Eigen::ScaledPermutationBase< Derived > Class Template Reference

#include <Eigen/src/Core/ScaledPermutationMatrix.h>

Detailed Description

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

Base class for scaled permutation matrices.

A scaled permutation is the product \(P D\) of a permutation matrix and a diagonal matrix: a square matrix with exactly one nonzero per row and per column. It is stored as the permutation's indices and one scale per column, so that coefficient (indices()(k), k) equals scales()(k).

The set is closed under products with permutations, diagonal matrices, scalars and other scaled permutations, and under inversion and transposition; all of these cost \(O(n)\) and return a plain ScaledPermutationMatrix. Products with a dense matrix scale and permute its rows or columns in \(O(nm)\), and assigning to a dense matrix scatters the scales, so writing P * D * x or P * D * P.inverse() never forms an \(n \times n\) intermediate. Sums with a dense matrix are lazy expressions.

See also

class ScaledPermutationMatrix, class PermutationBase, class DiagonalBase

Inheritance diagram for Eigen::ScaledPermutationBase< Derived >:

Public Member Functions
PlainObject	adjoint () const
Scalar	coeff (Index row, Index col) const
constexpr Index	cols () const
Scalar	determinant () const
constexpr const IndicesType &	indices () const
PlainObject	inverse () const
template<typename OtherDerived>
internal::scaled_permutation_product_result< Derived, OtherDerived, StorageIndex >::type	operator* (const DiagonalBase< OtherDerived > &other) const
template<typename OtherDerived>
PlainObject	operator* (const InverseImpl< OtherDerived, PermutationStorage > &other) const
template<typename OtherDerived>
const Product< Derived, OtherDerived, DefaultProduct >	operator* (const MatrixBase< OtherDerived > &other) const
template<typename OtherDerived>
PlainObject	operator* (const PermutationBase< OtherDerived > &other) const
PlainObject	operator* (const Scalar &alpha) const
template<typename OtherDerived>
internal::scaled_permutation_product_result< Derived, OtherDerived, StorageIndex >::type	operator* (const ScaledPermutationBase< OtherDerived > &other) const
template<typename OtherDerived>
const Product< Derived, OtherDerived, DefaultProduct >	operator* (const TriangularBase< OtherDerived > &other) const
PlainObject	operator- () const
const PermutationType &	permutation () const
constexpr Index	rows () const
const ScalesType &	scales () const
DenseMatrixType	toDenseMatrix () const
PlainObject	transpose () const
Public Member Functions inherited from Eigen::EigenBase< Derived >
constexpr Index	cols () const noexcept
constexpr Derived &	derived ()
constexpr const Derived &	derived () const
constexpr Index	rows () const noexcept
constexpr Index	size () const noexcept

Additional Inherited Members
Public Types inherited from Eigen::EigenBase< Derived >
using	Index
	The interface type of indices.

Member Function Documentation

adjoint()

template<typename Derived>

PlainObject Eigen::ScaledPermutationBase< Derived >::adjoint ( ) const

inline

Returns

the adjoint, the transpose with conjugated scales

coeff()

template<typename Derived>

Scalar Eigen::ScaledPermutationBase< Derived >::coeff ( Index row, Index col ) const

inline

Returns

the coefficient at (row, col) of the represented matrix

cols()

template<typename Derived>

Index Eigen::ScaledPermutationBase< Derived >::cols ( ) const

inlineconstexpr

Returns

the number of columns

determinant()

template<typename Derived>

Scalar Eigen::ScaledPermutationBase< Derived >::determinant ( ) const

inline

Returns

the determinant, the permutation's sign times the product of the scales

indices()

template<typename Derived>

const IndicesType & Eigen::ScaledPermutationBase< Derived >::indices ( ) const

inlineconstexpr

Returns

the permutation's indices: column k has its nonzero in row indices()(k)

inverse()

template<typename Derived>

PlainObject Eigen::ScaledPermutationBase< Derived >::inverse ( ) const

inline

Returns

the inverse, \((PD)^{-1} = D^{-1} P^{-1}\), which has \(1 / \text{scales}(k)\) at (k, indices()(k)). The scales must be nonzero.

operator*() [1/7]

template<typename Derived>

template<typename OtherDerived>

internal::scaled_permutation_product_result< Derived, OtherDerived, StorageIndex >::type Eigen::ScaledPermutationBase< Derived >::operator* ( const DiagonalBase< OtherDerived > & other ) const

inline

Returns

the scaled permutation *this times the diagonal matrix other

operator*() [2/7]

template<typename Derived>

template<typename OtherDerived>

PlainObject Eigen::ScaledPermutationBase< Derived >::operator* ( const InverseImpl< OtherDerived, PermutationStorage > & other ) const

inline

Returns

the scaled permutation *this times the inverse permutation other

operator*() [3/7]

template<typename Derived>

template<typename OtherDerived>

const Product< Derived, OtherDerived, DefaultProduct > Eigen::ScaledPermutationBase< Derived >::operator* ( const MatrixBase< OtherDerived > & other ) const

inline

Returns

the dense matrix product of *this by the dense matrix other: rows of other are scaled and permuted.

operator*() [4/7]

template<typename Derived>

template<typename OtherDerived>

PlainObject Eigen::ScaledPermutationBase< Derived >::operator* ( const PermutationBase< OtherDerived > & other ) const

inline

Returns

the scaled permutation *this times the permutation other

operator*() [5/7]

template<typename Derived>

PlainObject Eigen::ScaledPermutationBase< Derived >::operator* ( const Scalar & alpha ) const

inline

Returns

*this with its scales multiplied by alpha

operator*() [6/7]

template<typename Derived>

template<typename OtherDerived>

internal::scaled_permutation_product_result< Derived, OtherDerived, StorageIndex >::type Eigen::ScaledPermutationBase< Derived >::operator* ( const ScaledPermutationBase< OtherDerived > & other ) const

inline

Returns

the scaled permutation *this times the scaled permutation other

operator*() [7/7]

template<typename Derived>

template<typename OtherDerived>

const Product< Derived, OtherDerived, DefaultProduct > Eigen::ScaledPermutationBase< Derived >::operator* ( const TriangularBase< OtherDerived > & other ) const

inline

Returns

the dense matrix product of *this by the triangular or self-adjoint view other

operator-()

template<typename Derived>

PlainObject Eigen::ScaledPermutationBase< Derived >::operator- ( ) const

inline

Returns

*this with its scales negated

permutation()

template<typename Derived>

const PermutationType & Eigen::ScaledPermutationBase< Derived >::permutation ( ) const

inline

Returns

the permutation factor \(P\)

rows()

template<typename Derived>

Index Eigen::ScaledPermutationBase< Derived >::rows ( ) const

inlineconstexpr

Returns

the number of rows

scales()

template<typename Derived>

const ScalesType & Eigen::ScaledPermutationBase< Derived >::scales ( ) const

inline

Returns

the scales: column k's nonzero equals scales()(k)

toDenseMatrix()

template<typename Derived>

DenseMatrixType Eigen::ScaledPermutationBase< Derived >::toDenseMatrix ( ) const

inline

Returns

the represented matrix as a plain dense matrix

transpose()

template<typename Derived>

PlainObject Eigen::ScaledPermutationBase< Derived >::transpose ( ) const

inline

Returns

the transpose, which has scales()(k) at (k, indices()(k))

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The documentation for this class was generated from the following file:

• /builds/libeigen/eigen/Eigen/src/Core/ScaledPermutationMatrix.h