theoretica::dual2 Class Reference

Second order dual number class. More...

#include <dual2.h>

Public Member Functions
	dual2 ()
	Default constructor, initialize with null values.
	dual2 (real real_part, real dual1_part, real dual2_part)
	Initialize from two real numbers.
	dual2 (real real_part, real dual1_part)
	Initialize from two real numbers.
	dual2 (real real_part)
	Initialize from a real number.
	dual2 (const vec3 &v)
	Initialize from a vec3.
dual2 &	operator= (const vec3 &v)
	Initialize a dual number from a vec3.
dual2 &	operator= (real x)
	Initialize a dual number from a real number.
dual2 &	operator= (const std::array< real, 3 > &v)
	Initialize a dual number from a std::array.
real	Re () const
	Return real part.
real	Dual1 () const
	Return first order dual part.
real	Dual2 () const
	Return second order dual part.
dual2	conjugate () const
	Get the dual conjugate.
dual2	inverse () const
	Get the inverse of a dual number.
dual2	operator+ () const
	Identity (for consistency)
dual2	operator+ (const dual2 &other) const
	Sum two dual numbers.
dual2	operator+ (real r) const
	Sum a real number to a dual number.
dual2	operator- () const
	Get the opposite of a dual number.
dual2	operator- (const dual2 &other) const
	Subtract two dual numbers.
dual2	operator- (real r) const
	Subtract a real number from a dual number.
dual2	operator* (const dual2 &other) const
	Multiply two dual numbers.
dual2	operator* (real r) const
	Multiply a dual number by a real number.
dual2	operator/ (const dual2 &other) const
	Dual division.
dual2	operator/ (real r) const
	Divide a dual number by a real number.
dual2 &	operator+= (real r)
	Sum a real number to this dual number.
dual2 &	operator-= (const dual2 &other)
	Subtract a real number from this one.
dual2 &	operator-= (real r)
	Subtract a real number from this dual number.
dual2 &	operator*= (const dual2 &other)
	Multiply this dual number by another one.
dual2 &	operator*= (real r)
	Multiply this dual number by a real number.
dual2 &	operator/= (const dual2 &other)
	Divide this dual number by another one.
dual2 &	operator/= (real r)
	Divide a dual number by a real number.
bool	operator== (const dual2 &other)
	Check whether two dual numbers have the same real and dual parts.
vec3	to_vec () const
	Convert a dual number to a vector.
void	from_vec (const vec3 &v)
	Initialize from a vector.
std::string	to_string (const std::string &epsilon1="e1", const std::string &epsilon2="e2") const
	Convert the dual number to string representation. More...
	operator std::string ()
	Convert the dual number to string representation.

Public Attributes
real	a
real	b
real	c

Friends
dual2	operator+ (real a, const dual2 &d)
dual2	operator- (real a, const dual2 &d)
dual2	operator* (real a, const dual2 &d)
dual2	operator/ (real a, const dual2 &d)
std::ostream &	operator<< (std::ostream &out, const dual2 &obj)
	Stream the dual number in string representation to an output stream (std::ostream)

Detailed Description

Second order dual number class.

Implemented as \(a + b * \epsilon_1 + c * \epsilon_2\) where epsilon is such that \(\epsilon_1^3 = 0\) and \(\epsilon_1 * \epsilon_2 = 0\)

Member Function Documentation

to_string()

std::string theoretica::dual2::to_string ( const std::string &  epsilon1 = "e1", const std::string &  epsilon2 = "e2"  ) const

inline

Convert the dual number to string representation.

Parameters

epsilon1	The character to use to represent epsilon1
epsilon2	The character to use to represent epsilon2

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

• autodiff/dual2.h