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

#include <autodiff.h>

Inheritance diagram for DScalar1< _Scalar, _Gradient >:

Collaboration diagram for DScalar1< _Scalar, _Gradient >:

Public Types
typedef _Scalar	Scalar

typedef _Gradient	Gradient

typedef Eigen::Matrix< DScalar1, 2, 1 >	DVector2

typedef Eigen::Matrix< DScalar1, 3, 1 >	DVector3

Public Member Functions
Constructors and accessors
	DScalar1 (Scalar value_=(Scalar) 0)
	Create a new constant automatic differentiation scalar.

	DScalar1 (size_t index, const Scalar &value_)
	Construct a new scalar with the specified value and one first derivative set to 1.

	DScalar1 (Scalar value_, const Gradient &grad_)
	Construct a scalar associated with the given gradient.

	DScalar1 (const DScalar1 &s)
	Copy constructor.

const Scalar &	getValue () const

const Gradient &	getGradient () const

Comparison and assignment
void	operator= (const DScalar1 &s)

void	operator= (const Scalar &v)

bool	operator< (const DScalar1 &s) const

bool	operator<= (const DScalar1 &s) const

bool	operator> (const DScalar1 &s) const

bool	operator>= (const DScalar1 &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

Friends
Miscellaneous functions
DScalar1	sqrt (const DScalar1 &s)

DScalar1	pow (const DScalar1 &s, const Scalar &a)

DScalar1	exp (const DScalar1 &s)

DScalar1	log (const DScalar1 &s)

DScalar1	sin (const DScalar1 &s)

DScalar1	cos (const DScalar1 &s)

DScalar1	acos (const DScalar1 &s)

DScalar1	asin (const DScalar1 &s)

DScalar1	atan2 (const DScalar1 &y, const DScalar1 &x)

Addition
DScalar1 &	operator+= (const DScalar1 &s)

DScalar1 &	operator+= (const Scalar &v)

DScalar1	operator+ (const DScalar1 &lhs, const DScalar1 &rhs)

DScalar1	operator+ (const DScalar1 &lhs, const Scalar &rhs)

DScalar1	operator+ (const Scalar &lhs, const DScalar1 &rhs)

Subtraction
DScalar1 &	operator-= (const DScalar1 &s)

DScalar1 &	operator-= (const Scalar &v)

DScalar1	operator- (const DScalar1 &lhs, const DScalar1 &rhs)

DScalar1	operator- (const DScalar1 &lhs, const Scalar &rhs)

DScalar1	operator- (const Scalar &lhs, const DScalar1 &rhs)

DScalar1	operator- (const DScalar1 &s)

Division
DScalar1 &	operator/= (const Scalar &v)

DScalar1	operator/ (const DScalar1 &lhs, const Scalar &rhs)

DScalar1	operator/ (const Scalar &lhs, const DScalar1 &rhs)

DScalar1	operator/ (const DScalar1 &lhs, const DScalar1 &rhs)

DScalar1	inverse (const DScalar1 &s)

Multiplication
DScalar1 &	operator*= (const Scalar &v)

DScalar1	operator* (const DScalar1 &lhs, const Scalar &rhs)

DScalar1	operator* (const Scalar &lhs, const DScalar1 &rhs)

DScalar1	operator* (const DScalar1 &lhs, const DScalar1 &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>>
struct DScalar1< _Scalar, _Gradient >

Automatic differentiation scalar with first-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 -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 zero-finding, 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: DScalar2

Author: Wenzel Jakob

Definition at line 111 of file autodiff.h.

Member Typedef Documentation

◆ DVector2

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

typedef Eigen::Matrix<DScalar1, 2, 1> DScalar1< _Scalar, _Gradient >::DVector2

Definition at line 116 of file autodiff.h.

◆ DVector3

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

typedef Eigen::Matrix<DScalar1, 3, 1> DScalar1< _Scalar, _Gradient >::DVector3

Definition at line 117 of file autodiff.h.

◆ Gradient

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

typedef _Gradient DScalar1< _Scalar, _Gradient >::Gradient

Definition at line 115 of file autodiff.h.

◆ Scalar

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

typedef _Scalar DScalar1< _Scalar, _Gradient >::Scalar

Definition at line 114 of file autodiff.h.

Constructor & Destructor Documentation

◆ DScalar1() [1/4]

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

DScalar1< _Scalar, _Gradient >::DScalar1 ( Scalar value_ = (Scalar)0 )

inlineexplicit

Create a new constant automatic differentiation scalar.

Definition at line 124 of file autodiff.h.

References DiffScalarBase::getVariableCount(), and DScalar1< _Scalar, _Gradient >::grad.

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◆ DScalar1() [2/4]

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

DScalar1< _Scalar, _Gradient >::DScalar1	(	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 132 of file autodiff.h.

References DiffScalarBase::getVariableCount(), and DScalar1< _Scalar, _Gradient >::grad.

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◆ DScalar1() [3/4]

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

DScalar1< _Scalar, _Gradient >::DScalar1	(	Scalar	value_,
		const Gradient &	grad_
	)

inline

Construct a scalar associated with the given gradient.

Definition at line 142 of file autodiff.h.

◆ DScalar1() [4/4]

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

DScalar1< _Scalar, _Gradient >::DScalar1 ( const DScalar1< _Scalar, _Gradient > & s )

inline

Copy constructor.

Definition at line 146 of file autodiff.h.

Member Function Documentation

◆ getGradient()

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

const Gradient & DScalar1< _Scalar, _Gradient >::getGradient ( ) const

inline

Definition at line 150 of file autodiff.h.

References DScalar1< _Scalar, _Gradient >::grad.

Referenced by operator<<().

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◆ getValue()

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

const Scalar & DScalar1< _Scalar, _Gradient >::getValue ( ) const

inline

Definition at line 149 of file autodiff.h.

References DScalar1< _Scalar, _Gradient >::value.

Referenced by operator<<().

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◆ operator!=()

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

bool DScalar1< _Scalar, _Gradient >::operator!= ( const Scalar & s ) const

inline

Definition at line 404 of file autodiff.h.

References DScalar1< _Scalar, _Gradient >::value.

◆ operator*=()

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

DScalar1 & DScalar1< _Scalar, _Gradient >::operator*= ( const Scalar & v )

inline

Definition at line 285 of file autodiff.h.

References DScalar1< _Scalar, _Gradient >::grad, and DScalar1< _Scalar, _Gradient >::value.

◆ operator+=() [1/2]

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

DScalar1 & DScalar1< _Scalar, _Gradient >::operator+= ( const DScalar1< _Scalar, _Gradient > & s )

inline

Definition at line 170 of file autodiff.h.

References DScalar1< _Scalar, _Gradient >::grad, and DScalar1< _Scalar, _Gradient >::value.

◆ operator+=() [2/2]

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

DScalar1 & DScalar1< _Scalar, _Gradient >::operator+= ( const Scalar & v )

inline

Definition at line 177 of file autodiff.h.

References DScalar1< _Scalar, _Gradient >::value.

◆ operator-=() [1/2]

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

DScalar1 & DScalar1< _Scalar, _Gradient >::operator-= ( const DScalar1< _Scalar, _Gradient > & s )

inline

Definition at line 210 of file autodiff.h.

References DScalar1< _Scalar, _Gradient >::grad, and DScalar1< _Scalar, _Gradient >::value.

◆ operator-=() [2/2]

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

DScalar1 & DScalar1< _Scalar, _Gradient >::operator-= ( const Scalar & v )

inline

Definition at line 217 of file autodiff.h.

References DScalar1< _Scalar, _Gradient >::value.

◆ operator/=()

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

DScalar1 & DScalar1< _Scalar, _Gradient >::operator/= ( const Scalar & v )

inline

Definition at line 255 of file autodiff.h.

References DScalar1< _Scalar, _Gradient >::grad, and DScalar1< _Scalar, _Gradient >::value.

◆ operator<() [1/2]

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

bool DScalar1< _Scalar, _Gradient >::operator< ( const DScalar1< _Scalar, _Gradient > & s ) const

inline

Definition at line 395 of file autodiff.h.

References DScalar1< _Scalar, _Gradient >::value.

◆ operator<() [2/2]

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

bool DScalar1< _Scalar, _Gradient >::operator< ( const Scalar & s ) const

inline

Definition at line 399 of file autodiff.h.

References DScalar1< _Scalar, _Gradient >::value.

◆ operator<=() [1/2]

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

bool DScalar1< _Scalar, _Gradient >::operator<= ( const DScalar1< _Scalar, _Gradient > & s ) const

inline

Definition at line 396 of file autodiff.h.

References DScalar1< _Scalar, _Gradient >::value.

◆ operator<=() [2/2]

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

bool DScalar1< _Scalar, _Gradient >::operator<= ( const Scalar & s ) const

inline

Definition at line 400 of file autodiff.h.

References DScalar1< _Scalar, _Gradient >::value.

◆ operator=() [1/2]

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

void DScalar1< _Scalar, _Gradient >::operator= ( const DScalar1< _Scalar, _Gradient > & s )

inline

Definition at line 385 of file autodiff.h.

References DScalar1< _Scalar, _Gradient >::grad, and DScalar1< _Scalar, _Gradient >::value.

◆ operator=() [2/2]

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

void DScalar1< _Scalar, _Gradient >::operator= ( const Scalar & v )

inline

Definition at line 390 of file autodiff.h.

References DScalar1< _Scalar, _Gradient >::grad, and DScalar1< _Scalar, _Gradient >::value.

◆ operator==()

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

bool DScalar1< _Scalar, _Gradient >::operator== ( const Scalar & s ) const

inline

Definition at line 403 of file autodiff.h.

References DScalar1< _Scalar, _Gradient >::value.

◆ operator>() [1/2]

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

bool DScalar1< _Scalar, _Gradient >::operator> ( const DScalar1< _Scalar, _Gradient > & s ) const

inline

Definition at line 397 of file autodiff.h.

References DScalar1< _Scalar, _Gradient >::value.

◆ operator>() [2/2]

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

bool DScalar1< _Scalar, _Gradient >::operator> ( const Scalar & s ) const

inline

Definition at line 401 of file autodiff.h.

References DScalar1< _Scalar, _Gradient >::value.

◆ operator>=() [1/2]

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

bool DScalar1< _Scalar, _Gradient >::operator>= ( const DScalar1< _Scalar, _Gradient > & s ) const

inline

Definition at line 398 of file autodiff.h.

References DScalar1< _Scalar, _Gradient >::value.

◆ operator>=() [2/2]

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

bool DScalar1< _Scalar, _Gradient >::operator>= ( const Scalar & s ) const

inline

Definition at line 402 of file autodiff.h.

References DScalar1< _Scalar, _Gradient >::value.

◆ vector() [1/2]

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

static DVector2 DScalar1< _Scalar, _Gradient >::vector ( const Eigen::Matrix< Scalar, 2, 1 > & v )

inlinestatic

Initialize a constant two-dimensional vector.

Definition at line 414 of file autodiff.h.

◆ vector() [2/2]

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

static DVector3 DScalar1< _Scalar, _Gradient >::vector ( const Eigen::Matrix< Scalar, 3, 1 > & v )

inlinestatic

Create a constant three-dimensional vector.

Definition at line 420 of file autodiff.h.

Friends And Related Symbol Documentation

◆ acos

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

DScalar1 acos ( const DScalar1< _Scalar, _Gradient > & s )

friend

Definition at line 345 of file autodiff.h.

◆ asin

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

DScalar1 asin ( const DScalar1< _Scalar, _Gradient > & s )

friend

Definition at line 357 of file autodiff.h.

◆ atan2

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

DScalar1 atan2	(	const DScalar1< _Scalar, _Gradient > &	y,
		const DScalar1< _Scalar, _Gradient > &	x
	)

friend

Definition at line 369 of file autodiff.h.

◆ cos

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

DScalar1 cos ( const DScalar1< _Scalar, _Gradient > & s )

friend

Definition at line 339 of file autodiff.h.

◆ exp

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

DScalar1 exp ( const DScalar1< _Scalar, _Gradient > & s )

friend

Definition at line 317 of file autodiff.h.

◆ inverse

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

DScalar1 inverse ( const DScalar1< _Scalar, _Gradient > & s )

friend

Definition at line 246 of file autodiff.h.

◆ log

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

DScalar1 log ( const DScalar1< _Scalar, _Gradient > & s )

friend

Definition at line 325 of file autodiff.h.

◆ operator* [1/3]

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

DScalar1 operator*	(	const DScalar1< _Scalar, _Gradient > &	lhs,
		const DScalar1< _Scalar, _Gradient > &	rhs
	)

friend

Definition at line 278 of file autodiff.h.

◆ operator* [2/3]

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

DScalar1 operator*	(	const DScalar1< _Scalar, _Gradient > &	lhs,
		const Scalar &	rhs
	)

friend

Definition at line 268 of file autodiff.h.

◆ operator* [3/3]

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

DScalar1 operator*	(	const Scalar &	lhs,
		const DScalar1< _Scalar, _Gradient > &	rhs
	)

friend

Definition at line 273 of file autodiff.h.

◆ operator+ [1/3]

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

DScalar1 operator+	(	const DScalar1< _Scalar, _Gradient > &	lhs,
		const DScalar1< _Scalar, _Gradient > &	rhs
	)

friend

Definition at line 155 of file autodiff.h.

◆ operator+ [2/3]

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

DScalar1 operator+	(	const DScalar1< _Scalar, _Gradient > &	lhs,
		const Scalar &	rhs
	)

friend

Definition at line 160 of file autodiff.h.

◆ operator+ [3/3]

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

DScalar1 operator+	(	const Scalar &	lhs,
		const DScalar1< _Scalar, _Gradient > &	rhs
	)

friend

Definition at line 165 of file autodiff.h.

◆ operator- [1/4]

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

DScalar1 operator-	(	const DScalar1< _Scalar, _Gradient > &	lhs,
		const DScalar1< _Scalar, _Gradient > &	rhs
	)

friend

Definition at line 190 of file autodiff.h.

◆ operator- [2/4]

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

DScalar1 operator-	(	const DScalar1< _Scalar, _Gradient > &	lhs,
		const Scalar &	rhs
	)

friend

Definition at line 195 of file autodiff.h.

◆ operator- [3/4]

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

DScalar1 operator- ( const DScalar1< _Scalar, _Gradient > & s )

friend

Definition at line 205 of file autodiff.h.

◆ operator- [4/4]

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

DScalar1 operator-	(	const Scalar &	lhs,
		const DScalar1< _Scalar, _Gradient > &	rhs
	)

friend

Definition at line 200 of file autodiff.h.

◆ operator/ [1/3]

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

DScalar1 operator/	(	const DScalar1< _Scalar, _Gradient > &	lhs,
		const DScalar1< _Scalar, _Gradient > &	rhs
	)

friend

Definition at line 241 of file autodiff.h.

◆ operator/ [2/3]

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

DScalar1 operator/	(	const DScalar1< _Scalar, _Gradient > &	lhs,
		const Scalar &	rhs
	)

friend

Definition at line 228 of file autodiff.h.

◆ operator/ [3/3]

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

DScalar1 operator/	(	const Scalar &	lhs,
		const DScalar1< _Scalar, _Gradient > &	rhs
	)

friend

Definition at line 236 of file autodiff.h.

◆ pow

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

DScalar1 pow	(	const DScalar1< _Scalar, _Gradient > &	s,
		const Scalar &	a
	)

friend

Definition at line 309 of file autodiff.h.

◆ sin

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

DScalar1 sin ( const DScalar1< _Scalar, _Gradient > & s )

friend

Definition at line 333 of file autodiff.h.

◆ sqrt

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

DScalar1 sqrt ( const DScalar1< _Scalar, _Gradient > & s )

friend

Definition at line 299 of file autodiff.h.

Member Data Documentation

◆ grad

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

Gradient DScalar1< _Scalar, _Gradient >::grad

protected

Definition at line 455 of file autodiff.h.

Referenced by DScalar1< _Scalar, _Gradient >::DScalar1(), DScalar1< _Scalar, _Gradient >::DScalar1(), DScalar1< _Scalar, _Gradient >::getGradient(), DScalar1< _Scalar, _Gradient >::operator*=(), DScalar1< _Scalar, _Gradient >::operator+=(), DScalar1< _Scalar, _Gradient >::operator-=(), DScalar1< _Scalar, _Gradient >::operator/=(), DScalar1< _Scalar, _Gradient >::operator=(), and DScalar1< _Scalar, _Gradient >::operator=().

◆ value

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

Scalar DScalar1< _Scalar, _Gradient >::value

protected

Definition at line 454 of file autodiff.h.

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

src/polyfem/utils/autodiff.h

Public Types

Public Member Functions

Static Public Member Functions

Protected Attributes

Friends

Addition

Subtraction

Division

Multiplication

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ DVector2

◆ DVector3

◆ Gradient

◆ Scalar

Constructor & Destructor Documentation

◆ DScalar1() [1/4]

◆ DScalar1() [2/4]

◆ DScalar1() [3/4]

◆ DScalar1() [4/4]

Member Function Documentation

◆ getGradient()

◆ getValue()

◆ operator!=()

◆ 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 Symbol Documentation

◆ 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

◆ value