Eigen::PermutationBase< Derived > Class Template Reference

Base class for permutations. More...

Inheritance diagram for Eigen::PermutationBase< Derived >:

Public Member Functions
Derived &	applyTranspositionOnTheLeft (Index i, Index j)
Derived &	applyTranspositionOnTheRight (Index i, Index j)
Index	cols () const
Index	determinant () const
IndicesType &	indices ()
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 >
template<typename Dest >
void	addTo (Dest &dst) const
template<typename Dest >
void	applyThisOnTheLeft (Dest &dst) const
template<typename Dest >
void	applyThisOnTheRight (Dest &dst) const
EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT
Derived &	const_cast_derived () const
const Derived &	const_derived () const
Derived &	derived ()
const Derived &	derived () const
template<typename Dest >
void	evalTo (Dest &dst) const
EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT
EIGEN_CONSTEXPR Index	size () const EIGEN_NOEXCEPT
template<typename Dest >
void	subTo (Dest &dst) const

Private Types
typedef EigenBase< Derived >	Base
typedef internal::traits< Derived >	Traits

Additional Inherited Members
Public Types inherited from Eigen::EigenBase< Derived >
typedef Eigen::Index	Index
	The interface type of indices. More...
typedef internal::traits< Derived >::StorageKind	StorageKind

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

Definition at line 48 of file PermutationMatrix.h.

Member Typedef Documentation

Base

template<typename Derived >

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

private

Definition at line 51 of file PermutationMatrix.h.

Traits

template<typename Derived >

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

private

Definition at line 50 of file PermutationMatrix.h.

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)

Definition at line 157 of file PermutationMatrix.h.

    {
      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();
    }

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)

Definition at line 176 of file PermutationMatrix.h.

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

cols()

template<typename Derived >

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

inline

Returns

the number of columns

Definition at line 96 of file PermutationMatrix.h.

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

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.

Definition at line 244 of file PermutationMatrix.h.

    {
      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;
    }

indices() [1/2]

template<typename Derived >

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

inline

Returns

a reference to the stored array representing the permutation.

Definition at line 123 of file PermutationMatrix.h.

{ return derived().indices(); }

indices() [2/2]

template<typename Derived >

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

inline

const version of indices().

Definition at line 121 of file PermutationMatrix.h.

{ return derived().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).

Definition at line 187 of file PermutationMatrix.h.

    { return InverseReturnType(derived()); }

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).

Definition at line 229 of file PermutationMatrix.h.

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

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).

Definition at line 221 of file PermutationMatrix.h.

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

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

Definition at line 76 of file PermutationMatrix.h.

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

operator=() [2/2]

template<typename Derived >

template<typename OtherDerived >

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

inline

Assignment from the Transpositions tr

Definition at line 84 of file PermutationMatrix.h.

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

resize()

template<typename Derived >

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

inline

Resizes to given size.

Definition at line 127 of file PermutationMatrix.h.

    {
      indices().resize(newSize);
    }

rows()

template<typename Derived >

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

inline

Returns

the number of rows

Definition at line 93 of file PermutationMatrix.h.

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

setIdentity() [1/2]

template<typename Derived >

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

inline

Sets *this to be the identity permutation matrix

Definition at line 133 of file PermutationMatrix.h.

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

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.

Definition at line 142 of file PermutationMatrix.h.

    {
      resize(newSize);
      setIdentity();
    }

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

Definition at line 99 of file PermutationMatrix.h.

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

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.

Definition at line 115 of file PermutationMatrix.h.

    {
      return derived();
    }

transpose()

template<typename Derived >

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

inline

Returns

the tranpose 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).

Definition at line 193 of file PermutationMatrix.h.

    { return InverseReturnType(derived()); }

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

• PermutationMatrix.h