Eigen/src/Core/Transpositions.h - eigen - Git at Google

 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
 // Copyright (C) 2010-2011 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_TRANSPOSITIONS_H
 #define EIGEN_TRANSPOSITIONS_H

 namespace Eigen {

 template<typename Derived>
 class TranspositionsBase
 {
     typedef internal::traits<Derived> Traits;

   public:

     typedef typename Traits::IndicesType IndicesType;
     typedef typename IndicesType::Scalar StorageIndex;
     typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3

     Derived& derived() { return *static_cast<Derived*>(this); }
     const Derived& derived() const { return *static_cast<const Derived*>(this); }

     /** Copies the \a other transpositions into \c *this */
     template<typename OtherDerived>
     Derived& operator=(const TranspositionsBase<OtherDerived>& other)
     {
       indices() = other.indices();
       return 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=.
       */
     Derived& operator=(const TranspositionsBase& other)
     {
       indices() = other.indices();
       return derived();
     }
     #endif

     /** \returns the number of transpositions */
     Index size() const { return indices().size(); }
     /** \returns the number of rows of the equivalent permutation matrix */
     Index rows() const { return indices().size(); }
     /** \returns the number of columns of the equivalent permutation matrix */
     Index cols() const { return indices().size(); }

     /** Direct access to the underlying index vector */
     inline const StorageIndex& coeff(Index i) const { return indices().coeff(i); }
     /** Direct access to the underlying index vector */
     inline StorageIndex& coeffRef(Index i) { return indices().coeffRef(i); }
     /** Direct access to the underlying index vector */
     inline const StorageIndex& operator()(Index i) const { return indices()(i); }
     /** Direct access to the underlying index vector */
     inline StorageIndex& operator()(Index i) { return indices()(i); }
     /** Direct access to the underlying index vector */
     inline const StorageIndex& operator[](Index i) const { return indices()(i); }
     /** Direct access to the underlying index vector */
     inline StorageIndex& operator[](Index i) { return indices()(i); }

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

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

     /** Sets \c *this to represents an identity transformation */
     void setIdentity()
     {
       for(StorageIndex i = 0; i < indices().size(); ++i)
         coeffRef(i) = i;
     }

     // FIXME: do we want such methods ?
     // might be useful when the target matrix expression is complex, e.g.:
     // object.matrix().block(..,..,..,..) = trans * object.matrix().block(..,..,..,..);
     /*
     template<typename MatrixType>
     void applyForwardToRows(MatrixType& mat) const
     {
       for(Index k=0 ; k<size() ; ++k)
         if(m_indices(k)!=k)
           mat.row(k).swap(mat.row(m_indices(k)));
     }

     template<typename MatrixType>
     void applyBackwardToRows(MatrixType& mat) const
     {
       for(Index k=size()-1 ; k>=0 ; --k)
         if(m_indices(k)!=k)
           mat.row(k).swap(mat.row(m_indices(k)));
     }
     */

     /** \returns the inverse transformation */
     inline Transpose<TranspositionsBase> inverse() const
     { return Transpose<TranspositionsBase>(derived()); }

     /** \returns the tranpose transformation */
     inline Transpose<TranspositionsBase> transpose() const
     { return Transpose<TranspositionsBase>(derived()); }

   protected:
 };

 namespace internal {
 template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex>
 struct traits<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex> >
  : traits<PermutationMatrix<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex> >
 {
   typedef Matrix<_StorageIndex, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1> IndicesType;
   typedef TranspositionsStorage StorageKind;
 };
 }

 /** \class Transpositions
   * \ingroup Core_Module
   *
   * \brief Represents a sequence of transpositions (row/column interchange)
   *
   * \tparam SizeAtCompileTime the number of transpositions, or Dynamic
   * \tparam MaxSizeAtCompileTime the maximum number of transpositions, or Dynamic. This optional parameter defaults to SizeAtCompileTime. Most of the time, you should not have to specify it.
   *
   * This class represents a permutation transformation as a sequence of \em n transpositions
   * \f$[T_{n-1} \ldots T_{i} \ldots T_{0}]\f$. It is internally stored as a vector of integers \c indices.
   * Each transposition \f$ T_{i} \f$ applied on the left of a matrix (\f$ T_{i} M\f$) interchanges
   * the rows \c i and \c indices[i] of the matrix \c M.
   * A transposition applied on the right (e.g., \f$ M T_{i}\f$) yields a column interchange.
   *
   * Compared to the class PermutationMatrix, such a sequence of transpositions is what is
   * computed during a decomposition with pivoting, and it is faster when applying the permutation in-place.
   *
   * To apply a sequence of transpositions to a matrix, simply use the operator * as in the following example:
   * \code
   * Transpositions tr;
   * MatrixXf mat;
   * mat = tr * mat;
   * \endcode
   * In this example, we detect that the matrix appears on both side, and so the transpositions
   * are applied in-place without any temporary or extra copy.
   *
   * \sa class PermutationMatrix
   */

 template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex>
 class Transpositions : public TranspositionsBase<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex> >
 {
     typedef internal::traits<Transpositions> Traits;
   public:

     typedef TranspositionsBase<Transpositions> Base;
     typedef typename Traits::IndicesType IndicesType;
     typedef typename IndicesType::Scalar StorageIndex;

     inline Transpositions() {}

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

     #ifndef EIGEN_PARSED_BY_DOXYGEN
     /** Standard copy constructor. Defined only to prevent a default copy constructor
       * from hiding the other templated constructor */
     inline Transpositions(const Transpositions& other) : m_indices(other.indices()) {}
     #endif

     /** Generic constructor from expression of the transposition indices. */
     template<typename Other>
     explicit inline Transpositions(const MatrixBase<Other>& indices) : m_indices(indices)
     {}

     /** Copies the \a other transpositions into \c *this */
     template<typename OtherDerived>
     Transpositions& operator=(const TranspositionsBase<OtherDerived>& other)
     {
       return Base::operator=(other);
     }

     #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=.
       */
     Transpositions& operator=(const Transpositions& other)
     {
       m_indices = other.m_indices;
       return *this;
     }
     #endif

     /** Constructs an uninitialized permutation matrix of given size.
       */
     inline Transpositions(Index size) : m_indices(size)
     {}

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

   protected:

     IndicesType m_indices;
 };


 namespace internal {
 template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex, int _PacketAccess>
 struct traits<Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex>,_PacketAccess> >
  : traits<PermutationMatrix<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex> >
 {
   typedef Map<const Matrix<_StorageIndex,SizeAtCompileTime,1,0,MaxSizeAtCompileTime,1>, _PacketAccess> IndicesType;
   typedef _StorageIndex StorageIndex;
   typedef TranspositionsStorage StorageKind;
 };
 }

 template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex, int PacketAccess>
 class Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex>,PacketAccess>
  : public TranspositionsBase<Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex>,PacketAccess> >
 {
     typedef internal::traits<Map> Traits;
   public:

     typedef TranspositionsBase<Map> Base;
     typedef typename Traits::IndicesType IndicesType;
     typedef typename IndicesType::Scalar StorageIndex;

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

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

     /** Copies the \a other transpositions into \c *this */
     template<typename OtherDerived>
     Map& operator=(const TranspositionsBase<OtherDerived>& other)
     {
       return Base::operator=(other);
     }

     #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 transpositions. */
     IndicesType& indices() { return m_indices; }

   protected:

     IndicesType m_indices;
 };

 namespace internal {
 template<typename _IndicesType>
 struct traits<TranspositionsWrapper<_IndicesType> >
  : traits<PermutationWrapper<_IndicesType> >
 {
   typedef TranspositionsStorage StorageKind;
 };
 }

 template<typename _IndicesType>
 class TranspositionsWrapper
  : public TranspositionsBase<TranspositionsWrapper<_IndicesType> >
 {
     typedef internal::traits<TranspositionsWrapper> Traits;
   public:

     typedef TranspositionsBase<TranspositionsWrapper> Base;
     typedef typename Traits::IndicesType IndicesType;
     typedef typename IndicesType::Scalar StorageIndex;

     explicit inline TranspositionsWrapper(IndicesType& indices)
       : m_indices(indices)
     {}

     /** Copies the \a other transpositions into \c *this */
     template<typename OtherDerived>
     TranspositionsWrapper& operator=(const TranspositionsBase<OtherDerived>& other)
     {
       return Base::operator=(other);
     }

     #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=.
       */
     TranspositionsWrapper& operator=(const TranspositionsWrapper& 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 transpositions. */
     IndicesType& indices() { return m_indices; }

   protected:

     typename IndicesType::Nested m_indices;
 };


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

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

 // Template partial specialization for transposed/inverse transpositions

 namespace internal {

 template<typename Derived>
 struct traits<Transpose<TranspositionsBase<Derived> > >
  : traits<Derived>
 {};

 } // end namespace internal

 template<typename TranspositionsDerived>
 class Transpose<TranspositionsBase<TranspositionsDerived> >
 {
     typedef TranspositionsDerived TranspositionType;
     typedef typename TranspositionType::IndicesType IndicesType;
   public:

     explicit Transpose(const TranspositionType& t) : m_transpositions(t) {}

     Index size() const { return m_transpositions.size(); }
     Index rows() const { return m_transpositions.size(); }
     Index cols() const { return m_transpositions.size(); }

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

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

     const TranspositionType& nestedExpression() const { return m_transpositions; }

   protected:
     const TranspositionType& m_transpositions;
 };

 } // end namespace Eigen

 #endif // EIGEN_TRANSPOSITIONS_H
	// This file is part of Eigen, a lightweight C++ template library
	// for linear algebra.
	//
	// Copyright (C) 2010-2011 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_TRANSPOSITIONS_H
	#define EIGEN_TRANSPOSITIONS_H

	namespace Eigen {

	template<typename Derived>
	class TranspositionsBase
	{
	typedef internal::traits<Derived> Traits;

	public:

	typedef typename Traits::IndicesType IndicesType;
	typedef typename IndicesType::Scalar StorageIndex;
	typedef Eigen::Index Index; ///< \deprecated since Eigen 3.3

	Derived& derived() { return static_cast<Derived>(this); }
	const Derived& derived() const { return static_cast<const Derived>(this); }

	/** Copies the \a other transpositions into \c this /
	template<typename OtherDerived>
	Derived& operator=(const TranspositionsBase<OtherDerived>& other)
	{
	indices() = other.indices();
	return 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=.
	*/
	Derived& operator=(const TranspositionsBase& other)
	{
	indices() = other.indices();
	return derived();
	}
	#endif

	/** \returns the number of transpositions */
	Index size() const { return indices().size(); }
	/** \returns the number of rows of the equivalent permutation matrix */
	Index rows() const { return indices().size(); }
	/** \returns the number of columns of the equivalent permutation matrix */
	Index cols() const { return indices().size(); }

	/** Direct access to the underlying index vector */
	inline const StorageIndex& coeff(Index i) const { return indices().coeff(i); }
	/** Direct access to the underlying index vector */
	inline StorageIndex& coeffRef(Index i) { return indices().coeffRef(i); }
	/** Direct access to the underlying index vector */
	inline const StorageIndex& operator()(Index i) const { return indices()(i); }
	/** Direct access to the underlying index vector */
	inline StorageIndex& operator()(Index i) { return indices()(i); }
	/** Direct access to the underlying index vector */
	inline const StorageIndex& operator[](Index i) const { return indices()(i); }
	/** Direct access to the underlying index vector */
	inline StorageIndex& operator[](Index i) { return indices()(i); }

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

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

	/** Sets \c this to represents an identity transformation /
	void setIdentity()
	{
	for(StorageIndex i = 0; i < indices().size(); ++i)
	coeffRef(i) = i;
	}

	// FIXME: do we want such methods ?
	// might be useful when the target matrix expression is complex, e.g.:
	// object.matrix().block(..,..,..,..) = trans * object.matrix().block(..,..,..,..);
	/*
	template<typename MatrixType>
	void applyForwardToRows(MatrixType& mat) const
	{
	for(Index k=0 ; k<size() ; ++k)
	if(m_indices(k)!=k)
	mat.row(k).swap(mat.row(m_indices(k)));
	}

	template<typename MatrixType>
	void applyBackwardToRows(MatrixType& mat) const
	{
	for(Index k=size()-1 ; k>=0 ; --k)
	if(m_indices(k)!=k)
	mat.row(k).swap(mat.row(m_indices(k)));
	}
	*/

	/** \returns the inverse transformation */
	inline Transpose<TranspositionsBase> inverse() const
	{ return Transpose<TranspositionsBase>(derived()); }

	/** \returns the tranpose transformation */
	inline Transpose<TranspositionsBase> transpose() const
	{ return Transpose<TranspositionsBase>(derived()); }

	protected:
	};

	namespace internal {
	template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex>
	struct traits<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex> >
	: traits<PermutationMatrix<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex> >
	{
	typedef Matrix<_StorageIndex, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1> IndicesType;
	typedef TranspositionsStorage StorageKind;
	};
	}

	/** \class Transpositions
	* \ingroup Core_Module
	*
	* \brief Represents a sequence of transpositions (row/column interchange)
	*
	* \tparam SizeAtCompileTime the number of transpositions, or Dynamic
	* \tparam MaxSizeAtCompileTime the maximum number of transpositions, or Dynamic. This optional parameter defaults to SizeAtCompileTime. Most of the time, you should not have to specify it.
	*
	* This class represents a permutation transformation as a sequence of \em n transpositions
	* \f$[T_{n-1} \ldots T_{i} \ldots T_{0}]\f$. It is internally stored as a vector of integers \c indices.
	* Each transposition \f$ T_{i} \f$ applied on the left of a matrix (\f$ T_{i} M\f$) interchanges
	* the rows \c i and \c indices[i] of the matrix \c M.
	* A transposition applied on the right (e.g., \f$ M T_{i}\f$) yields a column interchange.
	*
	* Compared to the class PermutationMatrix, such a sequence of transpositions is what is
	* computed during a decomposition with pivoting, and it is faster when applying the permutation in-place.
	*
	* To apply a sequence of transpositions to a matrix, simply use the operator * as in the following example:
	* \code
	* Transpositions tr;
	* MatrixXf mat;
	* mat = tr * mat;
	* \endcode
	* In this example, we detect that the matrix appears on both side, and so the transpositions
	* are applied in-place without any temporary or extra copy.
	*
	* \sa class PermutationMatrix
	*/

	template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex>
	class Transpositions : public TranspositionsBase<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex> >
	{
	typedef internal::traits<Transpositions> Traits;
	public:

	typedef TranspositionsBase<Transpositions> Base;
	typedef typename Traits::IndicesType IndicesType;
	typedef typename IndicesType::Scalar StorageIndex;

	inline Transpositions() {}

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

	#ifndef EIGEN_PARSED_BY_DOXYGEN
	/** Standard copy constructor. Defined only to prevent a default copy constructor
	* from hiding the other templated constructor */
	inline Transpositions(const Transpositions& other) : m_indices(other.indices()) {}
	#endif

	/** Generic constructor from expression of the transposition indices. */
	template<typename Other>
	explicit inline Transpositions(const MatrixBase<Other>& indices) : m_indices(indices)
	{}

	/** Copies the \a other transpositions into \c this /
	template<typename OtherDerived>
	Transpositions& operator=(const TranspositionsBase<OtherDerived>& other)
	{
	return Base::operator=(other);
	}

	#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=.
	*/
	Transpositions& operator=(const Transpositions& other)
	{
	m_indices = other.m_indices;
	return *this;
	}
	#endif

	/** Constructs an uninitialized permutation matrix of given size.
	*/
	inline Transpositions(Index size) : m_indices(size)
	{}

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

	protected:

	IndicesType m_indices;
	};


	namespace internal {
	template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex, int _PacketAccess>
	struct traits<Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex>,_PacketAccess> >
	: traits<PermutationMatrix<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex> >
	{
	typedef Map<const Matrix<_StorageIndex,SizeAtCompileTime,1,0,MaxSizeAtCompileTime,1>, _PacketAccess> IndicesType;
	typedef _StorageIndex StorageIndex;
	typedef TranspositionsStorage StorageKind;
	};
	}

	template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename _StorageIndex, int PacketAccess>
	class Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex>,PacketAccess>
	: public TranspositionsBase<Map<Transpositions<SizeAtCompileTime,MaxSizeAtCompileTime,_StorageIndex>,PacketAccess> >
	{
	typedef internal::traits<Map> Traits;
	public:

	typedef TranspositionsBase<Map> Base;
	typedef typename Traits::IndicesType IndicesType;
	typedef typename IndicesType::Scalar StorageIndex;

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

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

	/** Copies the \a other transpositions into \c this /
	template<typename OtherDerived>
	Map& operator=(const TranspositionsBase<OtherDerived>& other)
	{
	return Base::operator=(other);
	}

	#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 transpositions. */
	IndicesType& indices() { return m_indices; }

	protected:

	IndicesType m_indices;
	};

	namespace internal {
	template<typename _IndicesType>
	struct traits<TranspositionsWrapper<_IndicesType> >
	: traits<PermutationWrapper<_IndicesType> >
	{
	typedef TranspositionsStorage StorageKind;
	};
	}

	template<typename _IndicesType>
	class TranspositionsWrapper
	: public TranspositionsBase<TranspositionsWrapper<_IndicesType> >
	{
	typedef internal::traits<TranspositionsWrapper> Traits;
	public:

	typedef TranspositionsBase<TranspositionsWrapper> Base;
	typedef typename Traits::IndicesType IndicesType;
	typedef typename IndicesType::Scalar StorageIndex;

	explicit inline TranspositionsWrapper(IndicesType& indices)
	: m_indices(indices)
	{}

	/** Copies the \a other transpositions into \c this /
	template<typename OtherDerived>
	TranspositionsWrapper& operator=(const TranspositionsBase<OtherDerived>& other)
	{
	return Base::operator=(other);
	}

	#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=.
	*/
	TranspositionsWrapper& operator=(const TranspositionsWrapper& 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 transpositions. */
	IndicesType& indices() { return m_indices; }

	protected:

	typename IndicesType::Nested m_indices;
	};



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

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

	// Template partial specialization for transposed/inverse transpositions

	namespace internal {

	template<typename Derived>
	struct traits<Transpose<TranspositionsBase<Derived> > >
	: traits<Derived>
	{};

	} // end namespace internal

	template<typename TranspositionsDerived>
	class Transpose<TranspositionsBase<TranspositionsDerived> >
	{
	typedef TranspositionsDerived TranspositionType;
	typedef typename TranspositionType::IndicesType IndicesType;
	public:

	explicit Transpose(const TranspositionType& t) : m_transpositions(t) {}

	Index size() const { return m_transpositions.size(); }
	Index rows() const { return m_transpositions.size(); }
	Index cols() const { return m_transpositions.size(); }

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

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

	const TranspositionType& nestedExpression() const { return m_transpositions; }

	protected:
	const TranspositionType& m_transpositions;
	};

	} // end namespace Eigen

	#endif // EIGEN_TRANSPOSITIONS_H