Eigen/src/Core/PermutationMatrix.h - eigen/fuchsia - 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

 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();
     }

     #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 PermutationBase& other)
     {
       indices() = other.indices();
       return derived();
     }
     #endif

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

     /** \returns the number of columns */
     inline 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 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;
 };
 }

 /** \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()) {}

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

     /** 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());
     }

     #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=.
       */
     PermutationMatrix& operator=(const PermutationMatrix& 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; }


     /**** 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;
 };
 }

 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
   };
 };
 }

 /** \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 typename internal::remove_all<typename IndicesType::Nested>::type&
     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

	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();
	}

	#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 PermutationBase& other)
	{
	indices() = other.indices();
	return derived();
	}
	#endif

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

	/** \returns the number of columns */
	inline 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 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;
	};
	}

	/** \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()) {}

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

	/** 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());
	}

	#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=.
	*/
	PermutationMatrix& operator=(const PermutationMatrix& 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; }


	/** 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;
	};
	}

	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
	};
	};
	}

	/** \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 typename internal::remove_all<typename IndicesType::Nested>::type&
	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