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PermutationBase< Derived > Class Template Reference

Base class for permutations. More...

#include <PermutationMatrix.h>

+ Inheritance diagram for PermutationBase< Derived >:

Public Member Functions

Derived & applyTranspositionOnTheLeft (Index i, Index j)
 
Derived & applyTranspositionOnTheRight (Index i, Index j)
 
Index cols () const
 
Derived & derived ()
 
const Derived & derived () const
 
const IndicesType & indices () const
 
IndicesType & indices ()
 
Transpose< PermutationBaseinverse () const
 
template<typename Other >
PlainPermutationType operator* (const PermutationBase< Other > &other) const
 
template<typename Other >
PlainPermutationType operator* (const Transpose< 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 size)
 
Index rows () const
 
void setIdentity ()
 
void setIdentity (Index size)
 
Index size () const
 
DenseMatrixType toDenseMatrix () const
 
Transpose< PermutationBasetranspose () const
 

Friends

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

Detailed Description

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

Base class for permutations.

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

Member Function Documentation

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(int,int): this has linear complexity and requires a lot of branching.
See Also
applyTranspositionOnTheRight(int,int)
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(int,int)

Referenced by PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, Index > >::operator=().

Index cols ( void  ) const
inline
Returns
the number of columns
Derived& derived ( )
inlineinherited
Returns
a reference to the derived object

Referenced by MatrixBase< Derived >::applyOnTheLeft(), MatrixBase< Derived >::applyOnTheRight(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, Index > >::applyTranspositionOnTheLeft(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, Index > >::applyTranspositionOnTheRight(), SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::binaryExpr(), EigenBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, Index > >::cols(), SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::cols(), SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::eval(), SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::imag(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, Index > >::indices(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, Index > >::inverse(), SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::nonZeros(), RotationBase< Derived, 3 >::operator*(), Translation< _Scalar, _Dim >::operator*(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, Index > >::operator*(), SparseMatrixBase< Derived >::operator*(), Transform< _Scalar, _Dim, _Mode, _Options >::operator*(), Eigen::operator*(), MatrixBase< Derived >::operator*=(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, Index > >::operator=(), DenseBase< Derived >::operator=(), Transform< _Scalar, _Dim, _Mode, _Options >::operator=(), PlainObjectBase< Matrix< int, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::operator=(), PlainObjectBase< Matrix< int, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::PlainObjectBase(), PlainObjectBase< Matrix< int, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::resizeLike(), EigenBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, Index > >::rows(), SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::rows(), SimplicialCholeskyBase< SimplicialLDLT< _MatrixType, _UpLo > >::solve(), IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >::solve(), CholmodBase< _MatrixType, _UpLo, CholmodSimplicialLLT< _MatrixType, _UpLo > >::solve(), SparseMatrix< Scalar, RowMajor >::SparseMatrix(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, Index > >::toDenseMatrix(), Transform< _Scalar, _Dim, _Mode, _Options >::Transform(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, Index > >::transpose(), and SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::twistedBy().

const Derived& derived ( ) const
inlineinherited
Returns
a const reference to the derived object
const IndicesType& indices ( ) const
inline
IndicesType& indices ( )
inline
Returns
a reference to the stored array representing the permutation.
Transpose<PermutationBase> 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).
PlainPermutationType 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).
PlainPermutationType operator* ( const Transpose< PermutationBase< Other > > &  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).
Derived& operator= ( const PermutationBase< OtherDerived > &  other)
inline

Copies the other permutation into *this

Referenced by PermutationMatrix< RowsAtCompileTime, MaxRowsAtCompileTime >::operator=().

Derived& operator= ( const TranspositionsBase< OtherDerived > &  tr)
inline

Assignment from the Transpositions tr

void resize ( Index  size)
inline
Index rows ( void  ) const
inline
Returns
the number of rows
void setIdentity ( )
inline
void setIdentity ( Index  size)
inline

Sets *this to be the identity permutation matrix of given size.

Index size ( ) const
inline
DenseMatrixType 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<PermutationBase> 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

PlainPermutationType operator* ( const Transpose< PermutationBase< Other > > &  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: