Eigen  3.3.3
Public Member Functions | Friends
Eigen::PermutationBase< Derived > Class Template 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 >:

List of all members.

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

Friends

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

Member Function Documentation

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)
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)
template<typename Derived>
Index Eigen::PermutationBase< Derived >::cols ( void  ) const [inline]
Returns:
the number of columns

Reimplemented from Eigen::EigenBase< Derived >.

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.

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

const version of indices().

Reimplemented in Eigen::PermutationWrapper< _IndicesType >, Eigen::PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex >, Eigen::PermutationMatrix< ColsAtCompileTime, MaxColsAtCompileTime >, Eigen::PermutationMatrix< Dynamic, Dynamic, StorageIndex >, and Eigen::PermutationMatrix< RowsAtCompileTime, MaxRowsAtCompileTime >.

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

Reimplemented in Eigen::PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, _StorageIndex >, Eigen::PermutationMatrix< ColsAtCompileTime, MaxColsAtCompileTime >, Eigen::PermutationMatrix< Dynamic, Dynamic, StorageIndex >, and Eigen::PermutationMatrix< RowsAtCompileTime, MaxRowsAtCompileTime >.

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).
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).
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).
template<typename Derived>
template<typename OtherDerived >
Derived& Eigen::PermutationBase< Derived >::operator= ( const PermutationBase< OtherDerived > &  other) [inline]

Copies the other permutation into *this

template<typename Derived>
template<typename OtherDerived >
Derived& Eigen::PermutationBase< Derived >::operator= ( const TranspositionsBase< OtherDerived > &  tr) [inline]

Assignment from the Transpositions tr

template<typename Derived>
void Eigen::PermutationBase< Derived >::resize ( Index  newSize) [inline]

Resizes to given size.

template<typename Derived>
Index Eigen::PermutationBase< Derived >::rows ( void  ) const [inline]
Returns:
the number of rows

Reimplemented from Eigen::EigenBase< Derived >.

template<typename Derived>
void Eigen::PermutationBase< Derived >::setIdentity ( ) [inline]

Sets *this to be the identity permutation matrix

template<typename Derived>
void Eigen::PermutationBase< Derived >::setIdentity ( Index  newSize) [inline]

Sets *this to be the identity permutation matrix of given 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

Reimplemented from Eigen::EigenBase< Derived >.

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.
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

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:
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