#include <math/Dual.hpp>

Public Types
Types
using	value_type = T
	The underlying implementation type.

Public Member Functions
constexpr BasicDual< T >	conjugate () const

constexpr T	magnitude () const

Constructors
constexpr	BasicDual ()=default
	Defaults to (0,0)

constexpr	BasicDual (const T &r)

constexpr	BasicDual (const T &r, const T &d)

Invalid Value Check
bool	isNaN () const

bool	isInf () const

Static Public Member Functions
Constants
static constexpr BasicDual< T >	identity ()

static constexpr BasicDual< T >	zero ()

Convenience Creation Functions
static constexpr BasicDual< T >	make_pure (const T &input)

Public Attributes
Element Access
T	real {}

T	dual {}

Friends
Equality
constexpr bool	operator== (const BasicDual< T > &left, const BasicDual< T > &right)

template<std::floating_point OT = T> requires std::is_floating_point_v<T>
constexpr bool	approximately_equal_to (const BasicDual< T > &value_to_test, const BasicDual< T > &value_it_should_be, OT tolerance=OT{0.0002})

Operators
constexpr BasicDual< T >	operator* (const BasicDual< T > &left, const BasicDual< T > &right)
	Defines multiplication of two Duals.

template<std::floating_point OT = double>
constexpr BasicDual< T >	operator* (OT scalar, const BasicDual< T > &d)

template<std::floating_point OT = double>
constexpr BasicDual< T >	operator* (const BasicDual< T > &d, OT scalar)

constexpr BasicDual< T >	operator/ (const BasicDual< T > &left, const BasicDual< T > &right)
	Defines division of two Duals.

template<std::floating_point OT = double>
constexpr BasicDual< T >	operator/ (OT scalar, const BasicDual< T > &d)

template<std::floating_point OT = double>
constexpr BasicDual< T >	operator/ (const BasicDual< T > &left, OT scalar)

constexpr BasicDual< T >	operator+ (const BasicDual< T > &left, const BasicDual< T > &right)
	Defines addition of two Duals.

template<std::floating_point OT = double>
constexpr BasicDual< T >	operator+ (OT scalar, const BasicDual< T > &d)
	Defines addition of a floating-point scalar and a Dual.

template<std::floating_point OT = double>
constexpr BasicDual< T >	operator+ (const BasicDual< T > &left, OT scalar)
	Defines addition of a Dual and a floating-point scalar.

constexpr BasicDual< T >	operator- (const BasicDual< T > &left, const BasicDual< T > &right)
	Defines subtraction of two Duals.

template<std::floating_point OT = double>
constexpr BasicDual< T >	operator- (OT scalar, const BasicDual< T > &d)
	Defines subtraction of a floating-point scalar and a Dual.

template<std::floating_point OT = double>
constexpr BasicDual< T >	operator- (const BasicDual< T > &left, OT scalar)
	Defines subtraction of a Dual and a floating-point scalar.

Check
template<std::floating_point OT = T> requires std::is_floating_point_v<T>
bool	check_if_equal (const BasicDual< T > &input, const BasicDual< T > &near_to, OT tolerance=OT{0.0002})

template<std::floating_point OT = T> requires std::is_floating_point_v<T>
bool	check_if_not_equal (const BasicDual< T > &input, const BasicDual< T > &near_to, OT tolerance=OT{0.0002})

Assert
template<std::floating_point OT = T> requires std::is_floating_point_v<T>
void	CHECK_IF_EQUAL (const BasicDual< T > &input, const BasicDual< T > &near_to, OT tolerance=OT{0.0002})

template<std::floating_point OT = T> requires std::is_floating_point_v<T>
void	CHECK_IF_NOT_EQUAL (const BasicDual< T > &input, const BasicDual< T > &near_to, OT tolerance=OT{0.0002})

template<std::floating_point OT = T> requires std::is_floating_point_v<T>
void	CHECK_IF_ZERO (const BasicDual< T > &input, OT tolerance=OT{0.0002})

Global Functions
constexpr T	dot (const BasicDual< T > &left, const BasicDual< T > &right)

constexpr BasicDual< T >	dualscalar_sqrt (const BasicDual< T > &input)

constexpr T	dualscalar_normsquared (const BasicDual< T > &d)

constexpr T	accumulate (const BasicDual< T > &input)

constexpr BasicDual< T >	conjugate (const BasicDual< T > &input)

std::string	format (const BasicDual< T > &input)

Related Symbols
(Note that these are not member symbols.)
Type Aliases
using	Dualf = BasicDual< float >

using	Duald = BasicDual< double >

using	Dual = BasicDual< double >

using	Duall = BasicDual< long double >

Detailed Description

template<class T>
class Math::BasicDual< T >

Class representing the concept of a dual number

Definition at line 25 of file Dual.hpp.

Member Typedef Documentation

◆ value_type

template<class T >

using value_type = T

The underlying implementation type.

Definition at line 31 of file Dual.hpp.

Constructor & Destructor Documentation

◆ BasicDual() [1/3]

template<class T >

constexpr BasicDual ( )

constexprdefault

Defaults to (0,0)

◆ BasicDual() [2/3]

template<class T >

constexpr BasicDual ( const T & r )

inlineconstexpr

Sets the real part to r and leaves the dual part as 0

Note: We don't make this an explicit constructor so that we may take advantage of operators using the hidden-friend idiom and allow for minimal code while allowing natural conversions to promote a scalar to a BasicDual to occur.

Definition at line 46 of file Dual.hpp.

◆ BasicDual() [3/3]

template<class T >

constexpr BasicDual	(	const T &	r,
		const T &	d
	)

inlineconstexpr

Definition at line 48 of file Dual.hpp.

Member Function Documentation

◆ conjugate()

template<class T >

constexpr BasicDual< T > conjugate ( ) const

inlineconstexpr

Definition at line 58 of file Dual.hpp.

◆ identity()

template<class T >

static constexpr BasicDual< T > identity ( )

inlinestaticconstexpr

Definition at line 54 of file Dual.hpp.

◆ isInf()

template<class T >

bool isInf ( ) const

inline

Definition at line 97 of file Dual.hpp.

◆ isNaN()

template<class T >

bool isNaN ( ) const

inline

Definition at line 89 of file Dual.hpp.

◆ magnitude()

template<class T >

constexpr T magnitude ( ) const

inlineconstexpr

Definition at line 66 of file Dual.hpp.

◆ make_pure()

template<class T >

static constexpr BasicDual< T > make_pure ( const T & input )

inlinestaticconstexpr

Creates a pure BasicDual with input

Parameters

input

Postcondition: output.real == 0 output.dual == input

Note: A pure BasicDual is one which has the real component set to 0

Definition at line 80 of file Dual.hpp.

◆ zero()

template<class T >

static constexpr BasicDual< T > zero ( )

inlinestaticconstexpr

Definition at line 55 of file Dual.hpp.

Friends And Related Symbol Documentation

◆ accumulate

template<class T >

constexpr T accumulate ( const BasicDual< T > & input )

friend

Accumulates the components of the input BasicDual

Returns: A scalar that is the sum of the components

Definition at line 454 of file Dual.hpp.

◆ approximately_equal_to

template<class T >

template<std::floating_point OT = T>
requires std::is_floating_point_v<T>

constexpr bool approximately_equal_to	(	const BasicDual< T > &	value_to_test,
		const BasicDual< T > &	value_it_should_be,
		OT	tolerance = `OT{0.0002}`
	)

friend

Compare two values for equality with a tolerance

Parameters

input	The first value to compare
near_to	The second value to compare
tolerance	The minimum value for being considered equal

Returns: true if the two are equal within tolerance , false otherwise

See also: Equality

Definition at line 146 of file Dual.hpp.

◆ conjugate

template<class T >

constexpr BasicDual< T > conjugate ( const BasicDual< T > & input )

friend

Computes the conjugate of the input

Note: This will just call input.conjugate()

Definition at line 463 of file Dual.hpp.

◆ dot

template<class T >

constexpr T dot	(	const BasicDual< T > &	left,
		const BasicDual< T > &	right
	)

friend

Calculates the dot-product of two Duals

Returns: The dot-product of the two inputs

Note: This treats the BasicDual number as a pair of numbers, or 2D vector, and calculates the dot product as as expected of that.

Definition at line 418 of file Dual.hpp.

◆ dualscalar_normsquared

template<class T >

constexpr T dualscalar_normsquared ( const BasicDual< T > & d )

friend

Calculates the square of the norm

Definition at line 441 of file Dual.hpp.

◆ dualscalar_sqrt

template<class T >

constexpr BasicDual< T > dualscalar_sqrt ( const BasicDual< T > & input )

friend

Calculates the square root of a BasicDual

This treats the input as a BasicDual scalar and calculates the square root based on that expectation.

Returns: The BasicDual as a dual scalar

Definition at line 431 of file Dual.hpp.

◆ format

template<class T >

std::string format ( const BasicDual< T > & input )

friend

Definition at line 468 of file Dual.hpp.

◆ operator==

template<class T >

constexpr bool operator==	(	const BasicDual< T > &	left,
		const BasicDual< T > &	right
	)

friend

Defines equality of two Duals

Note: Uses approximately_equal_to under-the-hood; Use C++20's ability to generate the operator !=() from operator ==()

See also: Equality

Definition at line 129 of file Dual.hpp.

Member Data Documentation

◆ dual

template<class T >

T dual {}

Definition at line 110 of file Dual.hpp.

◆ real

template<class T >

T real {}

Definition at line 109 of file Dual.hpp.

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

lib/include/Math/math/Dual.hpp

Public Types

Public Member Functions

Static Public Member Functions

Public Attributes

Friends

Related Symbols

Detailed Description

Member Typedef Documentation

◆ value_type

Constructor & Destructor Documentation

◆ BasicDual() [1/3]

◆ BasicDual() [2/3]

◆ BasicDual() [3/3]

Member Function Documentation

◆ conjugate()

◆ identity()

◆ isInf()

◆ isNaN()

◆ magnitude()

◆ make_pure()

◆ zero()

Friends And Related Symbol Documentation

◆ accumulate

◆ approximately_equal_to

◆ conjugate

◆ dot

◆ dualscalar_normsquared

◆ dualscalar_sqrt

◆ format

◆ operator==

Member Data Documentation

◆ dual

◆ real