Please, help us to better know about our user community by answering the following short survey: https://forms.gle/wpyrxWi18ox9Z5ae9 Eigen  3.3.9 Eigen::PermutationBase< Derived > Class Template Reference

## 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 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 >
Index cols () const

Derived & derived ()

const Derived & derived () const

Index rows () const

Index size () const

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

## ◆ 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)

## ◆ 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 ( void ) 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.

## ◆ indices() [1/2]

template<typename Derived >
 IndicesType& Eigen::PermutationBase< Derived >::indices ( )
inline
Returns
a reference to the stored array representing the permutation.

## ◆ indices() [2/2]

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

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 ( void ) 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 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).

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