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

#include <AutoDiffScalar.h>

Inheritance diagram for Eigen::AutoDiffScalar< DerivativeType >:

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 internal::traits< DerType >::Scalar	Scalar

typedef NumTraits< Scalar >::Real	Real

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, 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 AutoDiffScalar &other)

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

AutoDiffScalar &	operator= (const AutoDiffScalar &other)

AutoDiffScalar &	operator= (const Scalar &other)

const Scalar &	value () const

Scalar &	value ()

const DerType &	derivatives () const

DerType &	derivatives ()

bool	operator< (const Scalar &other) const

bool	operator<= (const Scalar &other) const

bool	operator> (const Scalar &other) const

bool	operator>= (const Scalar &other) const

bool	operator== (const Scalar &other) const

bool	operator!= (const Scalar &other) const

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

AutoDiffScalar &	operator*= (const Scalar &other)

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

AutoDiffScalar &	operator/= (const Scalar &other)

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

Protected Attributes
Scalar	m_value

DerType	m_derivatives

Friends
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)

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

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

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

Detailed Description

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

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.