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

#include <AutoDiffScalar.h>

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

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

typedef NumTraits< Scalar >::Real	Real

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

Public Member Functions
	AutoDiffScalar ()

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

	AutoDiffScalar (const Real &value)

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

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

	AutoDiffScalar (const AutoDiffScalar &other)

const DerType &	derivatives () const

DerType &	derivatives ()

const AutoDiffScalar< CwiseUnaryOp< internal::scalar_multiple_op< Scalar >, const DerType > >	operator * (const Scalar &other) const

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

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

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

bool	operator!= (const Scalar &other) const

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

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

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

AutoDiffScalar &	operator+= (const Scalar &other)

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

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

AutoDiffScalar &	operator-= (const Scalar &other)

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

const AutoDiffScalar< CwiseUnaryOp< internal::scalar_multiple_op< Scalar >, const DerType > >	operator/ (const Scalar &other) const

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

AutoDiffScalar &	operator/= (const Scalar &other)

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

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

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

AutoDiffScalar &	operator= (const AutoDiffScalar &other)

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

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

const Scalar &	value () const

Scalar &	value ()

Protected Attributes
DerType	m_derivatives

Scalar	m_value

Friends
const AutoDiffScalar< CwiseUnaryOp< internal::scalar_multiple_op< Scalar >, const DerType > >	operator * (const Scalar &other, const AutoDiffScalar &a)

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

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

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

const AutoDiffScalar< CwiseUnaryOp< internal::scalar_multiple_op< Scalar >, const DerType > >	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

template<typename _DerType>
class Eigen::AutoDiffScalar< _DerType >

A scalar type replacement with automatic differentation capability.

Parameters

_DerType 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 _DerType can also be a reference (e.g., VectorXf&) to wrap a existing vector into an AutoDiffScalar. Finally, _DerType 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, internal::pow, internal::exp, internal::log, internal::sin, internal::cos,
internal::conj, internal::real, internal::imag, internal::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.

Constructor & Destructor Documentation

◆ AutoDiffScalar() [1/4]

AutoDiffScalar ( )

inline

Default constructor without any initialization.

◆ AutoDiffScalar() [2/4]

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

◆ AutoDiffScalar() [3/4]

AutoDiffScalar ( const Real & value )

inline

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

◆ AutoDiffScalar() [4/4]

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

inline

Constructs an active scalar from its value and derivatives der

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

AutoDiffScalar.h

Public Types

Public Member Functions

Protected Attributes

Friends

Detailed Description

template<typename _DerType> class Eigen::AutoDiffScalar< _DerType >

Constructor & Destructor Documentation

◆ AutoDiffScalar() [1/4]

◆ AutoDiffScalar() [2/4]

◆ AutoDiffScalar() [3/4]

◆ AutoDiffScalar() [4/4]

template<typename _DerType>
class Eigen::AutoDiffScalar< _DerType >