Eigen::AutoDiffScalar< DerivativeType > Class Template Reference

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

Inherits Eigen::internal::auto_diff_special_op< DerivativeType, !internal::is_same< internal::traits< internal::remove_all_t< DerivativeType > >::Scalar, NumTraits< internal::traits< internal::remove_all_t< DerivativeType > >::Scalar >::Real >::value >.

Public Types
typedef internal::auto_diff_special_op< DerivativeType, !internal::is_same< typename internal::traits< internal::remove_all_t< DerivativeType > >::Scalar, typename NumTraits< typename internal::traits< internal::remove_all_t< DerivativeType > >::Scalar >::Real >::value >	Base
typedef internal::remove_all_t< DerivativeType >	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)
	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 >
AutoDiffScalar< CwiseBinaryOp< internal::scalar_sum_op< Scalar >, const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(DerType, Scalar, product), const EIGEN_EXPR_BINARYOP_SCALAR_RETURN_TYPE(internal::remove_all_t< OtherDerType >, Scalar, product) > >	operator* (const AutoDiffScalar< OtherDerType > &other) 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 >
AutoDiffScalar< CwiseBinaryOp< internal::scalar_sum_op< Scalar >, const DerType, const internal::remove_all_t< OtherDerType > > >	operator+ (const AutoDiffScalar< OtherDerType > &other) const
AutoDiffScalar< DerType & >	operator+ (const Scalar &other) const
template<typename OtherDerType >
AutoDiffScalar &	operator+= (const AutoDiffScalar< OtherDerType > &other)
AutoDiffScalar &	operator+= (const Scalar &other)
AutoDiffScalar< CwiseUnaryOp< internal::scalar_opposite_op< Scalar >, const DerType > >	operator- () const
template<typename OtherDerType >
AutoDiffScalar< CwiseBinaryOp< internal::scalar_difference_op< Scalar >, const DerType, const internal::remove_all_t< OtherDerType > > >	operator- (const AutoDiffScalar< OtherDerType > &other) 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 >
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(internal::remove_all_t< OtherDerType >, Scalar, product) >, Scalar, product) >	operator/ (const AutoDiffScalar< OtherDerType > &other) 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

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.

Definition at line 69 of file AutoDiffScalar.h.

Member Typedef Documentation

Base

template<typename DerivativeType >

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

Definition at line 77 of file AutoDiffScalar.h.

DerType

template<typename DerivativeType >

typedef internal::remove_all_t<DerivativeType> Eigen::AutoDiffScalar< DerivativeType >::DerType

Definition at line 78 of file AutoDiffScalar.h.

Real

template<typename DerivativeType >

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

Definition at line 80 of file AutoDiffScalar.h.

Scalar

template<typename DerivativeType >

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

Definition at line 79 of file AutoDiffScalar.h.

Constructor & Destructor Documentation

AutoDiffScalar() [1/6]

template<typename DerivativeType >

Eigen::AutoDiffScalar< DerivativeType >::AutoDiffScalar ( )

inline

Default constructor without any initialization.

Definition at line 86 of file AutoDiffScalar.h.

{}

Code

AutoDiffScalar() [2/6]

template<typename DerivativeType >

Eigen::AutoDiffScalar< DerivativeType >::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 90 of file AutoDiffScalar.h.

      : m_value(value), m_derivatives(DerType::Zero(nbDer))
    {
      m_derivatives.coeffRef(derNumber) = Scalar(1);
    }

Code

AutoDiffScalar() [3/6]

template<typename DerivativeType >

Eigen::AutoDiffScalar< DerivativeType >::AutoDiffScalar ( const Real &  value )

inline

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

Definition at line 98 of file AutoDiffScalar.h.

      : m_value(value)
    {
      if(m_derivatives.size()>0)
        m_derivatives.setZero();
    }

Code

AutoDiffScalar() [4/6]

template<typename DerivativeType >

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

inline

Constructs an active scalar from its value and derivatives der

Definition at line 106 of file AutoDiffScalar.h.

      : m_value(value), m_derivatives(der)
    {}

Code

AutoDiffScalar() [5/6]

template<typename DerivativeType >

template<typename OtherDerType >

Eigen::AutoDiffScalar< DerivativeType >::AutoDiffScalar ( const AutoDiffScalar< OtherDerType > &  other )

inline

Definition at line 111 of file AutoDiffScalar.h.

      : m_value(other.value()), m_derivatives(other.derivatives())
    {}

Code

AutoDiffScalar() [6/6]

template<typename DerivativeType >

Eigen::AutoDiffScalar< DerivativeType >::AutoDiffScalar ( const AutoDiffScalar< DerivativeType > &  other )

inline

Definition at line 126 of file AutoDiffScalar.h.

      : m_value(other.value()), m_derivatives(other.derivatives())
    {}

Code

Member Function Documentation

derivatives() [1/2]

template<typename DerivativeType >

DerType& Eigen::AutoDiffScalar< DerivativeType >::derivatives ( )

inline

Definition at line 160 of file AutoDiffScalar.h.

{ return m_derivatives; }

Code

derivatives() [2/2]

template<typename DerivativeType >

const DerType& Eigen::AutoDiffScalar< DerivativeType >::derivatives ( ) const

inline

Definition at line 159 of file AutoDiffScalar.h.

{ return m_derivatives; }

Code

operator!=() [1/2]

template<typename DerivativeType >

template<typename OtherDerType >

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

inline

Definition at line 181 of file AutoDiffScalar.h.

{ return m_value != b.value(); }

Code

operator!=() [2/2]

template<typename DerivativeType >

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

inline

Definition at line 167 of file AutoDiffScalar.h.

{ return m_value != other; }

Code

operator*() [1/2]

template<typename DerivativeType >

template<typename OtherDerType >

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

inline

Definition at line 345 of file AutoDiffScalar.h.

    {
      internal::make_coherent(m_derivatives, other.derivatives());
      return MakeAutoDiffScalar(
        m_value * other.value(),
        (m_derivatives * other.value()) + (other.derivatives() * m_value));
    }

Code

operator*() [2/2]

template<typename DerivativeType >

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

inline

Definition at line 272 of file AutoDiffScalar.h.

    {
      return MakeAutoDiffScalar(m_value * other, m_derivatives * other);
    }

Code

operator*=() [1/2]

template<typename DerivativeType >

template<typename OtherDerType >

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

inline

Definition at line 360 of file AutoDiffScalar.h.

    {
      *this = *this * other;
      return *this;
    }

Code

operator*=() [2/2]

template<typename DerivativeType >

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

inline

Definition at line 353 of file AutoDiffScalar.h.

    {
      *this = *this * other;
      return *this;
    }

Code

operator+() [1/2]

template<typename DerivativeType >

template<typename OtherDerType >

AutoDiffScalar<CwiseBinaryOp<internal::scalar_sum_op<Scalar>,const DerType,const internal::remove_all_t<OtherDerType> > > Eigen::AutoDiffScalar< DerivativeType >::operator+ ( const AutoDiffScalar< OtherDerType > &  other ) const

inline

Definition at line 211 of file AutoDiffScalar.h.

    {
      internal::make_coherent(m_derivatives, other.derivatives());
      return AutoDiffScalar<CwiseBinaryOp<internal::scalar_sum_op<Scalar>,const DerType,const internal::remove_all_t<OtherDerType>> >(
        m_value + other.value(),
        m_derivatives + other.derivatives());
    }

Code

operator+() [2/2]

template<typename DerivativeType >

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

inline

Definition at line 183 of file AutoDiffScalar.h.

    {
      return AutoDiffScalar<DerType&>(m_value + other, m_derivatives);
    }

Code

operator+=() [1/2]

template<typename DerivativeType >

template<typename OtherDerType >

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

inline

Definition at line 221 of file AutoDiffScalar.h.

    {
      (*this) = (*this) + other;
      return *this;
    }

Code

operator+=() [2/2]

template<typename DerivativeType >

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

inline

Definition at line 203 of file AutoDiffScalar.h.

    {
      value() += other;
      return *this;
    }

Code

operator-() [1/3]

template<typename DerivativeType >

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

inline

Definition at line 264 of file AutoDiffScalar.h.

    {
      return AutoDiffScalar<CwiseUnaryOp<internal::scalar_opposite_op<Scalar>, const DerType> >(
        -m_value,
        -m_derivatives);
    }

Code

operator-() [2/3]

template<typename DerivativeType >

template<typename OtherDerType >

AutoDiffScalar<CwiseBinaryOp<internal::scalar_difference_op<Scalar>, const DerType,const internal::remove_all_t<OtherDerType> > > Eigen::AutoDiffScalar< DerivativeType >::operator- ( const AutoDiffScalar< OtherDerType > &  other ) const

inline

Definition at line 247 of file AutoDiffScalar.h.

    {
      internal::make_coherent(m_derivatives, other.derivatives());
      return AutoDiffScalar<CwiseBinaryOp<internal::scalar_difference_op<Scalar>, const DerType,const internal::remove_all_t<OtherDerType>> >(
        m_value - other.value(),
        m_derivatives - other.derivatives());
    }

Code

operator-() [3/3]

template<typename DerivativeType >

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

inline

Definition at line 227 of file AutoDiffScalar.h.

    {
      return AutoDiffScalar<DerType&>(m_value - b, m_derivatives);
    }

Code

operator-=() [1/2]

template<typename DerivativeType >

template<typename OtherDerType >

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

inline

Definition at line 257 of file AutoDiffScalar.h.

    {
      *this = *this - other;
      return *this;
    }

Code

operator-=() [2/2]

template<typename DerivativeType >

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

inline

Definition at line 239 of file AutoDiffScalar.h.

    {
      value() -= other;
      return *this;
    }

Code

operator/() [1/2]

template<typename DerivativeType >

template<typename OtherDerType >

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(internal::remove_all_t<OtherDerType>,Scalar,product) >,Scalar,product) > Eigen::AutoDiffScalar< DerivativeType >::operator/ ( const AutoDiffScalar< OtherDerType > &  other ) const

inline

Definition at line 332 of file AutoDiffScalar.h.

    {
      internal::make_coherent(m_derivatives, other.derivatives());
      return MakeAutoDiffScalar(
        m_value / other.value(),
          ((m_derivatives * other.value()) - (other.derivatives() * m_value))
        * (Scalar(1)/(other.value()*other.value())));
    }

Code

operator/() [2/2]

template<typename DerivativeType >

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

inline

Definition at line 300 of file AutoDiffScalar.h.

    {
      return MakeAutoDiffScalar(m_value / other, (m_derivatives * (Scalar(1)/other)));
    }

Code

operator/=() [1/2]

template<typename DerivativeType >

template<typename OtherDerType >

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

inline

Definition at line 373 of file AutoDiffScalar.h.

    {
      *this = *this / other;
      return *this;
    }

Code

operator/=() [2/2]

template<typename DerivativeType >

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

inline

Definition at line 366 of file AutoDiffScalar.h.

    {
      *this = *this / other;
      return *this;
    }

Code

operator<() [1/2]

template<typename DerivativeType >

template<typename OtherDerType >

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

inline

Definition at line 176 of file AutoDiffScalar.h.

{ return m_value <  b.value(); }

Code

operator<() [2/2]

template<typename DerivativeType >

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

inline

Definition at line 162 of file AutoDiffScalar.h.

{ return m_value <  other; }

Code

operator<=() [1/2]

template<typename DerivativeType >

template<typename OtherDerType >

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

inline

Definition at line 177 of file AutoDiffScalar.h.

{ return m_value <= b.value(); }

Code

operator<=() [2/2]

template<typename DerivativeType >

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

inline

Definition at line 163 of file AutoDiffScalar.h.

{ return m_value <= other; }

Code

operator=() [1/3]

template<typename DerivativeType >

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

inline

Definition at line 138 of file AutoDiffScalar.h.

    {
      m_value = other.value();
      m_derivatives = other.derivatives();
      return *this;
    }

Code

operator=() [2/3]

template<typename DerivativeType >

template<typename OtherDerType >

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

inline

Definition at line 131 of file AutoDiffScalar.h.

    {
      m_value = other.value();
      m_derivatives = other.derivatives();
      return *this;
    }

Code

operator=() [3/3]

template<typename DerivativeType >

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

inline

Definition at line 145 of file AutoDiffScalar.h.

    {
      m_value = other;
      if(m_derivatives.size()>0)
        m_derivatives.setZero();
      return *this;
    }

Code

operator==() [1/2]

template<typename DerivativeType >

template<typename OtherDerType >

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

inline

Definition at line 180 of file AutoDiffScalar.h.

{ return m_value == b.value(); }

Code

operator==() [2/2]

template<typename DerivativeType >

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

inline

Definition at line 166 of file AutoDiffScalar.h.

{ return m_value == other; }

Code

operator>() [1/2]

template<typename DerivativeType >

template<typename OtherDerType >

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

inline

Definition at line 178 of file AutoDiffScalar.h.

{ return m_value >  b.value(); }

Code

operator>() [2/2]

template<typename DerivativeType >

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

inline

Definition at line 164 of file AutoDiffScalar.h.

{ return m_value >  other; }

Code

operator>=() [1/2]

template<typename DerivativeType >

template<typename OtherDerType >

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

inline

Definition at line 179 of file AutoDiffScalar.h.

{ return m_value >= b.value(); }

Code

operator>=() [2/2]

template<typename DerivativeType >

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

inline

Definition at line 165 of file AutoDiffScalar.h.

{ return m_value >= other; }

Code

value() [1/2]

template<typename DerivativeType >

Scalar& Eigen::AutoDiffScalar< DerivativeType >::value ( )

inline

Definition at line 157 of file AutoDiffScalar.h.

{ return m_value; }

Code

value() [2/2]

template<typename DerivativeType >

const Scalar& Eigen::AutoDiffScalar< DerivativeType >::value ( ) const

inline

Definition at line 156 of file AutoDiffScalar.h.

{ return m_value; }

Code

Member Data Documentation

m_derivatives

template<typename DerivativeType >

DerType Eigen::AutoDiffScalar< DerivativeType >::m_derivatives

protected

Definition at line 381 of file AutoDiffScalar.h.

m_value

template<typename DerivativeType >

Scalar Eigen::AutoDiffScalar< DerivativeType >::m_value

protected

Definition at line 380 of file AutoDiffScalar.h.

---

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

• AutoDiffScalar.h