DScalar2< _Scalar, _Gradient, _Hessian > Struct Template Reference

Automatic differentiation scalar with first- and second-order derivatives. More...

#include <autodiff.h>

Inheritance diagram for DScalar2< _Scalar, _Gradient, _Hessian >:

Collaboration diagram for DScalar2< _Scalar, _Gradient, _Hessian >:

Public Types
typedef _Scalar	Scalar
typedef _Gradient	Gradient
typedef _Hessian	Hessian
typedef Eigen::Matrix< DScalar2, 2, 1 >	DVector2
typedef Eigen::Matrix< DScalar2, 3, 1 >	DVector3

Public Member Functions
Constructors and accessors
	DScalar2 (Scalar value_=(Scalar) 0)
	Create a new constant automatic differentiation scalar.
	DScalar2 (size_t index, const Scalar &value_)
	Construct a new scalar with the specified value and one first derivative set to 1.
	DScalar2 (Scalar value_, const Gradient &grad_, const Hessian &hess_)
	Construct a scalar associated with the given gradient and Hessian.
	DScalar2 (const DScalar2 &s)
	Copy constructor.
const Scalar &	getValue () const
const Gradient &	getGradient () const
const Hessian &	getHessian () const
Comparison and assignment
void	operator= (const DScalar2 &s)
void	operator= (const Scalar &v)
bool	operator< (const DScalar2 &s) const
bool	operator<= (const DScalar2 &s) const
bool	operator> (const DScalar2 &s) const
bool	operator>= (const DScalar2 &s) const
bool	operator< (const Scalar &s) const
bool	operator<= (const Scalar &s) const
bool	operator> (const Scalar &s) const
bool	operator>= (const Scalar &s) const
bool	operator== (const Scalar &s) const
bool	operator!= (const Scalar &s) const

Static Public Member Functions
Vector helper functions
static DVector2	vector (const Eigen::Matrix< Scalar, 2, 1 > &v)
	Initialize a constant two-dimensional vector.
static DVector3	vector (const Eigen::Matrix< Scalar, 3, 1 > &v)
	Create a constant three-dimensional vector.
Static Public Member Functions inherited from DiffScalarBase
static void	setVariableCount (size_t value)
	Set the independent variable count used by the automatic differentiation layer.
static size_t	getVariableCount ()
	Get the variable count used by the automatic differentiation layer.

Protected Attributes
Scalar	value
Gradient	grad
Hessian	hess

Friends
Miscellaneous functions
DScalar2	sqrt (const DScalar2 &s)
DScalar2	pow (const DScalar2 &s, const Scalar &a)
DScalar2	exp (const DScalar2 &s)
DScalar2	log (const DScalar2 &s)
DScalar2	sin (const DScalar2 &s)
DScalar2	cos (const DScalar2 &s)
DScalar2	acos (const DScalar2 &s)
DScalar2	asin (const DScalar2 &s)
DScalar2	atan2 (const DScalar2 &y, const DScalar2 &x)

Addition
DScalar2 &	operator+= (const DScalar2 &s)
DScalar2 &	operator+= (const Scalar &v)
DScalar2	operator+ (const DScalar2 &lhs, const DScalar2 &rhs)
DScalar2	operator+ (const DScalar2 &lhs, const Scalar &rhs)
DScalar2	operator+ (const Scalar &lhs, const DScalar2 &rhs)

Subtraction
DScalar2 &	operator-= (const DScalar2 &s)
DScalar2 &	operator-= (const Scalar &v)
DScalar2	operator- (const DScalar2 &lhs, const DScalar2 &rhs)
DScalar2	operator- (const DScalar2 &lhs, const Scalar &rhs)
DScalar2	operator- (const Scalar &lhs, const DScalar2 &rhs)
DScalar2	operator- (const DScalar2 &s)

Division
DScalar2 &	operator/= (const Scalar &v)
DScalar2	operator/ (const DScalar2 &lhs, const Scalar &rhs)
DScalar2	operator/ (const Scalar &lhs, const DScalar2 &rhs)
DScalar2	operator/ (const DScalar2 &lhs, const DScalar2 &rhs)
DScalar2	inverse (const DScalar2 &s)

Multiplication
DScalar2 &	operator*= (const Scalar &v)
DScalar2	operator* (const DScalar2 &lhs, const Scalar &rhs)
DScalar2	operator* (const Scalar &lhs, const DScalar2 &rhs)
DScalar2	operator* (const DScalar2 &lhs, const DScalar2 &rhs)

Additional Inherited Members
Static Public Attributes inherited from DiffScalarBase
static thread_local size_t	m_variableCount

Detailed Description

template<typename _Scalar, typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>
struct DScalar2< _Scalar, _Gradient, _Hessian >

Automatic differentiation scalar with first- and second-order derivatives.

This class provides an instrumented "scalar" value, which may be dependent on a number of independent variables. The implementation keeps tracks of first and second-order drivatives with respect to these variables using a set of overloaded operations and implementations of special functions (sin, tan, exp, ..).

This is extremely useful for numerical optimization, particularly when analytic derivatives from programs like Maple or Mathematica suffer from excessively complicated expressions.

The class relies on templates, which makes it possible to fix the number of independent variables at compile-time so that instances can be allocated on the stack. Otherwise, they will be placed on the heap.

This is an extended C++ port of Jon Kaldor's implementation, which is based on a C version by Eitan Grinspun at Caltech)

See also

DScalar1

Author

Wenzel Jakob

Definition at line 492 of file autodiff.h.

Member Typedef Documentation

DVector2

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

typedef Eigen::Matrix<DScalar2, 2, 1> DScalar2< _Scalar, _Gradient, _Hessian >::DVector2

Definition at line 498 of file autodiff.h.

DVector3

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

typedef Eigen::Matrix<DScalar2, 3, 1> DScalar2< _Scalar, _Gradient, _Hessian >::DVector3

Definition at line 499 of file autodiff.h.

Gradient

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

typedef _Gradient DScalar2< _Scalar, _Gradient, _Hessian >::Gradient

Definition at line 496 of file autodiff.h.

Hessian

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

typedef _Hessian DScalar2< _Scalar, _Gradient, _Hessian >::Hessian

Definition at line 497 of file autodiff.h.

Scalar

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

typedef _Scalar DScalar2< _Scalar, _Gradient, _Hessian >::Scalar

Definition at line 495 of file autodiff.h.

Constructor & Destructor Documentation

DScalar2() [1/4]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2< _Scalar, _Gradient, _Hessian >::DScalar2 ( Scalar  value_ = (Scalar)0 )

inlineexplicit

Create a new constant automatic differentiation scalar.

Definition at line 506 of file autodiff.h.

References DiffScalarBase::getVariableCount(), DScalar2< _Scalar, _Gradient, _Hessian >::grad, and DScalar2< _Scalar, _Gradient, _Hessian >::hess.

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DScalar2() [2/4]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2< _Scalar, _Gradient, _Hessian >::DScalar2 ( size_t  index, const Scalar &  value_  )

inline

Construct a new scalar with the specified value and one first derivative set to 1.

Definition at line 517 of file autodiff.h.

References DiffScalarBase::getVariableCount(), DScalar2< _Scalar, _Gradient, _Hessian >::grad, and DScalar2< _Scalar, _Gradient, _Hessian >::hess.

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DScalar2() [3/4]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2< _Scalar, _Gradient, _Hessian >::DScalar2 ( Scalar  value_, const Gradient &  grad_, const Hessian &  hess_  )

inline

Construct a scalar associated with the given gradient and Hessian.

Definition at line 530 of file autodiff.h.

DScalar2() [4/4]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2< _Scalar, _Gradient, _Hessian >::DScalar2 ( const DScalar2< _Scalar, _Gradient, _Hessian > &  s )

inline

Copy constructor.

Definition at line 534 of file autodiff.h.

Member Function Documentation

getGradient()

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

const Gradient & DScalar2< _Scalar, _Gradient, _Hessian >::getGradient ( ) const

inline

Definition at line 538 of file autodiff.h.

References DScalar2< _Scalar, _Gradient, _Hessian >::grad.

Referenced by operator<<().

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getHessian()

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

const Hessian & DScalar2< _Scalar, _Gradient, _Hessian >::getHessian ( ) const

inline

Definition at line 539 of file autodiff.h.

References DScalar2< _Scalar, _Gradient, _Hessian >::hess.

Referenced by operator<<().

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getValue()

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

const Scalar & DScalar2< _Scalar, _Gradient, _Hessian >::getValue ( ) const

inline

Definition at line 537 of file autodiff.h.

References DScalar2< _Scalar, _Gradient, _Hessian >::value.

Referenced by operator<<().

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operator!=()

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

bool DScalar2< _Scalar, _Gradient, _Hessian >::operator!= ( const Scalar &  s ) const

inline

Definition at line 913 of file autodiff.h.

References DScalar2< _Scalar, _Gradient, _Hessian >::value.

operator*=()

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 & DScalar2< _Scalar, _Gradient, _Hessian >::operator*= ( const Scalar &  v )

inline

Definition at line 697 of file autodiff.h.

References DScalar2< _Scalar, _Gradient, _Hessian >::grad, DScalar2< _Scalar, _Gradient, _Hessian >::hess, and DScalar2< _Scalar, _Gradient, _Hessian >::value.

operator+=() [1/2]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 & DScalar2< _Scalar, _Gradient, _Hessian >::operator+= ( const DScalar2< _Scalar, _Gradient, _Hessian > &  s )

inline

Definition at line 560 of file autodiff.h.

References DScalar2< _Scalar, _Gradient, _Hessian >::grad, DScalar2< _Scalar, _Gradient, _Hessian >::hess, and DScalar2< _Scalar, _Gradient, _Hessian >::value.

operator+=() [2/2]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 & DScalar2< _Scalar, _Gradient, _Hessian >::operator+= ( const Scalar &  v )

inline

Definition at line 568 of file autodiff.h.

References DScalar2< _Scalar, _Gradient, _Hessian >::value.

operator-=() [1/2]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 & DScalar2< _Scalar, _Gradient, _Hessian >::operator-= ( const DScalar2< _Scalar, _Gradient, _Hessian > &  s )

inline

Definition at line 601 of file autodiff.h.

References DScalar2< _Scalar, _Gradient, _Hessian >::grad, DScalar2< _Scalar, _Gradient, _Hessian >::hess, and DScalar2< _Scalar, _Gradient, _Hessian >::value.

operator-=() [2/2]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 & DScalar2< _Scalar, _Gradient, _Hessian >::operator-= ( const Scalar &  v )

inline

Definition at line 609 of file autodiff.h.

References DScalar2< _Scalar, _Gradient, _Hessian >::value.

operator/=()

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 & DScalar2< _Scalar, _Gradient, _Hessian >::operator/= ( const Scalar &  v )

inline

Definition at line 658 of file autodiff.h.

References DScalar2< _Scalar, _Gradient, _Hessian >::grad, DScalar2< _Scalar, _Gradient, _Hessian >::hess, and DScalar2< _Scalar, _Gradient, _Hessian >::value.

operator<() [1/2]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

bool DScalar2< _Scalar, _Gradient, _Hessian >::operator< ( const DScalar2< _Scalar, _Gradient, _Hessian > &  s ) const

inline

Definition at line 904 of file autodiff.h.

References DScalar2< _Scalar, _Gradient, _Hessian >::value.

operator<() [2/2]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

bool DScalar2< _Scalar, _Gradient, _Hessian >::operator< ( const Scalar &  s ) const

inline

Definition at line 908 of file autodiff.h.

References DScalar2< _Scalar, _Gradient, _Hessian >::value.

operator<=() [1/2]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

bool DScalar2< _Scalar, _Gradient, _Hessian >::operator<= ( const DScalar2< _Scalar, _Gradient, _Hessian > &  s ) const

inline

Definition at line 905 of file autodiff.h.

References DScalar2< _Scalar, _Gradient, _Hessian >::value.

operator<=() [2/2]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

bool DScalar2< _Scalar, _Gradient, _Hessian >::operator<= ( const Scalar &  s ) const

inline

Definition at line 909 of file autodiff.h.

References DScalar2< _Scalar, _Gradient, _Hessian >::value.

operator=() [1/2]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

void DScalar2< _Scalar, _Gradient, _Hessian >::operator= ( const DScalar2< _Scalar, _Gradient, _Hessian > &  s )

inline

Definition at line 892 of file autodiff.h.

References DScalar2< _Scalar, _Gradient, _Hessian >::grad, DScalar2< _Scalar, _Gradient, _Hessian >::hess, and DScalar2< _Scalar, _Gradient, _Hessian >::value.

operator=() [2/2]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

void DScalar2< _Scalar, _Gradient, _Hessian >::operator= ( const Scalar &  v )

inline

Definition at line 898 of file autodiff.h.

References DScalar2< _Scalar, _Gradient, _Hessian >::grad, DScalar2< _Scalar, _Gradient, _Hessian >::hess, and DScalar2< _Scalar, _Gradient, _Hessian >::value.

operator==()

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

bool DScalar2< _Scalar, _Gradient, _Hessian >::operator== ( const Scalar &  s ) const

inline

Definition at line 912 of file autodiff.h.

References DScalar2< _Scalar, _Gradient, _Hessian >::value.

operator>() [1/2]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

bool DScalar2< _Scalar, _Gradient, _Hessian >::operator> ( const DScalar2< _Scalar, _Gradient, _Hessian > &  s ) const

inline

Definition at line 906 of file autodiff.h.

References DScalar2< _Scalar, _Gradient, _Hessian >::value.

operator>() [2/2]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

bool DScalar2< _Scalar, _Gradient, _Hessian >::operator> ( const Scalar &  s ) const

inline

Definition at line 910 of file autodiff.h.

References DScalar2< _Scalar, _Gradient, _Hessian >::value.

operator>=() [1/2]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

bool DScalar2< _Scalar, _Gradient, _Hessian >::operator>= ( const DScalar2< _Scalar, _Gradient, _Hessian > &  s ) const

inline

Definition at line 907 of file autodiff.h.

References DScalar2< _Scalar, _Gradient, _Hessian >::value.

operator>=() [2/2]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

bool DScalar2< _Scalar, _Gradient, _Hessian >::operator>= ( const Scalar &  s ) const

inline

Definition at line 911 of file autodiff.h.

References DScalar2< _Scalar, _Gradient, _Hessian >::value.

vector() [1/2]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

static DVector2 DScalar2< _Scalar, _Gradient, _Hessian >::vector ( const Eigen::Matrix< Scalar, 2, 1 > &  v )

inlinestatic

Initialize a constant two-dimensional vector.

Definition at line 949 of file autodiff.h.

vector() [2/2]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

static DVector3 DScalar2< _Scalar, _Gradient, _Hessian >::vector ( const Eigen::Matrix< Scalar, 3, 1 > &  v )

inlinestatic

Create a constant three-dimensional vector.

Definition at line 955 of file autodiff.h.

Friends And Related Symbol Documentation

acos

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 acos ( const DScalar2< _Scalar, _Gradient, _Hessian > &  s )

friend

Definition at line 818 of file autodiff.h.

asin

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 asin ( const DScalar2< _Scalar, _Gradient, _Hessian > &  s )

friend

Definition at line 839 of file autodiff.h.

atan2

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 atan2 ( const DScalar2< _Scalar, _Gradient, _Hessian > &  y, const DScalar2< _Scalar, _Gradient, _Hessian > &  x  )

friend

Definition at line 860 of file autodiff.h.

cos

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 cos ( const DScalar2< _Scalar, _Gradient, _Hessian > &  s )

friend

Definition at line 801 of file autodiff.h.

exp

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 exp ( const DScalar2< _Scalar, _Gradient, _Hessian > &  s )

friend

Definition at line 749 of file autodiff.h.

inverse

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 inverse ( const DScalar2< _Scalar, _Gradient, _Hessian > &  s )

friend

Definition at line 638 of file autodiff.h.

log

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 log ( const DScalar2< _Scalar, _Gradient, _Hessian > &  s )

friend

Definition at line 767 of file autodiff.h.

operator* [1/3]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 operator* ( const DScalar2< _Scalar, _Gradient, _Hessian > &  lhs, const DScalar2< _Scalar, _Gradient, _Hessian > &  rhs  )

friend

Product rule

Definition at line 681 of file autodiff.h.

operator* [2/3]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 operator* ( const DScalar2< _Scalar, _Gradient, _Hessian > &  lhs, const Scalar &  rhs  )

friend

Definition at line 671 of file autodiff.h.

operator* [3/3]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 operator* ( const Scalar &  lhs, const DScalar2< _Scalar, _Gradient, _Hessian > &  rhs  )

friend

Definition at line 676 of file autodiff.h.

operator+ [1/3]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 operator+ ( const DScalar2< _Scalar, _Gradient, _Hessian > &  lhs, const DScalar2< _Scalar, _Gradient, _Hessian > &  rhs  )

friend

Definition at line 544 of file autodiff.h.

operator+ [2/3]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 operator+ ( const DScalar2< _Scalar, _Gradient, _Hessian > &  lhs, const Scalar &  rhs  )

friend

Definition at line 550 of file autodiff.h.

operator+ [3/3]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 operator+ ( const Scalar &  lhs, const DScalar2< _Scalar, _Gradient, _Hessian > &  rhs  )

friend

Definition at line 555 of file autodiff.h.

operator- [1/4]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 operator- ( const DScalar2< _Scalar, _Gradient, _Hessian > &  lhs, const DScalar2< _Scalar, _Gradient, _Hessian > &  rhs  )

friend

Definition at line 581 of file autodiff.h.

operator- [2/4]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 operator- ( const DScalar2< _Scalar, _Gradient, _Hessian > &  lhs, const Scalar &  rhs  )

friend

Definition at line 586 of file autodiff.h.

operator- [3/4]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 operator- ( const DScalar2< _Scalar, _Gradient, _Hessian > &  s )

friend

Definition at line 596 of file autodiff.h.

operator- [4/4]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 operator- ( const Scalar &  lhs, const DScalar2< _Scalar, _Gradient, _Hessian > &  rhs  )

friend

Definition at line 591 of file autodiff.h.

operator/ [1/3]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 operator/ ( const DScalar2< _Scalar, _Gradient, _Hessian > &  lhs, const DScalar2< _Scalar, _Gradient, _Hessian > &  rhs  )

friend

Definition at line 633 of file autodiff.h.

operator/ [2/3]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 operator/ ( const DScalar2< _Scalar, _Gradient, _Hessian > &  lhs, const Scalar &  rhs  )

friend

Definition at line 620 of file autodiff.h.

operator/ [3/3]

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 operator/ ( const Scalar &  lhs, const DScalar2< _Scalar, _Gradient, _Hessian > &  rhs  )

friend

Definition at line 628 of file autodiff.h.

pow

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 pow ( const DScalar2< _Scalar, _Gradient, _Hessian > &  s, const Scalar &  a  )

friend

Definition at line 731 of file autodiff.h.

sin

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 sin ( const DScalar2< _Scalar, _Gradient, _Hessian > &  s )

friend

Definition at line 783 of file autodiff.h.

sqrt

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

DScalar2 sqrt ( const DScalar2< _Scalar, _Gradient, _Hessian > &  s )

friend

Definition at line 712 of file autodiff.h.

Member Data Documentation

grad

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

Gradient DScalar2< _Scalar, _Gradient, _Hessian >::grad

protected

Definition at line 964 of file autodiff.h.

Referenced by DScalar2< _Scalar, _Gradient, _Hessian >::DScalar2(), DScalar2< _Scalar, _Gradient, _Hessian >::DScalar2(), DScalar2< _Scalar, _Gradient, _Hessian >::getGradient(), DScalar2< _Scalar, _Gradient, _Hessian >::operator*=(), DScalar2< _Scalar, _Gradient, _Hessian >::operator+=(), DScalar2< _Scalar, _Gradient, _Hessian >::operator-=(), DScalar2< _Scalar, _Gradient, _Hessian >::operator/=(), DScalar2< _Scalar, _Gradient, _Hessian >::operator=(), and DScalar2< _Scalar, _Gradient, _Hessian >::operator=().

hess

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

Hessian DScalar2< _Scalar, _Gradient, _Hessian >::hess

protected

Definition at line 965 of file autodiff.h.

Referenced by DScalar2< _Scalar, _Gradient, _Hessian >::DScalar2(), DScalar2< _Scalar, _Gradient, _Hessian >::DScalar2(), DScalar2< _Scalar, _Gradient, _Hessian >::getHessian(), DScalar2< _Scalar, _Gradient, _Hessian >::operator*=(), DScalar2< _Scalar, _Gradient, _Hessian >::operator+=(), DScalar2< _Scalar, _Gradient, _Hessian >::operator-=(), DScalar2< _Scalar, _Gradient, _Hessian >::operator/=(), DScalar2< _Scalar, _Gradient, _Hessian >::operator=(), and DScalar2< _Scalar, _Gradient, _Hessian >::operator=().

value

template<typename _Scalar , typename _Gradient = Eigen::Matrix<_Scalar, Eigen::Dynamic, 1>, typename _Hessian = Eigen::Matrix<_Scalar, Eigen::Dynamic, Eigen::Dynamic>>

Scalar DScalar2< _Scalar, _Gradient, _Hessian >::value

protected

Definition at line 963 of file autodiff.h.

Referenced by DScalar2< _Scalar, _Gradient, _Hessian >::getValue(), DScalar2< _Scalar, _Gradient, _Hessian >::operator!=(), DScalar2< _Scalar, _Gradient, _Hessian >::operator*=(), DScalar2< _Scalar, _Gradient, _Hessian >::operator+=(), DScalar2< _Scalar, _Gradient, _Hessian >::operator+=(), DScalar2< _Scalar, _Gradient, _Hessian >::operator-=(), DScalar2< _Scalar, _Gradient, _Hessian >::operator-=(), DScalar2< _Scalar, _Gradient, _Hessian >::operator/=(), DScalar2< _Scalar, _Gradient, _Hessian >::operator<(), DScalar2< _Scalar, _Gradient, _Hessian >::operator<(), DScalar2< _Scalar, _Gradient, _Hessian >::operator<=(), DScalar2< _Scalar, _Gradient, _Hessian >::operator<=(), DScalar2< _Scalar, _Gradient, _Hessian >::operator=(), DScalar2< _Scalar, _Gradient, _Hessian >::operator=(), DScalar2< _Scalar, _Gradient, _Hessian >::operator==(), DScalar2< _Scalar, _Gradient, _Hessian >::operator>(), DScalar2< _Scalar, _Gradient, _Hessian >::operator>(), DScalar2< _Scalar, _Gradient, _Hessian >::operator>=(), and DScalar2< _Scalar, _Gradient, _Hessian >::operator>=().

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

• src/polyfem/utils/autodiff.h