Affine interval arithmetics. More...

#include <aa.h>

Public Member Functions
	Aa (double=0.0)
	Create the affine arithmetic interval equal to a real.

	Aa (double, const double , const unsigned , unsigned)
	Create an affine arithmetic interval.

	Aa (const Aa &)
	Copy constructor.

	Aa (const Ia &)
	Create an affine arithmetic interval from an interval.

	~Aa ()
	Destructor.

double	operator[] (unsigned) const
	Index operator.

bool	operator< (const Aa &) const
	Comparison.

bool	operator<= (const Aa &) const
	Comparison.

bool	operator> (const Aa &) const
	Comparison.

bool	operator>= (const Aa &) const
	Comparison.

bool	operator== (const Aa &) const
	Comparison.

Aa &	operator= (const Aa &)
	Overloaded.

Aa &	operator= (const double)
	Assignment operator.

Aa	operator+ (const Aa &) const
	Overloaded.

Aa	operator- (const Aa &) const
	Overloaded.

Aa	operator* (const Aa &)
	Overloaded.

Aa	operator/ (const Aa &)
	Division.

Aa	operator- () const
	Overloaded.

Aa &	operator+= (double)
	Destructive sum.

Aa &	operator-= (double)
	Destructive subtraction.

Aa &	*operator=** (double)
	Destructive multiply.

Aa &	operator/= (double)
	Overloaded.

Aa &	operator+= (const Aa &)
	Overloaded.

Aa &	operator-= (const Aa &)
	Overloaded.

Aa	operator* (double)
	Multiply.

Aa	operator/ (double)
	Division.

unsigned	getlength () const
	returns the number of partial deviations.

double	Radius () const
	Get the radius.

Ia	GetIa () const
	Convert to an interval.

Aa	Pow (int) const
	Power.

Static Public Member Functions
static void	SetApproximation (ApproximationType)
	sets the approximation type

static unsigned	getDefault ()
	returns the highest symbol

Protected Attributes
double	cvalue = 0.0
	Central value.

double	radius = 0.0
	Radius.

unsigned	length = 0
	Length of indexes.

unsigned	size = 0
	Array size of indexes and deviations.

double *	deviations = nullptr
	values of parial deviations

unsigned *	indexes = nullptr
	indexes of partial deviations

Friends
Aa	operator* (double cst, const Aa P)
	Overloaded.

Aa	operator/ (double x, const Aa a)
	Division.

Aa	operator+ (double cst, const Aa P)
	Overloaded.

Aa	operator- (double cst, const Aa P)
	Overloaded.

Aa	sqrt (const Aa &P)
	Square root.

Aa	isqrt (const Aa &P)
	Inverse square root.

Aa	sin (const Aa &P)
	Sine.

Aa	cos (const Aa &P)
	Cosine.

Aa	tan (const Aa &P)
	Tangent.

Aa	exp (const Aa &P)
	Exponential.

Aa	log (const Aa &P)
	Logarithm.

Aa	logexp (const Aa &P)
	Chained log(1+exp(x)).

Aa	atan (const Aa &P)
	Arctangent.

Aa	tanh (const Aa &P)
	Tangent hyperbolic.

std::ostream &	operator<< (std::ostream &s, const Aa &x)
	Overloaded output-stream operator.

Aa	sqrt (const Aa &P)
	Square root.

Aa	sqr (const Aa &P)
	Square.

Aa	isqrt (const Aa &P)
	Inverse square root.

Aa	exp (const Aa &P)
	Exponential.

Aa	log (const Aa &P)
	Logarithm.

Aa	logexp (const Aa &P)
	Chained log(1+exp(x)).

Aa	atan (const Aa &P)
	Arctangent.

Aa	tanh (const Aa &P)
	Tangent hyperbolic.

Aa	inv (const Aa &P)
	Inverse.

Aa	Aa_pow (const Aa &base, const Aa &exp)
	Power.

Aa	Aa_pow (const Aa &base, const double &exp)
	Power.

Aa	Aa_pow (const double &base, const Aa &exp)
	Power.

Detailed Description

Affine interval arithmetics.

Rewritten from Aalib, an Affine Arithmetic class.

Constructor & Destructor Documentation

◆ Aa() [1/4]

Aa::Aa ( double x = 0.0 )

Create the affine arithmetic interval equal to a real.

Parameters

x Real.

◆ Aa() [2/4]

Aa::Aa	(	double	x,
		const double *	t1,
		const unsigned *	t2,
		unsigned	T )

explicit

Create an affine arithmetic interval.

Parameters

x	Center value.
t1	array of index values
t2	array of indices
T	Number of indices.

◆ Aa() [3/4]

Aa::Aa ( const Aa & a )

Copy constructor.

Parameters

a	Affine arithmetic interval.

◆ Aa() [4/4]

Aa::Aa ( const Ia & iv )

Create an affine arithmetic interval from an interval.

Parameters

iv Interval.

Member Function Documentation

◆ operator=() [1/2]

Aa & Aa::operator= ( const Aa & P )

Overloaded.

Parameters

P	Affine arithmetic interval.

◆ operator=() [2/2]

Aa & Aa::operator= ( const double x )

Assignment operator.

Parameters

x Real.

◆ operator[]()

double Aa::operator[] ( unsigned ind ) const

Index operator.

Parameters

ind	The index.

◆ Pow()

Aa Aa::Pow ( int exponent ) const

Power.

Parameters

exponent Integer exponent.

◆ Radius()

double Aa::Radius ( ) const

inline

Get the radius.

The radius is the total deviation of an Aa, i.e. the sum of all deviations.

Friends And Related Symbol Documentation

◆ Aa_pow [1/3]

Aa Aa_pow	(	const Aa &	base,
		const Aa &	exp )

friend

Power.

Parameters

base	Affine arithmetic base.
exp	Affine arithmetic exponent.

◆ Aa_pow [2/3]

Aa Aa_pow	(	const Aa &	base,
		const double &	exp )

friend

Power.

Parameters

base	Affine arithmetic base.
exp	Exponent.

◆ Aa_pow [3/3]

Aa Aa_pow	(	const double &	base,
		const Aa &	exp )

friend

Power.

Parameters

base	Base.
exp	Affine arithmetic exponent.

◆ atan [1/2]

Aa atan ( const Aa & P )

friend

Arctangent.

Parameters

P	Affine arithmetic interval.

◆ atan [2/2]

Aa atan ( const Aa & P )

friend

Arctangent.

Parameters

P	Affine arithmetic interval.

◆ cos

Aa cos ( const Aa & P )

friend

Cosine.

Parameters

P	Affine arithmetic interval.

◆ exp [1/2]

Aa exp ( const Aa & P )

friend

Exponential.

Parameters

P	Affine arithmetic interval.

◆ exp [2/2]

Aa exp ( const Aa & P )

friend

Exponential.

Parameters

P	Affine arithmetic interval.

◆ inv

Aa inv ( const Aa & P )

friend

Inverse.

Parameters

P	Affine arithmetic interval.

◆ isqrt [1/2]

Aa isqrt ( const Aa & P )

friend

Inverse square root.

Parameters

P	Affine arithmetic interval.

◆ isqrt [2/2]

Aa isqrt ( const Aa & P )

friend

Inverse square root.

Parameters

P	Affine arithmetic interval.

◆ log [1/2]

Aa log ( const Aa & P )

friend

Logarithm.

Parameters

P	Affine arithmetic interval.

◆ log [2/2]

Aa log ( const Aa & P )

friend

Logarithm.

Parameters

P	Affine arithmetic interval.

◆ operator<<

std::ostream & operator<<	(	std::ostream &	s,
		const Aa &	x )

friend

Overloaded output-stream operator.

Parameters

s	Stream.
x	Affine arithmetic interval.

◆ sin

Aa sin ( const Aa & P )

friend

Sine.

Parameters

P	Affine arithmetic interval.

◆ sqr

Aa sqr ( const Aa & P )

friend

Square.

Parameters

P	Affine interval.

◆ sqrt [1/2]

Aa sqrt ( const Aa & P )

friend

Square root.

Parameters

P	Affine arithmetic interval.

◆ sqrt [2/2]

Aa sqrt ( const Aa & P )

friend

Square root.

Parameters

P	Affine arithmetic interval.

◆ tan

Aa tan ( const Aa & P )

friend

Tangent.

Parameters

P	Affine arithmetic interval.

◆ tanh [1/2]

Aa tanh ( const Aa & P )

friend

Tangent hyperbolic.

Parameters

P	Affine arithmetic interval.

The tanh function is strictly (monotonic) increasing but it has two possible turning points which has to be considered for the Chebyshev approximation.

◆ tanh [2/2]

Aa tanh ( const Aa & P )

friend

Tangent hyperbolic.

Parameters

P	Affine arithmetic interval.

The tanh function is strictly (monotonic) increasing but it has two possible turning points which has to be considered for the Chebyshev approximation.

Public Member Functions

Static Public Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Aa() [1/4]

◆ Aa() [2/4]

◆ Aa() [3/4]

◆ Aa() [4/4]

Member Function Documentation

◆ operator=() [1/2]

◆ operator=() [2/2]

◆ operator[]()

◆ Pow()

◆ Radius()

Friends And Related Symbol Documentation

◆ Aa_pow [1/3]

◆ Aa_pow [2/3]

◆ Aa_pow [3/3]

◆ atan [1/2]

◆ atan [2/2]

◆ cos

◆ exp [1/2]

◆ exp [2/2]

◆ inv

◆ isqrt [1/2]

◆ isqrt [2/2]

◆ log [1/2]

◆ log [2/2]

◆ operator<<

◆ sin

◆ sqr

◆ sqrt [1/2]

◆ sqrt [2/2]

◆ tan

◆ tanh [1/2]

◆ tanh [2/2]