// 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) 2009-2011 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_PERMUTATIONMATRIX_H
#define EIGEN_PERMUTATIONMATRIX_H
namespace Eigen {
template<int RowCol,typename IndicesType,typename MatrixType, typename StorageKind> class PermutedImpl;
/** \class PermutationBase
* \ingroup Core_Module
*
* \brief Base class for permutations
*
* \param 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
*/
namespace internal {
template<typename PermutationType, typename MatrixType, int Side, bool Transposed=false>
struct permut_matrix_product_retval;
template<typename PermutationType, typename MatrixType, int Side, bool Transposed=false>
struct permut_sparsematrix_product_retval;
enum PermPermProduct_t {PermPermProduct};
} // end namespace internal
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,
CoeffReadCost = Traits::CoeffReadCost,
RowsAtCompileTime = Traits::RowsAtCompileTime,
ColsAtCompileTime = Traits::ColsAtCompileTime,
MaxRowsAtCompileTime = Traits::MaxRowsAtCompileTime,
MaxColsAtCompileTime = Traits::MaxColsAtCompileTime
};
typedef typename Traits::Scalar Scalar;
typedef typename Traits::Index Index;
typedef Matrix<Scalar,RowsAtCompileTime,ColsAtCompileTime,0,MaxRowsAtCompileTime,MaxColsAtCompileTime>
DenseMatrixType;
typedef PermutationMatrix<IndicesType::SizeAtCompileTime,IndicesType::MaxSizeAtCompileTime,Index>
PlainPermutationType;
using Base::derived;
#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 indices().size(); }
/** \returns the number of columns */
inline Index cols() const { return indices().size(); }
/** \returns the size of a side of the respective square matrix, i.e., the number of indices */
inline Index size() const { return indices().size(); }
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename DenseDerived>
void evalTo(MatrixBase<DenseDerived>& other) const
{
other.setZero();
for (int 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 size)
{
indices().resize(size);
}
/** Sets *this to be the identity permutation matrix */
void setIdentity()
{
for(Index i = 0; i < size(); ++i)
indices().coeffRef(i) = i;
}
/** Sets *this to be the identity permutation matrix of given size.
*/
void setIdentity(Index size)
{
resize(size);
setIdentity();
}
/** Multiplies *this by the transposition \f$(ij)\f$ on the left.
*
* \returns a reference to *this.
*
* \warning This is much slower than applyTranspositionOnTheRight(int,int):
* this has linear complexity and requires a lot of branching.
*
* \sa applyTranspositionOnTheRight(int,int)
*/
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) = j;
else if(indices().coeff(k) == j) indices().coeffRef(k) = 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(int,int)
*/
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 \note_try_to_help_rvo
*/
inline Transpose<PermutationBase> inverse() const
{ return derived(); }
/** \returns the tranpose permutation matrix.
*
* \note \note_try_to_help_rvo
*/
inline Transpose<PermutationBase> transpose() const
{ return derived(); }
/**** multiplication helpers to hopefully get RVO ****/
#ifndef EIGEN_PARSED_BY_DOXYGEN
protected:
template<typename OtherDerived>
void assignTranspose(const PermutationBase<OtherDerived>& other)
{
for (int 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 (int i=0; i<rows();++i) indices().coeffRef(i) = lhs.indices().coeff(rhs.indices().coeff(i));
}
#endif
public:
/** \returns the product permutation matrix.
*
* \note \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 \note_try_to_help_rvo
*/
template<typename Other>
inline PlainPermutationType operator*(const Transpose<PermutationBase<Other> >& other) const
{ return PlainPermutationType(internal::PermPermProduct, *this, other.eval()); }
/** \returns the product of an inverse permutation with another permutation.
*
* \note \note_try_to_help_rvo
*/
template<typename Other> friend
inline PlainPermutationType operator*(const Transpose<PermutationBase<Other> >& other, const PermutationBase& perm)
{ return PlainPermutationType(internal::PermPermProduct, other.eval(), perm); }
protected:
};
/** \class PermutationMatrix
* \ingroup Core_Module
*
* \brief Permutation matrix
*
* \param SizeAtCompileTime the number of rows/cols, or Dynamic
* \param MaxSizeAtCompileTime the maximum number of rows/cols, or Dynamic. This optional parameter defaults to SizeAtCompileTime. Most of the time, you should not have to specify it.
* \param IndexType the interger type of the indices
*
* This class represents a permutation matrix, internally stored as a vector of integers.
*
* \sa class PermutationBase, class PermutationWrapper, class DiagonalMatrix
*/
namespace internal {
template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType>
struct traits<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType> >
: traits<Matrix<IndexType,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
{
typedef IndexType Index;
typedef Matrix<IndexType, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1> IndicesType;
};
}
template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType>
class PermutationMatrix : public PermutationBase<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType> >
{
typedef PermutationBase<PermutationMatrix> Base;
typedef internal::traits<PermutationMatrix> Traits;
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef typename Traits::IndicesType IndicesType;
#endif
inline PermutationMatrix()
{}
/** Constructs an uninitialized permutation matrix of given size.
*/
inline PermutationMatrix(int size) : m_indices(size)
{}
/** 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 Transpose<PermutationBase<Other> >& other)
: m_indices(other.nestedPermutation().size())
{
for (int i=0; i<m_indices.size();++i) m_indices.coeffRef(other.nestedPermutation().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 IndexType, int _PacketAccess>
struct traits<Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType>,_PacketAccess> >
: traits<Matrix<IndexType,SizeAtCompileTime,SizeAtCompileTime,0,MaxSizeAtCompileTime,MaxSizeAtCompileTime> >
{
typedef IndexType Index;
typedef Map<const Matrix<IndexType, SizeAtCompileTime, 1, 0, MaxSizeAtCompileTime, 1>, _PacketAccess> IndicesType;
};
}
template<int SizeAtCompileTime, int MaxSizeAtCompileTime, typename IndexType, int _PacketAccess>
class Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType>,_PacketAccess>
: public PermutationBase<Map<PermutationMatrix<SizeAtCompileTime, MaxSizeAtCompileTime, IndexType>,_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 Index;
#endif
inline Map(const Index* indices)
: m_indices(indices)
{}
inline Map(const Index* indices, Index size)
: m_indices(indices,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;
};
/** \class PermutationWrapper
* \ingroup Core_Module
*
* \brief Class to view a vector of integers as a permutation matrix
*
* \param _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
*/
struct PermutationStorage {};
template<typename _IndicesType> class TranspositionsWrapper;
namespace internal {
template<typename _IndicesType>
struct traits<PermutationWrapper<_IndicesType> >
{
typedef PermutationStorage StorageKind;
typedef typename _IndicesType::Scalar Scalar;
typedef typename _IndicesType::Scalar Index;
typedef _IndicesType IndicesType;
enum {
RowsAtCompileTime = _IndicesType::SizeAtCompileTime,
ColsAtCompileTime = _IndicesType::SizeAtCompileTime,
MaxRowsAtCompileTime = IndicesType::MaxRowsAtCompileTime,
MaxColsAtCompileTime = IndicesType::MaxColsAtCompileTime,
Flags = 0,
CoeffReadCost = _IndicesType::CoeffReadCost
};
};
}
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 Derived, typename PermutationDerived>
inline const internal::permut_matrix_product_retval<PermutationDerived, Derived, OnTheRight>
operator*(const MatrixBase<Derived>& matrix,
const PermutationBase<PermutationDerived> &permutation)
{
return internal::permut_matrix_product_retval
<PermutationDerived, Derived, OnTheRight>
(permutation.derived(), matrix.derived());
}
/** \returns the matrix with the permutation applied to the rows.
*/
template<typename Derived, typename PermutationDerived>
inline const internal::permut_matrix_product_retval
<PermutationDerived, Derived, OnTheLeft>
operator*(const PermutationBase<PermutationDerived> &permutation,
const MatrixBase<Derived>& matrix)
{
return internal::permut_matrix_product_retval
<PermutationDerived, Derived, OnTheLeft>
(permutation.derived(), matrix.derived());
}
namespace internal {
template<typename PermutationType, typename MatrixType, int Side, bool Transposed>
struct traits<permut_matrix_product_retval<PermutationType, MatrixType, Side, Transposed> >
{
typedef typename MatrixType::PlainObject ReturnType;
};
template<typename PermutationType, typename MatrixType, int Side, bool Transposed>
struct permut_matrix_product_retval
: public ReturnByValue<permut_matrix_product_retval<PermutationType, MatrixType, Side, Transposed> >
{
typedef typename remove_all<typename MatrixType::Nested>::type MatrixTypeNestedCleaned;
permut_matrix_product_retval(const PermutationType& perm, const MatrixType& matrix)
: m_permutation(perm), m_matrix(matrix)
{}
inline int rows() const { return m_matrix.rows(); }
inline int cols() const { return m_matrix.cols(); }
template<typename Dest> inline void evalTo(Dest& dst) const
{
const int n = Side==OnTheLeft ? rows() : cols();
if(is_same<MatrixTypeNestedCleaned,Dest>::value && extract_data(dst) == extract_data(m_matrix))
{
// apply the permutation inplace
Matrix<bool,PermutationType::RowsAtCompileTime,1,0,PermutationType::MaxRowsAtCompileTime> mask(m_permutation.size());
mask.fill(false);
int r = 0;
while(r < m_permutation.size())
{
// search for the next seed
while(r<m_permutation.size() && mask[r]) r++;
if(r>=m_permutation.size())
break;
// we got one, let's follow it until we are back to the seed
int k0 = r++;
int kPrev = k0;
mask.coeffRef(k0) = true;
for(int k=m_permutation.indices().coeff(k0); k!=k0; k=m_permutation.indices().coeff(k))
{
Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>(dst, k)
.swap(Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>
(dst,((Side==OnTheLeft) ^ Transposed) ? k0 : kPrev));
mask.coeffRef(k) = true;
kPrev = k;
}
}
}
else
{
for(int i = 0; i < n; ++i)
{
Block<Dest, Side==OnTheLeft ? 1 : Dest::RowsAtCompileTime, Side==OnTheRight ? 1 : Dest::ColsAtCompileTime>
(dst, ((Side==OnTheLeft) ^ Transposed) ? m_permutation.indices().coeff(i) : i)
=
Block<const MatrixTypeNestedCleaned,Side==OnTheLeft ? 1 : MatrixType::RowsAtCompileTime,Side==OnTheRight ? 1 : MatrixType::ColsAtCompileTime>
(m_matrix, ((Side==OnTheRight) ^ Transposed) ? m_permutation.indices().coeff(i) : i);
}
}
}
protected:
const PermutationType& m_permutation;
typename MatrixType::Nested m_matrix;
};
/* Template partial specialization for transposed/inverse permutations */
template<typename Derived>
struct traits<Transpose<PermutationBase<Derived> > >
: traits<Derived>
{};
} // end namespace internal
template<typename Derived>
class Transpose<PermutationBase<Derived> >
: public EigenBase<Transpose<PermutationBase<Derived> > >
{
typedef Derived PermutationType;
typedef typename PermutationType::IndicesType IndicesType;
typedef typename PermutationType::PlainPermutationType PlainPermutationType;
public:
#ifndef EIGEN_PARSED_BY_DOXYGEN
typedef internal::traits<PermutationType> Traits;
typedef typename Derived::DenseMatrixType DenseMatrixType;
enum {
Flags = Traits::Flags,
CoeffReadCost = Traits::CoeffReadCost,
RowsAtCompileTime = Traits::RowsAtCompileTime,
ColsAtCompileTime = Traits::ColsAtCompileTime,
MaxRowsAtCompileTime = Traits::MaxRowsAtCompileTime,
MaxColsAtCompileTime = Traits::MaxColsAtCompileTime
};
typedef typename Traits::Scalar Scalar;
#endif
Transpose(const PermutationType& p) : m_permutation(p) {}
inline int rows() const { return m_permutation.rows(); }
inline int cols() const { return m_permutation.cols(); }
#ifndef EIGEN_PARSED_BY_DOXYGEN
template<typename DenseDerived>
void evalTo(MatrixBase<DenseDerived>& other) const
{
other.setZero();
for (int i=0; i<rows();++i)
other.coeffRef(i, m_permutation.indices().coeff(i)) = typename DenseDerived::Scalar(1);
}
#endif
/** \return the equivalent permutation matrix */
PlainPermutationType eval() const { return *this; }
DenseMatrixType toDenseMatrix() const { return *this; }
/** \returns the matrix with the inverse permutation applied to the columns.
*/
template<typename OtherDerived> friend
inline const internal::permut_matrix_product_retval<PermutationType, OtherDerived, OnTheRight, true>
operator*(const MatrixBase<OtherDerived>& matrix, const Transpose& trPerm)
{
return internal::permut_matrix_product_retval<PermutationType, OtherDerived, OnTheRight, true>(trPerm.m_permutation, matrix.derived());
}
/** \returns the matrix with the inverse permutation applied to the rows.
*/
template<typename OtherDerived>
inline const internal::permut_matrix_product_retval<PermutationType, OtherDerived, OnTheLeft, true>
operator*(const MatrixBase<OtherDerived>& matrix) const
{
return internal::permut_matrix_product_retval<PermutationType, OtherDerived, OnTheLeft, true>(m_permutation, matrix.derived());
}
const PermutationType& nestedPermutation() const { return m_permutation; }
protected:
const PermutationType& m_permutation;
};
template<typename Derived>
const PermutationWrapper<const Derived> MatrixBase<Derived>::asPermutation() const
{
return derived();
}
} // end namespace Eigen
#endif // EIGEN_PERMUTATIONMATRIX_H