coco::interval Class Reference
[Classes and types for basic data management]

Interval wrapper class. More...

#include <interval_boost.h>

List of all members.

Public Member Functions

interval (double lo, double up)

interval (double d=0)

interval (int d)

interval (unsigned d)

interval (long d)

interval (unsigned long d)

interval (const interval &x)

interval (const interval_st &x)

void set (double lo, double up)

double inf () const

double sup () const

__Base base () const

bool empty () const

bool is_empty () const

bool is_thin () const

bool is_unbounded_below () const

bool is_unbounded_above () const

bool is_entire () const

bool is_bounded () const

bool subset (const interval &x) const

bool superset (const interval &x) const

bool proper_subset (const interval &x) const

bool proper_superset (const interval &x) const

bool disjoint (const interval &x) const

double rel_width () const

interval & intersect (const interval &x)

interval & hull (const interval &x)

interval & hulldiff (const interval &x)

bool contains (const interval &x) const

void setpair (double &lo, double &up) const

void get_bounds (double &a, double &b) const

void set_bounds (double a, double b)

void set_lb (double d)

void set_ub (double d)

interval & operator= (const interval &x)

interval & operator= (double d)

interval & operator= (int d)

interval & operator= (unsigned d)

interval & operator= (long d)

interval & operator= (unsigned long d)

interval operator- () const

interval & ipow (int n)

interval & imin (const interval &x)

interval & imax (const interval &x)

interval & round_to_integer ()

interval & intersect_div (const interval &__i, const interval &__j)

interval & intersect_power (const interval &__i, int __n)

interval & intersect_invsqr_wc (const interval &__i, double __l, double __d)

interval & intersect_invpower_wc (const interval &__i, double __l, int __n)

interval & intersect_invsin_wc (const interval &__i, double __l, double __d)

interval & intersect_invcos_wc (const interval &__i, double __l, double __d)

interval & intersect_invgauss_wc (const interval &__i, double __l, double __m, double __s)

double project (double __d) const

interval & operator+= (const interval &a)

interval & operator+= (double a)

interval & operator-= (const interval &a)

interval & operator-= (double a)

interval & operator*= (const interval &a)

interval & operator*= (double a)

interval & operator/= (const interval &a)

interval & operator/= (double a)

double mid () const

double diam () const

double width () const

double relDiam () const

double rad () const

double mig () const

double mag () const

double dist (const interval &x) const

double safeguarded_mid () const

interval (double lo, double up)

interval (double d=0)

interval (int d)

interval (unsigned d)

interval (long d)

interval (unsigned long d)

interval (const __Base &x)

interval (const interval &x)

interval (const interval_st &x)

void set (double lo, double up)

double sup () const

double inf () const

__Base base () const

bool empty () const

bool is_empty () const

bool is_thin () const

bool is_unbounded_below () const

bool is_unbounded_above () const

bool is_entire () const

bool is_bounded () const

bool subset (const interval &x) const

bool superset (const interval &x) const

bool proper_subset (const interval &x) const

bool proper_superset (const interval &x) const

bool disjoint (const interval &x) const

double rel_width () const

interval & intersectwith (const interval &x)

interval & hullwith (const interval &x)

interval & hulldiffwith (const interval &x)

interval intersect (const interval &x) const

interval hull (const interval &x) const

interval hulldiff (const interval &x) const

bool contains (const interval &x) const

void setpair (double &lo, double &up) const

void get_bounds (double &a, double &b) const

void set_bounds (double a, double b)

void set_lb (double d)

void set_ub (double d)

interval & operator= (const __Base &_x)

interval operator- () const

interval & ipow (int n)

interval & imin (const interval &x)

interval & imax (const interval &x)

interval & round_to_integer ()

interval & intersect_div (const interval &__i, const interval &__j)

interval & intersect_power (const interval &__i, int __n)

interval & intersect_invsqr_wc (const interval &__i, double __l, double __d)

interval & intersect_invpower_wc (const interval &__i, double __l, int __n)

interval & intersect_invsin_wc (const interval &__i, double __l, double __d)

interval & intersect_invcos_wc (const interval &__i, double __l, double __d)

interval & intersect_invgauss_wc (const interval &__i, double __l, double __m, double __s)

double project (double __d) const

interval & operator+= (const interval &a)

interval & operator+= (double a)

interval & operator-= (const interval &a)

interval & operator-= (double a)

interval & operator*= (const interval &a)

interval & operator*= (double a)

interval & operator/= (const interval &a)

interval & operator/= (double a)

double mid () const

double relDiam () const

double rad () const

double mig () const

double mag () const

double dist (const interval &x) const

double safeguarded_mid () const

interval (double lo, double up)

interval (double d=0)

interval (int d)

interval (unsigned d)

interval (long d)

interval (unsigned long d)

interval (const __Base &x)

interval (const interval &x)

interval (const interval_st &x)

void set (double lo, double up)

__Base base () const

bool empty () const

bool is_empty () const

bool is_thin () const

bool is_unbounded_below () const

bool is_unbounded_above () const

bool is_entire () const

bool is_bounded () const

bool subset (const interval &x) const

bool superset (const interval &x) const

bool proper_subset (const interval &x) const

bool proper_superset (const interval &x) const

bool disjoint (const interval &x) const

double rel_width () const

interval & intersect (const interval &x)

interval & hull (const interval &x)

interval & hulldiff (const interval &x)

bool contains (const interval &x) const

void setpair (double &lo, double &up) const

void get_bounds (double &a, double &b) const

void set_bounds (double a, double b)

void set_lb (double d)

void set_ub (double d)

interval & operator= (const __Base &_x)

interval operator- () const

interval & ipow (int n)

interval & imin (const interval &x)

interval & imax (const interval &x)

interval & intersect_div (const interval &__i, const interval &__j)

interval & intersect_power (const interval &__i, int __n)

interval & intersect_invsqr_wc (const interval &__i, double __l, double __d)

interval & intersect_invpower_wc (const interval &__i, double __l, int __n)

interval & intersect_invsin_wc (const interval &__i, double __l, double __d)

interval & intersect_invcos_wc (const interval &__i, double __l, double __d)

interval & intersect_invgauss_wc (const interval &__i, double __l, double __m, double __s)

double project (double __d) const

interval & operator+= (const interval &a)

interval & operator+= (double a)

interval & operator-= (const interval &a)

interval & operator-= (double a)

interval & operator*= (const interval &a)

interval & operator*= (double a)

interval & operator/= (const interval &a)

interval & operator/= (double a)

double mid () const

double relDiam () const

double rad () const

double mig () const

double mag () const

double dist (const interval &x) const

double safeguarded_mid () const

interval & operator= (double d)

interval & operator= (int d)

interval & operator= (unsigned d)

interval & operator= (long d)

interval & operator= (unsigned long d)

double diam () const

double width () const

interval & operator= (double d)

interval & operator= (int d)

interval & operator= (unsigned d)

interval & operator= (long d)

interval & operator= (unsigned long d)

double diam () const

double width () const

Static Public Member Functions

static interval EMPTY ()

static int const & precision ()

static int precision (int const &p)

static interval EMPTY ()

static int const & precision ()

static int precision (int const &p)

static interval EMPTY ()

static int const & precision ()

static int precision (int const &p)

Friends

std::ostream & operator<< (std::ostream &s, const interval &a)

interval operator+ (const interval &a, const interval &b)

interval operator+ (const interval &a, double b)

interval operator+ (double b, const interval &a)

interval operator- (const interval &a, const interval &b)

interval operator- (const interval &a, double b)

interval operator- (double b, const interval &a)

interval cancel (const interval &a, const interval &b)

interval operator* (const interval &a, const interval &b)

interval operator* (const interval &a, double b)

interval operator* (double b, const interval &a)

interval operator/ (const interval &a, const interval &b)

interval operator/ (const interval &a, double b)

interval operator/ (double b, const interval &a)

interval acos (const interval &x)

interval abs (const interval &x)

interval acosh (const interval &x)

interval acot (const interval &x)

interval acoth (const interval &x)

interval asin (const interval &x)

interval asinh (const interval &x)

interval atan (const interval &x)

interval atanh (const interval &x)

interval cos (const interval &x)

interval cosh (const interval &x)

interval cot (const interval &x)

interval coth (const interval &x)

interval exp (const interval &x)

interval exp10 (const interval &x)

interval exp2 (const interval &x)

interval expm1 (const interval &x)

interval log (const interval &x)

interval log10 (const interval &x)

interval log1p (const interval &x)

interval log2 (const interval &x)

interval power (const interval &x, int n)

interval pow (const interval &x, const interval &y)

interval sin (const interval &x)

interval sinh (const interval &x)

interval sqr (const interval &x)

interval sqrt (const interval &x)

interval tan (const interval &x)

interval tanh (const interval &x)

interval imax (const interval &x, const interval &y)

interval imin (const interval &x, const interval &y)

interval division_part1 (const interval &x, const interval &y, bool &b)

interval division_part2 (const interval &x, const interval &y, bool b)

bool operator== (const interval &__i, const interval &__d)

template<class _TC >

bool operator== (const interval &__i, const _TC &__d)

bool operator!= (const interval &__i, const interval &__d)

template<class _TC >

bool operator!= (const interval &__i, const _TC &__d)

std::ostream & operator<< (std::ostream &, const interval &)

interval tanh (const interval &x)

interval tan (const interval &x)

interval sqrt (const interval &x)

interval sqr (const interval &x)

interval sinh (const interval &x)

interval sin (const interval &x)

interval pow (const interval &x, const interval &y)

interval power (const interval &x, int n)

interval log2 (const interval &x)

interval log1p (const interval &x)

interval log10 (const interval &x)

interval log (const interval &x)

interval expm1 (const interval &x)

interval exp2 (const interval &x)

interval exp10 (const interval &x)

interval exp (const interval &x)

interval coth (const interval &x)

interval cot (const interval &x)

interval cosh (const interval &x)

interval cos (const interval &x)

interval atanh (const interval &x)

interval atan (const interval &x)

interval asinh (const interval &x)

interval asin (const interval &x)

interval acoth (const interval &x)

interval acot (const interval &x)

interval acosh (const interval &x)

interval abs (const interval &x)

interval acos (const interval &x)

double dist (const interval &x, const interval &y)

double mag (const interval &)

double mig (const interval &)

double rad (const interval &)

double relDiam (const interval &)

double width (const interval &)

double diam (const interval &)

double mid (const interval &)

interval operator/ (double a, const interval &b)

interval operator/ (const interval &a, double b)

interval operator/ (const interval &a, const interval &b)

interval operator* (double a, const interval &b)

interval operator* (const interval &a, double b)

interval operator* (const interval &a, const interval &b)

interval cancel (const interval &a, const interval &b)

interval operator- (const interval &a, const interval &b)

interval operator- (const interval &a, double b)

interval operator- (double a, const interval &b)

interval operator+ (const interval &a, const interval &b)

interval operator+ (const interval &a, double b)

interval operator+ (double b, const interval &a)

double upward_divides (const double &a, const double &b)

double downward_divides (const double &a, const double &b)

double upward_multiplies (const double &a, const double &b)

double downward_multiplies (const double &a, const double &b)

double upward_minus (const double &a, const double &b)

double downward_minus (const double &a, const double &b)

double upward_plus (const double &a, const double &b)

double downward_plus (const double &a, const double &b)

interval imin (const interval &x, const interval &y)

interval imax (const interval &x, const interval &y)

Detailed Description

This is a wrapper class to make the COCONUT environment independent from a <it>specific</it> interval library. Currently, the FILIB++ library works underneath.

This is a wrapper class to make the COCONUT environment independent from a <it>specific</it> interval library.

Definition at line 112 of file interval_boost.h.

Constructor & Destructor Documentation

coco::interval::interval	(	double	lo,
		double	up
	)			`[inline]`

Definition at line 134 of file interval_boost.h.

coco::interval::interval ( double d = 0 ) [inline]

Definition at line 135 of file interval_boost.h.

coco::interval::interval ( int d ) [inline]

Definition at line 136 of file interval_boost.h.

coco::interval::interval ( unsigned d ) [inline]

Definition at line 137 of file interval_boost.h.

coco::interval::interval ( long d ) [inline]

Definition at line 138 of file interval_boost.h.

coco::interval::interval ( unsigned long d ) [inline]

Definition at line 139 of file interval_boost.h.

coco::interval::interval ( const interval & x ) [inline]

Definition at line 140 of file interval_boost.h.

coco::interval::interval ( const interval_st & x ) [inline]

Definition at line 141 of file interval_boost.h.

coco::interval::interval	(	double	lo,
		double	up
	)			`[inline]`

Constructor, setting the interval to [lo,up].

Definition at line 86 of file interval_filib.h.

coco::interval::interval ( double d = 0 ) [inline]

Constructor, setting the interval to the thin interval [d,d].

Definition at line 88 of file interval_filib.h.

coco::interval::interval ( int d ) [inline]

Constructor, setting the interval to the thin interval [d,d].

Definition at line 90 of file interval_filib.h.

coco::interval::interval ( unsigned d ) [inline]

Constructor, setting the interval to the thin interval [d,d].

Definition at line 92 of file interval_filib.h.

coco::interval::interval ( long d ) [inline]

Constructor, setting the interval to the thin interval [d,d].

Definition at line 94 of file interval_filib.h.

coco::interval::interval ( unsigned long d ) [inline]

Constructor, setting the interval to the thin interval [d,d].

Definition at line 96 of file interval_filib.h.

coco::interval::interval ( const __Base & x ) [inline, explicit]

Constructor, setting the interval from a base class interval.

Definition at line 98 of file interval_filib.h.

coco::interval::interval ( const interval & x ) [inline]

Standard Copy Constructor

Definition at line 100 of file interval_filib.h.

coco::interval::interval ( const interval_st & x ) [inline]

Constructor, setting the interval from a interval_st interval storage.

Definition at line 102 of file interval_filib.h.

coco::interval::interval	(	double	lo,
		double	up
	)			`[inline]`

Constructor, setting the interval to [lo,up].

Definition at line 68 of file interval_profil.h.

coco::interval::interval ( double d = 0 ) [inline]

Constructor, setting the interval to the thin interval [d,d].

Definition at line 70 of file interval_profil.h.

coco::interval::interval ( int d ) [inline]

Constructor, setting the interval to the thin interval [d,d].

Definition at line 72 of file interval_profil.h.

coco::interval::interval ( unsigned d ) [inline]

Constructor, setting the interval to the thin interval [d,d].

Definition at line 74 of file interval_profil.h.

coco::interval::interval ( long d ) [inline]

Constructor, setting the interval to the thin interval [d,d].

Definition at line 76 of file interval_profil.h.

coco::interval::interval ( unsigned long d ) [inline]

Constructor, setting the interval to the thin interval [d,d].

Definition at line 78 of file interval_profil.h.

coco::interval::interval ( const __Base & x ) [inline, explicit]

Constructor, setting the interval from a base class interval.

Definition at line 80 of file interval_profil.h.

coco::interval::interval ( const interval & x ) [inline]

Standard Copy Constructor

Definition at line 82 of file interval_profil.h.

coco::interval::interval ( const interval_st & x ) [inline]

Constructor, setting the interval from a interval_st interval storage.

Definition at line 84 of file interval_profil.h.

Member Function Documentation

__Base coco::interval::base ( ) const [inline]

This method returns a base class representing the same interval.

Definition at line 93 of file interval_profil.h.

__Base coco::interval::base ( ) const [inline]

This method returns a base class representing the same interval.

Definition at line 116 of file interval_filib.h.

__Base coco::interval::base ( ) const [inline]

Definition at line 152 of file interval_boost.h.

bool coco::interval::contains ( const interval & x ) const [inline]

Check whether this interval contains x.

Definition at line 172 of file interval_profil.h.

bool coco::interval::contains ( const interval & x ) const [inline]

Check whether this interval contains x.

Definition at line 215 of file interval_filib.h.

bool coco::interval::contains ( const interval & x ) const [inline]

Definition at line 207 of file interval_boost.h.

double coco::interval::diam ( ) const

Returns an upper bound for the diameter (width) of this interval, i.e.

a.diam() == a.sup()-a.inf()

Special cases in the extended system:

a.diam() == NaN for a == [ EMPTY ]
a.diam() == +INF for any infinite interval

double coco::interval::diam ( ) const

Returns an upper bound for the diameter (width) of this interval, i.e.

a.diam() == a.sup()-a.inf()

Special cases in the extended system:

a.diam() == NaN for a == [ EMPTY ]
a.diam() == +INF for any infinite interval

double coco::interval::diam ( ) const

bool coco::interval::disjoint ( const interval & x ) const [inline]

This method checks whether this interval and x are disjoint.

Definition at line 133 of file interval_profil.h.

bool coco::interval::disjoint ( const interval & x ) const [inline]

This method checks whether this interval and x are disjoint.

Definition at line 151 of file interval_filib.h.

bool coco::interval::disjoint ( const interval & x ) const [inline]

Definition at line 173 of file interval_boost.h.

double coco::interval::dist ( const interval & x ) const

Returns an upper bound for the Hausdorff distance of this interval and the interval x, i.e.

x.dist(y) == max{ abs(x.inf()-y.inf()), abs(x.sup() - y.sup()) }

Special cases in the extended system:

x.dist(y) == NaN for x == [ EMPTY ] or y == [ EMPTY ]

double coco::interval::dist ( const interval & x ) const

Returns an upper bound for the Hausdorff distance of this interval and the interval x, i.e.

x.dist(y) == max{ abs(x.inf()-y.inf()), abs(x.sup() - y.sup()) }

Special cases in the extended system:

x.dist(y) == NaN for x == [ EMPTY ] or y == [ EMPTY ]

double coco::interval::dist ( const interval & x ) const

Returns an upper bound for the Hausdorff distance of this interval and the interval x, i.e.

x.dist(y) == max{ abs(x.inf()-y.inf()), abs(x.sup() - y.sup()) }

Special cases in the extended system:

x.dist(y) == NaN for x == [ EMPTY ] or y == [ EMPTY ]

bool coco::interval::empty ( ) const [inline]

This method checks whether the interval is empty.

Definition at line 100 of file interval_profil.h.

static interval coco::interval::EMPTY ( ) [inline, static]

This returns a new empty interval.

Definition at line 97 of file interval_profil.h.

bool coco::interval::empty ( ) const [inline]

This method checks whether the interval is empty.

Definition at line 121 of file interval_filib.h.

static interval coco::interval::EMPTY ( ) [inline, static]

This returns a new empty interval.

Definition at line 118 of file interval_filib.h.

bool coco::interval::empty ( ) const [inline]

Definition at line 156 of file interval_boost.h.

static interval coco::interval::EMPTY ( ) [inline, static]

Definition at line 153 of file interval_boost.h.

void coco::interval::get_bounds	(	double &	a,
		double &	b
	)			const `[inline]`

Set the pair a and b to the bounds of the interval.

Definition at line 183 of file interval_profil.h.

void coco::interval::get_bounds	(	double &	a,
		double &	b
	)			const `[inline]`

Set the pair a and b to the bounds of the interval.

Definition at line 226 of file interval_filib.h.

void coco::interval::get_bounds	(	double &	a,
		double &	b
	)			const `[inline]`

Definition at line 216 of file interval_boost.h.

interval& coco::interval::hull ( const interval & x ) [inline]

y.hull(x) builds the hull of y with x.

Definition at line 150 of file interval_profil.h.

interval coco::interval::hull ( const interval & x ) const [inline]

y.hull(x) returns the hull of y and x.

Definition at line 193 of file interval_filib.h.

interval& coco::interval::hull ( const interval & x ) [inline]

Definition at line 186 of file interval_boost.h.

interval& coco::interval::hulldiff ( const interval & x ) [inline]

y.hulldiff(x) constructs the hull of the set difference of y and x.

Definition at line 157 of file interval_profil.h.

interval coco::interval::hulldiff ( const interval & x ) const [inline]

y.hulldiff(x) returns the hull of the set difference of y and x.

Definition at line 200 of file interval_filib.h.

interval& coco::interval::hulldiff ( const interval & x ) [inline]

Definition at line 192 of file interval_boost.h.

interval& coco::interval::hulldiffwith ( const interval & x ) [inline]

y.hulldiffwith(x) constructs the hull of the set difference of y and x.

Definition at line 172 of file interval_filib.h.

interval& coco::interval::hullwith ( const interval & x ) [inline]

y.hullwith(x) builds the hull of y with x.

Definition at line 165 of file interval_filib.h.

interval& coco::interval::imax ( const interval & x )

The method changes this interval to the maximum of itself and x.

interval& coco::interval::imax ( const interval & x )

The method changes this interval to the maximum of itself and x.

interval& coco::interval::imax ( const interval & x )

The method changes this interval to the maximum of itself and x.

interval& coco::interval::imin ( const interval & x )

The method changes this interval to the minimum of itself and x.

interval& coco::interval::imin ( const interval & x )

The method changes this interval to the minimum of itself and x.

interval& coco::interval::imin ( const interval & x )

The method changes this interval to the minimum of itself and x.

double coco::interval::inf ( ) const [inline]

This method returns the lower bound of the interval.

Definition at line 113 of file interval_filib.h.

double coco::interval::inf ( ) const [inline]

Definition at line 150 of file interval_boost.h.

interval& coco::interval::intersect ( const interval & x ) [inline]

y.intersect(x) intersects y with x.

Definition at line 142 of file interval_profil.h.

interval coco::interval::intersect ( const interval & x ) const [inline]

y.intersect(x) returns the intersection of y and x.

Definition at line 187 of file interval_filib.h.

interval& coco::interval::intersect ( const interval & x ) [inline]

Definition at line 179 of file interval_boost.h.

interval& coco::interval::intersect_div	(	const interval &	__i,
		const interval &	__j
	)

i.intersect_div(j,k) computes the interval hull of the set $i\cap(j/k)$ .

interval& coco::interval::intersect_div	(	const interval &	__i,
		const interval &	__j
	)

i.intersect_div(j,k) computes the interval hull of the set $i\cap(j/k)$ .

interval& coco::interval::intersect_div	(	const interval &	__i,
		const interval &	__j
	)

interval& coco::interval::intersect_invcos_wc	(	const interval &	__i,
		double	__l,
		double	__d
	)

i.intersect_infcos_wc(j,l,d) computes the interval hull of the set $i\cap f(j,l,n)$ , where $f$ is the inverse image of $j$ under the function $x\mapsto \cos(lx+d)$ .

interval& coco::interval::intersect_invcos_wc	(	const interval &	__i,
		double	__l,
		double	__d
	)

i.intersect_infcos_wc(j,l,d) computes the interval hull of the set $i\cap f(j,l,n)$ , where $f$ is the inverse image of $j$ under the function $x\mapsto \cos(lx+d)$ .

interval& coco::interval::intersect_invcos_wc	(	const interval &	__i,
		double	__l,
		double	__d
	)

interval& coco::interval::intersect_invgauss_wc	(	const interval &	__i,
		double	__l,
		double	__m,
		double	__s
	)

i.intersect_infgauss_wc(j,l,m,s) computes the interval hull of the set $i\cap f(j,l,m,s)$ , where $f$ is the inverse image of $j$ under the function $x\mapsto e^{-(\frac{lx-m}{s})^2}$ .

interval& coco::interval::intersect_invgauss_wc	(	const interval &	__i,
		double	__l,
		double	__m,
		double	__s
	)

i.intersect_infgauss_wc(j,l,m,s) computes the interval hull of the set $i\cap f(j,l,m,s)$ , where $f$ is the inverse image of $j$ under the function $x\mapsto e^{-(\frac{lx-m}{s})^2}$ .

interval& coco::interval::intersect_invgauss_wc	(	const interval &	__i,
		double	__l,
		double	__m,
		double	__s
	)

interval& coco::interval::intersect_invpower_wc	(	const interval &	__i,
		double	__l,
		int	__n
	)

i.intersect_infpower_wc(j,l,n) computes the interval hull of the set $i\cap f(j,l,n)$ , where $f$ is the inverse image of $j$ under the function $x\mapsto (lx)^n$ .

interval& coco::interval::intersect_invpower_wc	(	const interval &	__i,
		double	__l,
		int	__n
	)

i.intersect_infpower_wc(j,l,n) computes the interval hull of the set $i\cap f(j,l,n)$ , where $f$ is the inverse image of $j$ under the function $x\mapsto (lx)^n$ .

interval& coco::interval::intersect_invpower_wc	(	const interval &	__i,
		double	__l,
		int	__n
	)

interval& coco::interval::intersect_invsin_wc	(	const interval &	__i,
		double	__l,
		double	__d
	)

i.intersect_infsin_wc(j,l,d) computes the interval hull of the set $i\cap f(j,l,n)$ , where $f$ is the inverse image of $j$ under the function $x\mapsto \sin(lx+d)$ .

interval& coco::interval::intersect_invsin_wc	(	const interval &	__i,
		double	__l,
		double	__d
	)

i.intersect_infsin_wc(j,l,d) computes the interval hull of the set $i\cap f(j,l,n)$ , where $f$ is the inverse image of $j$ under the function $x\mapsto \sin(lx+d)$ .

interval& coco::interval::intersect_invsin_wc	(	const interval &	__i,
		double	__l,
		double	__d
	)

interval& coco::interval::intersect_invsqr_wc	(	const interval &	__i,
		double	__l,
		double	__d
	)

i.intersect_infsqr_wc(j,l,d) computes the interval hull of the set $i\cap f(j,l,d)$ , where $f$ is the inverse image of $j$ under the function $x\mapsto (lx+d)^2$ .

interval& coco::interval::intersect_invsqr_wc	(	const interval &	__i,
		double	__l,
		double	__d
	)

i.intersect_infsqr_wc(j,l,d) computes the interval hull of the set $i\cap f(j,l,d)$ , where $f$ is the inverse image of $j$ under the function $x\mapsto (lx+d)^2$ .

interval& coco::interval::intersect_invsqr_wc	(	const interval &	__i,
		double	__l,
		double	__d
	)

interval& coco::interval::intersect_power	(	const interval &	__i,
		int	__n
	)

i.intersect_power(j,n) computes the interval hull of the set $i\cap j^n$ .

interval& coco::interval::intersect_power	(	const interval &	__i,
		int	__n
	)

i.intersect_power(j,n) computes the interval hull of the set $i\cap j^n$ .

interval& coco::interval::intersect_power	(	const interval &	__i,
		int	__n
	)

interval& coco::interval::intersectwith ( const interval & x ) [inline]

y.intersectwith(x) intersects y with x.

Definition at line 159 of file interval_filib.h.

interval& coco::interval::ipow ( int n )

The method changes this interval to the n-th power.

interval& coco::interval::ipow ( int n )

The method changes this interval to the n-th power.

interval& coco::interval::ipow ( int n )

The method changes this interval to the n-th power.

bool coco::interval::is_bounded ( ) const [inline]

This method checks whether the interval is bounded.

Definition at line 118 of file interval_profil.h.

bool coco::interval::is_bounded ( ) const [inline]

This method checks whether the interval is bounded.

Definition at line 136 of file interval_filib.h.

bool coco::interval::is_bounded ( ) const [inline]

Definition at line 162 of file interval_boost.h.

bool coco::interval::is_empty ( ) const [inline]

This method checks whether the interval is empty.

Definition at line 102 of file interval_profil.h.

bool coco::interval::is_empty ( ) const [inline]

This method checks whether the interval is empty.

Definition at line 123 of file interval_filib.h.

bool coco::interval::is_empty ( ) const [inline]

Definition at line 157 of file interval_boost.h.

bool coco::interval::is_entire ( ) const [inline]

This method checks whether the interval is all $\mathbb R$ .

Definition at line 116 of file interval_profil.h.

bool coco::interval::is_entire ( ) const [inline]

This method checks whether the interval is all $\mathbb R$ .

Definition at line 134 of file interval_filib.h.

bool coco::interval::is_entire ( ) const [inline]

Definition at line 161 of file interval_boost.h.

bool coco::interval::is_thin ( ) const [inline]

This method checks whether the interval is thin (contains only one point).

Definition at line 106 of file interval_profil.h.

bool coco::interval::is_thin ( ) const [inline]

This method checks whether the interval is thin (contains only one point).

Definition at line 126 of file interval_filib.h.

bool coco::interval::is_thin ( ) const [inline]

Definition at line 158 of file interval_boost.h.

bool coco::interval::is_unbounded_above ( ) const [inline]

This method checks whether the interval is unbounded above ( $[a,\infty]$ ).

Definition at line 114 of file interval_profil.h.

bool coco::interval::is_unbounded_above ( ) const [inline]

This method checks whether the interval is unbounded above ( $[a,\infty]$ ).

Definition at line 132 of file interval_filib.h.

bool coco::interval::is_unbounded_above ( ) const [inline]

Definition at line 160 of file interval_boost.h.

bool coco::interval::is_unbounded_below ( ) const [inline]

This method checks whether the interval is unbounded below ( $[-\infty,a]$ ).

Definition at line 111 of file interval_profil.h.

bool coco::interval::is_unbounded_below ( ) const [inline]

This method checks whether the interval is unbounded below ( $[-\infty,a]$ ).

Definition at line 129 of file interval_filib.h.

bool coco::interval::is_unbounded_below ( ) const [inline]

Definition at line 159 of file interval_boost.h.

double coco::interval::mag ( ) const

Returns the magnitude of this interval, i.e.

a.mag() == max{abs(y) : y in a }

Special cases in the extended system:

a.mag() == NaN for a == [ EMPTY ]
a.mag() == +INF for any infinite interval

double coco::interval::mag ( ) const

Returns the magnitude of this interval, i.e.

a.mag() == max{abs(y) : y in a }

Special cases in the extended system:

a.mag() == NaN for a == [ EMPTY ]
a.mag() == +INF for any infinite interval

double coco::interval::mag ( ) const

Returns the magnitude of this interval, i.e.

a.mag() == max{abs(y) : y in a }

Special cases in the extended system:

a.mag() == NaN for a == [ EMPTY ]
a.mag() == +INF for any infinite interval

double coco::interval::mid ( ) const

Returns the midpoint of this interval, i.e.

a.mid() == (a.inf()+a.sup())/2

The following special cases are distinguished:

a.mid() == NaN for a == [ EMPTY ]
a.mid() == 0 for a == [ ENTIRE ]
a.mid() == +INF for a == [ a, INFTY ]
a.mid() == -INF for a == [ -INFTY, a ]

double coco::interval::mid ( ) const

Returns the midpoint of this interval, i.e.

a.mid() == (a.inf()+a.sup())/2

The following special cases are distinguished:

a.mid() == NaN for a == [ EMPTY ]
a.mid() == 0 for a == [ ENTIRE ]
a.mid() == +INF for a == [ a, INFTY ]
a.mid() == -INF for a == [ -INFTY, a ]

double coco::interval::mid ( ) const

Returns the midpoint of this interval, i.e.

a.mid() == (a.inf()+a.sup())/2

The following special cases are distinguished:

a.mid() == NaN for a == [ EMPTY ]
a.mid() == 0 for a == [ ENTIRE ]
a.mid() == +INF for a == [ a, INFTY ]
a.mid() == -INF for a == [ -INFTY, a ]

double coco::interval::mig ( ) const

Returns the mignitude of this interval, i.e.

a.mig() == min{abs(y) : y in x }

Special cases in the extended system:

a.mig() == NaN for a == [ EMPTY ]

double coco::interval::mig ( ) const

Returns the mignitude of this interval, i.e.

a.mig() == min{abs(y) : y in x }

Special cases in the extended system:

a.mig() == NaN for a == [ EMPTY ]

double coco::interval::mig ( ) const

Returns the mignitude of this interval, i.e.

a.mig() == min{abs(y) : y in a }

Special cases in the extended system:

a.mig() == NaN for a == [ EMPTY ]

interval& coco::interval::operator*= ( double a )

unary operator*= for number

interval& coco::interval::operator*= ( const interval & a )

unary operator*=

interval& coco::interval::operator*= ( double a )

unary operator*= for number

interval& coco::interval::operator*= ( const interval & a )

unary operator*=

interval& coco::interval::operator*= ( double a )

interval& coco::interval::operator*= ( const interval & a )

interval& coco::interval::operator+= ( double a )

unary += for number

interval& coco::interval::operator+= ( const interval & a )

unary +=

interval& coco::interval::operator+= ( double a )

unary += for number

interval& coco::interval::operator+= ( const interval & a )

unary +=

interval& coco::interval::operator+= ( double a )

interval& coco::interval::operator+= ( const interval & a )

interval coco::interval::operator- ( ) const [inline]

Unary interval minus operation

Definition at line 204 of file interval_profil.h.

interval coco::interval::operator- ( ) const [inline]

Unary interval minus operation

Definition at line 247 of file interval_filib.h.

interval coco::interval::operator- ( ) const [inline]

Definition at line 230 of file interval_boost.h.

interval& coco::interval::operator-= ( double a )

unary -= for number

interval& coco::interval::operator-= ( const interval & a )

unary -=

interval& coco::interval::operator-= ( double a )

unary -= for number

interval& coco::interval::operator-= ( const interval & a )

unary -=

interval& coco::interval::operator-= ( double a )

interval& coco::interval::operator-= ( const interval & a )

interval& coco::interval::operator/= ( double a )

unary operator/= for number

interval& coco::interval::operator/= ( const interval & a )

unary operator/=

interval& coco::interval::operator/= ( double a )

unary operator/= for number

interval& coco::interval::operator/= ( const interval & a )

unary operator/=

interval& coco::interval::operator/= ( double a )

interval& coco::interval::operator/= ( const interval & a )

interval& coco::interval::operator= ( const __Base & _x ) [inline]

Assignment from the base interval class

Definition at line 200 of file interval_profil.h.

interval& coco::interval::operator= ( unsigned long d ) [inline]

Assign the thin interval [d,d].

Definition at line 197 of file interval_profil.h.

interval& coco::interval::operator= ( long d ) [inline]

Assign the thin interval [d,d].

Definition at line 196 of file interval_profil.h.

interval& coco::interval::operator= ( unsigned d ) [inline]

Assign the thin interval [d,d].

Definition at line 195 of file interval_profil.h.

interval& coco::interval::operator= ( int d ) [inline]

Assign the thin interval [d,d].

Definition at line 194 of file interval_profil.h.

interval& coco::interval::operator= ( double d ) [inline]

Assign the thin interval [d,d].

Definition at line 193 of file interval_profil.h.

interval& coco::interval::operator= ( const __Base & _x ) [inline]

Assignment from the base interval class

Definition at line 243 of file interval_filib.h.

interval& coco::interval::operator= ( unsigned long d ) [inline]

Assign the thin interval [d,d].

Definition at line 240 of file interval_filib.h.

interval& coco::interval::operator= ( long d ) [inline]

Assign the thin interval [d,d].

Definition at line 239 of file interval_filib.h.

interval& coco::interval::operator= ( unsigned d ) [inline]

Assign the thin interval [d,d].

Definition at line 238 of file interval_filib.h.

interval& coco::interval::operator= ( int d ) [inline]

Assign the thin interval [d,d].

Definition at line 237 of file interval_filib.h.

interval& coco::interval::operator= ( double d ) [inline]

Assign the thin interval [d,d].

Definition at line 236 of file interval_filib.h.

interval& coco::interval::operator= ( unsigned long d ) [inline]

Definition at line 226 of file interval_boost.h.

interval& coco::interval::operator= ( long d ) [inline]

Definition at line 225 of file interval_boost.h.

interval& coco::interval::operator= ( unsigned d ) [inline]

Definition at line 224 of file interval_boost.h.

interval& coco::interval::operator= ( int d ) [inline]

Definition at line 223 of file interval_boost.h.

interval& coco::interval::operator= ( double d ) [inline]

Definition at line 222 of file interval_boost.h.

interval& coco::interval::operator= ( const interval & x ) [inline]

Definition at line 221 of file interval_boost.h.

static int coco::interval::precision ( int const & p ) [static]

This method sets the output precision to p. The default value is 3.

static int const& coco::interval::precision ( ) [static]

This method returns the output precision that is used by the output operator <<.

static int coco::interval::precision ( int const & p ) [static]

This method sets the output precision to p. The default value is 3.

static int const& coco::interval::precision ( ) [static]

This method returns the output precision that is used by the output operator <<.

static int coco::interval::precision ( int const & p ) [static]

This method sets the output precision to p. The default value is 3.

static int const& coco::interval::precision ( ) [static]

This method returns the output precision that is used by the output operator <<.

double coco::interval::project ( double __d ) const

This method returns the projection of __d to the interval, i.e. to the double number in the interval which is closest to __d.

double coco::interval::project ( double __d ) const

This method returns the projection of __d to the interval, i.e. to the double number in the interval which is closest to __d.

double coco::interval::project ( double __d ) const [inline]

Definition at line 802 of file interval_boost.h.

bool coco::interval::proper_subset ( const interval & x ) const [inline]

This method checks whether this interval is a proper subset of x.

Definition at line 127 of file interval_profil.h.

bool coco::interval::proper_subset ( const interval & x ) const [inline]

This method checks whether this interval is a proper subset of x.

Definition at line 145 of file interval_filib.h.

bool coco::interval::proper_subset ( const interval & x ) const [inline]

Definition at line 169 of file interval_boost.h.

bool coco::interval::proper_superset ( const interval & x ) const [inline]

This method checks whether this interval is a proper superset of x.

Definition at line 130 of file interval_profil.h.

bool coco::interval::proper_superset ( const interval & x ) const [inline]

This method checks whether this interval is a proper superset of x.

Definition at line 148 of file interval_filib.h.

bool coco::interval::proper_superset ( const interval & x ) const [inline]

Definition at line 171 of file interval_boost.h.

double coco::interval::rad ( ) const

Returns an upper bound for the radius of this interval, i.e.

a.rad() = (a.sup() - a.inf()) / 2

Special cases in the extended system:

a.rad() == NaN for a == [ EMPTY ]
a.rad() == +INF for any infinite interval

double coco::interval::rad ( ) const

Returns an upper bound for the radius of this interval, i.e.

a.rad() = (a.sup() - a.inf()) / 2

Special cases in the extended system:

a.rad() == NaN for a == [ EMPTY ]
a.rad() == +INF for any infinite interval

double coco::interval::rad ( ) const

Returns an upper bound for the radius of this interval, i.e.

a.rad() = (a.sup() - a.inf()) / 2

Special cases in the extended system:

a.rad() == NaN for a == [ EMPTY ]
a.rad() == +INF for any infinite interval

double coco::interval::rel_width ( ) const

i.rel_width() computes the relative width (diameter) of i.

double coco::interval::rel_width ( ) const

i.rel_width() computes the relative width (diameter) of i.

double coco::interval::rel_width ( ) const

double coco::interval::relDiam ( ) const

Returns an upper bound for the relative diameter (width) of this interval, i.e.

a.relDiam == a.diam() if a.mig() is less than the smallest normalized number

a.relDiam == a.diam() / a.mig() else

Special cases in the extended system:

a.relDiam() == NaN for a == [ EMPTY ]
a.relDiam() == +INF for any infinite interval

double coco::interval::relDiam ( ) const

Returns an upper bound for the relative diameter (width) of this interval, i.e.

a.relDiam == a.diam() if a.mig() is less than the smallest normalized number

a.relDiam == a.diam() / a.mig() else

Special cases in the extended system:

a.relDiam() == NaN for a == [ EMPTY ]
a.relDiam() == +INF for any infinite interval

double coco::interval::relDiam ( ) const

Returns an upper bound for the relative diameter (width) of this interval, i.e.

a.relDiam == a.diam() if a.mig() is less than the smallest normalized number

a.relDiam == a.diam() / a.mig() else

Special cases in the extended system:

a.relDiam() == NaN for a == [ EMPTY ]
a.relDiam() == +INF for any infinite interval

interval& coco::interval::round_to_integer ( )

This method rounds the interval inward to integer borders.

interval& coco::interval::round_to_integer ( )

This method rounds the interval inward to integer borders.

double coco::interval::safeguarded_mid ( ) const

Returns the safeguarded midpoint of this interval, i.e.

a.safeguarded_mid() ==

if a contains 0,
$2*\overline a$ if a is unbounded below and does not contain 0,
$2*\underline a$ if a is unbounded above and does not contain 0,
the geometric mean of the endpoints if contained in a,
the arithmetic mean of the endpoints otherwise.

double coco::interval::safeguarded_mid ( ) const

Returns the safeguarded midpoint of this interval, i.e.

a.safeguarded_mid() ==

if a contains 0,
$2*\overline a$ if a is unbounded below and does not contain 0,
$2*\underline a$ if a is unbounded above and does not contain 0,
the geometric mean of the endpoints if contained in a,
the arithmetic mean of the endpoints otherwise.

double coco::interval::safeguarded_mid ( ) const

Returns the magnitude of this interval, i.e.

a.mag() == max{abs(y) : y in a }

Special cases in the extended system:

a.mag() == NaN for a == [ EMPTY ]
a.mag() == +INF for any infinite interval

void coco::interval::set	(	double	lo,
		double	up
	)			`[inline]`

i.set(lo,up) sets i to [lo,up].

Definition at line 87 of file interval_profil.h.

void coco::interval::set	(	double	lo,
		double	up
	)			`[inline]`

i.set(lo,up) sets i to [lo,up].

Definition at line 105 of file interval_filib.h.

void coco::interval::set	(	double	lo,
		double	up
	)			`[inline]`

Definition at line 144 of file interval_boost.h.

void coco::interval::set_bounds	(	double	a,
		double	b
	)			`[inline]`

Set the bounds of the interval to a and b.

Definition at line 185 of file interval_profil.h.

void coco::interval::set_bounds	(	double	a,
		double	b
	)			`[inline]`

Set the bounds of the interval to a and b.

Definition at line 228 of file interval_filib.h.

void coco::interval::set_bounds	(	double	a,
		double	b
	)			`[inline]`

Definition at line 217 of file interval_boost.h.

void coco::interval::set_lb ( double d ) [inline]

Set the lower bound of the interval to d.

Definition at line 187 of file interval_profil.h.

void coco::interval::set_lb ( double d ) [inline]

Set the lower bound of the interval to d.

Definition at line 230 of file interval_filib.h.

void coco::interval::set_lb ( double d ) [inline]

Definition at line 218 of file interval_boost.h.

void coco::interval::set_ub ( double d ) [inline]

Set the upper bound of the interval to d.

Definition at line 189 of file interval_profil.h.

void coco::interval::set_ub ( double d ) [inline]

Set the upper bound of the interval to d.

Definition at line 232 of file interval_filib.h.

void coco::interval::set_ub ( double d ) [inline]

Definition at line 219 of file interval_boost.h.

void coco::interval::setpair	(	double &	lo,
		double &	up
	)			const `[inline]`

Set the pair lo and up to the bounds of the interval.

Definition at line 181 of file interval_profil.h.

void coco::interval::setpair	(	double &	lo,
		double &	up
	)			const `[inline]`

Set the pair lo and up to the bounds of the interval.

Definition at line 224 of file interval_filib.h.

void coco::interval::setpair	(	double &	lo,
		double &	up
	)			const `[inline]`

Definition at line 215 of file interval_boost.h.

bool coco::interval::subset ( const interval & x ) const [inline]

This method checks whether this interval is a subset of x.

Definition at line 121 of file interval_profil.h.

bool coco::interval::subset ( const interval & x ) const [inline]

This method checks whether this interval is a subset of x.

Definition at line 139 of file interval_filib.h.

bool coco::interval::subset ( const interval & x ) const [inline]

Definition at line 165 of file interval_boost.h.

double coco::interval::sup ( ) const [inline]

This method returns the upper bound of the interval.

Definition at line 111 of file interval_filib.h.

double coco::interval::sup ( ) const [inline]

Definition at line 151 of file interval_boost.h.

bool coco::interval::superset ( const interval & x ) const [inline]

This method checks whether this interval is a superset of x.

Definition at line 124 of file interval_profil.h.

bool coco::interval::superset ( const interval & x ) const [inline]

This method checks whether this interval is a superset of x.

Definition at line 142 of file interval_filib.h.

bool coco::interval::superset ( const interval & x ) const [inline]

Definition at line 167 of file interval_boost.h.

double coco::interval::width ( ) const

Returns an upper bound for the diameter (width) of this interval, i.e.

a.diam() == a.sup()-a.inf()

Special cases in the extended system:

a.diam() == NaN for a == [ EMPTY ]
a.diam() == +INF for any infinite interval

double coco::interval::width ( ) const

Returns an upper bound for the diameter (width) of this interval, i.e.

a.diam() == a.sup()-a.inf()

Special cases in the extended system:

a.diam() == NaN for a == [ EMPTY ]
a.diam() == +INF for any infinite interval

double coco::interval::width ( ) const

Friends And Related Function Documentation

interval abs ( const interval & x ) [friend]

Returns an interval enclosure of the absolute value of the interval x.

interval abs ( const interval & x ) [friend]

Returns an interval enclosure of the absolute value of the interval x.

interval acos ( const interval & x ) [friend]

Returns an interval enclosure of the inverse cosine of the interval x.

interval acos ( const interval & x ) [friend]

Returns an interval enclosure of the inverse cosine of the interval x.

interval acosh ( const interval & x ) [friend]

Returns an interval enclosure of the inverse hyperbolic cosine of the interval x.

interval acosh ( const interval & x ) [friend]

Returns an interval enclosure of the inverse hyperbolic cosine of the interval x.

interval acot ( const interval & x ) [friend]

Returns an interval enclosure of the inverse cotangent of the interval x.

interval acot ( const interval & x ) [friend]

Returns an interval enclosure of the inverse cotangent of the interval x.

interval acoth ( const interval & x ) [friend]

Returns an interval enclosure of the inverse hyperbolic cotangent of the interval x.

interval acoth ( const interval & x ) [friend]

Returns an interval enclosure of the inverse hyperbolic cotangent of the interval x.

interval asin ( const interval & x ) [friend]

Returns an interval enclosure of the inverse sine of the interval x.

interval asin ( const interval & x ) [friend]

Returns an interval enclosure of the inverse sine of the interval x.

interval asinh ( const interval & x ) [friend]

Returns an interval enclosure of the inverse hyperbolic sine of the interval x.

interval asinh ( const interval & x ) [friend]

Returns an interval enclosure of the inverse hyperbolic sine of the interval x.

interval atan ( const interval & x ) [friend]

Returns an interval enclosure of the inverse tangent of the interval x.

interval atan ( const interval & x ) [friend]

Returns an interval enclosure of the inverse tangent of the interval x.

interval atanh ( const interval & x ) [friend]

Returns an interval enclosure of the inverse hyperbolic tangent of the interval x.

interval atanh ( const interval & x ) [friend]

Returns an interval enclosure of the inverse hyperbolic tangent of the interval x.

interval cancel	(	const interval &	a,
		const interval &	b
	)			`[friend]`

interval cancel	(	const interval &	a,
		const interval &	b
	)			`[friend]`

interval cos ( const interval & x ) [friend]

Returns an interval enclosure of the cosine of the interval x.

interval cos ( const interval & x ) [friend]

Returns an interval enclosure of the cosine of the interval x.

interval cosh ( const interval & x ) [friend]

Returns an interval enclosure of the hyperbolic cosine of the interval x.

interval cosh ( const interval & x ) [friend]

Returns an interval enclosure of the hyperbolic cosine of the interval x.

interval cot ( const interval & x ) [friend]

Returns an interval enclosure of the cotangent of the interval x.

interval cot ( const interval & x ) [friend]

Returns an interval enclosure of the cotangent of the interval x.

interval coth ( const interval & x ) [friend]

Returns an interval enclosure of the hyperbolic cotangent of the interval x.

interval coth ( const interval & x ) [friend]

Returns an interval enclosure of the hyperbolic cotangent of the interval x.

double diam ( const interval & ) [friend]

diam(a) == a.diam()

double dist	(	const interval &	x,
		const interval &	y
	)			`[friend]`

Same as x.dist(y)

interval division_part1	(	const interval &	x,
		const interval &	y,
		bool &	b
	)			`[friend]`

The division_part? functions return the result of x/y in the following sense, even if the smallest set containing the result is a union of two intervals. For example, the narrowest closed set containg $[2,3]/[-2,1]$ is not $]-\infty,\infty[$ but $]-\infty,-1]\cup[2,\infty[$ . When the result of the division is representable by only one interval, division_part1 returns this interval and sets the boolean reference to false. However, if the result needs two intervals, division_part1 returns the negative part and sets the boolean reference to true; a call to division_part2 is now needed to get the positive part. This second function can take the boolean returned by the first function as last argument. If this bool is not given, its value is assumed to be true, and the behavior of the function is then undetermined if the division does not produce a second interval.

interval division_part2	(	const interval &	x,
		const interval &	y,
		bool	b
	)			`[friend]`

double downward_divides	(	const double &	a,
		const double &	b
	)			`[friend]`

This function divides a by b, rounding downwards.

double downward_minus	(	const double &	a,
		const double &	b
	)			`[friend]`

This function subtracts b from a, rounding downwards.

double downward_multiplies	(	const double &	a,
		const double &	b
	)			`[friend]`

This function multiplies a by b, rounding downwards.

double downward_plus	(	const double &	a,
		const double &	b
	)			`[friend]`

This function adds a and b, rounding downwards.

interval exp ( const interval & x ) [friend]

Returns an interval enclosure of the exponential of the interval x.

interval exp ( const interval & x ) [friend]

Returns an interval enclosure of the exponential of the interval x.

interval exp10 ( const interval & x ) [friend]

Returns an interval enclosure of the exponential (base 10) of the interval x.

interval exp10 ( const interval & x ) [friend]

Returns an interval enclosure of the exponential (base 10) of the interval x.

interval exp2 ( const interval & x ) [friend]

Returns an interval enclosure of the exponential (base 2) of the interval x.

interval exp2 ( const interval & x ) [friend]

Returns an interval enclosure of the exponential (base 2) of the interval x.

interval expm1 ( const interval & x ) [friend]

Returns an interval enclosure of exp(x)-1

interval expm1 ( const interval & x ) [friend]

Returns an interval enclosure of exp(x)-1

interval imax	(	const interval &	x,
		const interval &	y
	)			`[friend]`

Returns an interval enclosure of the maximum of two intervals x and y.

interval imax	(	const interval &	x,
		const interval &	y
	)			`[friend]`

Returns an interval enclosure of the maximum of two intervals x and y.

interval imin	(	const interval &	x,
		const interval &	y
	)			`[friend]`

Returns an interval enclosure of the minimum of two intervals x and y.

interval imin	(	const interval &	x,
		const interval &	y
	)			`[friend]`

Returns an interval enclosure of the minimum of two intervals x and y.

interval log ( const interval & x ) [friend]

Returns an interval enclosure of the natural logarithm of the interval x.

interval log ( const interval & x ) [friend]

Returns an interval enclosure of the natural logarithm of the interval x.

interval log10 ( const interval & x ) [friend]

Returns an interval enclosure of the logarithm (base 10) of the interval x.

interval log10 ( const interval & x ) [friend]

Returns an interval enclosure of the logarithm (base 10) of the interval x.

interval log1p ( const interval & x ) [friend]

Returns an interval enclosure of log(1+x).

interval log1p ( const interval & x ) [friend]

Returns an interval enclosure of log(1+x).

interval log2 ( const interval & x ) [friend]

Returns an interval enclosure of the logarithm (base 2) of the interval x.

interval log2 ( const interval & x ) [friend]

Returns an interval enclosure of the logarithm (base 2) of the interval x.

double mag ( const interval & ) [friend]

mag(a) == a.mag()

double mid ( const interval & ) [friend]

mid(a) == a.mid()

double mig ( const interval & ) [friend]

mig(a) == a.mig()

template<class _TC >

bool operator!=	(	const interval &	__i,
		const _TC &	__d
	)			`[friend]`

bool operator!=	(	const interval &	__i,
		const interval &	__d
	)			`[friend]`

Comparison operator (not equal)

Definition at line 490 of file interval_boost.h.

interval operator*	(	const interval &	a,
		const interval &	b
	)			`[friend]`

This operator computes a*b as interval.

interval operator*	(	const interval &	a,
		double	b
	)			`[friend]`

interval operator*	(	double	a,
		const interval &	b
	)			`[friend]`

interval operator*	(	double	b,
		const interval &	a
	)			`[friend]`

interval operator*	(	const interval &	a,
		double	b
	)			`[friend]`

interval operator*	(	const interval &	a,
		const interval &	b
	)			`[friend]`

This operator computes a*b as interval.

interval operator+	(	double	b,
		const interval &	a
	)			`[friend]`

interval operator+	(	const interval &	a,
		double	b
	)			`[friend]`

interval operator+	(	const interval &	a,
		const interval &	b
	)			`[friend]`

This operator computes a+b as interval.

interval operator+	(	double	b,
		const interval &	a
	)			`[friend]`

interval operator+	(	const interval &	a,
		double	b
	)			`[friend]`

interval operator+	(	const interval &	a,
		const interval &	b
	)			`[friend]`

This operator computes a+b as interval.

interval operator-	(	double	a,
		const interval &	b
	)			`[friend]`

interval operator-	(	const interval &	a,
		double	b
	)			`[friend]`

interval operator-	(	const interval &	a,
		const interval &	b
	)			`[friend]`

This operator computes a-b as interval.

interval operator-	(	double	b,
		const interval &	a
	)			`[friend]`

interval operator-	(	const interval &	a,
		double	b
	)			`[friend]`

interval operator-	(	const interval &	a,
		const interval &	b
	)			`[friend]`

This operator computes a-b as interval.

interval operator/	(	const interval &	a,
		const interval &	b
	)			`[friend]`

This operator computes a/b as interval.

interval operator/	(	const interval &	a,
		double	b
	)			`[friend]`

interval operator/	(	double	a,
		const interval &	b
	)			`[friend]`

interval operator/	(	double	b,
		const interval &	a
	)			`[friend]`

interval operator/	(	const interval &	a,
		double	b
	)			`[friend]`

interval operator/	(	const interval &	a,
		const interval &	b
	)			`[friend]`

This operator computes a/b as interval.

std::ostream& operator<<	(	std::ostream &	s,
		const interval &	a
	)			`[friend]`

std::ostream& operator<<	(	std::ostream &	s,
		const interval &	a
	)			`[friend]`

template<class _TC >

bool operator==	(	const interval &	__i,
		const _TC &	__d
	)			`[friend]`

bool operator==	(	const interval &	__i,
		const interval &	__d
	)			`[friend]`

friends

Comparison operator (equal)

Definition at line 486 of file interval_boost.h.

interval pow	(	const interval &	x,
		const interval &	y
	)			`[friend]`

Returns an interval enclosure of x^y = exp(y*log(x)).

interval pow	(	const interval &	x,
		const interval &	y
	)			`[friend]`

Returns an interval enclosure of x^y = exp(y*log(x)).

interval power	(	const interval &	x,
		int	n
	)			`[friend]`

Returns an interval enclosure of x^n.

interval power	(	const interval &	x,
		int	n
	)			`[friend]`

Returns an interval enclosure of x^n.

double rad ( const interval & ) [friend]

rad(a) == a.rad()

double relDiam ( const interval & ) [friend]

relDiam(a) == a.relDiam()

interval sin ( const interval & x ) [friend]

Returns an interval enclosure of the sine of the interval x.

interval sin ( const interval & x ) [friend]

Returns an interval enclosure of the sine of the interval x.

interval sinh ( const interval & x ) [friend]

Returns an interval enclosure of the hyperbolic sine of the interval x.

interval sinh ( const interval & x ) [friend]

Returns an interval enclosure of the hyperbolic sine of the interval x.

interval sqr ( const interval & x ) [friend]

Returns an interval enclosure of x^2.

interval sqr ( const interval & x ) [friend]

Returns an interval enclosure of x^2.

interval sqrt ( const interval & x ) [friend]

Returns an interval enclosure of the square root of the interval x.

interval sqrt ( const interval & x ) [friend]

Returns an interval enclosure of the square root of the interval x.

interval tan ( const interval & x ) [friend]

Returns an interval enclosure of the tangent of the interval x.

interval tan ( const interval & x ) [friend]

Returns an interval enclosure of the tangent of the interval x.

interval tanh ( const interval & x ) [friend]

Returns an interval enclosure of the hyperbolic tangent of the interval x.

interval tanh ( const interval & x ) [friend]

Returns an interval enclosure of the hyperbolic tangent of the interval x.

double upward_divides	(	const double &	a,
		const double &	b
	)			`[friend]`

This function divides a by b, rounding upwards.

double upward_minus	(	const double &	a,
		const double &	b
	)			`[friend]`

This function subtracts b from a, rounding upwards.

double upward_multiplies	(	const double &	a,
		const double &	b
	)			`[friend]`

This function multiplies a by b, rounding upwards.

double upward_plus	(	const double &	a,
		const double &	b
	)			`[friend]`

This function adds a and b, rounding upwards.

double width ( const interval & ) [friend]

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


Public Member Functions
	interval (double lo, double up)
	interval (double d=0)
	interval (int d)
	interval (unsigned d)
	interval (long d)
	interval (unsigned long d)
	interval (const interval &x)
	interval (const interval_st &x)
void	set (double lo, double up)
double	inf () const
double	sup () const
__Base	base () const
bool	empty () const
bool	is_empty () const
bool	is_thin () const
bool	is_unbounded_below () const
bool	is_unbounded_above () const
bool	is_entire () const
bool	is_bounded () const
bool	subset (const interval &x) const
bool	superset (const interval &x) const
bool	proper_subset (const interval &x) const
bool	proper_superset (const interval &x) const
bool	disjoint (const interval &x) const
double	rel_width () const
interval &	intersect (const interval &x)
interval &	hull (const interval &x)
interval &	hulldiff (const interval &x)
bool	contains (const interval &x) const
void	setpair (double &lo, double &up) const
void	get_bounds (double &a, double &b) const
void	set_bounds (double a, double b)
void	set_lb (double d)
void	set_ub (double d)
interval &	operator= (const interval &x)
interval &	operator= (double d)
interval &	operator= (int d)
interval &	operator= (unsigned d)
interval &	operator= (long d)
interval &	operator= (unsigned long d)
interval	operator- () const
interval &	ipow (int n)
interval &	imin (const interval &x)
interval &	imax (const interval &x)
interval &	round_to_integer ()
interval &	intersect_div (const interval &__i, const interval &__j)
interval &	intersect_power (const interval &__i, int __n)
interval &	intersect_invsqr_wc (const interval &__i, double __l, double __d)
interval &	intersect_invpower_wc (const interval &__i, double __l, int __n)
interval &	intersect_invsin_wc (const interval &__i, double __l, double __d)
interval &	intersect_invcos_wc (const interval &__i, double __l, double __d)
interval &	intersect_invgauss_wc (const interval &__i, double __l, double __m, double __s)
double	project (double __d) const
interval &	operator+= (const interval &a)
interval &	operator+= (double a)
interval &	operator-= (const interval &a)
interval &	operator-= (double a)
interval &	operator*= (const interval &a)
interval &	operator*= (double a)
interval &	operator/= (const interval &a)
interval &	operator/= (double a)
double	mid () const
double	diam () const
double	width () const
double	relDiam () const
double	rad () const
double	mig () const
double	mag () const
double	dist (const interval &x) const
double	safeguarded_mid () const
	interval (double lo, double up)
	interval (double d=0)
	interval (int d)
	interval (unsigned d)
	interval (long d)
	interval (unsigned long d)
	interval (const __Base &x)
	interval (const interval &x)
	interval (const interval_st &x)
void	set (double lo, double up)
double	sup () const
double	inf () const
__Base	base () const
bool	empty () const
bool	is_empty () const
bool	is_thin () const
bool	is_unbounded_below () const
bool	is_unbounded_above () const
bool	is_entire () const
bool	is_bounded () const
bool	subset (const interval &x) const
bool	superset (const interval &x) const
bool	proper_subset (const interval &x) const
bool	proper_superset (const interval &x) const
bool	disjoint (const interval &x) const
double	rel_width () const
interval &	intersectwith (const interval &x)
interval &	hullwith (const interval &x)
interval &	hulldiffwith (const interval &x)
interval	intersect (const interval &x) const
interval	hull (const interval &x) const
interval	hulldiff (const interval &x) const
bool	contains (const interval &x) const
void	setpair (double &lo, double &up) const
void	get_bounds (double &a, double &b) const
void	set_bounds (double a, double b)
void	set_lb (double d)
void	set_ub (double d)
interval &	operator= (const __Base &_x)
interval	operator- () const
interval &	ipow (int n)
interval &	imin (const interval &x)
interval &	imax (const interval &x)
interval &	round_to_integer ()
interval &	intersect_div (const interval &__i, const interval &__j)
interval &	intersect_power (const interval &__i, int __n)
interval &	intersect_invsqr_wc (const interval &__i, double __l, double __d)
interval &	intersect_invpower_wc (const interval &__i, double __l, int __n)
interval &	intersect_invsin_wc (const interval &__i, double __l, double __d)
interval &	intersect_invcos_wc (const interval &__i, double __l, double __d)
interval &	intersect_invgauss_wc (const interval &__i, double __l, double __m, double __s)
double	project (double __d) const
interval &	operator+= (const interval &a)
interval &	operator+= (double a)
interval &	operator-= (const interval &a)
interval &	operator-= (double a)
interval &	operator*= (const interval &a)
interval &	operator*= (double a)
interval &	operator/= (const interval &a)
interval &	operator/= (double a)
double	mid () const
double	relDiam () const
double	rad () const
double	mig () const
double	mag () const
double	dist (const interval &x) const
double	safeguarded_mid () const
	interval (double lo, double up)
	interval (double d=0)
	interval (int d)
	interval (unsigned d)
	interval (long d)
	interval (unsigned long d)
	interval (const __Base &x)
	interval (const interval &x)
	interval (const interval_st &x)
void	set (double lo, double up)
__Base	base () const
bool	empty () const
bool	is_empty () const
bool	is_thin () const
bool	is_unbounded_below () const
bool	is_unbounded_above () const
bool	is_entire () const
bool	is_bounded () const
bool	subset (const interval &x) const
bool	superset (const interval &x) const
bool	proper_subset (const interval &x) const
bool	proper_superset (const interval &x) const
bool	disjoint (const interval &x) const
double	rel_width () const
interval &	intersect (const interval &x)
interval &	hull (const interval &x)
interval &	hulldiff (const interval &x)
bool	contains (const interval &x) const
void	setpair (double &lo, double &up) const
void	get_bounds (double &a, double &b) const
void	set_bounds (double a, double b)
void	set_lb (double d)
void	set_ub (double d)
interval &	operator= (const __Base &_x)
interval	operator- () const
interval &	ipow (int n)
interval &	imin (const interval &x)
interval &	imax (const interval &x)
interval &	intersect_div (const interval &__i, const interval &__j)
interval &	intersect_power (const interval &__i, int __n)
interval &	intersect_invsqr_wc (const interval &__i, double __l, double __d)
interval &	intersect_invpower_wc (const interval &__i, double __l, int __n)
interval &	intersect_invsin_wc (const interval &__i, double __l, double __d)
interval &	intersect_invcos_wc (const interval &__i, double __l, double __d)
interval &	intersect_invgauss_wc (const interval &__i, double __l, double __m, double __s)
double	project (double __d) const
interval &	operator+= (const interval &a)
interval &	operator+= (double a)
interval &	operator-= (const interval &a)
interval &	operator-= (double a)
interval &	operator*= (const interval &a)
interval &	operator*= (double a)
interval &	operator/= (const interval &a)
interval &	operator/= (double a)
double	mid () const
double	relDiam () const
double	rad () const
double	mig () const
double	mag () const
double	dist (const interval &x) const
double	safeguarded_mid () const

interval &	operator= (double d)
interval &	operator= (int d)
interval &	operator= (unsigned d)
interval &	operator= (long d)
interval &	operator= (unsigned long d)

double	diam () const
double	width () const

interval &	operator= (double d)
interval &	operator= (int d)
interval &	operator= (unsigned d)
interval &	operator= (long d)
interval &	operator= (unsigned long d)

double	diam () const
double	width () const
Static Public Member Functions
static interval	EMPTY ()
static int const &	precision ()
static int	precision (int const &p)
static interval	EMPTY ()
static int const &	precision ()
static int	precision (int const &p)
static interval	EMPTY ()
static int const &	precision ()
static int	precision (int const &p)
Friends
std::ostream &	operator<< (std::ostream &s, const interval &a)
interval	operator+ (const interval &a, const interval &b)
interval	operator+ (const interval &a, double b)
interval	operator+ (double b, const interval &a)
interval	operator- (const interval &a, const interval &b)
interval	operator- (const interval &a, double b)
interval	operator- (double b, const interval &a)
interval	cancel (const interval &a, const interval &b)
interval	operator* (const interval &a, const interval &b)
interval	operator* (const interval &a, double b)
interval	operator* (double b, const interval &a)
interval	operator/ (const interval &a, const interval &b)
interval	operator/ (const interval &a, double b)
interval	operator/ (double b, const interval &a)
interval	acos (const interval &x)
interval	abs (const interval &x)
interval	acosh (const interval &x)
interval	acot (const interval &x)
interval	acoth (const interval &x)
interval	asin (const interval &x)
interval	asinh (const interval &x)
interval	atan (const interval &x)
interval	atanh (const interval &x)
interval	cos (const interval &x)
interval	cosh (const interval &x)
interval	cot (const interval &x)
interval	coth (const interval &x)
interval	exp (const interval &x)
interval	exp10 (const interval &x)
interval	exp2 (const interval &x)
interval	expm1 (const interval &x)
interval	log (const interval &x)
interval	log10 (const interval &x)
interval	log1p (const interval &x)
interval	log2 (const interval &x)
interval	power (const interval &x, int n)
interval	pow (const interval &x, const interval &y)
interval	sin (const interval &x)
interval	sinh (const interval &x)
interval	sqr (const interval &x)
interval	sqrt (const interval &x)
interval	tan (const interval &x)
interval	tanh (const interval &x)
interval	imax (const interval &x, const interval &y)
interval	imin (const interval &x, const interval &y)
interval	division_part1 (const interval &x, const interval &y, bool &b)
interval	division_part2 (const interval &x, const interval &y, bool b)
bool	operator== (const interval &__i, const interval &__d)
template<class _TC >
bool	operator== (const interval &__i, const _TC &__d)
bool	operator!= (const interval &__i, const interval &__d)
template<class _TC >
bool	operator!= (const interval &__i, const _TC &__d)
std::ostream &	operator<< (std::ostream &, const interval &)
interval	tanh (const interval &x)
interval	tan (const interval &x)
interval	sqrt (const interval &x)
interval	sqr (const interval &x)
interval	sinh (const interval &x)
interval	sin (const interval &x)
interval	pow (const interval &x, const interval &y)
interval	power (const interval &x, int n)
interval	log2 (const interval &x)
interval	log1p (const interval &x)
interval	log10 (const interval &x)
interval	log (const interval &x)
interval	expm1 (const interval &x)
interval	exp2 (const interval &x)
interval	exp10 (const interval &x)
interval	exp (const interval &x)
interval	coth (const interval &x)
interval	cot (const interval &x)
interval	cosh (const interval &x)
interval	cos (const interval &x)
interval	atanh (const interval &x)
interval	atan (const interval &x)
interval	asinh (const interval &x)
interval	asin (const interval &x)
interval	acoth (const interval &x)
interval	acot (const interval &x)
interval	acosh (const interval &x)
interval	abs (const interval &x)
interval	acos (const interval &x)
double	dist (const interval &x, const interval &y)
double	mag (const interval &)
double	mig (const interval &)
double	rad (const interval &)
double	relDiam (const interval &)
double	width (const interval &)
double	diam (const interval &)
double	mid (const interval &)
interval	operator/ (double a, const interval &b)
interval	operator/ (const interval &a, double b)
interval	operator/ (const interval &a, const interval &b)
interval	operator* (double a, const interval &b)
interval	operator* (const interval &a, double b)
interval	operator* (const interval &a, const interval &b)
interval	cancel (const interval &a, const interval &b)
interval	operator- (const interval &a, const interval &b)
interval	operator- (const interval &a, double b)
interval	operator- (double a, const interval &b)
interval	operator+ (const interval &a, const interval &b)
interval	operator+ (const interval &a, double b)
interval	operator+ (double b, const interval &a)
double	upward_divides (const double &a, const double &b)
double	downward_divides (const double &a, const double &b)
double	upward_multiplies (const double &a, const double &b)
double	downward_multiplies (const double &a, const double &b)
double	upward_minus (const double &a, const double &b)
double	downward_minus (const double &a, const double &b)
double	upward_plus (const double &a, const double &b)
double	downward_plus (const double &a, const double &b)
interval	imin (const interval &x, const interval &y)
interval	imax (const interval &x, const interval &y)

coco::interval Class Reference [Classes and types for basic data management]

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

coco::interval Class Reference
[Classes and types for basic data management]