Base class for permutations. More...

#include <PermutationMatrix.h>

Inheritance diagram for PermutationBase< Derived >:

Public Types
enum	{ Flags = Traits::Flags, CoeffReadCost = Traits::CoeffReadCost, RowsAtCompileTime = Traits::RowsAtCompileTime, ColsAtCompileTime = Traits::ColsAtCompileTime, MaxRowsAtCompileTime = Traits::MaxRowsAtCompileTime, MaxColsAtCompileTime = Traits::MaxColsAtCompileTime }
typedef Matrix< Scalar, RowsAtCompileTime, ColsAtCompileTime, 0, MaxRowsAtCompileTime, MaxColsAtCompileTime >	DenseMatrixType
typedef Traits::Index	Index
typedef Traits::IndicesType	IndicesType
typedef PermutationMatrix < IndicesType::SizeAtCompileTime, IndicesType::MaxSizeAtCompileTime, Index >	PlainPermutationType
typedef Traits::Scalar	Scalar
Public Member Functions
Derived &	applyTranspositionOnTheLeft (Index i, Index j)
Derived &	applyTranspositionOnTheRight (Index i, Index j)
Index	cols () const
template<typename DenseDerived >
void	evalTo (MatrixBase< DenseDerived > &other) const
const IndicesType &	indices () const
IndicesType &	indices ()
Transpose< PermutationBase >	inverse () const
template<typename Other >
PlainPermutationType	operator* (const PermutationBase< Other > &other) const
template<typename Other >
PlainPermutationType	operator* (const Transpose< PermutationBase< Other > > &other) const
template<typename OtherDerived >
Derived &	operator= (const PermutationBase< OtherDerived > &other)
template<typename OtherDerived >
Derived &	operator= (const TranspositionsBase< OtherDerived > &tr)
Derived &	operator= (const PermutationBase &other)
void	resize (Index size)
Index	rows () const
void	setIdentity ()
void	setIdentity (Index size)
Index	size () const
DenseMatrixType	toDenseMatrix () const
Transpose< PermutationBase >	transpose () const
Protected Member Functions
template<typename Lhs , typename Rhs >
void	assignProduct (const Lhs &lhs, const Rhs &rhs)
template<typename OtherDerived >
void	assignTranspose (const PermutationBase< OtherDerived > &other)
Private Types
typedef EigenBase< Derived >	Base
typedef internal::traits< Derived >	Traits
Friends
template<typename Other >
PlainPermutationType	operator* (const Transpose< PermutationBase< Other > > &other, const PermutationBase &perm)

Detailed Description

template<typename Derived>
class 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

Definition at line 64 of file PermutationMatrix.h.

Member Typedef Documentation

template<typename Derived>

typedef EigenBase<Derived> PermutationBase< Derived >::Base [private]

Reimplemented in PermutationWrapper< _IndicesType >, Map< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType >, _PacketAccess >, PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType >, PermutationMatrix< Dynamic >, PermutationMatrix< Dynamic, Dynamic >, PermutationMatrix< ColsAtCompileTime, MaxColsAtCompileTime >, and PermutationMatrix< RowsAtCompileTime, MaxRowsAtCompileTime >.

Definition at line 67 of file PermutationMatrix.h.

template<typename Derived>

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

Definition at line 83 of file PermutationMatrix.h.

template<typename Derived>

typedef Traits::Index PermutationBase< Derived >::Index

Reimplemented from EigenBase< Derived >.

Reimplemented in Map< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType >, _PacketAccess >.

Definition at line 81 of file PermutationMatrix.h.

template<typename Derived>

typedef Traits::IndicesType PermutationBase< Derived >::IndicesType

Reimplemented in PermutationWrapper< _IndicesType >, Map< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType >, _PacketAccess >, PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType >, PermutationMatrix< Dynamic >, PermutationMatrix< Dynamic, Dynamic >, PermutationMatrix< ColsAtCompileTime, MaxColsAtCompileTime >, and PermutationMatrix< RowsAtCompileTime, MaxRowsAtCompileTime >.

Definition at line 71 of file PermutationMatrix.h.

template<typename Derived>

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

Definition at line 85 of file PermutationMatrix.h.

template<typename Derived>

typedef Traits::Scalar PermutationBase< Derived >::Scalar

Definition at line 80 of file PermutationMatrix.h.

template<typename Derived>

typedef internal::traits<Derived> PermutationBase< Derived >::Traits [private]

Reimplemented in PermutationWrapper< _IndicesType >, Map< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType >, _PacketAccess >, PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType >, PermutationMatrix< Dynamic >, PermutationMatrix< Dynamic, Dynamic >, PermutationMatrix< ColsAtCompileTime, MaxColsAtCompileTime >, and PermutationMatrix< RowsAtCompileTime, MaxRowsAtCompileTime >.

Definition at line 66 of file PermutationMatrix.h.

Member Enumeration Documentation

template<typename Derived>

anonymous enum

Enumerator:

Flags
CoeffReadCost
RowsAtCompileTime
ColsAtCompileTime
MaxRowsAtCompileTime
MaxColsAtCompileTime

Definition at line 72 of file PermutationMatrix.h.

Member Function Documentation

template<typename Derived>

Derived& 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)

Definition at line 182 of file PermutationMatrix.h.

template<typename Derived>

Derived& 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)

Definition at line 201 of file PermutationMatrix.h.

template<typename Derived>

template<typename Lhs , typename Rhs >

void PermutationBase< Derived >::assignProduct	(	const Lhs &	lhs,
		const Rhs &	rhs
	)		`[inline, protected]`

Definition at line 232 of file PermutationMatrix.h.

template<typename Derived>

template<typename OtherDerived >

void PermutationBase< Derived >::assignTranspose ( const PermutationBase< OtherDerived > & other ) [inline, protected]

Definition at line 227 of file PermutationMatrix.h.

template<typename Derived>

Index PermutationBase< Derived >::cols ( void ) const [inline]

Returns:: the number of columns

Reimplemented from EigenBase< Derived >.

Definition at line 122 of file PermutationMatrix.h.

template<typename Derived>

template<typename DenseDerived >

void PermutationBase< Derived >::evalTo ( MatrixBase< DenseDerived > & other ) const [inline]

Definition at line 129 of file PermutationMatrix.h.

template<typename Derived>

const IndicesType& PermutationBase< Derived >::indices ( ) const [inline]

const version of indices().

Reimplemented in PermutationWrapper< _IndicesType >, Map< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType >, _PacketAccess >, PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType >, PermutationMatrix< Dynamic >, PermutationMatrix< Dynamic, Dynamic >, PermutationMatrix< ColsAtCompileTime, MaxColsAtCompileTime >, and PermutationMatrix< RowsAtCompileTime, MaxRowsAtCompileTime >.

Definition at line 147 of file PermutationMatrix.h.

template<typename Derived>

IndicesType& PermutationBase< Derived >::indices ( ) [inline]

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

Reimplemented in Map< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType >, _PacketAccess >, PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType >, PermutationMatrix< Dynamic >, PermutationMatrix< Dynamic, Dynamic >, PermutationMatrix< ColsAtCompileTime, MaxColsAtCompileTime >, and PermutationMatrix< RowsAtCompileTime, MaxRowsAtCompileTime >.

Definition at line 149 of file PermutationMatrix.h.

template<typename Derived>

Transpose<PermutationBase> PermutationBase< Derived >::inverse ( ) const [inline]

Returns:: the inverse permutation matrix.

Note:

Definition at line 212 of file PermutationMatrix.h.

template<typename Derived>

template<typename Other >

PlainPermutationType PermutationBase< Derived >::operator* ( const PermutationBase< Other > & other ) const [inline]

Returns:: the product permutation matrix.

Note:

Definition at line 246 of file PermutationMatrix.h.

template<typename Derived>

template<typename Other >

PlainPermutationType PermutationBase< Derived >::operator* ( const Transpose< PermutationBase< Other > > & other ) const [inline]

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

Note:

Definition at line 254 of file PermutationMatrix.h.

template<typename Derived>

template<typename OtherDerived >

Derived& PermutationBase< Derived >::operator= ( const PermutationBase< OtherDerived > & other ) [inline]

Copies the other permutation into *this

Definition at line 91 of file PermutationMatrix.h.

template<typename Derived>

template<typename OtherDerived >

Derived& PermutationBase< Derived >::operator= ( const TranspositionsBase< OtherDerived > & tr ) [inline]

Assignment from the Transpositions tr

Definition at line 99 of file PermutationMatrix.h.

template<typename Derived>

Derived& 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=.

Definition at line 111 of file PermutationMatrix.h.

template<typename Derived>

void PermutationBase< Derived >::resize ( Index size ) [inline]

Resizes to given size.

Definition at line 153 of file PermutationMatrix.h.

template<typename Derived>

Index PermutationBase< Derived >::rows ( void ) const [inline]

Returns:: the number of rows

Reimplemented from EigenBase< Derived >.

Definition at line 119 of file PermutationMatrix.h.

template<typename Derived>

void PermutationBase< Derived >::setIdentity ( ) [inline]

Sets *this to be the identity permutation matrix

Definition at line 159 of file PermutationMatrix.h.

template<typename Derived>

void PermutationBase< Derived >::setIdentity ( Index size ) [inline]

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

Definition at line 167 of file PermutationMatrix.h.

template<typename Derived>

Index PermutationBase< Derived >::size ( ) const [inline]

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

Reimplemented from EigenBase< Derived >.

Definition at line 125 of file PermutationMatrix.h.

template<typename Derived>

DenseMatrixType 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.

Definition at line 141 of file PermutationMatrix.h.

template<typename Derived>

Transpose<PermutationBase> PermutationBase< Derived >::transpose ( ) const [inline]

Returns:: the tranpose permutation matrix.

Note:

Definition at line 218 of file PermutationMatrix.h.

Friends And Related Function Documentation

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:

Definition at line 262 of file PermutationMatrix.h.

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

PermutationMatrix.h

Public Types

Public Member Functions

Protected Member Functions

Private Types

Friends

Detailed Description

template<typename Derived> class PermutationBase< Derived >

Member Typedef Documentation

Member Enumeration Documentation

Member Function Documentation

Friends And Related Function Documentation

template<typename Derived>
class PermutationBase< Derived >