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

#include <mitsuba/core/autodiff.h>

Inheritance 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. More...

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

	DScalar1 (Scalar value, const Gradient &grad)
	Construct a scalar associated with the given gradient. More...

	DScalar1 (const DScalar1 &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...

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

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 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>>
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