Eigen::PermutationBase< Derived > Class Template Reference

Base class for permutations. More...

#include <PermutationMatrix.h>

Inheritance diagram for Eigen::PermutationBase< Derived >:

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
Public Types inherited from Eigen::EigenBase< Derived >
typedef Eigen::Index	Index
	The interface type of indices. More...
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)
EIGEN_DEVICE_FUNC Index	rows () const
EIGEN_DEVICE_FUNC Index	cols () const
EIGEN_DEVICE_FUNC 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
constexpr EIGEN_DEVICE_FUNC Derived &	derived ()
constexpr EIGEN_DEVICE_FUNC const Derived &	derived () const
Public Member Functions inherited from Eigen::EigenBase< Derived >
constexpr EIGEN_DEVICE_FUNC Derived &	derived ()
constexpr EIGEN_DEVICE_FUNC const Derived &	derived () const
EIGEN_DEVICE_FUNC Derived &	const_cast_derived () const
EIGEN_DEVICE_FUNC const Derived &	const_derived () const
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT
EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	size () const EIGEN_NOEXCEPT
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
template<typename Device >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DeviceWrapper< Derived, Device >	device (Device &device)
template<typename Device >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DeviceWrapper< const Derived, Device >	device (Device &device) 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

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

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

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, i, Eigen::PermutationBase< Derived >::indices(), j, k, and Eigen::PermutationBase< Derived >::size().

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, i, Eigen::PermutationBase< Derived >::indices(), j, Eigen::PermutationBase< Derived >::size(), and swap().

Referenced by Eigen::ColPivHouseholderQR< MatrixType_, PermutationIndex_ >::computeInPlace(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::computeInPlace(), and Eigen::PermutationBase< Derived >::operator=().

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

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

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

cols()

template<typename Derived >

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

inline

Returns

the number of columns

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

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

Referenced by gdb.printers._MatrixEntryIterator::__next__(), gdb.printers.EigenMatrixPrinter::children(), gdb.printers.EigenSparseMatrixPrinter::children(), gdb.printers.EigenMatrixPrinter::to_string(), and gdb.printers.EigenSparseMatrixPrinter::to_string().

derived() [1/2]

template<typename Derived >

constexpr EIGEN_DEVICE_FUNC Derived& Eigen::EigenBase< Derived >::derived

inlineconstexpr

Returns

a reference to the derived object

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

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

derived() [2/2]

template<typename Derived >

constexpr EIGEN_DEVICE_FUNC const Derived& Eigen::EigenBase< Derived >::derived

inlineconstexpr

Returns

a const reference to the derived object

{ 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::Matrix< Scalar_, Rows_, Cols_, Options_, MaxRows_, MaxCols_ >::coeffRef(), Eigen::PermutationBase< Derived >::indices(), k, n, UniformPSDSelfTest::r, res, and Eigen::PermutationBase< Derived >::size().

evalTo()

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

indices() [1/2]

template<typename Derived >

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

inline

Returns

a reference to the stored array representing the permutation.

{ return derived().indices(); }

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

indices() [2/2]

template<typename Derived >

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

inline

const version of indices().

{ return derived().indices(); }

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

Referenced by Eigen::PermutationBase< Derived >::applyTranspositionOnTheLeft(), Eigen::PermutationBase< Derived >::applyTranspositionOnTheRight(), Eigen::PermutationBase< Derived >::assignProduct(), Eigen::PermutationBase< Derived >::assignTranspose(), Eigen::PermutationBase< Derived >::cols(), Eigen::PermutationBase< Derived >::determinant(), Eigen::PermutationBase< Derived >::evalTo(), Eigen::PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, StorageIndex_ >::operator=(), Eigen::PermutationBase< Derived >::operator=(), Eigen::PermutationBase< Derived >::resize(), Eigen::PermutationBase< Derived >::rows(), Eigen::PermutationBase< Derived >::setIdentity(), and Eigen::PermutationBase< Derived >::size().

inverse()

template<typename Derived >

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

inline

Returns

the inverse permutation matrix.

Note

\blank \note_try_to_help_rvo

{ return InverseReturnType(derived()); }

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

Referenced by Eigen::SparseLU< MatrixType_, OrderingType_ >::_solve_impl(), and Eigen::FullPivLU< MatrixType_, PermutationIndex_ >::_solve_impl_transposed().

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

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

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

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

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

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

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

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

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

operator=() [2/2]

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(), k, Eigen::PermutationBase< Derived >::setIdentity(), Eigen::PermutationBase< Derived >::size(), and Eigen::TranspositionsBase< Derived >::size().

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::ColPivHouseholderQR< MatrixType_, PermutationIndex_ >::init(), Eigen::internal::minimum_degree_ordering(), Eigen::NaturalOrdering< StorageIndex >::operator()(), Eigen::MetisOrdering< StorageIndex >::operator()(), Eigen::COLAMDOrdering< StorageIndex >::operator()(), and Eigen::PermutationBase< Derived >::setIdentity().

rows()

template<typename Derived >

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

inline

Returns

the number of rows

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

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

Referenced by gdb.printers._MatrixEntryIterator::__next__(), Eigen::PermutationBase< Derived >::assignProduct(), Eigen::PermutationBase< Derived >::assignTranspose(), gdb.printers.EigenMatrixPrinter::children(), gdb.printers.EigenSparseMatrixPrinter::children(), Eigen::PermutationBase< Derived >::evalTo(), gdb.printers.EigenMatrixPrinter::to_string(), and gdb.printers.EigenSparseMatrixPrinter::to_string().

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

Referenced by Eigen::ColPivHouseholderQR< MatrixType_, PermutationIndex_ >::computeInPlace(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::computeInPlace(), Eigen::PermutationBase< Derived >::operator=(), and Eigen::PermutationBase< Derived >::setIdentity().

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().

size()

template<typename Derived >

EIGEN_DEVICE_FUNC Index Eigen::PermutationBase< Derived >::size ( ) const

inline

Returns

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

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

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

Referenced by Eigen::SimplicialCholeskyBase< Derived >::_solve_impl(), Eigen::SparseQR< MatrixType_, OrderingType_ >::_solve_impl(), Eigen::PermutationBase< Derived >::applyTranspositionOnTheLeft(), Eigen::PermutationBase< Derived >::applyTranspositionOnTheRight(), Eigen::PermutationBase< Derived >::cols(), Eigen::PermutationBase< Derived >::determinant(), Eigen::SimplicialCholeskyBase< Derived >::dumpMemory(), Eigen::SimplicialCholeskyBase< Derived >::factorize(), Eigen::PermutationBase< Derived >::operator=(), Eigen::PermutationBase< Derived >::rows(), Eigen::PermutationBase< Derived >::setIdentity(), and Eigen::PermutationBase< Derived >::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.

{ return derived(); }

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

transpose()

template<typename Derived >

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

inline

Returns

the transpose permutation matrix.

Note

\blank \note_try_to_help_rvo

{ return InverseReturnType(derived()); }

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

Referenced by Eigen::PartialPivLU< MatrixType_, PermutationIndex_ >::_solve_impl_transposed(), Eigen::ColPivHouseholderQR< MatrixType_, PermutationIndex_ >::_solve_impl_transposed(), Eigen::FullPivHouseholderQR< MatrixType_, PermutationIndex_ >::_solve_impl_transposed(), and Eigen::SparseInverse< Scalar >::computeInverse().

Friends And Related Function 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

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

---

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

• PermutationMatrix.h