C-XSC - A C++ Class Library for Extended Scientific Computing 2.5.4
cxsc::interval Class Reference

The Scalar Type interval. More...

#include <interval.hpp>

Collaboration diagram for cxsc::interval:
Collaboration graph

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.
 
intervaloperator= (const dotprecision &) noexcept
 Implementation of standard assigning operator.
 
intervaloperator= (const idotprecision &) noexcept
 Implementation of standard assigning operator.
 
intervaloperator= (const l_interval &) noexcept
 Implementation of standard assigning operator.
 
intervaloperator= (const l_real &) noexcept
 Implementation of standard assigning operator.
 
intervaloperator= (const lx_interval &) noexcept
 Implementation of standard assigning operator.
 
intervaloperator= (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 realInf (const interval &a)
 Returns the infimum of an interval.
 
realInf (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.
 
intervaloperator&= (interval &a, const interval &b)
 Allocates the intersection of the arguments to the first argument.
 
intervaloperator&= (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.
 
intervaloperator*= (interval &a, const interval &b)
 Implementation of standard algebraic multiplication and allocation operation.
 
intervaloperator*= (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.
 
intervaloperator+= (interval &a, const interval &b)
 Implementation of standard algebraic addition and allocation operation.
 
intervaloperator+= (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.
 
intervaloperator-= (interval &a, const interval &b)
 Implementation of standard algebraic subtraction and allocation operation.
 
intervaloperator-= (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.
 
intervaloperator/= (interval &a, const interval &b)
 Implementation of standard algebraic division and allocation operation.
 
intervaloperator/= (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.
 
intervaloperator|= (interval &a, const interval &b)
 Allocates the convex hull of the arguments to the first argument.
 
intervaloperator|= (interval &a, const real &b)
 Allocates the convex hull of the arguments to the first argument.
 
intervalSetInf (interval &a, const real &b)
 Returns the interval with the new given infimum value.
 
intervalSetSup (interval &a, const real &b)
 Returns the interval with the new given supremum value.
 
const realSup (const interval &a)
 Returns the supremum of an interval.
 
realSup (interval &a)
 Returns the supremum of an interval.
 
void times2pown (interval &x, const int &n)
 Multiplication of interval with $ 2^n $.
 
intervalUncheckedSetInf (interval &a, const real &b)
 Returns the interval with the unchecked new given infimum value.
 
intervalUncheckedSetSup (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.

Friends And Related Symbol Documentation

◆ _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: