operator*(
	const PermutationBase<PermutationDerived>& permutation, const MatrixBase<MatrixDerived>& matrix) {
	return Product<PermutationDerived, MatrixDerived, AliasFreeProduct>(permutation.derived(), matrix.derived());
	}

	template <typename PermutationType>
	class InverseImpl<PermutationType, PermutationStorage> : public EigenBase<Inverse<PermutationType> > {
	typedef typename PermutationType::PlainPermutationType PlainPermutationType;
	typedef internal::traits<PermutationType> PermTraits;

	protected:
	InverseImpl() {}

	public:
	typedef Inverse<PermutationType> InverseType;
	using EigenBase<Inverse<PermutationType> >::derived;

	#ifndef EIGEN_PARSED_BY_DOXYGEN
	typedef typename PermutationType::DenseMatrixType DenseMatrixType;
	enum {
	RowsAtCompileTime = PermTraits::RowsAtCompileTime,
	ColsAtCompileTime = PermTraits::ColsAtCompileTime,
	MaxRowsAtCompileTime = PermTraits::MaxRowsAtCompileTime,
	MaxColsAtCompileTime = PermTraits::MaxColsAtCompileTime
	};
	#endif

	#ifndef EIGEN_PARSED_BY_DOXYGEN
	template <typename DenseDerived>
	void evalTo(MatrixBase<DenseDerived>& other) const {
	other.setZero();
	for (Index i = 0; i < derived().rows(); ++i)
	other.coeffRef(i, derived().nestedExpression().indices().coeff(i)) = typename DenseDerived::Scalar(1);
	}
	#endif

	/** \return the equivalent permutation matrix */
	PlainPermutationType eval() const { return derived(); }

	DenseMatrixType toDenseMatrix() const { return derived(); }

	/** \returns the matrix with the inverse permutation applied to the columns.
	*/
	template <typename OtherDerived>
	friend const Product<OtherDerived, InverseType, AliasFreeProduct> operator*(const MatrixBase<OtherDerived>& matrix,
	const InverseType& trPerm) {
	return Product<OtherDerived, InverseType, AliasFreeProduct>(matrix.derived(), trPerm.derived());
	}

	/** \returns the matrix with the inverse permutation applied to the rows.
	*/
	template <typename OtherDerived>
	const Product<InverseType, OtherDerived, AliasFreeProduct> operator*(const MatrixBase<OtherDerived>& matrix) const {
	return Product<InverseType, OtherDerived, AliasFreeProduct>(derived(), matrix.derived());
	}
	};

	template <typename Derived>
	const PermutationWrapper<const Derived> MatrixBase<Derived>::asPermutation() const {
	return derived();
	}

	namespace internal {

	template <>
	struct AssignmentKind<DenseShape, PermutationShape> {
	typedef EigenBase2EigenBase Kind;
	};

	} // end namespace internal

	} // end namespace Eigen

	#endif // EIGEN_PERMUTATIONMATRIX_H