Base class for skew symmetric matrices and expressions. More...

#include <SkewSymmetricMatrix3.h>

Inheritance diagram for Eigen::SkewSymmetricBase< Derived >:

Public Types
enum	{ RowsAtCompileTime = SkewSymmetricVectorType::SizeAtCompileTime , ColsAtCompileTime = SkewSymmetricVectorType::SizeAtCompileTime , MaxRowsAtCompileTime = SkewSymmetricVectorType::MaxSizeAtCompileTime , MaxColsAtCompileTime = SkewSymmetricVectorType::MaxSizeAtCompileTime , IsVectorAtCompileTime = 0 , Flags = NoPreferredStorageOrderBit }

typedef internal::traits< Derived >::SkewSymmetricVectorType	SkewSymmetricVectorType

typedef SkewSymmetricVectorType::Scalar	Scalar

typedef SkewSymmetricVectorType::RealScalar	RealScalar

typedef internal::traits< Derived >::StorageKind	StorageKind

typedef internal::traits< Derived >::StorageIndex	StorageIndex

typedef Matrix< Scalar, RowsAtCompileTime, ColsAtCompileTime, 0, MaxRowsAtCompileTime, MaxColsAtCompileTime >	DenseMatrixType

typedef DenseMatrixType	DenseType

typedef SkewSymmetricMatrix3< Scalar >	PlainObject

template<typename OtherDerived >
using	SkewSymmetricProductReturnType = SkewSymmetricWrapper< const EIGEN_CWISE_BINARY_RETURN_TYPE(SkewSymmetricVectorType, typename OtherDerived::SkewSymmetricVectorType, product)>

using	SkewSymmetricScaleReturnType = SkewSymmetricWrapper< const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(SkewSymmetricVectorType, Scalar, product)>

using	ScaleSkewSymmetricReturnType = SkewSymmetricWrapper< const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar, SkewSymmetricVectorType, product)>

template<typename OtherDerived >
using	SkewSymmetricSumReturnType = SkewSymmetricWrapper< const EIGEN_CWISE_BINARY_RETURN_TYPE(SkewSymmetricVectorType, typename OtherDerived::SkewSymmetricVectorType, sum)>

template<typename OtherDerived >
using	SkewSymmetricDifferenceReturnType = SkewSymmetricWrapper< const EIGEN_CWISE_BINARY_RETURN_TYPE(SkewSymmetricVectorType, typename OtherDerived::SkewSymmetricVectorType, difference)>

Public Types inherited from Eigen::EigenBase< Derived >
typedef Eigen::Index	Index
	The interface type of indices. More...

typedef internal::traits< Derived >::StorageKind	StorageKind

Public Member Functions
EIGEN_DEVICE_FUNC const Derived &	derived () const

EIGEN_DEVICE_FUNC Derived &	derived ()

EIGEN_DEVICE_FUNC DenseMatrixType	toDenseMatrix () const

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Scalar	determinant () const

EIGEN_DEVICE_FUNC PlainObject	transpose () const

EIGEN_DEVICE_FUNC DenseMatrixType	exponential () const

EIGEN_DEVICE_FUNC const SkewSymmetricVectorType &	vector () const

EIGEN_DEVICE_FUNC SkewSymmetricVectorType &	vector ()

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	rows () const

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	cols () const

template<typename MatrixDerived >
EIGEN_DEVICE_FUNC Product< Derived, MatrixDerived, LazyProduct >	operator* (const MatrixBase< MatrixDerived > &matrix) const

template<typename MatrixDerived >
EIGEN_DEVICE_FUNC Product< Derived, MatrixDerived, LazyProduct >	operator* (const SkewSymmetricBase< MatrixDerived > &matrix) const

template<typename OtherDerived >
EIGEN_DEVICE_FUNC SkewSymmetricProductReturnType< OtherDerived >	wedge (const SkewSymmetricBase< OtherDerived > &other) const

EIGEN_DEVICE_FUNC SkewSymmetricScaleReturnType	operator* (const Scalar &scalar) const

template<typename OtherDerived >
EIGEN_DEVICE_FUNC SkewSymmetricSumReturnType< OtherDerived >	operator+ (const SkewSymmetricBase< OtherDerived > &other) const

template<typename OtherDerived >
EIGEN_DEVICE_FUNC SkewSymmetricDifferenceReturnType< OtherDerived >	operator- (const SkewSymmetricBase< OtherDerived > &other) const

Public Member Functions inherited from Eigen::EigenBase< Derived >
constexpr EIGEN_DEVICE_FUNC Derived &	derived ()

constexpr EIGEN_DEVICE_FUNC const Derived &	derived () const

EIGEN_DEVICE_FUNC Derived &	const_cast_derived () const

EIGEN_DEVICE_FUNC const Derived &	const_derived () const

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index	size () const EIGEN_NOEXCEPT

template<typename Dest >
EIGEN_DEVICE_FUNC void	evalTo (Dest &dst) const

template<typename Dest >
EIGEN_DEVICE_FUNC void	addTo (Dest &dst) const

template<typename Dest >
EIGEN_DEVICE_FUNC void	subTo (Dest &dst) const

template<typename Dest >
EIGEN_DEVICE_FUNC void	applyThisOnTheRight (Dest &dst) const

template<typename Dest >
EIGEN_DEVICE_FUNC void	applyThisOnTheLeft (Dest &dst) const

template<typename Device >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DeviceWrapper< Derived, Device >	device (Device &device)

template<typename Device >
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE DeviceWrapper< const Derived, Device >	device (Device &device) const

Friends
EIGEN_DEVICE_FUNC friend ScaleSkewSymmetricReturnType	operator* (const Scalar &scalar, const SkewSymmetricBase &other)

Detailed Description

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

Base class for skew symmetric matrices and expressions.

This is the base class that is inherited by SkewSymmetricMatrix3 and related expression types, which internally use a three vector for storing the entries. SkewSymmetric types always represent square three times three matrices.

This implementations follows class DiagonalMatrix

Template Parameters

Derived is the derived type, a SkewSymmetricMatrix3 or SkewSymmetricWrapper.

See also: class SkewSymmetricMatrix3, class SkewSymmetricWrapper

Member Typedef Documentation

◆ DenseMatrixType

template<typename Derived >

typedef Matrix<Scalar, RowsAtCompileTime, ColsAtCompileTime, 0, MaxRowsAtCompileTime, MaxColsAtCompileTime> Eigen::SkewSymmetricBase< Derived >::DenseMatrixType

◆ DenseType

template<typename Derived >

typedef DenseMatrixType Eigen::SkewSymmetricBase< Derived >::DenseType

◆ PlainObject

template<typename Derived >

typedef SkewSymmetricMatrix3<Scalar> Eigen::SkewSymmetricBase< Derived >::PlainObject

◆ RealScalar

template<typename Derived >

typedef SkewSymmetricVectorType::RealScalar Eigen::SkewSymmetricBase< Derived >::RealScalar

◆ Scalar

template<typename Derived >

typedef SkewSymmetricVectorType::Scalar Eigen::SkewSymmetricBase< Derived >::Scalar

◆ ScaleSkewSymmetricReturnType

template<typename Derived >

using Eigen::SkewSymmetricBase< Derived >::ScaleSkewSymmetricReturnType = SkewSymmetricWrapper<const EIGEN_SCALAR_BINARYOP_EXPR_RETURN_TYPE(Scalar, SkewSymmetricVectorType, product)>

◆ SkewSymmetricDifferenceReturnType

template<typename Derived >

template<typename OtherDerived >

using Eigen::SkewSymmetricBase< Derived >::SkewSymmetricDifferenceReturnType = SkewSymmetricWrapper<const EIGEN_CWISE_BINARY_RETURN_TYPE( SkewSymmetricVectorType, typename OtherDerived::SkewSymmetricVectorType, difference)>

◆ SkewSymmetricProductReturnType

template<typename Derived >

template<typename OtherDerived >

using Eigen::SkewSymmetricBase< Derived >::SkewSymmetricProductReturnType = SkewSymmetricWrapper<const EIGEN_CWISE_BINARY_RETURN_TYPE( SkewSymmetricVectorType, typename OtherDerived::SkewSymmetricVectorType, product)>

◆ SkewSymmetricScaleReturnType

template<typename Derived >

using Eigen::SkewSymmetricBase< Derived >::SkewSymmetricScaleReturnType = SkewSymmetricWrapper<const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(SkewSymmetricVectorType, Scalar, product)>

◆ SkewSymmetricSumReturnType

template<typename Derived >

template<typename OtherDerived >

using Eigen::SkewSymmetricBase< Derived >::SkewSymmetricSumReturnType = SkewSymmetricWrapper<const EIGEN_CWISE_BINARY_RETURN_TYPE( SkewSymmetricVectorType, typename OtherDerived::SkewSymmetricVectorType, sum)>

◆ SkewSymmetricVectorType

template<typename Derived >

typedef internal::traits<Derived>::SkewSymmetricVectorType Eigen::SkewSymmetricBase< Derived >::SkewSymmetricVectorType

◆ StorageIndex

template<typename Derived >

typedef internal::traits<Derived>::StorageIndex Eigen::SkewSymmetricBase< Derived >::StorageIndex

◆ StorageKind

template<typename Derived >

typedef internal::traits<Derived>::StorageKind Eigen::SkewSymmetricBase< Derived >::StorageKind

Member Enumeration Documentation

◆ anonymous enum

template<typename Derived >

anonymous enum

Enumerator
RowsAtCompileTime
ColsAtCompileTime
MaxRowsAtCompileTime
MaxColsAtCompileTime
IsVectorAtCompileTime
Flags

        {
     RowsAtCompileTime = SkewSymmetricVectorType::SizeAtCompileTime,
     ColsAtCompileTime = SkewSymmetricVectorType::SizeAtCompileTime,
     MaxRowsAtCompileTime = SkewSymmetricVectorType::MaxSizeAtCompileTime,
     MaxColsAtCompileTime = SkewSymmetricVectorType::MaxSizeAtCompileTime,
     IsVectorAtCompileTime = 0,
     Flags = NoPreferredStorageOrderBit
   };

Member Function Documentation

◆ cols()

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index Eigen::SkewSymmetricBase< Derived >::cols ( ) const

inline

Returns: the number of columns.

96 { return 3; }

Referenced by gdb.printers._MatrixEntryIterator::__next__(), gdb.printers.EigenMatrixPrinter::children(), gdb.printers.EigenSparseMatrixPrinter::children(), anonymous_namespace{skew_symmetric_matrix3.cpp}::constructors(), gdb.printers.EigenMatrixPrinter::to_string(), and gdb.printers.EigenSparseMatrixPrinter::to_string().

◆ derived() [1/2]

template<typename Derived >

EIGEN_DEVICE_FUNC Derived& Eigen::SkewSymmetricBase< Derived >::derived ( )

inline

Returns: a const reference to the derived object.

60 { return *static_cast<Derived*>(this); }

◆ derived() [2/2]

template<typename Derived >

EIGEN_DEVICE_FUNC const Derived& Eigen::SkewSymmetricBase< Derived >::derived ( ) const

inline

Returns: a reference to the derived object.

58 { return *static_cast<const Derived*>(this); }

Referenced by Eigen::SkewSymmetricBase< Derived >::exponential(), Eigen::SkewSymmetricBase< Derived >::operator*(), Eigen::MatrixBase< Derived >::operator*(), Eigen::SkewSymmetricBase< Derived >::toDenseMatrix(), and Eigen::SkewSymmetricBase< Derived >::vector().

◆ determinant()

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Scalar Eigen::SkewSymmetricBase< Derived >::determinant ( ) const

inline

Determinant vanishes

69 { return 0; }

◆ exponential()

template<typename Derived >

EIGEN_DEVICE_FUNC DenseMatrixType Eigen::SkewSymmetricBase< Derived >::exponential ( ) const

inline

Returns: the exponential of this matrix using Rodrigues’ formula

                                                         {
     DenseMatrixType retVal = DenseMatrixType::Identity();
     const SkewSymmetricVectorType& v = vector();
     if (v.isZero()) {
       return retVal;
     }
     const Scalar norm2 = v.squaredNorm();
     const Scalar norm = numext::sqrt(norm2);
     retVal += ((((1 - numext::cos(norm)) / norm2) * derived()) * derived()) +
               (numext::sin(norm) / norm) * derived().toDenseMatrix();
     return retVal;
   }

References Eigen::numext::cos(), Eigen::SkewSymmetricBase< Derived >::derived(), Eigen::numext::sin(), Eigen::numext::sqrt(), v, and Eigen::SkewSymmetricBase< Derived >::vector().

◆ operator*() [1/3]

template<typename Derived >

template<typename MatrixDerived >

EIGEN_DEVICE_FUNC Product<Derived, MatrixDerived, LazyProduct> Eigen::SkewSymmetricBase< Derived >::operator* ( const MatrixBase< MatrixDerived > & matrix ) const

inline

Returns: the matrix product of *this by the dense matrix, matrix

                                                      {
     return Product<Derived, MatrixDerived, LazyProduct>(derived(), matrix.derived());
   }

References Eigen::SkewSymmetricBase< Derived >::derived(), and matrix().

◆ operator*() [2/3]

template<typename Derived >

EIGEN_DEVICE_FUNC SkewSymmetricScaleReturnType Eigen::SkewSymmetricBase< Derived >::operator* ( const Scalar & scalar ) const

inline

Returns: the product of *this by the scalar scalar

                                                                                               {
     return (vector() * scalar).asSkewSymmetric();
   }

References Eigen::SkewSymmetricBase< Derived >::vector().

◆ operator*() [3/3]

template<typename Derived >

template<typename MatrixDerived >

EIGEN_DEVICE_FUNC Product<Derived, MatrixDerived, LazyProduct> Eigen::SkewSymmetricBase< Derived >::operator* ( const SkewSymmetricBase< MatrixDerived > & matrix ) const

inline

Returns: the matrix product of *this by the skew symmetric matrix, matrix

                                                             {
     return Product<Derived, MatrixDerived, LazyProduct>(derived(), matrix.derived());
   }

References Eigen::SkewSymmetricBase< Derived >::derived(), and matrix().

◆ operator+()

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC SkewSymmetricSumReturnType<OtherDerived> Eigen::SkewSymmetricBase< Derived >::operator+ ( const SkewSymmetricBase< OtherDerived > & other ) const

inline

Returns: the sum of *this and the skew symmetric matrix other

                                                           {
     return (vector() + other.vector()).asSkewSymmetric();
   }

References Eigen::SkewSymmetricBase< Derived >::vector().

◆ operator-()

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC SkewSymmetricDifferenceReturnType<OtherDerived> Eigen::SkewSymmetricBase< Derived >::operator- ( const SkewSymmetricBase< OtherDerived > & other ) const

inline

Returns: the difference of *this and the skew symmetric matrix other

                                                           {
     return (vector() - other.vector()).asSkewSymmetric();
   }

References Eigen::SkewSymmetricBase< Derived >::vector().

◆ rows()

template<typename Derived >

EIGEN_DEVICE_FUNC EIGEN_CONSTEXPR Index Eigen::SkewSymmetricBase< Derived >::rows ( ) const

inline

Returns: the number of rows.

94 { return 3; }

Referenced by gdb.printers._MatrixEntryIterator::__next__(), gdb.printers.EigenMatrixPrinter::children(), gdb.printers.EigenSparseMatrixPrinter::children(), anonymous_namespace{skew_symmetric_matrix3.cpp}::constructors(), gdb.printers.EigenMatrixPrinter::to_string(), and gdb.printers.EigenSparseMatrixPrinter::to_string().

◆ toDenseMatrix()

template<typename Derived >

EIGEN_DEVICE_FUNC DenseMatrixType Eigen::SkewSymmetricBase< Derived >::toDenseMatrix ( ) const

inline

Constructs a dense matrix from *this. Note, this directly returns a dense matrix type, not an expression.

Returns: A dense matrix, with its entries set from the the derived object.

66 { return derived(); }

References Eigen::SkewSymmetricBase< Derived >::derived().

Referenced by anonymous_namespace{skew_symmetric_matrix3.cpp}::constructors().

◆ transpose()

template<typename Derived >

EIGEN_DEVICE_FUNC PlainObject Eigen::SkewSymmetricBase< Derived >::transpose ( ) const

inline

A.transpose() = -A

72 { return (-vector()).asSkewSymmetric(); }

References Eigen::SkewSymmetricBase< Derived >::vector().

◆ vector() [1/2]

template<typename Derived >

EIGEN_DEVICE_FUNC SkewSymmetricVectorType& Eigen::SkewSymmetricBase< Derived >::vector ( )

inline

Returns: a const reference to the derived object's vector of coefficients.

91 { return derived().vector(); }

References Eigen::SkewSymmetricBase< Derived >::derived().

◆ vector() [2/2]

template<typename Derived >

EIGEN_DEVICE_FUNC const SkewSymmetricVectorType& Eigen::SkewSymmetricBase< Derived >::vector ( ) const

inline

Returns: a reference to the derived object's vector of coefficients.

89 { return derived().vector(); }

References Eigen::SkewSymmetricBase< Derived >::derived().

Referenced by Eigen::SkewSymmetricBase< Derived >::exponential(), Eigen::SkewSymmetricBase< Derived >::operator*(), Eigen::SkewSymmetricBase< Derived >::operator+(), Eigen::SkewSymmetricBase< Derived >::operator-(), Eigen::SkewSymmetricMatrix3< Scalar_ >::operator=(), Eigen::SkewSymmetricBase< Derived >::transpose(), and Eigen::SkewSymmetricBase< Derived >::wedge().

◆ wedge()

template<typename Derived >

template<typename OtherDerived >

EIGEN_DEVICE_FUNC SkewSymmetricProductReturnType<OtherDerived> Eigen::SkewSymmetricBase< Derived >::wedge ( const SkewSymmetricBase< OtherDerived > & other ) const

inline

Returns: the wedge product of *this by the skew symmetric matrix other A wedge B = AB - BA

                                                           {
     return vector().cross(other.vector()).asSkewSymmetric();
   }

References Eigen::SkewSymmetricBase< Derived >::vector().

Friends And Related Function Documentation

◆ operator*

template<typename Derived >

EIGEN_DEVICE_FUNC friend ScaleSkewSymmetricReturnType operator*	(	const Scalar &	scalar,
		const SkewSymmetricBase< Derived > &	other
	)

friend

Returns: the product of a scalar and the skew symmetric matrix other

                                                                                                          {
     return (scalar * other.vector()).asSkewSymmetric();
   }

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

SkewSymmetricMatrix3.h

Public Types

Public Member Functions

Friends

Detailed Description

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

Member Typedef Documentation

◆ DenseMatrixType

◆ DenseType

◆ PlainObject

◆ RealScalar

◆ Scalar

◆ ScaleSkewSymmetricReturnType

◆ SkewSymmetricDifferenceReturnType

◆ SkewSymmetricProductReturnType

◆ SkewSymmetricScaleReturnType

◆ SkewSymmetricSumReturnType

◆ SkewSymmetricVectorType

◆ StorageIndex

◆ StorageKind

Member Enumeration Documentation

◆ anonymous enum

Member Function Documentation

◆ cols()

◆ derived() [1/2]

◆ derived() [2/2]

◆ determinant()

◆ exponential()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator+()

◆ operator-()

◆ rows()

◆ toDenseMatrix()

◆ transpose()

◆ vector() [1/2]

◆ vector() [2/2]

◆ wedge()

Friends And Related Function Documentation

◆ operator*

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