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

#include <mitsuba/core/autodiff.h>

Inheritance 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
	Create a new constant automatic differentiation scalar. More...

const Gradient &	getGradient () const
	Create a new constant automatic differentiation scalar. More...

const Hessian &	getHessian () const
	Create a new constant automatic differentiation scalar. More...

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

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 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...

Static Public Attributes inherited from DiffScalarBase
static __thread 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