Eigen  3.3.4
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Eigen::PermutationBase< Derived > Class Template Reference
Dense matrix and array manipulation » Reference » Core module

Detailed Description

template<typename Derived>
class Eigen::PermutationBase< Derived >

Base class for permutations.

Template Parameters
Derivedthe 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
 
const IndicesType & indices () const
 
IndicesType & indices ()
 
InverseReturnType inverse () const
 
template<typename Other >
PlainPermutationType operator* (const PermutationBase< Other > &other) const
 
template<typename Other >
PlainPermutationType operator* (const InverseImpl< Other, PermutationStorage > &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
 

Friends

template<typename Other >
PlainPermutationType operator* (const InverseImpl< Other, PermutationStorage > &other, const PermutationBase &perm)
 

Additional Inherited Members

- Public Types inherited from Eigen::EigenBase< Derived >
typedef Eigen::Index Index
 The interface type of indices. More...
 

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)

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

const version of indices().

◆ indices() [2/2]

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

◆ 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 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*() [2/2]

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=() [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).

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
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: