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)
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)
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
template<typename OtherDerType >
const AutoDiffScalar < CwiseUnaryOp < internal::scalar_opposite_op < Scalar >, const DerType > >	operator- () const
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
template<typename OtherDerType >
AutoDiffScalar &	operator= (const AutoDiffScalar< OtherDerType > &other)
AutoDiffScalar &	operator= (const AutoDiffScalar &other)
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)
const AutoDiffScalar< 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)
std::ostream &	operator<< (std::ostream &s, const AutoDiffScalar &a)

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.

Definition at line 75 of file AutoDiffScalar.h.

Member Typedef Documentation

template<typename _DerType>

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> Eigen::AutoDiffScalar< _DerType >::Base

Definition at line 83 of file AutoDiffScalar.h.

template<typename _DerType>

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

Definition at line 84 of file AutoDiffScalar.h.

template<typename _DerType>

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

Definition at line 86 of file AutoDiffScalar.h.

template<typename _DerType>

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

Definition at line 85 of file AutoDiffScalar.h.

Constructor & Destructor Documentation

template<typename _DerType>

Eigen::AutoDiffScalar< _DerType >::AutoDiffScalar ( ) [inline]

Default constructor without any initialization.

Definition at line 92 of file AutoDiffScalar.h.

template<typename _DerType>

Eigen::AutoDiffScalar< _DerType >::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 96 of file AutoDiffScalar.h.

template<typename _DerType>

Eigen::AutoDiffScalar< _DerType >::AutoDiffScalar ( const Real & value ) [inline, explicit]

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

Definition at line 104 of file AutoDiffScalar.h.

template<typename _DerType>

Eigen::AutoDiffScalar< _DerType >::AutoDiffScalar	(	const Scalar &	value,
		const DerType &	der
	)		`[inline]`

Constructs an active scalar from its value and derivatives der

Definition at line 112 of file AutoDiffScalar.h.

template<typename _DerType>

template<typename OtherDerType >

Eigen::AutoDiffScalar< _DerType >::AutoDiffScalar ( const AutoDiffScalar< OtherDerType > & other ) [inline]

Definition at line 117 of file AutoDiffScalar.h.

template<typename _DerType>

Eigen::AutoDiffScalar< _DerType >::AutoDiffScalar ( const AutoDiffScalar< _DerType > & other ) [inline]

Definition at line 126 of file AutoDiffScalar.h.

Member Function Documentation

template<typename _DerType>

const DerType& Eigen::AutoDiffScalar< _DerType >::derivatives ( ) const [inline]

Definition at line 151 of file AutoDiffScalar.h.

template<typename _DerType>

DerType& Eigen::AutoDiffScalar< _DerType >::derivatives ( ) [inline]

Definition at line 152 of file AutoDiffScalar.h.

template<typename _DerType>

const AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> > Eigen::AutoDiffScalar< _DerType >::operator* ( const Scalar & other ) const [inline]

Definition at line 226 of file AutoDiffScalar.h.

template<typename _DerType>

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> > > Eigen::AutoDiffScalar< _DerType >::operator* ( const AutoDiffScalar< OtherDerType > & other ) const [inline]

Definition at line 310 of file AutoDiffScalar.h.

template<typename _DerType>

AutoDiffScalar& Eigen::AutoDiffScalar< _DerType >::operator*= ( const Scalar & other ) [inline]

Definition at line 320 of file AutoDiffScalar.h.

template<typename _DerType>

template<typename OtherDerType >

AutoDiffScalar& Eigen::AutoDiffScalar< _DerType >::operator*= ( const AutoDiffScalar< OtherDerType > & other ) [inline]

Definition at line 327 of file AutoDiffScalar.h.

template<typename _DerType>

const AutoDiffScalar<DerType&> Eigen::AutoDiffScalar< _DerType >::operator+ ( const Scalar & other ) const [inline]

Definition at line 154 of file AutoDiffScalar.h.

template<typename _DerType>

template<typename OtherDerType >

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

Definition at line 182 of file AutoDiffScalar.h.

template<typename _DerType>

AutoDiffScalar& Eigen::AutoDiffScalar< _DerType >::operator+= ( const Scalar & other ) [inline]

Definition at line 174 of file AutoDiffScalar.h.

template<typename _DerType>

template<typename OtherDerType >

AutoDiffScalar& Eigen::AutoDiffScalar< _DerType >::operator+= ( const AutoDiffScalar< OtherDerType > & other ) [inline]

Definition at line 192 of file AutoDiffScalar.h.

template<typename _DerType>

template<typename OtherDerType >

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

Definition at line 200 of file AutoDiffScalar.h.

template<typename _DerType>

template<typename OtherDerType >

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

Definition at line 218 of file AutoDiffScalar.h.

template<typename _DerType>

template<typename OtherDerType >

AutoDiffScalar& Eigen::AutoDiffScalar< _DerType >::operator-= ( const AutoDiffScalar< OtherDerType > & other ) [inline]

Definition at line 210 of file AutoDiffScalar.h.

template<typename _DerType>

const AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> > Eigen::AutoDiffScalar< _DerType >::operator/ ( const Scalar & other ) const [inline]

Definition at line 258 of file AutoDiffScalar.h.

template<typename _DerType>

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 > > > > Eigen::AutoDiffScalar< _DerType >::operator/ ( const AutoDiffScalar< OtherDerType > & other ) const [inline]

Definition at line 294 of file AutoDiffScalar.h.

template<typename _DerType>

template<typename OtherDerType >

AutoDiffScalar& Eigen::AutoDiffScalar< _DerType >::operator= ( const AutoDiffScalar< OtherDerType > & other ) [inline]

Definition at line 131 of file AutoDiffScalar.h.

template<typename _DerType>

AutoDiffScalar& Eigen::AutoDiffScalar< _DerType >::operator= ( const AutoDiffScalar< _DerType > & other ) [inline]

Definition at line 138 of file AutoDiffScalar.h.

template<typename _DerType>

const Scalar& Eigen::AutoDiffScalar< _DerType >::value ( ) const [inline]

Definition at line 148 of file AutoDiffScalar.h.

template<typename _DerType>

Scalar& Eigen::AutoDiffScalar< _DerType >::value ( ) [inline]

Definition at line 149 of file AutoDiffScalar.h.

Friends And Related Function Documentation

template<typename _DerType>

const AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> > operator*	(	const Scalar &	other,
		const AutoDiffScalar< _DerType > &	a
	)		`[friend]`

Definition at line 234 of file AutoDiffScalar.h.

template<typename _DerType>

const AutoDiffScalar<DerType&> operator+	(	const Scalar &	a,
		const AutoDiffScalar< _DerType > &	b
	)		`[friend]`

Definition at line 159 of file AutoDiffScalar.h.

template<typename _DerType>

const AutoDiffScalar<CwiseUnaryOp<internal::scalar_multiple_op<Scalar>, const DerType> > operator/	(	const Scalar &	other,
		const AutoDiffScalar< _DerType > &	a
	)		`[friend]`

Definition at line 266 of file AutoDiffScalar.h.

template<typename _DerType>

std::ostream& operator<<	(	std::ostream &	s,
		const AutoDiffScalar< _DerType > &	a
	)		`[friend]`

Definition at line 121 of file AutoDiffScalar.h.

Member Data Documentation

template<typename _DerType>

DerType Eigen::AutoDiffScalar< _DerType >::m_derivatives [protected]

Definition at line 335 of file AutoDiffScalar.h.

template<typename _DerType>

Scalar Eigen::AutoDiffScalar< _DerType >::m_value [protected]

Definition at line 334 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

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

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation

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