Base class for permutations. More...

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

Inheritance diagram for Eigen::PermutationBase< Derived >:

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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

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)

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

Derived &	operator= (const PermutationBase &other)

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

IndicesType &	indices ()

void	resize (Index newSize)

void	setIdentity ()

void	setIdentity (Index newSize)

Derived &	applyTranspositionOnTheLeft (Index i, Index j)

Derived &	applyTranspositionOnTheRight (Index i, Index j)

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

EIGEN_DEVICE_FUNC Derived &	const_cast_derived () const

EIGEN_DEVICE_FUNC const Derived &	const_derived () 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)

Private Types
typedef internal::traits< Derived >	Traits

typedef EigenBase< Derived >	Base

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.

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.

See also: class PermutationMatrix, class PermutationWrapper

Member Typedef Documentation

◆ Base

template<typename Derived >

typedef EigenBase<Derived> Eigen::PermutationBase< Derived >::Base

private

◆ DenseMatrixType

template<typename Derived >

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

◆ Index

template<typename Derived >

typedef Eigen::Index Eigen::EigenBase< Derived >::Index

inherited

The interface type of indices.

To change this, #define the preprocessor symbol EIGEN_DEFAULT_DENSE_INDEX_TYPE.

See also: StorageIndex, TopicPreprocessorDirectives.

◆ IndicesType

template<typename Derived >

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

◆ InverseReturnType

template<typename Derived >

typedef Inverse<Derived> Eigen::PermutationBase< Derived >::InverseReturnType

◆ PlainObject

template<typename Derived >

typedef PlainPermutationType Eigen::PermutationBase< Derived >::PlainObject

◆ PlainPermutationType

template<typename Derived >

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

◆ Scalar

template<typename Derived >

typedef void Eigen::PermutationBase< Derived >::Scalar

◆ StorageIndex

template<typename Derived >

typedef Traits::StorageIndex Eigen::PermutationBase< Derived >::StorageIndex

◆ StorageKind

template<typename Derived >

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

inherited

◆ Traits

template<typename Derived >

typedef internal::traits<Derived> Eigen::PermutationBase< Derived >::Traits

private

Member Enumeration Documentation

◆ anonymous enum

template<typename Derived >

anonymous enum

Enumerator
Flags
RowsAtCompileTime
ColsAtCompileTime
MaxRowsAtCompileTime
MaxColsAtCompileTime

         {
      Flags = Traits::Flags,
      RowsAtCompileTime = Traits::RowsAtCompileTime,
      ColsAtCompileTime = Traits::ColsAtCompileTime,
      MaxRowsAtCompileTime = Traits::MaxRowsAtCompileTime,
      MaxColsAtCompileTime = Traits::MaxColsAtCompileTime
    };

Member Function Documentation

◆ addTo()

template<typename Derived >

template<typename Dest >

EIGEN_DEVICE_FUNC void Eigen::EigenBase< Derived >::addTo ( Dest & dst ) const

inlineinherited

  {
    // This is the default implementation,
    // derived class can reimplement it in a more optimized way.
    typename Dest::PlainObject res(rows(),cols());
    evalTo(res);
    dst += res;
  }

◆ applyThisOnTheLeft()

template<typename Derived >

template<typename Dest >

EIGEN_DEVICE_FUNC void Eigen::EigenBase< Derived >::applyThisOnTheLeft ( Dest & dst ) const

inlineinherited

  {
    // This is the default implementation,
    // derived class can reimplement it in a more optimized way.
    dst = this->derived() * dst;
  }

References Eigen::EigenBase< Derived >::derived().

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◆ applyThisOnTheRight()

template<typename Derived >

template<typename Dest >

EIGEN_DEVICE_FUNC void Eigen::EigenBase< Derived >::applyThisOnTheRight ( Dest & dst ) const

inlineinherited

  {
    // This is the default implementation,
    // derived class can reimplement it in a more optimized way.
    dst = dst * this->derived();
  }

References Eigen::EigenBase< Derived >::derived().

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◆ 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)

    {
      eigen_assert(i>=0 && j>=0 && i<size() && j<size());
      for(Index k = 0; k < size(); ++k)
      {
        if(indices().coeff(k) == i) indices().coeffRef(k) = StorageIndex(j);
        else if(indices().coeff(k) == j) indices().coeffRef(k) = StorageIndex(i);
      }
      return derived();
    }

References Eigen::PermutationBase< Derived >::derived(), eigen_assert, Eigen::PermutationBase< Derived >::indices(), and Eigen::PermutationBase< Derived >::size().

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◆ 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)

    {
      eigen_assert(i>=0 && j>=0 && i<size() && j<size());
      std::swap(indices().coeffRef(i), indices().coeffRef(j));
      return derived();
    }

References Eigen::PermutationBase< Derived >::derived(), eigen_assert, Eigen::PermutationBase< Derived >::indices(), and Eigen::PermutationBase< Derived >::size().

Referenced by Eigen::PermutationBase< Derived >::operator=().

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◆ assignProduct()

template<typename Derived >

template<typename Lhs , typename Rhs >

void Eigen::PermutationBase< Derived >::assignProduct	(	const Lhs &	lhs,
		const Rhs &	rhs
	)

inlineprotected

    {
      eigen_assert(lhs.cols() == rhs.rows());
      for (Index i=0; i<rows();++i) indices().coeffRef(i) = lhs.indices().coeff(rhs.indices().coeff(i));
    }

References eigen_assert, Eigen::PermutationBase< Derived >::indices(), and Eigen::PermutationBase< Derived >::rows().

Referenced by Eigen::PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex >::PermutationMatrix().

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◆ assignTranspose()

template<typename Derived >

template<typename OtherDerived >

void Eigen::PermutationBase< Derived >::assignTranspose ( const PermutationBase< OtherDerived > & other )

inlineprotected

    {
      for (Index i=0; i<rows();++i) indices().coeffRef(other.indices().coeff(i)) = i;
    }

References Eigen::PermutationBase< Derived >::indices(), and Eigen::PermutationBase< Derived >::rows().

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◆ cols()

template<typename Derived >

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

inline

Returns: the number of columns

105{ return Index(indices().size()); }

References Eigen::PermutationBase< Derived >::indices(), and Eigen::PermutationBase< Derived >::size().

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◆ const_cast_derived()

template<typename Derived >

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

inlineinherited

52 { return *static_cast<Derived*>(const_cast<EigenBase*>(this)); }

Referenced by Eigen::TriangularViewImpl< _MatrixType, _Mode, Dense >::swap().

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◆ const_derived()

template<typename Derived >

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

inlineinherited

55 { return *static_cast<const Derived*>(this); }

◆ derived() [1/2]

template<typename Derived >

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

inline

Returns: a reference to the derived object

45{ return *static_cast<Derived*>(this); }

Referenced by Eigen::PermutationBase< Derived >::applyTranspositionOnTheLeft(), Eigen::PermutationBase< Derived >::applyTranspositionOnTheRight(), Eigen::PermutationBase< Derived >::indices(), Eigen::PermutationBase< Derived >::indices(), Eigen::PermutationBase< Derived >::inverse(), Eigen::operator*(), Eigen::PermutationBase< Derived >::operator*(), Eigen::operator*(), Eigen::operator*(), Eigen::operator*(), Eigen::PermutationBase< Derived >::operator=(), Eigen::Map< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex >, _PacketAccess >::operator=(), Eigen::PermutationBase< Derived >::operator=(), Eigen::PermutationBase< Derived >::operator=(), Eigen::PermutationBase< Derived >::toDenseMatrix(), and Eigen::PermutationBase< Derived >::transpose().

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◆ 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

48{ return *static_cast<const Derived*>(this); }

◆ 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.

    {
      Index res = 1;
      Index n = size();
      Matrix<bool,RowsAtCompileTime,1,0,MaxRowsAtCompileTime> mask(n);
      mask.fill(false);
      Index r = 0;
      while(r < n)
      {
        // search for the next seed
        while(r<n && mask[r]) r++;
        if(r>=n)
          break;
        // we got one, let's follow it until we are back to the seed
        Index k0 = r++;
        mask.coeffRef(k0) = true;
        for(Index k=indices().coeff(k0); k!=k0; k=indices().coeff(k))
        {
          mask.coeffRef(k) = true;
          res = -res;
        }
      }
      return res;
    }

References Eigen::PermutationBase< Derived >::size().

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◆ evalTo() [1/2]

template<typename Derived >

template<typename Dest >

EIGEN_DEVICE_FUNC void Eigen::EigenBase< Derived >::evalTo ( Dest & dst ) const

inlineinherited

72 { derived().evalTo(dst); }

Referenced by Eigen::EigenBase< Derived >::subTo().

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◆ evalTo() [2/2]

template<typename Derived >

template<typename DenseDerived >

void Eigen::PermutationBase< Derived >::evalTo ( MatrixBase< DenseDerived > & other ) const

inline

    {
      other.setZero();
      for (Index i=0; i<rows(); ++i)
        other.coeffRef(indices().coeff(i),i) = typename DenseDerived::Scalar(1);
    }

References Eigen::PermutationBase< Derived >::indices(), Eigen::PermutationBase< Derived >::rows(), and Eigen::DenseBase< Derived >::setZero().

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◆ indices() [1/2]

template<typename Derived >

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

inline

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

132{ return derived().indices(); }

References Eigen::PermutationBase< Derived >::derived().

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◆ indices() [2/2]

template<typename Derived >

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

inline

const version of indices().

130{ return derived().indices(); }

References Eigen::PermutationBase< Derived >::derived().

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◆ inverse()

template<typename Derived >

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

inline

Returns: the inverse permutation matrix.

Note: \blank \note_try_to_help_rvo

197 { return InverseReturnType(derived()); }

Eigen::PermutationBase::InverseReturnType

Inverse< Derived > InverseReturnType

Definition PermutationMatrix.h:68

References Eigen::PermutationBase< Derived >::derived().

Referenced by Eigen::SparseLU< _MatrixType, _OrderingType >::_solve_impl(), and Eigen::FullPivLU< _MatrixType >::_solve_impl_transposed().

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◆ 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: \blank \note_try_to_help_rvo

239 { return PlainPermutationType(internal::PermPermProduct, *this, other.eval()); }

Eigen::PermutationBase::PlainPermutationType

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

Definition PermutationMatrix.h:65

Eigen::internal::PermPermProduct

@ PermPermProduct

Definition PermutationMatrix.h:18

References Eigen::internal::PermPermProduct.

◆ 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: \blank \note_try_to_help_rvo

231 { return PlainPermutationType(internal::PermPermProduct, derived(), other.derived()); }

References Eigen::PermutationBase< Derived >::derived(), and Eigen::internal::PermPermProduct.

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◆ operator=() [1/3]

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=.

    {
      indices() = other.indices();
      return derived();
    }

References Eigen::PermutationBase< Derived >::derived(), and Eigen::PermutationBase< Derived >::indices().

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◆ operator=() [2/3]

template<typename Derived >

template<typename OtherDerived >

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

inline

Copies the other permutation into *this

    {
      indices() = other.indices();
      return derived();
    }

References Eigen::PermutationBase< Derived >::derived(), and Eigen::PermutationBase< Derived >::indices().

Referenced by Eigen::PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex >::operator=().

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◆ operator=() [3/3]

template<typename Derived >

template<typename OtherDerived >

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

inline

Assignment from the Transpositions tr

    {
      setIdentity(tr.size());
      for(Index k=size()-1; k>=0; --k)
        applyTranspositionOnTheRight(k,tr.coeff(k));
      return derived();
    }

References Eigen::PermutationBase< Derived >::applyTranspositionOnTheRight(), Eigen::TranspositionsBase< Derived >::coeff(), Eigen::PermutationBase< Derived >::derived(), Eigen::PermutationBase< Derived >::setIdentity(), Eigen::PermutationBase< Derived >::size(), and Eigen::TranspositionsBase< Derived >::size().

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◆ resize()

template<typename Derived >

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

inline

Resizes to given size.

    {
      indices().resize(newSize);
    }

References Eigen::PermutationBase< Derived >::indices().

Referenced by Eigen::internal::minimum_degree_ordering(), Eigen::NaturalOrdering< StorageIndex >::operator()(), Eigen::MetisOrdering< StorageIndex >::operator()(), Eigen::COLAMDOrdering< StorageIndex >::operator()(), and Eigen::PermutationBase< Derived >::setIdentity().

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◆ rows()

template<typename Derived >

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

inline

Returns: the number of rows

102{ return Index(indices().size()); }

References Eigen::PermutationBase< Derived >::indices(), and Eigen::PermutationBase< Derived >::size().

Referenced by Eigen::PermutationBase< Derived >::assignProduct(), Eigen::PermutationBase< Derived >::assignTranspose(), and Eigen::PermutationBase< Derived >::evalTo().

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◆ setIdentity() [1/2]

template<typename Derived >

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

inline

Sets *this to be the identity permutation matrix

    {
      StorageIndex n = StorageIndex(size());
      for(StorageIndex i = 0; i < n; ++i)
        indices().coeffRef(i) = i;
    }

References Eigen::PermutationBase< Derived >::indices(), and Eigen::PermutationBase< Derived >::size().

Referenced by Eigen::PermutationBase< Derived >::operator=(), and Eigen::PermutationBase< Derived >::setIdentity().

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◆ 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.

    {
      resize(newSize);
      setIdentity();
    }

References Eigen::PermutationBase< Derived >::resize(), and Eigen::PermutationBase< Derived >::setIdentity().

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◆ 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

108{ return Index(indices().size()); }

References Eigen::PermutationBase< Derived >::indices(), and Eigen::PermutationBase< Derived >::size().

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◆ subTo()

template<typename Derived >

template<typename Dest >

EIGEN_DEVICE_FUNC void Eigen::EigenBase< Derived >::subTo ( Dest & dst ) const

inlineinherited

  {
    // This is the default implementation,
    // derived class can reimplement it in a more optimized way.
    typename Dest::PlainObject res(rows(),cols());
    evalTo(res);
    dst -= res;
  }

References Eigen::EigenBase< Derived >::cols(), Eigen::EigenBase< Derived >::evalTo(), and Eigen::EigenBase< Derived >::rows().

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◆ 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.

    {
      return derived();
    }

References Eigen::PermutationBase< Derived >::derived().

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◆ transpose()

template<typename Derived >

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

inline

Returns: the tranpose permutation matrix.

Note: \blank \note_try_to_help_rvo

203 { return InverseReturnType(derived()); }

References Eigen::PermutationBase< Derived >::derived().

Referenced by Eigen::PartialPivLU< _MatrixType >::_solve_impl_transposed(), and Eigen::internal::permutation_matrix_product< ExpressionType, Side, Transposed, SparseShape >::run().

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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: \blank \note_try_to_help_rvo

247 { return PlainPermutationType(internal::PermPermProduct, other.eval(), perm); }

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

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

Public Types

Public Member Functions

Protected Member Functions

Private Types

Friends

Detailed Description

Member Typedef Documentation

◆ Base

◆ DenseMatrixType

◆ Index

◆ IndicesType

◆ InverseReturnType

◆ PlainObject

◆ PlainPermutationType

◆ Scalar

◆ StorageIndex

◆ StorageKind

◆ Traits

Member Enumeration Documentation

◆ anonymous enum

Member Function Documentation

◆ addTo()

◆ applyThisOnTheLeft()

◆ applyThisOnTheRight()

◆ applyTranspositionOnTheLeft()

◆ applyTranspositionOnTheRight()

◆ assignProduct()

◆ assignTranspose()

◆ cols()

◆ const_cast_derived()

◆ const_derived()

◆ derived() [1/2]

◆ derived() [2/2]

◆ determinant()

◆ evalTo() [1/2]

◆ evalTo() [2/2]

◆ indices() [1/2]

◆ indices() [2/2]

◆ inverse()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator=() [1/3]

◆ operator=() [2/3]

◆ operator=() [3/3]

◆ resize()

◆ rows()

◆ setIdentity() [1/2]

◆ setIdentity() [2/2]

◆ size()

◆ subTo()

◆ toDenseMatrix()

◆ transpose()

Friends And Related Symbol Documentation

◆ operator*