Eigen  3.2.7
•All Classes Namespaces Functions Variables Typedefs Enumerations Enumerator Friends Groups Pages
List of all members | Public Member Functions | Friends
PermutationBase< Derived > Class Template Reference
Core module

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
+ 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
 
Index determinant () const
 
const IndicesType & indices () const
 
IndicesType & indices ()
 
Transpose< PermutationBase > inverse () 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 newSize)
 
Index rows () const
 
void setIdentity ()
 
void setIdentity (Index newSize)
 
Index size () const
 
DenseMatrixType toDenseMatrix () const
 
Transpose< PermutationBase > transpose () const
 

Friends

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

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, IndexType > >::operator=().

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

Referenced by IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >::analyzePattern(), MatrixBase< Derived >::applyOnTheLeft(), MatrixBase< Derived >::applyOnTheRight(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::applyTranspositionOnTheLeft(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::applyTranspositionOnTheRight(), SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::bottomRows(), EigenBase< SparseSymmetricPermutationProduct< MatrixType, UpLo > >::cols(), SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::cols(), IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >::compute(), SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::eval(), IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >::factorize(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::indices(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::inverse(), IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >::IterativeSolverBase(), RotationBase< Derived, 3 >::operator*(), SparseSelfAdjointView< MatrixType, UpLo >::operator*(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::operator*(), SparseMatrixBase< Derived >::operator*(), SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::operator*(), Transform< Scalar, Dim, Mode, _Options >::operator*(), Eigen::operator*(), MatrixBase< Derived >::operator*=(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::operator=(), DenseBase< Derived >::operator=(), Transform< Scalar, Dim, Mode, _Options >::operator=(), PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::operator=(), PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::PlainObjectBase(), SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::real(), PlainObjectBase< Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols > >::resizeLike(), EigenBase< SparseSymmetricPermutationProduct< MatrixType, UpLo > >::rows(), SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::rows(), SimplicialCholeskyBase< SimplicialLDLT< _MatrixType, _UpLo, _Ordering > >::solve(), IterativeSolverBase< ConjugateGradient< _MatrixType, _UpLo, _Preconditioner > >::solve(), SparseLU< _MatrixType, _OrderingType >::solve(), UmfPackLU< _MatrixType >::solve(), CholmodBase< _MatrixType, _UpLo, CholmodSimplicialLLT< _MatrixType, _UpLo > >::solve(), SuperLUBase< _MatrixType, SuperILU< _MatrixType > >::solve(), SparseMatrix< Scalar, RowMajor >::SparseMatrix(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::toDenseMatrix(), SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::topLeftCorner(), Transform< Scalar, Dim, Mode, _Options >::Transform(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::transpose(), and SparseMatrixBase< CwiseBinaryOp< BinaryOp, Lhs, Rhs > >::twistedBy().

const Derived& derived ( ) const
inlineinherited
Returns
a const reference to the derived object
Index 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.

const IndicesType& indices ( ) const
inline

const version of indices().

Referenced by PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::applyTranspositionOnTheLeft(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::applyTranspositionOnTheRight(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::cols(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::determinant(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::operator=(), PermutationMatrix< RowsAtCompileTime, MaxRowsAtCompileTime >::operator=(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::resize(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::rows(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::setIdentity(), and PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::size().

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  newSize)
inline

Resizes to given size.

Referenced by NaturalOrdering< Index >::operator()(), COLAMDOrdering< Index >::operator()(), and PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::setIdentity().

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

Sets *this to be the identity permutation matrix

Referenced by PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::operator=(), and PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::setIdentity().

void setIdentity ( Index  newSize)
inline

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

Index size ( ) const
inline
Returns
the size of a side of the respective square matrix, i.e., the number of indices

Referenced by PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::applyTranspositionOnTheLeft(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::applyTranspositionOnTheRight(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::cols(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::determinant(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::operator=(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::rows(), PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::setIdentity(), and PermutationBase< PermutationMatrix< SizeAtCompileTime, MaxSizeAtCompileTime, IndexType > >::size().

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: