W3cubDocs
/Eigen3Eigen::PermutationBase
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
| 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 >
| |
| EIGEN_CONSTEXPR Index | cols () const EIGEN_NOEXCEPT |
| Derived & | derived () |
| const Derived & | derived () const |
| EIGEN_CONSTEXPR Index | rows () const EIGEN_NOEXCEPT |
| EIGEN_CONSTEXPR Index | size () const EIGEN_NOEXCEPT |
|
Public Types inherited from Eigen::EigenBase< Derived >
| |
| typedef Eigen::Index | Index |
| The interface type of indices. More... |
|
applyTranspositionOnTheLeft()
template<typename Derived >
| 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.
applyTranspositionOnTheRight()
template<typename Derived >
| 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.
cols()
template<typename Derived >
| inline |
- Returns
- the number of columns
determinant()
template<typename Derived >
| 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 >
| inline |
- Returns
- a reference to the stored array representing the permutation.
indices() [2/2]
template<typename Derived >
| inline |
const version of indices().
inverse()
template<typename Derived >
| 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 >
| 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 >
| 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 >
| inline |
Copies the other permutation into *this
operator=() [2/2]
template<typename Derived >
template<typename OtherDerived >
| inline |
Assignment from the Transpositions tr
resize()
template<typename Derived >
| inline |
Resizes to given size.
rows()
template<typename Derived >
| inline |
- Returns
- the number of rows
setIdentity() [1/2]
template<typename Derived >
| inline |
Sets *this to be the identity permutation matrix
setIdentity() [2/2]
template<typename Derived >
| inline |
Sets *this to be the identity permutation matrix of given size.
size()
template<typename Derived >
| inline |
- Returns
- the size of a side of the respective square matrix, i.e., the number of indices
toDenseMatrix()
template<typename Derived >
| inline |
transpose()
template<typename Derived >
| 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:
© Eigen.
Licensed under the MPL2 License.
https://eigen.tuxfamily.org/dox/classEigen_1_1PermutationBase.html