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

Inheritance diagram for Eigen::SkewSymmetricBase< Derived >:

Public Types
enum	{ RowsAtCompileTime , ColsAtCompileTime , MaxRowsAtCompileTime , MaxColsAtCompileTime , IsVectorAtCompileTime , Flags }

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

typedef DenseMatrixType	DenseType

typedef SkewSymmetricMatrix3< Scalar >	PlainObject

typedef SkewSymmetricVectorType::RealScalar	RealScalar

typedef SkewSymmetricVectorType::Scalar	Scalar

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

template<typename OtherDerived >
using	SkewSymmetricDifferenceReturnType = SkewSymmetricWrapper< const CwiseBinaryOp< internal::scalar_difference_op< SkewSymmetricVectorType ::Scalar, typename OtherDerived::SkewSymmetricVectorType ::Scalar >, const SkewSymmetricVectorType, const typename OtherDerived::SkewSymmetricVectorType > >

template<typename OtherDerived >
using	SkewSymmetricProductReturnType = SkewSymmetricWrapper< const CwiseBinaryOp< internal::scalar_product_op< SkewSymmetricVectorType ::Scalar, typename OtherDerived::SkewSymmetricVectorType ::Scalar >, const SkewSymmetricVectorType, const typename OtherDerived::SkewSymmetricVectorType > >

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

template<typename OtherDerived >
using	SkewSymmetricSumReturnType = SkewSymmetricWrapper< const CwiseBinaryOp< internal::scalar_sum_op< SkewSymmetricVectorType ::Scalar, typename OtherDerived::SkewSymmetricVectorType ::Scalar >, const SkewSymmetricVectorType, const typename OtherDerived::SkewSymmetricVectorType > >

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

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

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

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_CONSTEXPR Index	cols () const

Derived &	derived ()

const Derived &	derived () const

EIGEN_CONSTEXPR Scalar	determinant () const

DenseMatrixType	exponential () const

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

SkewSymmetricScaleReturnType	operator* (const Scalar &scalar) const

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

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

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

EIGEN_CONSTEXPR Index	rows () const

DenseMatrixType	toDenseMatrix () const

PlainObject	transpose () const

SkewSymmetricVectorType &	vector ()

const SkewSymmetricVectorType &	vector () const

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

Public Member Functions inherited from Eigen::EigenBase< Derived >
template<typename Dest >
void	addTo (Dest &dst) const

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

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

EIGEN_CONSTEXPR Index	cols () const EIGEN_NOEXCEPT

Derived &	const_cast_derived () const

const Derived &	const_derived () const

Derived &	derived ()

const Derived &	derived () const

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

EIGEN_CONSTEXPR Index	rows () const EIGEN_NOEXCEPT

EIGEN_CONSTEXPR Index	size () const EIGEN_NOEXCEPT

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

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

Definition at line 34 of file SkewSymmetricMatrix3.h.

Member Typedef Documentation

◆ DenseMatrixType

template<typename Derived >

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

Definition at line 52 of file SkewSymmetricMatrix3.h.

◆ DenseType

template<typename Derived >

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

Definition at line 53 of file SkewSymmetricMatrix3.h.

◆ PlainObject

template<typename Derived >

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

Definition at line 54 of file SkewSymmetricMatrix3.h.

◆ RealScalar

template<typename Derived >

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

Definition at line 39 of file SkewSymmetricMatrix3.h.

◆ Scalar

template<typename Derived >

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

Definition at line 38 of file SkewSymmetricMatrix3.h.

◆ ScaleSkewSymmetricReturnType

template<typename Derived >

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

Definition at line 145 of file SkewSymmetricMatrix3.h.

◆ SkewSymmetricDifferenceReturnType

template<typename Derived >

template<typename OtherDerived >

using Eigen::SkewSymmetricBase< Derived >::SkewSymmetricDifferenceReturnType = SkewSymmetricWrapper<const CwiseBinaryOp< internal::scalar_difference_op < SkewSymmetricVectorType ::Scalar, typename OtherDerived::SkewSymmetricVectorType ::Scalar>, const SkewSymmetricVectorType , const typename OtherDerived::SkewSymmetricVectorType > >

Definition at line 166 of file SkewSymmetricMatrix3.h.

◆ SkewSymmetricProductReturnType

template<typename Derived >

template<typename OtherDerived >

using Eigen::SkewSymmetricBase< Derived >::SkewSymmetricProductReturnType = SkewSymmetricWrapper<const CwiseBinaryOp< internal::scalar_product_op < SkewSymmetricVectorType ::Scalar, typename OtherDerived::SkewSymmetricVectorType ::Scalar>, const SkewSymmetricVectorType , const typename OtherDerived::SkewSymmetricVectorType > >

Definition at line 125 of file SkewSymmetricMatrix3.h.

◆ SkewSymmetricScaleReturnType

template<typename Derived >

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

Definition at line 136 of file SkewSymmetricMatrix3.h.

◆ SkewSymmetricSumReturnType

template<typename Derived >

template<typename OtherDerived >

using Eigen::SkewSymmetricBase< Derived >::SkewSymmetricSumReturnType = SkewSymmetricWrapper<const CwiseBinaryOp< internal::scalar_sum_op < SkewSymmetricVectorType ::Scalar, typename OtherDerived::SkewSymmetricVectorType ::Scalar>, const SkewSymmetricVectorType , const typename OtherDerived::SkewSymmetricVectorType > >

Definition at line 155 of file SkewSymmetricMatrix3.h.

◆ SkewSymmetricVectorType

template<typename Derived >

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

Definition at line 37 of file SkewSymmetricMatrix3.h.

◆ StorageIndex

template<typename Derived >

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

Definition at line 41 of file SkewSymmetricMatrix3.h.

◆ StorageKind

template<typename Derived >

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

Definition at line 40 of file SkewSymmetricMatrix3.h.

Member Enumeration Documentation

◆ anonymous enum

template<typename Derived >

anonymous enum

Enumerator
RowsAtCompileTime
ColsAtCompileTime
MaxRowsAtCompileTime
MaxColsAtCompileTime
IsVectorAtCompileTime
Flags

Definition at line 43 of file SkewSymmetricMatrix3.h.

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

Member Function Documentation

◆ cols()

template<typename Derived >

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

inline

Returns: the number of columns.

Definition at line 104 of file SkewSymmetricMatrix3.h.

104 { return 3; }

◆ derived() [1/2]

template<typename Derived >

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

inline

Returns: a const reference to the derived object.

Definition at line 61 of file SkewSymmetricMatrix3.h.

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

◆ derived() [2/2]

template<typename Derived >

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

inline

Returns: a reference to the derived object.

Definition at line 58 of file SkewSymmetricMatrix3.h.

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

◆ determinant()

template<typename Derived >

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

inline

Determinant vanishes

Definition at line 72 of file SkewSymmetricMatrix3.h.

72 { return 0; }

◆ exponential()

template<typename Derived >

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

inline

Returns: the exponential of this matrix using Rodrigues’ formula

Definition at line 80 of file SkewSymmetricMatrix3.h.

                                         {
       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;
     }

◆ operator*() [1/3]

template<typename Derived >

template<typename MatrixDerived >

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

Definition at line 110 of file SkewSymmetricMatrix3.h.

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

◆ operator*() [2/3]

template<typename Derived >

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

inline

Returns: the product of *this by the scalar scalar

Definition at line 141 of file SkewSymmetricMatrix3.h.

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

◆ operator*() [3/3]

template<typename Derived >

template<typename MatrixDerived >

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

Definition at line 119 of file SkewSymmetricMatrix3.h.

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

◆ operator+()

template<typename Derived >

template<typename OtherDerived >

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

inline

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

Definition at line 160 of file SkewSymmetricMatrix3.h.

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

◆ operator-()

template<typename Derived >

template<typename OtherDerived >

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

inline

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

Definition at line 171 of file SkewSymmetricMatrix3.h.

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

◆ rows()

template<typename Derived >

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

inline

Returns: the number of rows.

Definition at line 101 of file SkewSymmetricMatrix3.h.

101 { return 3; }

◆ toDenseMatrix()

template<typename Derived >

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.

Definition at line 68 of file SkewSymmetricMatrix3.h.

68 { return derived(); }

◆ transpose()

template<typename Derived >

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

inline

A.transpose() = -A

Definition at line 76 of file SkewSymmetricMatrix3.h.

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

◆ vector() [1/2]

template<typename Derived >

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

inline

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

Definition at line 97 of file SkewSymmetricMatrix3.h.

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

◆ vector() [2/2]

template<typename Derived >

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

inline

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

Definition at line 94 of file SkewSymmetricMatrix3.h.

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

◆ wedge()

template<typename Derived >

template<typename OtherDerived >

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

Definition at line 131 of file SkewSymmetricMatrix3.h.

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

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

SkewSymmetricMatrix3.h

Public Types

Public Member Functions

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()

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