Eigen: Eigen::PermutationBase< Derived > Class Template Reference

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#include <Eigen/src/Core/PermutationMatrix.h>

Detailed Description

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

Base class for permutations.

Template 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, and with a diagonal matrix (DiagonalBase) on either side, which yields a ScaledPermutationMatrix.

See also: class PermutationMatrix, class PermutationWrapper

Inheritance diagram for Eigen::PermutationBase< Derived >:

Public Member Functions
InverseReturnType	adjoint () const

Derived &	applyTranspositionOnTheLeft (Index i, Index j)

Derived &	applyTranspositionOnTheRight (Index i, Index j)

Index	cols () const

Index	determinant () const

DenseMatrixType	eval () const

constexpr IndicesType &	indices ()

constexpr const IndicesType &	indices () const

InverseReturnType	inverse () const

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

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

template<typename OtherDerived>
Derived &	operator= (const PermutationBase< OtherDerived > &other)

template<typename OtherDerived>
Derived &	operator= (const TranspositionsBase< OtherDerived > &tr)

void	resize (Index newSize)

Index	rows () const

void	setIdentity ()

void	setIdentity (Index newSize)

Index	size () const

DenseMatrixType	toDenseMatrix () const

InverseReturnType	transpose () const

Public Member Functions inherited from Eigen::EigenBase< Derived >
constexpr Index	cols () const noexcept

constexpr Derived &	derived ()

constexpr const Derived &	derived () const

constexpr Index	rows () const noexcept

constexpr Index	size () const noexcept

Additional Inherited Members
Public Types inherited from Eigen::EigenBase< Derived >
using	Index
	The interface type of indices.

Member Function Documentation

◆ adjoint()

template<typename Derived>

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

inline

Returns: the adjoint of the permutation matrix. Its entries are real and it is orthogonal, so this equals transpose() and inverse().

Note: This function returns the result by value. In order to make that efficient, it is implemented as just a return statement using a special constructor, hopefully allowing the compiler to perform a RVO (return value optimization).

◆ 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.

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

◆ 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.

◆ eval()

template<typename Derived>

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

inline

Returns: the plain matrix representation of the permutation.

◆ indices() [1/2]

template<typename Derived>

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

inlineconstexpr

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

◆ indices() [2/2]

template<typename Derived>

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

inlineconstexpr

const version of indices().

◆ inverse()

template<typename Derived>

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

inline

Returns: the inverse permutation matrix.

Note: This function returns the result by value. In order to make that efficient, it is implemented as just a return statement using a special constructor, hopefully allowing the compiler to perform a RVO (return value optimization).

◆ 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: This function returns the result by value. In order to make that efficient, it is implemented as just a return statement using a special constructor, hopefully allowing the compiler to perform a RVO (return value optimization).

◆ 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: This function returns the result by value. In order to make that efficient, it is implemented as just a return statement using a special constructor, hopefully allowing the compiler to perform a RVO (return value optimization).

◆ operator=() [1/2]

template<typename Derived>

template<typename OtherDerived>

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

inline

Copies the other permutation into *this

◆ operator=() [2/2]

template<typename Derived>

template<typename OtherDerived>

Derived & Eigen::PermutationBase< Derived >::operator= ( const TranspositionsBase< OtherDerived > & tr )

inline

Assignment from the Transpositions tr

◆ resize()

template<typename Derived>

void Eigen::PermutationBase< Derived >::resize ( Index newSize )

inline

Resizes to given size.

◆ rows()

template<typename Derived>

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

inline

Returns: the number of rows

◆ setIdentity() [1/2]

template<typename Derived>

void Eigen::PermutationBase< Derived >::setIdentity ( )

inline

Sets *this to be the identity permutation matrix

◆ setIdentity() [2/2]

template<typename Derived>

void Eigen::PermutationBase< Derived >::setIdentity ( Index newSize )

inline

Sets *this to be the identity permutation matrix of given size.

◆ 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 transpose permutation matrix.

Note: This function returns the result by value. In order to make that efficient, it is implemented as just a return statement using a special constructor, hopefully allowing the compiler to perform a RVO (return value optimization).

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

/builds/libeigen/eigen/Eigen/src/Core/PermutationMatrix.h

Detailed Description

Public Member Functions

Additional Inherited Members

Member Function Documentation

◆ adjoint()

◆ applyTranspositionOnTheLeft()

◆ applyTranspositionOnTheRight()

◆ cols()

◆ determinant()

◆ eval()

◆ indices() [1/2]

◆ indices() [2/2]

◆ inverse()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ resize()

◆ rows()

◆ setIdentity() [1/2]

◆ setIdentity() [2/2]

◆ size()

◆ toDenseMatrix()

◆ transpose()