The Scalar Type cinterval. More...

#include <cinterval.hpp>

Public Member Functions
	cinterval (void) throw ()
	Constructor of class cinterval.
	cinterval (const interval &a, const interval &b) throw ()
	Constructor of class cinterval.
	cinterval (const complex &a, const complex &b) throw (ERROR_CINTERVAL_EMPTY_INTERVAL)
	Constructor of class cinterval.
	cinterval (const civector &) throw ()
	Constructor of class cinterval.
	cinterval (const civector_slice &) throw ()
	Constructor of class cinterval.
	cinterval (const cimatrix &) throw ()
	Constructor of class cinterval.
	cinterval (const cimatrix_slice &) throw ()
	Constructor of class cinterval.
	cinterval (const real &a) throw ()
	Constructor of class cinterval.
	cinterval (const interval &a) throw ()
	Constructor of class cinterval.
	cinterval (const complex &a) throw ()
	Constructor of class cinterval.
	cinterval (const dotprecision &) throw ()
	Constructor of class cinterval.
	cinterval (const cdotprecision &) throw ()
	Constructor of class cinterval.
	cinterval (const idotprecision &) throw ()
	Constructor of class cinterval.
	cinterval (const cidotprecision &) throw ()
	Constructor of class cinterval.
	cinterval (const l_cinterval &) throw ()
	Constructor of class cinterval.
cinterval &	operator= (const real &) throw ()
	Implementation of standard assigning operator.
cinterval &	operator= (const interval &) throw ()
	Implementation of standard assigning operator.
cinterval &	operator= (const complex &) throw ()
	Implementation of standard assigning operator.
cinterval &	operator= (const cinterval &) throw ()
	Implementation of standard assigning operator.
cinterval &	operator= (const dotprecision &) throw ()
	Implementation of standard assigning operator.
cinterval &	operator= (const idotprecision &) throw ()
	Implementation of standard assigning operator.
cinterval &	operator= (const cdotprecision &) throw ()
	Implementation of standard assigning operator.
cinterval &	operator= (const cidotprecision &) throw ()
	Implementation of standard assigning operator.
cinterval &	operator= (const l_cinterval &) throw ()
	Implementation of standard assigning operator.
cinterval &	operator= (const lx_cinterval &) throw ()
	Implementation of standard assigning operator.
Friends
cinterval	_cinterval (const real &) throw ()
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
cinterval	_cinterval (const interval &) throw ()
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
cinterval	_cinterval (const complex &) throw ()
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
cinterval	_cinterval (const dotprecision &) throw ()
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
cinterval	_cinterval (const idotprecision &) throw ()
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
cinterval	_cinterval (const cdotprecision &) throw ()
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
cinterval	_cinterval (const cidotprecision &) throw ()
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
cinterval	_cinterval (const interval &, const interval &) throw ()
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
cinterval	_cinterval (const real &, const interval &) throw ()
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
cinterval	_cinterval (const interval &, const real &) throw ()
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
cinterval	_cinterval (const complex &, const complex &) throw ()
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
cinterval	_cinterval (const real &, const complex &) throw ()
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
cinterval	_cinterval (const complex &, const real &) throw ()
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
cinterval	_unchecked_cinterval (const complex &, const complex &) throw ()
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
cinterval	_unchecked_cinterval (const real &, const complex &) throw ()
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
cinterval	_unchecked_cinterval (const complex &, const real &) throw ()
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
interval	abs (const cinterval &) throw ()
	Returns the absolute value of a complex interval.
cinterval	conj (const cinterval &) throw ()
	Returns the conjugated complex interval.
complex	diam (const cinterval &) throw ()
	Returns the rounded diameter of the complex interval.
interval &	Im (cinterval &a) throw ()
	Returns the imaginary interval of the complex interval.
interval	Im (const cinterval &a) throw ()
	Returns the imaginary interval of the complex interval.
complex	Inf (const cinterval &) throw ()
	Returns the infimum of a complex interval.
real	InfIm (const cinterval &a) throw ()
	Returns the infimum of the imaginary interval of the complex interval.
real &	InfIm (cinterval &a) throw ()
	Returns the infimum of the imaginary interval of the complex interval.
real	InfRe (const cinterval &a) throw ()
	Returns the infimum of the real interval of the complex interval.
real &	InfRe (cinterval &a) throw ()
	Returns the infimum of the real interval of the complex interval.
complex	mid (const cinterval &) throw ()
	Returns the rounded middle of the complex interval.
bool	operator! (const cinterval &a) throw ()
	Implementation of standard negation operation.
bool	operator!= (const cinterval &a, const cinterval &b) throw ()
	Implementation of standard negated equality operation.
bool	operator!= (const cinterval &a, const real &b) throw ()
	Implementation of standard negated equality operation.
bool	operator!= (const real &a, const cinterval &b) throw ()
	Implementation of standard negated equality operation.
bool	operator!= (const cinterval &a, const interval &b) throw ()
	Implementation of standard negated equality operation.
bool	operator!= (const interval &a, const cinterval &b) throw ()
	Implementation of standard negated equality operation.
bool	operator!= (const cinterval &a, const complex &b) throw ()
	Implementation of standard negated equality operation.
bool	operator!= (const complex &a, const cinterval &b) throw ()
	Implementation of standard negated equality operation.
cinterval	operator& (const cinterval &, const cinterval &) throw (ERROR_CINTERVAL_EMPTY_INTERVAL)
	Returns the intersection of the arguments.
cinterval	operator& (const cinterval &, const real &) throw ()
	Returns the intersection of the arguments.
cinterval	operator& (const real &, const cinterval &) throw ()
	Returns the intersection of the arguments.
cinterval	operator& (const cinterval &, const interval &) throw ()
	Returns the intersection cinterval of the arguments.
cinterval	operator& (const interval &, const cinterval &) throw ()
	Returns the intersection cinterval of the arguments.
cinterval	operator& (const cinterval &, const complex &) throw ()
	Returns the intersection of the arguments.
cinterval	operator& (const complex &, const cinterval &) throw ()
	Returns the intersection of the arguments.
cinterval	operator& (const complex &, const interval &) throw ()
	Returns the intersection of the arguments.
cinterval	operator& (const interval &, const complex &) throw ()
	Returns the intersection of the arguments.
cinterval &	operator&= (cinterval &, const cinterval &) throw (ERROR_CINTERVAL_EMPTY_INTERVAL)
	Allocates the intersection of the arguments to the first argument.
cinterval &	operator&= (cinterval &, const real &) throw ()
	Allocates the intersection of the arguments to the first argument.
cinterval &	operator&= (cinterval &, const interval &) throw ()
	Allocates the intersection cinterval of the arguments to the first argument.
cinterval &	operator&= (cinterval &, const complex &) throw ()
	Allocates the intersection of the arguments to the first argument.
cinterval	operator* (const cinterval &, const cinterval &) throw ()
	Implementation of standard algebraic multiplication operation.
cinterval	operator* (const cinterval &, const real &) throw ()
	Implementation of standard algebraic multiplication operation.
cinterval	operator* (const real &, const cinterval &) throw ()
	Implementation of standard algebraic multiplication operation.
cinterval	operator* (const cinterval &, const interval &) throw ()
	Implementation of standard algebraic multiplication operation.
cinterval	operator* (const interval &, const cinterval &) throw ()
	Implementation of standard algebraic multiplication operation.
cinterval	operator* (const cinterval &, const complex &) throw ()
	Implementation of standard algebraic multiplication operation.
cinterval	operator* (const complex &, const cinterval &) throw ()
	Implementation of standard algebraic multiplication operation.
cinterval	operator* (const complex &, const interval &) throw ()
	Implementation of standard algebraic multiplication operation.
cinterval	operator* (const interval &, const complex &) throw ()
	Implementation of standard algebraic multiplication operation.
cinterval &	operator*= (cinterval &, const cinterval &) throw ()
	Implementation of standard algebraic multiplication and allocation operation.
cinterval &	operator*= (cinterval &, const real &) throw ()
	Implementation of standard algebraic multiplication and allocation operation.
cinterval &	operator*= (cinterval &, const interval &) throw ()
	Implementation of standard algebraic multiplication and allocation operation.
cinterval &	operator*= (cinterval &, const complex &) throw ()
	Implementation of standard algebraic multiplication and allocation operation.
cinterval	operator+ (const cinterval &) throw ()
	Implementation of standard algebraic positive sign operation.
cinterval	operator+ (const cinterval &, const cinterval &) throw ()
	Implementation of standard algebraic addition operation.
cinterval	operator+ (const cinterval &, const real &) throw ()
	Implementation of standard algebraic addition operation.
cinterval	operator+ (const real &, const cinterval &) throw ()
	Implementation of standard algebraic addition operation.
cinterval	operator+ (const cinterval &, const interval &) throw ()
	Implementation of standard algebraic addition operation.
cinterval	operator+ (const interval &, const cinterval &) throw ()
	Implementation of standard algebraic addition operation.
cinterval	operator+ (const cinterval &, const complex &) throw ()
	Implementation of standard algebraic addition operation.
cinterval	operator+ (const complex &, const cinterval &) throw ()
	Implementation of standard algebraic addition operation.
cinterval	operator+ (const complex &, const interval &) throw ()
	Implementation of standard algebraic addition operation.
cinterval	operator+ (const interval &, const complex &) throw ()
	Implementation of standard algebraic addition operation.
cinterval &	operator+= (cinterval &, const cinterval &) throw ()
	Implementation of standard algebraic addition and allocation operation.
cinterval &	operator+= (cinterval &, const real &) throw ()
	Implementation of standard algebraic addition and allocation operation.
cinterval &	operator+= (cinterval &, const interval &) throw ()
	Implementation of standard algebraic addition and allocation operation.
cinterval &	operator+= (cinterval &, const complex &) throw ()
	Implementation of standard algebraic addition and allocation operation.
cinterval	operator- (const cinterval &) throw ()
	Implementation of standard algebraic negative sign operation.
cinterval	operator- (const cinterval &, const cinterval &) throw ()
	Implementation of standard algebraic subtraction operation.
cinterval	operator- (const cinterval &, const real &) throw ()
	Implementation of standard algebraic subtraction operation.
cinterval	operator- (const real &, const cinterval &) throw ()
	Implementation of standard algebraic subtraction operation.
cinterval	operator- (const cinterval &, const interval &) throw ()
	Implementation of standard algebraic subtraction operation.
cinterval	operator- (const interval &, const cinterval &) throw ()
	Implementation of standard algebraic subtraction operation.
cinterval	operator- (const cinterval &, const complex &) throw ()
	Implementation of standard algebraic subtraction operation.
cinterval	operator- (const complex &, const cinterval &) throw ()
	Implementation of standard algebraic subtraction operation.
cinterval	operator- (const complex &, const interval &) throw ()
	Implementation of standard algebraic subtraction operation.
cinterval	operator- (const interval &, const complex &) throw ()
	Implementation of standard algebraic subtraction operation.
cinterval &	operator-= (cinterval &, const cinterval &) throw ()
	Implementation of standard algebraic subtraction and allocation operation.
cinterval &	operator-= (cinterval &, const real &) throw ()
	Implementation of standard algebraic subtraction and allocation operation.
cinterval &	operator-= (cinterval &, const interval &) throw ()
	Implementation of standard algebraic subtraction and allocation operation.
cinterval &	operator-= (cinterval &, const complex &) throw ()
	Implementation of standard algebraic subtraction and allocation operation.
cinterval	operator/ (const cinterval &, const cinterval &) throw (DIV_BY_ZERO)
	Implementation of standard algebraic division operation.
cinterval	operator/ (const cinterval &, const real &) throw ()
	Implementation of standard algebraic division operation.
cinterval	operator/ (const real &, const cinterval &) throw ()
	Implementation of standard algebraic division operation.
cinterval	operator/ (const cinterval &, const interval &) throw ()
	Implementation of standard algebraic division operation.
cinterval	operator/ (const interval &, const cinterval &) throw ()
	Implementation of standard algebraic division operation.
cinterval	operator/ (const cinterval &, const complex &) throw ()
	Implementation of standard algebraic division operation.
cinterval	operator/ (const complex &, const cinterval &) throw ()
	Implementation of standard algebraic division operation.
cinterval	operator/ (const complex &, const interval &) throw ()
	Implementation of standard algebraic division operation.
cinterval	operator/ (const interval &, const complex &) throw ()
	Implementation of standard algebraic division operation.
cinterval &	operator/= (cinterval &, const cinterval &) throw ()
	Implementation of standard algebraic division and allocation operation.
cinterval &	operator/= (cinterval &, const real &) throw ()
	Implementation of standard algebraic division and allocation operation.
cinterval &	operator/= (cinterval &, const interval &) throw ()
	Implementation of standard algebraic division and allocation operation.
cinterval &	operator/= (cinterval &, const complex &) throw ()
	Implementation of standard algebraic division and allocation operation.
bool	operator< (const cinterval &, const cinterval &) throw ()
	Implementation of standard less-than operation.
bool	operator< (const real &, const cinterval &) throw ()
	Implementation of standard less-than operation.
bool	operator< (const cinterval &, const real &) throw ()
	Implementation of standard less-than operation.
bool	operator< (const interval &, const cinterval &) throw ()
	Implementation of standard less-than operation.
bool	operator< (const cinterval &, const interval &) throw ()
	Implementation of standard less-than operation.
bool	operator< (const complex &, const cinterval &) throw ()
	Implementation of standard less-than operation.
bool	operator< (const cinterval &, const complex &) throw ()
	Implementation of standard less-than operation.
std::ostream &	operator<< (std::ostream &, const cinterval &) throw ()
	Implementation of standard output method.
std::string &	operator<< (std::string &, const cinterval &) throw ()
	Implementation of standard output method.
bool	operator<= (const cinterval &, const cinterval &) throw ()
	Implementation of standard less-or-equal-than operation.
bool	operator<= (const real &, const cinterval &) throw ()
	Implementation of standard less-or-equal-than operation.
bool	operator<= (const cinterval &, const real &) throw ()
	Implementation of standard less-or-equal-than operation.
bool	operator<= (const interval &, const cinterval &) throw ()
	Implementation of standard less-or-equal-than operation.
bool	operator<= (const cinterval &, const interval &) throw ()
	Implementation of standard less-or-equal-than operation.
bool	operator<= (const complex &, const cinterval &) throw ()
	Implementation of standard less-or-equal-than operation.
bool	operator<= (const cinterval &, const complex &) throw ()
	Implementation of standard less-or-equal-than operation.
bool	operator== (const cinterval &a, const cinterval &b) throw ()
	Implementation of standard equality operation.
bool	operator== (const cinterval &a, const real &b) throw ()
	Implementation of standard equality operation.
bool	operator== (const real &a, const cinterval &b) throw ()
	Implementation of standard equality operation.
bool	operator== (const cinterval &a, const interval &b) throw ()
	Implementation of standard equality operation.
bool	operator== (const interval &a, const cinterval &b) throw ()
	Implementation of standard equality operation.
bool	operator== (const cinterval &a, const complex &b) throw ()
	Implementation of standard equality operation.
bool	operator== (const complex &a, const cinterval &b) throw ()
	Implementation of standard equality operation.
bool	operator> (const cinterval &, const cinterval &) throw ()
	Implementation of standard greater-than operation.
bool	operator> (const real &, const cinterval &) throw ()
	Implementation of standard greater-than operation.
bool	operator> (const cinterval &, const real &) throw ()
	Implementation of standard greater-than operation.
bool	operator> (const interval &, const cinterval &) throw ()
	Implementation of standard greater-than operation.
bool	operator> (const cinterval &, const interval &) throw ()
	Implementation of standard greater-than operation.
bool	operator> (const complex &, const cinterval &) throw ()
	Implementation of standard greater-than operation.
bool	operator> (const cinterval &, const complex &) throw ()
	Implementation of standard greater-than operation.
bool	operator>= (const cinterval &, const cinterval &) throw ()
	Implementation of standard more-or-equal-than operation.
bool	operator>= (const real &, const cinterval &) throw ()
	Implementation of standard more-or-equal-than operation.
bool	operator>= (const cinterval &, const real &) throw ()
	Implementation of standard more-or-equal-than operation.
bool	operator>= (const interval &, const cinterval &) throw ()
	Implementation of standard more-or-equal-than operation.
bool	operator>= (const cinterval &, const interval &) throw ()
	Implementation of standard more-or-equal-than operation.
bool	operator>= (const complex &, const cinterval &) throw ()
	Implementation of standard more-or-equal-than operation.
bool	operator>= (const cinterval &, const complex &) throw ()
	Implementation of standard greater-or-equal-than operation.
std::istream &	operator>> (std::istream &, cinterval &) throw (ERROR_CINTERVAL_EMPTY_INTERVAL)
	Implementation of standard input method.
std::string &	operator>> (std::string &, cinterval &) throw (ERROR_CINTERVAL_EMPTY_INTERVAL)
	Implementation of standard input method.
void	operator>> (const char *, cinterval &) throw (ERROR_CINTERVAL_EMPTY_INTERVAL)
	Implementation of standard input method.
void	operator>> (const std::string &, cinterval &) throw (ERROR_CINTERVAL_EMPTY_INTERVAL)
	Implementation of standard input method.
cinterval	operator\| (const cinterval &, const cinterval &) throw ()
	Returns the convex hull of the arguments.
cinterval	operator\| (const cinterval &, const real &) throw ()
	Returns the convex hull of the arguments.
cinterval	operator\| (const real &, const cinterval &) throw ()
	Returns the convex hull of the arguments.
cinterval	operator\| (const cinterval &, const interval &) throw ()
	Returns the convex hull of the arguments.
cinterval	operator\| (const interval &, const cinterval &) throw ()
	Returns the convex hull of the arguments.
cinterval	operator\| (const cinterval &, const complex &) throw ()
	Returns the convex hull of the arguments.
cinterval	operator\| (const complex &, const cinterval &) throw ()
	Returns the convex hull of the arguments.
cinterval	operator\| (const complex &, const real &) throw ()
	Returns the union cinterval of the arguments.
cinterval	operator\| (const real &, const complex &) throw ()
	Returns the union cinterval of the arguments.
cinterval	operator\| (const complex &, const interval &) throw ()
	Returns the convex hull of the arguments.
cinterval	operator\| (const interval &, const complex &) throw ()
	Returns the convex hull of the arguments.
cinterval	operator\| (const complex &, const complex &) throw ()
	Returns the union cinterval of the arguments.
cinterval &	operator\|= (cinterval &, const cinterval &) throw ()
	Allocates the convex hull of the arguments to the first argument.
cinterval &	operator\|= (cinterval &, const real &) throw ()
	Allocates the convex hull of the arguments to the first argument.
cinterval &	operator\|= (cinterval &, const interval &) throw ()
	Allocates the convex hull of the arguments to the first argument.
cinterval &	operator\|= (cinterval &, const complex &) throw ()
	Allocates the convex hull of the arguments to the first argument.
interval &	Re (cinterval &a) throw ()
	Returns the real interval of the complex interval.
interval	Re (const cinterval &a) throw ()
	Returns the real interval of the complex interval.
cinterval &	SetIm (cinterval &a, const interval &b)
	Sets the imaginary interval of the complex interval.
cinterval &	SetIm (cinterval &a, const real &b)
	Sets the imaginary interval of the complex interval.
cinterval &	SetInf (cinterval &, const complex &) throw (ERROR_CINTERVAL_EMPTY_INTERVAL)
	Returns the complex interval with the new given infimum value.
cinterval &	SetInf (cinterval &, const real &) throw (ERROR_CINTERVAL_EMPTY_INTERVAL)
	Returns the complex interval with the new given infimum value.
cinterval &	SetRe (cinterval &a, const interval &b)
	Sets the real interval of the complex interval.
cinterval &	SetRe (cinterval &a, const real &b)
	Sets the real interval of the complex interval.
cinterval &	SetSup (cinterval &, const complex &) throw (ERROR_CINTERVAL_EMPTY_INTERVAL)
	Returns the complex interval with the new given supremum value.
cinterval &	SetSup (cinterval &, const real &) throw (ERROR_CINTERVAL_EMPTY_INTERVAL)
	Returns the complex interval with the new given supremum value.
complex	Sup (const cinterval &) throw ()
	Returns the supremum of a complex interval.
real	SupIm (const cinterval &a) throw ()
	Returns the supremum of the imaginary interval of the complex interval.
real &	SupIm (cinterval &a) throw ()
	Returns the supremum of the imaginary interval of the complex interval.
real	SupRe (const cinterval &a) throw ()
	Returns the supremum of the real interval of the complex interval.
real &	SupRe (cinterval &a) throw ()
	Returns the supremum of the real interval of the complex interval.
cinterval &	UncheckedSetInf (cinterval &, const complex &) throw ()
	Returns the complex interval with the unchecked new given infimum value.
cinterval &	UncheckedSetInf (cinterval &, const real &) throw ()
	Returns the complex interval with the unchecked new given infimum value.
cinterval &	UncheckedSetSup (cinterval &, const complex &) throw ()
	Returns the complex interval with the unchecked new given supremum value.
cinterval &	UncheckedSetSup (cinterval &, const real &) throw ()
	Returns the cinterval with the unchecked new given supremum value.

Detailed Description

The Scalar Type cinterval.

The data type cinterval is used to store complex intervals. They are defined as rectangles of the form $z = \left[ x \right] + i \left[ y \right] \in C$ (real part $\left[ x \right] \in R$ and imaginary part $\left[ y \right] \in R$ ) with sides parallel to the axes in the complex plane, as indicated in the figure below.

Complex Interval [3.0, 4.5] + [1.0, 2.0]i

Definition at line 54 of file cinterval.hpp.