Base class for permutations. More...

#include <PermutationMatrix.h>

Inheritance diagram for Eigen::PermutationBase< Derived >:

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

typedef Traits::IndicesType	IndicesType

typedef Traits::Scalar	Scalar

typedef Traits::Index	Index

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

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

Public Types inherited from Eigen::EigenBase< Derived >
typedef internal::traits< Derived >::StorageKind	StorageKind

typedef internal::traits< Derived >::Index	Index

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=. More...

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(). More...

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 \((ij)\) on the left. More...

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

Transpose< PermutationBase >	inverse () const

Transpose< PermutationBase >	transpose () const

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

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

Index	determinant () const

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

const Derived &	derived () const

Derived &	const_cast_derived () const

const Derived &	const_derived () const

Index	rows () const

Index	cols () const

Index	size () const

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

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

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

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

template<typename Dest >
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 Transpose< PermutationBase< Other > > &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(int,int): this has linear complexity and requires a lot of branching.

See also: applyTranspositionOnTheRight(int,int)

§ 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(int,int)

§ cols()

template<typename Derived>

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

inline

Returns: the number of columns

§ 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() [1/2]

template<typename Derived>

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

inline

const version of indices().

§ indices() [2/2]

template<typename Derived>

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

inline

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

§ inverse()

template<typename Derived>

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

inline

Returns: the inverse permutation matrix.

Note

§ operator*() [1/2]

template<typename Derived>

template<typename Other >

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

inline

Returns: the product permutation matrix.

Note

§ operator*() [2/2]

template<typename Derived>

template<typename Other >

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

inline

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

Note

§ 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 ( void ) 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>

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

inline

Returns: the tranpose permutation matrix.

Note

Friends And Related Function Documentation

§ operator*

template<typename Derived>

template<typename Other >

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

friend

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

Note

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

vendor/eigen/Eigen/src/Core/PermutationMatrix.h

Public Types

Public Member Functions

Protected Member Functions

Friends

Detailed Description

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

Member Function Documentation

§ applyTranspositionOnTheLeft()

§ applyTranspositionOnTheRight()

§ cols()

§ determinant()

§ indices() [1/2]

§ indices() [2/2]

§ inverse()

§ operator*() [1/2]

§ operator*() [2/2]

§ operator=()

§ rows()

§ size()

§ toDenseMatrix()

§ transpose()

Friends And Related Function Documentation

§ operator*

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