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

The Scalar Type interval. More...

#include <interval.hpp>

List of all members.

Public Member Functions

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

Friends

interval _interval (const ivector &) throw ()
 Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
interval _interval (const ivector_slice &) throw ()
 Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
interval _interval (const imatrix &m) throw ()
 Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
interval _interval (const imatrix_slice &m) throw ()
 Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
interval _interval (const l_real &a) throw ()
 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) throw (ERROR_INTERVAL_EMPTY_INTERVAL)
 Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
interval _interval (const l_interval &a) throw ()
 Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
interval _unchecked_interval (const real &, const real &)
 Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
interval abs (const interval &) throw ()
 Returns the absolute value of the interval.
real diam (const interval &) throw ()
 Returns the rounded diameter of the interval.
real & Inf (interval &) throw ()
 Returns the infimum of an interval.
const real & Inf (const interval &) throw ()
 Returns the infimum of an interval.
bool IsEmpty (const interval &) throw ()
 Returns true if the interval is empty.
real mid (const interval &) throw ()
 Returns the rounded middle of the interval.
bool operator! (const interval &) throw ()
 Implementation of standard negation operation.
bool operator!= (const interval &, const interval &) throw ()
 Implementation of standard negated equality operation.
bool operator!= (const real &, const interval &) throw ()
 Implementation of standard negated equality operation.
bool operator!= (const interval &, const real &) throw ()
 Implementation of standard negated equality operation.
bool operator!= (const dotprecision &, const interval &) throw ()
 Implementation of standard negated equality operation.
bool operator!= (const interval &, const dotprecision &) throw ()
 Implementation of standard negated equality operation.
bool operator!= (const int &, const interval &) throw ()
 Implementation of standard negated equality operation.
bool operator!= (const interval &, const int &) throw ()
 Implementation of standard negated equality operation.
bool operator!= (const long &, const interval &) throw ()
 Implementation of standard negated equality operation.
bool operator!= (const interval &, const long &) throw ()
 Implementation of standard negated equality operation.
bool operator!= (const double &, const interval &) throw ()
 Implementation of standard negated equality operation.
bool operator!= (const interval &, const double &) throw ()
 Implementation of standard negated equality operation.
interval operator& (const interval &, const interval &) throw (ERROR_INTERVAL_EMPTY_INTERVAL)
 Returns the intersection of the arguments.
interval operator& (const real &, const interval &) throw (ERROR_INTERVAL_EMPTY_INTERVAL)
 Returns the intersection of the arguments.
interval operator& (const interval &, const real &) throw (ERROR_INTERVAL_EMPTY_INTERVAL)
 Returns the intersection of the arguments.
idotprecision operator& (const interval &, const idotprecision &) throw (ERROR_IDOTPRECISION_EMPTY_INTERVAL)
 Returns the intersection of the arguments.
idotprecision operator& (const idotprecision &, const interval &) throw (ERROR_IDOTPRECISION_EMPTY_INTERVAL)
 Returns the intersection of the arguments.
interval & operator&= (interval &, const interval &) throw (ERROR_INTERVAL_EMPTY_INTERVAL)
 Allocates the intersection of the arguments to the first argument.
interval & operator&= (interval &, const real &) throw (ERROR_INTERVAL_EMPTY_INTERVAL)
 Allocates the intersection of the arguments to the first argument.
interval operator* (const interval &, const interval &) throw ()
 Implementation of standard algebraic multiplication operation.
interval operator* (const interval &, const real &) throw ()
 Implementation of standard algebraic multiplication operation.
interval operator* (const real &, const interval &) throw ()
 Implementation of standard algebraic multiplication operation.
interval & operator*= (interval &, const interval &) throw ()
 Implementation of standard algebraic multiplication and allocation operation.
interval & operator*= (interval &, const real &) throw ()
 Implementation of standard algebraic multiplication and allocation operation.
interval operator+ (const interval &) throw ()
 Implementation of standard algebraic positive sign operation.
interval operator+ (const interval &, const interval &) throw ()
 Implementation of standard algebraic addition operation.
interval operator+ (const interval &, const real &) throw ()
 Implementation of standard algebraic addition operation.
interval operator+ (const real &, const interval &) throw ()
 Implementation of standard algebraic addition operation.
idotprecision operator+ (const idotprecision &, const interval &) throw ()
 Implementation of standard algebraic addition operation.
idotprecision operator+ (const interval &, const idotprecision &) throw ()
 Implementation of standard algebraic addition operation.
interval & operator+= (interval &, const interval &) throw ()
 Implementation of standard algebraic addition and allocation operation.
interval & operator+= (interval &, const real &) throw ()
 Implementation of standard algebraic addition and allocation operation.
interval operator- (const interval &) throw ()
 Implementation of standard algebraic negative sign operation.
interval operator- (const interval &, const interval &) throw ()
 Implementation of standard algebraic subtraction operation.
interval operator- (const interval &, const real &) throw ()
 Implementation of standard algebraic subtraction operation.
interval operator- (const real &, const interval &) throw ()
 Implementation of standard algebraic subtraction operation.
idotprecision operator- (const idotprecision &, const interval &) throw ()
 Implementation of standard algebraic subtraction operation.
idotprecision operator- (const interval &, const idotprecision &) throw ()
 Implementation of standard algebraic subtraction operation.
interval & operator-= (interval &, const interval &) throw ()
 Implementation of standard algebraic subtraction and allocation operation.
interval & operator-= (interval &, const real &) throw ()
 Implementation of standard algebraic subtraction and allocation operation.
interval operator/ (const interval &, const interval &) throw (DIV_BY_ZERO)
 Implementation of standard algebraic division operation.
interval operator/ (const interval &, const real &) throw ()
 Implementation of standard algebraic division operation.
interval operator/ (const real &, const interval &) throw ()
 Implementation of standard algebraic division operation.
interval & operator/= (interval &, const interval &) throw ()
 Implementation of standard algebraic division and allocation operation.
interval & operator/= (interval &, const real &) throw ()
 Implementation of standard algebraic division and allocation operation.
bool operator< (const interval &, const interval &) throw ()
 Implementation of standard less-than operation.
bool operator< (const real &, const interval &) throw ()
 Implementation of standard less-than operation.
bool operator< (const interval &, const real &) throw ()
 Implementation of standard less-than operation.
bool operator< (const dotprecision &, const interval &) throw ()
 Implementation of standard less-than operation.
bool operator< (const interval &, const dotprecision &) throw ()
 Implementation of standard less-than operation.
std::ostream & operator<< (std::ostream &, const interval &) throw ()
 Implementation of standard output method.
std::string & operator<< (std::string &, const interval &) throw ()
 Implementation of standard output method.
bool operator<= (const interval &, const interval &) throw ()
 Implementation of standard less-or-equal-than operation.
bool operator<= (const real &, const interval &) throw ()
 Implementation of standard less-or-equal-than operation.
bool operator<= (const interval &, const real &) throw ()
 Implementation of standard less-or-equal-than operation.
bool operator<= (const dotprecision &, const interval &) throw ()
 Implementation of standard less-or-equal-than operation.
bool operator<= (const interval &, const dotprecision &) throw ()
 Implementation of standard less-or-equal-than operation.
bool operator== (const interval &, const interval &) throw ()
 Implementation of standard equality operation.
bool operator== (const real &, const interval &) throw ()
 Implementation of standard equality operation.
bool operator== (const interval &, const real &) throw ()
 Implementation of standard equality operation.
bool operator== (const dotprecision &, const interval &) throw ()
 Implementation of standard equality operation.
bool operator== (const interval &, const dotprecision &) throw ()
 Implementation of standard equality operation.
bool operator== (const int &, const interval &) throw ()
 Implementation of standard equality operation.
bool operator== (const interval &, const int &) throw ()
 Implementation of standard equality operation.
bool operator== (const long &, const interval &) throw ()
 Implementation of standard equality operation.
bool operator== (const interval &, const long &) throw ()
 Implementation of standard equality operation.
bool operator== (const double &, const interval &) throw ()
 Implementation of standard equality operation.
bool operator== (const interval &, const double &) throw ()
 Implementation of standard equality operation.
bool operator> (const interval &, const interval &) throw ()
 Implementation of standard greater-than operation.
bool operator> (const real &, const interval &) throw ()
 Implementation of standard greater-than operation.
bool operator> (const interval &, const real &) throw ()
 Implementation of standard greater-than operation.
bool operator> (const dotprecision &, const interval &) throw ()
 Implementation of standard greater-than operation.
bool operator> (const interval &, const dotprecision &) throw ()
 Implementation of standard greater-than operation.
bool operator>= (const interval &, const interval &) throw ()
 Implementation of standard greater-or-equal-than operation.
bool operator>= (const real &, const interval &) throw ()
 Implementation of standard greater-or-equal-than operation.
bool operator>= (const interval &, const real &) throw ()
 Implementation of standard greater-or-equal-than operation.
bool operator>= (const dotprecision &, const interval &) throw ()
 Implementation of standard greater-or-equal-than operation.
bool operator>= (const interval &, const dotprecision &) throw ()
 Implementation of standard greater-or-equal-than operation.
std::istream & operator>> (std::istream &, interval &) throw ()
 Implementation of standard input method.
std::string & operator>> (std::string &, interval &) throw ()
 Implementation of standard input method.
void operator>> (const std::string &, interval &) throw ()
 Implementation of standard input method.
void operator>> (const char *, interval &) throw ()
 Implementation of standard input method.
interval operator| (const interval &, const interval &) throw ()
 Returns the convex hull of the arguments.
interval operator| (const real &, const interval &) throw ()
 Returns the convex hull of the arguments.
interval operator| (const interval &, const real &) throw ()
 Returns the convex hull of the arguments.
interval operator| (const real &, const real &) throw ()
 Returns the convex hull of the arguments.
idotprecision operator| (const interval &, const idotprecision &) throw ()
 Returns the convex hull of the arguments.
idotprecision operator| (const idotprecision &, const interval &) throw ()
 Returns the convex hull of the arguments.
interval & operator|= (interval &, const interval &) throw ()
 Allocates the convex hull of the arguments to the first argument.
interval & operator|= (interval &, const real &) throw ()
 Allocates the convex hull of the arguments to the first argument.
interval & SetInf (interval &, const real &) throw ()
 Returns the interval with the new given infimum value.
interval & SetSup (interval &, const real &) throw ()
 Returns the interval with the new given supremum value.
real & Sup (interval &) throw ()
 Returns the supremum of an interval.
const real & Sup (const interval &) throw ()
 Returns the supremum of an interval.
void times2pown (interval &, const int &) throw ()
 Multiplication of interval with $ 2^n $.
interval & UncheckedSetInf (interval &, const real &) throw ()
 Returns the interval with the unchecked new given infimum value.
interval & UncheckedSetSup (interval &, const real &) throw ()
 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 Function Documentation

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: