The Scalar Type interval. More...

#include <interval.hpp>

Collaboration diagram for cxsc::interval:

Public Member Functions
	interval ()
	Constructor of class interval.
	interval (const dotprecision &) noexcept
	Constructor of class interval.
	interval (const dotprecision &, const dotprecision &)
	Constructor of class interval.
	interval (const idotprecision &) noexcept
	Constructor of class interval.
	interval (const imatrix &m) noexcept
	Constructor of class interval.
	interval (const imatrix_slice &m) noexcept
	Constructor of class interval.
	interval (const ivector &) noexcept
	Constructor of class interval.
	interval (const ivector_slice &) noexcept
	Constructor of class interval.
	interval (const l_interval &) noexcept
	Constructor of class interval.
	interval (const l_real &) noexcept
	Constructor of class interval.
	interval (const l_real &, const l_real &)
	Constructor of class interval.
	interval (const real &, const real &)
	Constructor of class interval.
	interval (const real &r) noexcept
	Typecast for converting a real value in an interval.
interval &	operator= (const dotprecision &) noexcept
	Implementation of standard assigning operator.
interval &	operator= (const idotprecision &) noexcept
	Implementation of standard assigning operator.
interval &	operator= (const l_interval &) noexcept
	Implementation of standard assigning operator.
interval &	operator= (const l_real &) noexcept
	Implementation of standard assigning operator.
interval &	operator= (const lx_interval &) noexcept
	Implementation of standard assigning operator.
interval &	operator= (const real &a)
	Implementation of standard assigning operator.

Friends
interval	_interval (const imatrix &m) noexcept
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
interval	_interval (const imatrix_slice &m) noexcept
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
interval	_interval (const ivector &) noexcept
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
interval	_interval (const ivector_slice &) noexcept
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
interval	_interval (const l_interval &a)
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
interval	_interval (const l_real &a)
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
interval	_interval (const l_real &a, const l_real &b)
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
interval	_unchecked_interval (const real &a, const real &b)
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
interval	abs (const interval &a)
	Returns the absolute value of the interval.
real	diam (const interval &a)
	Returns the rounded diameter of the interval.
const real &	Inf (const interval &a)
	Returns the infimum of an interval.
real &	Inf (interval &a)
	Returns the infimum of an interval.
bool	IsEmpty (const interval &a)
	Returns true if the interval is empty.
real	mid (const interval &a)
	Returns the rounded middle of the interval.
bool	operator! (const interval &a)
	Implementation of standard negation operation.
bool	operator!= (const dotprecision &r, const interval &a)
	Implementation of standard negated equality operation.
bool	operator!= (const double &r, const interval &a)
	Implementation of standard negated equality operation.
bool	operator!= (const int &r, const interval &a)
	Implementation of standard negated equality operation.
bool	operator!= (const interval &a, const dotprecision &r)
	Implementation of standard negated equality operation.
bool	operator!= (const interval &a, const double &r)
	Implementation of standard negated equality operation.
bool	operator!= (const interval &a, const int &r)
	Implementation of standard negated equality operation.
bool	operator!= (const interval &a, const interval &b)
	Implementation of standard negated equality operation.
bool	operator!= (const interval &a, const long &r)
	Implementation of standard negated equality operation.
bool	operator!= (const interval &a, const real &r)
	Implementation of standard negated equality operation.
bool	operator!= (const long &r, const interval &a)
	Implementation of standard negated equality operation.
bool	operator!= (const real &r, const interval &a)
	Implementation of standard negated equality operation.
idotprecision	operator& (const idotprecision &a, const interval &b)
	Returns the intersection of the arguments.
idotprecision	operator& (const interval &a, const idotprecision &b)
	Returns the intersection of the arguments.
interval	operator& (const interval &a, const interval &b)
	Returns the intersection of the arguments.
interval	operator& (const interval &a, const real &b)
	Returns the intersection of the arguments.
interval	operator& (const real &a, const interval &b)
	Returns the intersection of the arguments.
interval &	operator&= (interval &a, const interval &b)
	Allocates the intersection of the arguments to the first argument.
interval &	operator&= (interval &a, const real &b)
	Allocates the intersection of the arguments to the first argument.
interval	operator* (const interval &a, const interval &b)
	Implementation of standard algebraic multiplication operation.
interval	operator* (const interval &a, const real &b)
	Implementation of standard algebraic multiplication operation.
interval	operator* (const real &a, const interval &b)
	Implementation of standard algebraic multiplication operation.
interval &	*operator=** (interval &a, const interval &b)
	Implementation of standard algebraic multiplication and allocation operation.
interval &	*operator=** (interval &a, const real &b)
	Implementation of standard algebraic multiplication and allocation operation.
idotprecision	operator+ (const idotprecision &a, const interval &b)
	Implementation of standard algebraic addition operation.
interval	operator+ (const interval &a)
	Implementation of standard algebraic positive sign operation.
interval	operator+ (const interval &a, const interval &b)
	Implementation of standard algebraic addition operation.
interval	operator+ (const interval &a, const real &b)
	Implementation of standard algebraic addition operation.
idotprecision	operator+ (const interval &b, const idotprecision &a)
	Implementation of standard algebraic addition operation.
interval	operator+ (const real &a, const interval &b)
	Implementation of standard algebraic addition operation.
interval &	operator+= (interval &a, const interval &b)
	Implementation of standard algebraic addition and allocation operation.
interval &	operator+= (interval &a, const real &b)
	Implementation of standard algebraic addition and allocation operation.
idotprecision	operator- (const idotprecision &a, const interval &b)
	Implementation of standard algebraic subtraction operation.
interval	operator- (const interval &a)
	Implementation of standard algebraic negative sign operation.
idotprecision	operator- (const interval &a, const idotprecision &b)
	Implementation of standard algebraic subtraction operation.
interval	operator- (const interval &a, const interval &b)
	Implementation of standard algebraic subtraction operation.
interval	operator- (const interval &a, const real &b)
	Implementation of standard algebraic subtraction operation.
interval	operator- (const real &a, const interval &b)
	Implementation of standard algebraic subtraction operation.
interval &	operator-= (interval &a, const interval &b)
	Implementation of standard algebraic subtraction and allocation operation.
interval &	operator-= (interval &a, const real &b)
	Implementation of standard algebraic subtraction and allocation operation.
interval	operator/ (const interval &a, const interval &b)
	Implementation of standard algebraic division operation.
interval	operator/ (const interval &a, const real &b)
	Implementation of standard algebraic division operation.
interval	operator/ (const real &a, const interval &b)
	Implementation of standard algebraic division operation.
interval &	operator/= (interval &a, const interval &b)
	Implementation of standard algebraic division and allocation operation.
interval &	operator/= (interval &a, const real &b)
	Implementation of standard algebraic division and allocation operation.
bool	operator< (const dotprecision &a, const interval &b)
	Implementation of standard less-than operation.
bool	operator< (const interval &, const dotprecision &) noexcept
	Implementation of standard less-than operation.
bool	operator< (const interval &, const real &) noexcept
	Implementation of standard less-than operation.
bool	operator< (const interval &a, const interval &b)
	Implementation of standard less-than operation.
bool	operator< (const real &a, const interval &b)
	Implementation of standard less-than operation.
std::ostream &	operator<< (std::ostream &s, const interval &a)
	Implementation of standard output method.
std::string &	operator<< (std::string &s, const interval &a)
	Implementation of standard output method.
bool	operator<= (const dotprecision &a, const interval &b)
	Implementation of standard less-or-equal-than operation.
bool	operator<= (const interval &a, const dotprecision &b)
	Implementation of standard less-or-equal-than operation.
bool	operator<= (const interval &a, const interval &b)
	Implementation of standard less-or-equal-than operation.
bool	operator<= (const interval &a, const real &b)
	Implementation of standard less-or-equal-than operation.
bool	operator<= (const real &a, const interval &b)
	Implementation of standard less-or-equal-than operation.
bool	operator== (const dotprecision &r, const interval &a)
	Implementation of standard equality operation.
bool	operator== (const double &r, const interval &a)
	Implementation of standard equality operation.
bool	operator== (const int &r, const interval &a)
	Implementation of standard equality operation.
bool	operator== (const interval &a, const dotprecision &r)
	Implementation of standard equality operation.
bool	operator== (const interval &a, const double &r)
	Implementation of standard equality operation.
bool	operator== (const interval &a, const int &r)
	Implementation of standard equality operation.
bool	operator== (const interval &a, const interval &b)
	Implementation of standard equality operation.
bool	operator== (const interval &a, const long &r)
	Implementation of standard equality operation.
bool	operator== (const interval &a, const real &r)
	Implementation of standard equality operation.
bool	operator== (const long &r, const interval &a)
	Implementation of standard equality operation.
bool	operator== (const real &r, const interval &a)
	Implementation of standard equality operation.
bool	operator> (const dotprecision &, const interval &) noexcept
	Implementation of standard greater-than operation.
bool	operator> (const interval &a, const dotprecision &b)
	Implementation of standard greater-than operation.
bool	operator> (const interval &a, const interval &b)
	Implementation of standard greater-than operation.
bool	operator> (const interval &a, const real &b)
	Implementation of standard greater-than operation.
bool	operator> (const real &, const interval &) noexcept
	Implementation of standard greater-than operation.
bool	operator>= (const dotprecision &a, const interval &b)
	Implementation of standard greater-or-equal-than operation.
bool	operator>= (const interval &a, const dotprecision &b)
	Implementation of standard greater-or-equal-than operation.
bool	operator>= (const interval &a, const interval &b)
	Implementation of standard greater-or-equal-than operation.
bool	operator>= (const interval &a, const real &b)
	Implementation of standard greater-or-equal-than operation.
bool	operator>= (const real &a, const interval &b)
	Implementation of standard greater-or-equal-than operation.
void	operator>> (const char *s, interval &a)
	Implementation of standard input method.
void	operator>> (const std::string &s, interval &a)
	Implementation of standard input method.
std::istream &	operator>> (std::istream &s, interval &a)
	Implementation of standard input method.
std::string &	operator>> (std::string &s, interval &a)
	Implementation of standard input method.
idotprecision	operator\| (const idotprecision &a, const interval &b)
	Returns the convex hull of the arguments.
idotprecision	operator\| (const interval &a, const idotprecision &b)
	Returns the convex hull of the arguments.
interval	operator\| (const interval &a, const interval &b)
	Returns the convex hull of the arguments.
interval	operator\| (const interval &a, const real &b)
	Returns the convex hull of the arguments.
interval	operator\| (const real &a, const interval &b)
	Returns the convex hull of the arguments.
interval	operator\| (const real &a, const real &b)
	Returns the convex hull of the arguments.
interval &	operator\|= (interval &a, const interval &b)
	Allocates the convex hull of the arguments to the first argument.
interval &	operator\|= (interval &a, const real &b)
	Allocates the convex hull of the arguments to the first argument.
interval &	SetInf (interval &a, const real &b)
	Returns the interval with the new given infimum value.
interval &	SetSup (interval &a, const real &b)
	Returns the interval with the new given supremum value.
const real &	Sup (const interval &a)
	Returns the supremum of an interval.
real &	Sup (interval &a)
	Returns the supremum of an interval.
void	times2pown (interval &x, const int &n)
	Multiplication of interval with .
interval &	UncheckedSetInf (interval &a, const real &b)
	Returns the interval with the unchecked new given infimum value.
interval &	UncheckedSetSup (interval &a, const real &b)
	Returns the interval with the unchecked new given supremum value.

Detailed Description

The Scalar Type interval.

The data type interval is used to represent intervals over the real floating-point numbers:

$\‍[\left[ a \right] = \left[ \underline a , \overline a \right] := \left\{ x \in R | \underline a \le x \le \overline a \right\} \in R \‍]$

i.e. $\left[ a \right]$ represents the set of all real numbers enclosed within the bounds $\underline a , \overline a \in R$ .

The notation $\underline a$ denotes the lower bound (infimum), and $\overline a$ denotes the upper bound (supremum) of the interval $\left[ a \right]$ .

Definition at line 54 of file interval.hpp.

◆ _unchecked_interval

interval _unchecked_interval	(	const real &	a,
		const real &	b )

friend

Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.

Deprecated: use standard contructors for typecasting

See also: cxsc::interval::interval(const real&, const real&)

Definition at line 66 of file interval.inl.

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

Public Member Functions

Friends

Detailed Description

Friends And Related Symbol Documentation

◆ _unchecked_interval