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. More...

	DScalar2 (size_t index, const Scalar &value_)
	Construct a new scalar with the specified value and one first derivative set to 1. More...

	DScalar2 (Scalar value_, const Gradient &grad_, const Hessian &hess_)
	Construct a scalar associated with the given gradient and Hessian. More...

	DScalar2 (const DScalar2 &s)
	Copy constructor. More...

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 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. More...

static DVector3	vector (const Eigen::Matrix< Scalar, 3, 1 > &v)
	Create a constant three-dimensional vector. More...

Static Public Member Functions inherited from DiffScalarBase
static void	setVariableCount (size_t value)
	Set the independent variable count used by the automatic differentiation layer. More...

static size_t	getVariableCount ()
	Get the variable count used by the automatic differentiation layer. More...

Protected Attributes
Scalar	value

Gradient	grad

Hessian	hess

Friends
Miscellaneous functions
DScalar2	abs (const DScalar2 &s)

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 500 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 506 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 507 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 504 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 505 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 503 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 514 of file autodiff.h.

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

Referenced by DScalar2< _Scalar, _Gradient, _Hessian >::vector().

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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 525 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 538 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 542 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 546 of file autodiff.h.

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

Referenced by wmtk::function::PerSimplexAutodiffFunction::get_gradient(), and 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 547 of file autodiff.h.

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

Referenced by wmtk::function::PerSimplexAutodiffFunction::get_hessian(), and 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 545 of file autodiff.h.

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

Referenced by wmtk::function::PerSimplexAutodiffFunction::get_value(), and operator<<().

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◆ 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 921 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 928 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 705 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 568 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 576 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 609 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 617 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 666 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 917 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 923 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 918 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 924 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 905 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 911 of file autodiff.h.

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

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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 927 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 919 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 925 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 920 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 926 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 964 of file autodiff.h.

References DScalar2< _Scalar, _Gradient, _Hessian >::DScalar2().

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◆ 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 970 of file autodiff.h.

References DScalar2< _Scalar, _Gradient, _Hessian >::DScalar2().

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Friends And Related Function Documentation

◆ abs

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

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

friend

Definition at line 720 of file autodiff.h.

◆ 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 831 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 852 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 873 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 814 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 762 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 646 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 780 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 689 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 679 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 684 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 552 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 558 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 563 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 589 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 594 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 604 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 599 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 641 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 628 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 636 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 744 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 796 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 725 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 979 of file autodiff.h.

Referenced by 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/=(), 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 980 of file autodiff.h.

Referenced by 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/=(), 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 978 of file autodiff.h.

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

src/wmtk/function/utils/autodiff.h

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Friends

Addition

Subtraction

Division

Multiplication

Additional Inherited Members

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 >

Member Typedef Documentation

◆ DVector2

◆ DVector3

◆ Gradient

◆ Hessian

◆ Scalar

Constructor & Destructor Documentation

◆ DScalar2() [1/4]

◆ DScalar2() [2/4]

◆ DScalar2() [3/4]

◆ DScalar2() [4/4]

Member Function Documentation

◆ getGradient()

◆ getHessian()

◆ getValue()

◆ operator!=() [1/2]

◆ operator!=() [2/2]

◆ operator*=()

◆ operator+=() [1/2]

◆ operator+=() [2/2]

◆ operator-=() [1/2]

◆ operator-=() [2/2]

◆ operator/=()

◆ operator<() [1/2]

◆ operator<() [2/2]

◆ operator<=() [1/2]

◆ operator<=() [2/2]

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator==()

◆ operator>() [1/2]

◆ operator>() [2/2]

◆ operator>=() [1/2]

◆ operator>=() [2/2]

◆ vector() [1/2]

◆ vector() [2/2]

Friends And Related Function Documentation

◆ abs

◆ acos

◆ asin

◆ atan2

◆ cos

◆ exp

◆ inverse

◆ log

◆ operator* [1/3]

◆ operator* [2/3]

◆ operator* [3/3]

◆ operator+ [1/3]

◆ operator+ [2/3]

◆ operator+ [3/3]

◆ operator- [1/4]

◆ operator- [2/4]

◆ operator- [3/4]

◆ operator- [4/4]

◆ operator/ [1/3]

◆ operator/ [2/3]

◆ operator/ [3/3]

◆ pow

◆ sin

◆ sqrt

Member Data Documentation

◆ grad

◆ hess

◆ value

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 >