A scalar type replacement with automatic differentiation capability. More...

#include <AutoDiffScalar.h>

Public Types
typedef internal::auto_diff_special_op< DerivativeType, !internal::is_same< typename internal::traits< typename internal::remove_all< DerivativeType >::type >::Scalar, typename NumTraits< typename internal::traits< typename internal::remove_all< DerivativeType >::type >::Scalar >::Real >::value >	Base

typedef internal::remove_all< DerivativeType >::type	DerType

typedef NumTraits< Scalar >::Real	Real

typedef internal::traits< DerType >::Scalar	Scalar

Public Member Functions
	AutoDiffScalar ()

	AutoDiffScalar (const AutoDiffScalar &other)

template<typename OtherDerType >
	AutoDiffScalar (const AutoDiffScalar< OtherDerType > &other, typename internal::enable_if< internal::is_same< Scalar, typename internal::traits< typename internal::remove_all< OtherDerType >::type >::Scalar >::value &&internal::is_convertible< OtherDerType, DerType >::value, void * >::type=0)

	AutoDiffScalar (const Real &value)

	AutoDiffScalar (const Scalar &value, const DerType &der)

	AutoDiffScalar (const Scalar &value, int nbDer, int derNumber)

DerType &	derivatives ()

const DerType &	derivatives () const

template<typename OtherDerType >
bool	operator!= (const AutoDiffScalar< OtherDerType > &b) const

bool	operator!= (const Scalar &other) const

template<typename OtherDerType >
const AutoDiffScalar< CwiseBinaryOp< internal::scalar_sum_op< Scalar >, const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType, Scalar, product), const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(typename internal::remove_all< OtherDerType >::type, Scalar, product) > >	operator* (const AutoDiffScalar< OtherDerType > &other) const

const AutoDiffScalar< EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType, Scalar, product) >	operator* (const Scalar &other) const

template<typename OtherDerType >
AutoDiffScalar &	operator*= (const AutoDiffScalar< OtherDerType > &other)

AutoDiffScalar &	operator*= (const Scalar &other)

template<typename OtherDerType >
const AutoDiffScalar< CwiseBinaryOp< internal::scalar_sum_op< Scalar >, const DerType, const typename internal::remove_all< OtherDerType >::type > >	operator+ (const AutoDiffScalar< OtherDerType > &other) const

const AutoDiffScalar< DerType & >	operator+ (const Scalar &other) const

template<typename OtherDerType >
AutoDiffScalar &	operator+= (const AutoDiffScalar< OtherDerType > &other)

AutoDiffScalar &	operator+= (const Scalar &other)

const AutoDiffScalar< CwiseUnaryOp< internal::scalar_opposite_op< Scalar >, const DerType > >	operator- () const

template<typename OtherDerType >
const AutoDiffScalar< CwiseBinaryOp< internal::scalar_difference_op< Scalar >, const DerType, const typename internal::remove_all< OtherDerType >::type > >	operator- (const AutoDiffScalar< OtherDerType > &other) const

const AutoDiffScalar< DerType & >	operator- (const Scalar &b) const

template<typename OtherDerType >
AutoDiffScalar &	operator-= (const AutoDiffScalar< OtherDerType > &other)

AutoDiffScalar &	operator-= (const Scalar &other)

template<typename OtherDerType >
const AutoDiffScalar< EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(CwiseBinaryOp< internal::scalar_difference_op< Scalar > EIGEN_COMMA const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType, Scalar, product) EIGEN_COMMA const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(typename internal::remove_all< OtherDerType >::type, Scalar, product) >, Scalar, product) >	operator/ (const AutoDiffScalar< OtherDerType > &other) const

const AutoDiffScalar< EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType, Scalar, product) >	operator/ (const Scalar &other) const

template<typename OtherDerType >
AutoDiffScalar &	operator/= (const AutoDiffScalar< OtherDerType > &other)

AutoDiffScalar &	operator/= (const Scalar &other)

template<typename OtherDerType >
bool	operator< (const AutoDiffScalar< OtherDerType > &b) const

bool	operator< (const Scalar &other) const

template<typename OtherDerType >
bool	operator<= (const AutoDiffScalar< OtherDerType > &b) const

bool	operator<= (const Scalar &other) const

AutoDiffScalar &	operator= (const AutoDiffScalar &other)

template<typename OtherDerType >
AutoDiffScalar &	operator= (const AutoDiffScalar< OtherDerType > &other)

AutoDiffScalar &	operator= (const Scalar &other)

template<typename OtherDerType >
bool	operator== (const AutoDiffScalar< OtherDerType > &b) const

bool	operator== (const Scalar &other) const

template<typename OtherDerType >
bool	operator> (const AutoDiffScalar< OtherDerType > &b) const

bool	operator> (const Scalar &other) const

template<typename OtherDerType >
bool	operator>= (const AutoDiffScalar< OtherDerType > &b) const

bool	operator>= (const Scalar &other) const

Scalar &	value ()

const Scalar &	value () const

Protected Attributes
DerType	m_derivatives

Scalar	m_value

Friends
bool	operator!= (const Scalar &a, const AutoDiffScalar &b)

const friend AutoDiffScalar< EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType, Scalar, product) >	operator* (const Scalar &other, const AutoDiffScalar &a)

const friend AutoDiffScalar< DerType & >	operator+ (const Scalar &a, const AutoDiffScalar &b)

const friend AutoDiffScalar< CwiseUnaryOp< internal::scalar_opposite_op< Scalar >, const DerType > >	operator- (const Scalar &a, const AutoDiffScalar &b)

const friend AutoDiffScalar< EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType, Scalar, product) >	operator/ (const Scalar &other, const AutoDiffScalar &a)

bool	operator< (const Scalar &a, const AutoDiffScalar &b)

std::ostream &	operator<< (std::ostream &s, const AutoDiffScalar &a)

bool	operator<= (const Scalar &a, const AutoDiffScalar &b)

bool	operator== (const Scalar &a, const AutoDiffScalar &b)

bool	operator> (const Scalar &a, const AutoDiffScalar &b)

bool	operator>= (const Scalar &a, const AutoDiffScalar &b)

Detailed Description

A scalar type replacement with automatic differentiation capability.

Parameters

DerivativeType the vector type used to store/represent the derivatives. The base scalar type as well as the number of derivatives to compute are determined from this type. Typical choices include, e.g., Vector4f for 4 derivatives, or VectorXf if the number of derivatives is not known at compile time, and/or, the number of derivatives is large. Note that DerivativeType can also be a reference (e.g., VectorXf&) to wrap a existing vector into an AutoDiffScalar. Finally, DerivativeType can also be any Eigen compatible expression.

This class represents a scalar value while tracking its respective derivatives using Eigen's expression template mechanism.

It supports the following list of global math function:

std::abs, std::sqrt, std::pow, std::exp, std::log, std::sin, std::cos,
internal::abs, internal::sqrt, numext::pow, internal::exp, internal::log, internal::sin, internal::cos,
internal::conj, internal::real, internal::imag, numext::abs2.

AutoDiffScalar can be used as the scalar type of an Eigen::Matrix object. However, in that case, the expression template mechanism only occurs at the top Matrix level, while derivatives are computed right away.

Definition at line 33 of file AutoDiffScalar.h.

Member Typedef Documentation

◆ Base

typedef internal::auto_diff_special_op<DerivativeType, !internal::is_same<typename internal::traits<typename internal::remove_all<DerivativeType>::type>::Scalar, typename NumTraits<typename internal::traits<typename internal::remove_all<DerivativeType>::type>::Scalar>::Real>::value> Eigen::AutoDiffScalar::Base

Definition at line 75 of file AutoDiffScalar.h.

◆ DerType

typedef internal::remove_all<DerivativeType>::type Eigen::AutoDiffScalar::DerType

Definition at line 76 of file AutoDiffScalar.h.

◆ Real

typedef NumTraits<Scalar>::Real Eigen::AutoDiffScalar::Real

Definition at line 78 of file AutoDiffScalar.h.

◆ Scalar

typedef internal::traits<DerType>::Scalar Eigen::AutoDiffScalar::Scalar

Definition at line 77 of file AutoDiffScalar.h.

Constructor & Destructor Documentation

◆ AutoDiffScalar() [1/6]

Eigen::AutoDiffScalar::AutoDiffScalar ( )

inline

Default constructor without any initialization.

Definition at line 84 of file AutoDiffScalar.h.

◆ AutoDiffScalar() [2/6]

Eigen::AutoDiffScalar::AutoDiffScalar	(	const Scalar &	value,
		int	nbDer,
		int	derNumber
	)

inline

Constructs an active scalar from its value, and initializes the nbDer derivatives such that it corresponds to the derNumber -th variable

Definition at line 88 of file AutoDiffScalar.h.

◆ AutoDiffScalar() [3/6]

Eigen::AutoDiffScalar::AutoDiffScalar ( const Real & value )

inline

Conversion from a scalar constant to an active scalar. The derivatives are set to zero.

Definition at line 96 of file AutoDiffScalar.h.

◆ AutoDiffScalar() [4/6]

Eigen::AutoDiffScalar::AutoDiffScalar	(	const Scalar &	value,
		const DerType &	der
	)

inline

Constructs an active scalar from its value and derivatives der

Definition at line 104 of file AutoDiffScalar.h.

◆ AutoDiffScalar() [5/6]

template<typename OtherDerType >

Eigen::AutoDiffScalar::AutoDiffScalar	(	const AutoDiffScalar< OtherDerType > &	other,
		typename internal::enable_if< internal::is_same< Scalar, typename internal::traits< typename internal::remove_all< OtherDerType >::type >::Scalar >::value &&internal::is_convertible< OtherDerType, DerType >::value, void * >::type	= `0`
	)

inline

Definition at line 109 of file AutoDiffScalar.h.

◆ AutoDiffScalar() [6/6]

Eigen::AutoDiffScalar::AutoDiffScalar ( const AutoDiffScalar & other )

inline

Definition at line 124 of file AutoDiffScalar.h.

Member Function Documentation

◆ derivatives() [1/2]

DerType& Eigen::AutoDiffScalar::derivatives ( )

inline

Definition at line 158 of file AutoDiffScalar.h.

◆ derivatives() [2/2]

const DerType& Eigen::AutoDiffScalar::derivatives ( ) const

inline

Definition at line 157 of file AutoDiffScalar.h.

◆ operator!=() [1/2]

template<typename OtherDerType >

bool Eigen::AutoDiffScalar::operator!= ( const AutoDiffScalar< OtherDerType > & b ) const

inline

Definition at line 179 of file AutoDiffScalar.h.

◆ operator!=() [2/2]

bool Eigen::AutoDiffScalar::operator!= ( const Scalar & other ) const

inline

Definition at line 165 of file AutoDiffScalar.h.

◆ operator*() [1/2]

template<typename OtherDerType >

const AutoDiffScalar<CwiseBinaryOp<internal::scalar_sum_op<Scalar>, const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product), const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(typename internal::remove_all<OtherDerType>::type,Scalar,product) > > Eigen::AutoDiffScalar::operator* ( const AutoDiffScalar< OtherDerType > & other ) const

inline

Definition at line 343 of file AutoDiffScalar.h.

◆ operator*() [2/2]

const AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) > Eigen::AutoDiffScalar::operator* ( const Scalar & other ) const

inline

Definition at line 270 of file AutoDiffScalar.h.

◆ operator*=() [1/2]

template<typename OtherDerType >

AutoDiffScalar& Eigen::AutoDiffScalar::operator*= ( const AutoDiffScalar< OtherDerType > & other )

inline

Definition at line 358 of file AutoDiffScalar.h.

◆ operator*=() [2/2]

AutoDiffScalar& Eigen::AutoDiffScalar::operator*= ( const Scalar & other )

inline

Definition at line 351 of file AutoDiffScalar.h.

◆ operator+() [1/2]

template<typename OtherDerType >

const AutoDiffScalar<CwiseBinaryOp<internal::scalar_sum_op<Scalar>,const DerType,const typename internal::remove_all<OtherDerType>::type> > Eigen::AutoDiffScalar::operator+ ( const AutoDiffScalar< OtherDerType > & other ) const

inline

Definition at line 209 of file AutoDiffScalar.h.

◆ operator+() [2/2]

const AutoDiffScalar<DerType&> Eigen::AutoDiffScalar::operator+ ( const Scalar & other ) const

inline

Definition at line 181 of file AutoDiffScalar.h.

◆ operator+=() [1/2]

template<typename OtherDerType >

AutoDiffScalar& Eigen::AutoDiffScalar::operator+= ( const AutoDiffScalar< OtherDerType > & other )

inline

Definition at line 219 of file AutoDiffScalar.h.

◆ operator+=() [2/2]

AutoDiffScalar& Eigen::AutoDiffScalar::operator+= ( const Scalar & other )

inline

Definition at line 201 of file AutoDiffScalar.h.

◆ operator-() [1/3]

const AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const DerType> > Eigen::AutoDiffScalar::operator- ( ) const

inline

Definition at line 262 of file AutoDiffScalar.h.

◆ operator-() [2/3]

template<typename OtherDerType >

const AutoDiffScalar<CwiseBinaryOp<internal::scalar_difference_op<Scalar>, const DerType,const typename internal::remove_all<OtherDerType>::type> > Eigen::AutoDiffScalar::operator- ( const AutoDiffScalar< OtherDerType > & other ) const

inline

Definition at line 245 of file AutoDiffScalar.h.

◆ operator-() [3/3]

const AutoDiffScalar<DerType&> Eigen::AutoDiffScalar::operator- ( const Scalar & b ) const

inline

Definition at line 225 of file AutoDiffScalar.h.

◆ operator-=() [1/2]

template<typename OtherDerType >

AutoDiffScalar& Eigen::AutoDiffScalar::operator-= ( const AutoDiffScalar< OtherDerType > & other )

inline

Definition at line 255 of file AutoDiffScalar.h.

◆ operator-=() [2/2]

AutoDiffScalar& Eigen::AutoDiffScalar::operator-= ( const Scalar & other )

inline

Definition at line 237 of file AutoDiffScalar.h.

◆ operator/() [1/2]

template<typename OtherDerType >

const AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE( CwiseBinaryOp<internal::scalar_difference_op<Scalar> EIGEN_COMMA const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) EIGEN_COMMA const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(typename internal::remove_all<OtherDerType>::type,Scalar,product) >,Scalar,product) > Eigen::AutoDiffScalar::operator/ ( const AutoDiffScalar< OtherDerType > & other ) const

inline

Definition at line 330 of file AutoDiffScalar.h.

◆ operator/() [2/2]

const AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) > Eigen::AutoDiffScalar::operator/ ( const Scalar & other ) const

inline

Definition at line 298 of file AutoDiffScalar.h.

◆ operator/=() [1/2]

template<typename OtherDerType >

AutoDiffScalar& Eigen::AutoDiffScalar::operator/= ( const AutoDiffScalar< OtherDerType > & other )

inline

Definition at line 371 of file AutoDiffScalar.h.

◆ operator/=() [2/2]

AutoDiffScalar& Eigen::AutoDiffScalar::operator/= ( const Scalar & other )

inline

Definition at line 364 of file AutoDiffScalar.h.

◆ operator<() [1/2]

template<typename OtherDerType >

bool Eigen::AutoDiffScalar::operator< ( const AutoDiffScalar< OtherDerType > & b ) const

inline

Definition at line 174 of file AutoDiffScalar.h.

◆ operator<() [2/2]

bool Eigen::AutoDiffScalar::operator< ( const Scalar & other ) const

inline

Definition at line 160 of file AutoDiffScalar.h.

◆ operator<=() [1/2]

template<typename OtherDerType >

bool Eigen::AutoDiffScalar::operator<= ( const AutoDiffScalar< OtherDerType > & b ) const

inline

Definition at line 175 of file AutoDiffScalar.h.

◆ operator<=() [2/2]

bool Eigen::AutoDiffScalar::operator<= ( const Scalar & other ) const

inline

Definition at line 161 of file AutoDiffScalar.h.

◆ operator=() [1/3]

AutoDiffScalar& Eigen::AutoDiffScalar::operator= ( const AutoDiffScalar & other )

inline

Definition at line 136 of file AutoDiffScalar.h.

◆ operator=() [2/3]

template<typename OtherDerType >

AutoDiffScalar& Eigen::AutoDiffScalar::operator= ( const AutoDiffScalar< OtherDerType > & other )

inline

Definition at line 129 of file AutoDiffScalar.h.

◆ operator=() [3/3]

AutoDiffScalar& Eigen::AutoDiffScalar::operator= ( const Scalar & other )

inline

Definition at line 143 of file AutoDiffScalar.h.

◆ operator==() [1/2]

template<typename OtherDerType >

bool Eigen::AutoDiffScalar::operator== ( const AutoDiffScalar< OtherDerType > & b ) const

inline

Definition at line 178 of file AutoDiffScalar.h.

◆ operator==() [2/2]

bool Eigen::AutoDiffScalar::operator== ( const Scalar & other ) const

inline

Definition at line 164 of file AutoDiffScalar.h.

◆ operator>() [1/2]

template<typename OtherDerType >

bool Eigen::AutoDiffScalar::operator> ( const AutoDiffScalar< OtherDerType > & b ) const

inline

Definition at line 176 of file AutoDiffScalar.h.

◆ operator>() [2/2]

bool Eigen::AutoDiffScalar::operator> ( const Scalar & other ) const

inline

Definition at line 162 of file AutoDiffScalar.h.

◆ operator>=() [1/2]

template<typename OtherDerType >

bool Eigen::AutoDiffScalar::operator>= ( const AutoDiffScalar< OtherDerType > & b ) const

inline

Definition at line 177 of file AutoDiffScalar.h.

◆ operator>=() [2/2]

bool Eigen::AutoDiffScalar::operator>= ( const Scalar & other ) const

inline

Definition at line 163 of file AutoDiffScalar.h.

◆ value() [1/2]

Scalar& Eigen::AutoDiffScalar::value ( )

inline

Definition at line 155 of file AutoDiffScalar.h.

◆ value() [2/2]

const Scalar& Eigen::AutoDiffScalar::value ( ) const

inline

Definition at line 154 of file AutoDiffScalar.h.

Friends And Related Function Documentation

◆ operator!=

bool operator!=	(	const Scalar &	a,
		const AutoDiffScalar &	b
	)

friend

Definition at line 172 of file AutoDiffScalar.h.

◆ operator*

const friend AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) > operator*	(	const Scalar &	other,
		const AutoDiffScalar &	a
	)

friend

Definition at line 276 of file AutoDiffScalar.h.

◆ operator+

const friend AutoDiffScalar<DerType&> operator+	(	const Scalar &	a,
		const AutoDiffScalar &	b
	)

friend

Definition at line 186 of file AutoDiffScalar.h.

◆ operator-

const friend AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const DerType> > operator-	(	const Scalar &	a,
		const AutoDiffScalar &	b
	)

friend

Definition at line 231 of file AutoDiffScalar.h.

◆ operator/

const friend AutoDiffScalar<EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType,Scalar,product) > operator/	(	const Scalar &	other,
		const AutoDiffScalar &	a
	)

friend

Definition at line 304 of file AutoDiffScalar.h.

◆ operator<

bool operator<	(	const Scalar &	a,
		const AutoDiffScalar &	b
	)

friend

Definition at line 167 of file AutoDiffScalar.h.

◆ operator<<

std::ostream& operator<<	(	std::ostream &	s,
		const AutoDiffScalar &	a
	)

friend

Definition at line 119 of file AutoDiffScalar.h.

◆ operator<=

bool operator<=	(	const Scalar &	a,
		const AutoDiffScalar &	b
	)

friend

Definition at line 168 of file AutoDiffScalar.h.

◆ operator==

bool operator==	(	const Scalar &	a,
		const AutoDiffScalar &	b
	)

friend

Definition at line 171 of file AutoDiffScalar.h.

◆ operator>

bool operator>	(	const Scalar &	a,
		const AutoDiffScalar &	b
	)

friend

Definition at line 169 of file AutoDiffScalar.h.

◆ operator>=

bool operator>=	(	const Scalar &	a,
		const AutoDiffScalar &	b
	)

friend

Definition at line 170 of file AutoDiffScalar.h.

Member Data Documentation

◆ m_derivatives

DerType Eigen::AutoDiffScalar::m_derivatives

protected

Definition at line 379 of file AutoDiffScalar.h.

◆ m_value

Scalar Eigen::AutoDiffScalar::m_value

protected

Definition at line 378 of file AutoDiffScalar.h.

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

AutoDiffScalar.h

Public Types

Public Member Functions

Protected Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ Base

◆ DerType

◆ Real

◆ Scalar

Constructor & Destructor Documentation

◆ AutoDiffScalar() [1/6]

◆ AutoDiffScalar() [2/6]

◆ AutoDiffScalar() [3/6]

◆ AutoDiffScalar() [4/6]

◆ AutoDiffScalar() [5/6]

◆ AutoDiffScalar() [6/6]

Member Function Documentation

◆ derivatives() [1/2]

◆ derivatives() [2/2]

◆ operator!=() [1/2]

◆ operator!=() [2/2]

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+() [1/2]

◆ operator+() [2/2]

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-() [1/3]

◆ operator-() [2/3]

◆ operator-() [3/3]

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/() [1/2]

◆ operator/() [2/2]

◆ operator/=() [1/2]

◆ operator/=() [2/2]

◆ operator<() [1/2]

◆ operator<() [2/2]

◆ operator<=() [1/2]

◆ operator<=() [2/2]

◆ operator=() [1/3]

◆ operator=() [2/3]

◆ operator=() [3/3]

◆ operator==() [1/2]

◆ operator==() [2/2]

◆ operator>() [1/2]

◆ operator>() [2/2]

◆ operator>=() [1/2]

◆ operator>=() [2/2]

◆ value() [1/2]

◆ value() [2/2]

Friends And Related Function Documentation

◆ operator!=

◆ operator*

◆ operator+

◆ operator-

◆ operator/

◆ operator<

◆ operator<<

◆ operator<=

◆ operator==

◆ operator>

◆ operator>=

Member Data Documentation

◆ m_derivatives

◆ m_value