Base class for permutations. More...

#include <PermutationMatrix.h>

Inheritance diagram for Eigen::PermutationBase< Derived >:

Public Types
enum	{ Flags = Traits::Flags , RowsAtCompileTime = Traits::RowsAtCompileTime , ColsAtCompileTime = Traits::ColsAtCompileTime , MaxRowsAtCompileTime = Traits::MaxRowsAtCompileTime , MaxColsAtCompileTime = Traits::MaxColsAtCompileTime }

typedef Traits::IndicesType	IndicesType

typedef Traits::StorageIndex	StorageIndex

typedef Matrix< StorageIndex, RowsAtCompileTime, ColsAtCompileTime, 0, MaxRowsAtCompileTime, MaxColsAtCompileTime >	DenseMatrixType

typedef PermutationMatrix< IndicesType::SizeAtCompileTime, IndicesType::MaxSizeAtCompileTime, StorageIndex >	PlainPermutationType

typedef PlainPermutationType	PlainObject

typedef Inverse< Derived >	InverseReturnType

typedef void	Scalar

Public Types inherited from Eigen::EigenBase< Derived >
typedef Eigen::Index	Index
	The interface type of indices.

typedef internal::traits< Derived >::StorageKind	StorageKind

Public Member Functions
template<typename OtherDerived >
Derived &	operator= (const PermutationBase< OtherDerived > &other)
	Copies the other permutation into *this.

template<typename OtherDerived >
Derived &	operator= (const TranspositionsBase< OtherDerived > &tr)
	Assignment from the Transpositions tr.

Derived &	operator= (const PermutationBase &other)
	This is a special case of the templated operator=.

Index	rows () const

Index	cols () const

Index	size () const

template<typename DenseDerived >
void	evalTo (MatrixBase< DenseDerived > &other) const

DenseMatrixType	toDenseMatrix () const

const IndicesType &	indices () const
	const version of indices().

IndicesType &	indices ()

void	resize (Index newSize)
	Resizes to given size.

void	setIdentity ()
	Sets *this to be the identity permutation matrix.

void	setIdentity (Index newSize)
	Sets *this to be the identity permutation matrix of given size.

Derived &	applyTranspositionOnTheLeft (Index i, Index j)
	Multiplies *this by the transposition on the left.

Derived &	applyTranspositionOnTheRight (Index i, Index j)
	Multiplies *this by the transposition on the right.

InverseReturnType	inverse () const

InverseReturnType	transpose () const

template<typename Other >
PlainPermutationType	operator* (const PermutationBase< Other > &other) const

template<typename Other >
PlainPermutationType	operator* (const InverseImpl< Other, PermutationStorage > &other) const

Index	determinant () const

EIGEN_DEVICE_FUNC Derived &	derived ()

EIGEN_DEVICE_FUNC const Derived &	derived () const

Public Member Functions inherited from Eigen::EigenBase< Derived >
EIGEN_DEVICE_FUNC Derived &	derived ()

EIGEN_DEVICE_FUNC const Derived &	derived () const

EIGEN_DEVICE_FUNC Derived &	const_cast_derived () const

EIGEN_DEVICE_FUNC const Derived &	const_derived () const

EIGEN_DEVICE_FUNC Index	rows () const

EIGEN_DEVICE_FUNC Index	cols () const

EIGEN_DEVICE_FUNC Index	size () const

template<typename Dest >
EIGEN_DEVICE_FUNC void	evalTo (Dest &dst) const

template<typename Dest >
EIGEN_DEVICE_FUNC void	addTo (Dest &dst) const

template<typename Dest >
EIGEN_DEVICE_FUNC void	subTo (Dest &dst) const

template<typename Dest >
EIGEN_DEVICE_FUNC void	applyThisOnTheRight (Dest &dst) const

template<typename Dest >
EIGEN_DEVICE_FUNC void	applyThisOnTheLeft (Dest &dst) const

Protected Member Functions
template<typename OtherDerived >
void	assignTranspose (const PermutationBase< OtherDerived > &other)

template<typename Lhs , typename Rhs >
void	assignProduct (const Lhs &lhs, const Rhs &rhs)

Friends
template<typename Other >
PlainPermutationType	operator* (const InverseImpl< Other, PermutationStorage > &other, const PermutationBase &perm)

Detailed Description

template<typename Derived>
class Eigen::PermutationBase< Derived >

Base class for permutations.

Parameters

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 $\sigma$ is a permutation, the corresponding permutation matrix $P_\sigma$ is such that if $(e_1,\ldots,e_p)$ is the canonical basis, we have:

$P_\sigma(e_i) = e_{\sigma(i)}.$

This convention ensures that for any two permutations $\sigma, \tau$ , we have:

$P_{\sigma\circ\tau} = P_\sigma P_\tau.$

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.

See also: class PermutationMatrix, class PermutationWrapper

Member Function Documentation

◆ applyTranspositionOnTheLeft()

template<typename Derived >

Derived & Eigen::PermutationBase< Derived >::applyTranspositionOnTheLeft	(	Index	i,
		Index	j
	)

inline

Multiplies *this by the transposition $(ij)$ 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.

See also: applyTranspositionOnTheRight(Index,Index)

◆ applyTranspositionOnTheRight()

template<typename Derived >

Derived & Eigen::PermutationBase< Derived >::applyTranspositionOnTheRight	(	Index	i,
		Index	j
	)

inline

Multiplies *this by the transposition $(ij)$ on the right.

Returns: a reference to *this.

This is a fast operation, it only consists in swapping two indices.

See also: applyTranspositionOnTheLeft(Index,Index)

◆ cols()

template<typename Derived >

Index Eigen::PermutationBase< Derived >::cols ( ) const

inline

Returns: the number of columns

◆ derived() [1/2]

template<typename Derived >

EIGEN_DEVICE_FUNC Derived & Eigen::EigenBase< Derived >::derived ( )

inline

Returns: a reference to the derived object

◆ derived() [2/2]

template<typename Derived >

EIGEN_DEVICE_FUNC const Derived & Eigen::EigenBase< Derived >::derived ( ) const

inline

Returns: a const reference to the derived object

◆ determinant()

template<typename Derived >

Index Eigen::PermutationBase< Derived >::determinant ( ) const

inline

Returns: the determinant of the permutation matrix, which is either 1 or -1 depending on the parity of the permutation.

This function is O(n) procedure allocating a buffer of n booleans.

◆ indices()

template<typename Derived >

IndicesType & Eigen::PermutationBase< Derived >::indices ( )

inline

Returns: a reference to the stored array representing the permutation.

◆ inverse()

template<typename Derived >

InverseReturnType Eigen::PermutationBase< Derived >::inverse ( ) const

inline

Returns: the inverse permutation matrix.

Note: \note_try_to_help_rvo

◆ operator*() [1/2]

template<typename Derived >

template<typename Other >

PlainPermutationType Eigen::PermutationBase< Derived >::operator* ( const InverseImpl< Other, PermutationStorage > & other ) const

inline

Returns: the product of a permutation with another inverse permutation.

Note: \note_try_to_help_rvo

◆ operator*() [2/2]

template<typename Derived >

template<typename Other >

PlainPermutationType Eigen::PermutationBase< Derived >::operator* ( const PermutationBase< Other > & other ) const

inline

Returns: the product permutation matrix.

Note: \note_try_to_help_rvo

◆ operator=()

template<typename Derived >

Derived & Eigen::PermutationBase< Derived >::operator= ( const PermutationBase< Derived > & other )

inline

This is a special case of the templated operator=.

Its purpose is to prevent a default operator= from hiding the templated operator=.

◆ rows()

template<typename Derived >

Index Eigen::PermutationBase< Derived >::rows ( ) const

inline

Returns: the number of rows

◆ size()

template<typename Derived >

Index Eigen::PermutationBase< Derived >::size ( ) const

inline

Returns: the size of a side of the respective square matrix, i.e., the number of indices

◆ toDenseMatrix()

template<typename Derived >

DenseMatrixType Eigen::PermutationBase< Derived >::toDenseMatrix ( ) const

inline

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.

◆ transpose()

template<typename Derived >

InverseReturnType Eigen::PermutationBase< Derived >::transpose ( ) const

inline

Returns: the tranpose permutation matrix.

Note: \note_try_to_help_rvo

Friends And Related Symbol Documentation

◆ operator*

template<typename Derived >

template<typename Other >

PlainPermutationType operator*	(	const InverseImpl< Other, PermutationStorage > &	other,
		const PermutationBase< Derived > &	perm
	)

friend

Returns: the product of an inverse permutation with another permutation.

Note: \note_try_to_help_rvo

The documentation for this class was generated from the following file:

External/Eigen/src/Core/PermutationMatrix.h

Public Types

Public Member Functions

Protected Member Functions

Friends

Detailed Description

Member Function Documentation

◆ applyTranspositionOnTheLeft()

◆ applyTranspositionOnTheRight()

◆ cols()

◆ derived() [1/2]

◆ derived() [2/2]

◆ determinant()

◆ indices()

◆ inverse()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator=()

◆ rows()

◆ size()

◆ toDenseMatrix()

◆ transpose()

Friends And Related Symbol Documentation

◆ operator*