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Transpositions.h
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Transpositions.h
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// 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
EIGEN_DEVICE_FUNC
Derived& derived() { return *static_cast<Derived*>(this); }
EIGEN_DEVICE_FUNC
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();
}
/** \returns the number of transpositions */
EIGEN_DEVICE_FUNC
Index size() const { return indices().size(); }
/** \returns the number of rows of the equivalent permutation matrix */
EIGEN_DEVICE_FUNC
Index rows() const { return indices().size(); }
/** \returns the number of columns of the equivalent permutation matrix */
EIGEN_DEVICE_FUNC
Index cols() const { return indices().size(); }
/** Direct access to the underlying index vector */
EIGEN_DEVICE_FUNC
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(). */
EIGEN_DEVICE_FUNC
const IndicesType& indices() const { return derived().indices(); }
/** \returns a reference to the stored array representing the transpositions. */
EIGEN_DEVICE_FUNC
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()) {}
/** 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);
}
/** Constructs an uninitialized permutation matrix of given size.
*/
inline Transpositions(Index size) : m_indices(size)
{}
/** const version of indices(). */
EIGEN_DEVICE_FUNC
const IndicesType& indices() const { return m_indices; }
/** \returns a reference to the stored array representing the transpositions. */
EIGEN_DEVICE_FUNC
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(). */
EIGEN_DEVICE_FUNC
const IndicesType& indices() const { return m_indices; }
/** \returns a reference to the stored array representing the transpositions. */
EIGEN_DEVICE_FUNC
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);
}
/** const version of indices(). */
EIGEN_DEVICE_FUNC
const IndicesType& indices() const { return m_indices; }
/** \returns a reference to the stored array representing the transpositions. */
EIGEN_DEVICE_FUNC
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) {}
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
Index size() const EIGEN_NOEXCEPT { return m_transpositions.size(); }
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
Index rows() const EIGEN_NOEXCEPT { return m_transpositions.size(); }
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR
Index cols() const EIGEN_NOEXCEPT { 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());
}
EIGEN_DEVICE_FUNC
const TranspositionType& nestedExpression() const { return m_transpositions; }
protected:
const TranspositionType& m_transpositions;
};
} // end namespace Eigen
#endif // EIGEN_TRANSPOSITIONS_H

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