The Scalar Type complex. More...

#include <complex.hpp>

Public Member Functions
	complex (void) throw ()
	Constructor of class complex.
	complex (const real &a, const real &b) throw ()
	Constructor of class complex.
	complex (const real &r) throw ()
	Constructor of class complex.
	complex (const cvector &) throw ()
	Constructor of class complex.
	complex (const cvector_slice &) throw ()
	Constructor of class complex.
	complex (const cmatrix &) throw ()
	Constructor of class complex.
	complex (const cmatrix_slice &) throw ()
	Constructor of class complex.
	complex (const cdotprecision &) throw ()
	Constructor of class complex.
complex &	operator= (const real &r) throw ()
	Implementation of standard assigning operator.
complex &	operator= (const cdotprecision &) throw ()
	Implementation of standard assigning operator.
complex &	operator= (const lx_complex &) throw ()
	Assigning lx_complex to complex.
complex &	operator= (const l_complex &) throw ()
	Assigning l_complex to complex.
Friends
complex	_complex (const cvector &) throw ()
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
complex	_complex (const cvector_slice &) throw ()
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
complex	_complex (const cmatrix &) throw ()
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
complex	_complex (const cmatrix_slice &) throw ()
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
complex	_complex (const cdotprecision &a) throw ()
	Deprecated typecast, which only exist for the reason of compatibility with older versions of C-XSC.
real	abs (complex) throw ()
	Returns the absolute value of a complex value.
real	abs2 (const complex &) throw ()
	Returns the absolute value of a complex value.
complex	adddown (const complex &, const complex &) throw ()
	Returns the downward rounded result of the addition operation.
complex	adddown (const complex &, const real &) throw ()
	Returns the downward rounded result of the addition operation.
complex	adddown (const real &, const complex &) throw ()
	Returns the downward rounded result of the addition operation.
complex	addup (const complex &, const complex &) throw ()
	Returns the upward rounded result of the addition operation.
complex	addup (const complex &, const real &) throw ()
	Returns the upward rounded result of the addition operation.
complex	addup (const real &, const complex &) throw ()
	Returns the upward rounded result of the addition operation.
complex	conj (const complex &) throw ()
	Returns the conjugated complex value.
complex	divdown (const complex &, const complex &)
	Returns the downward rounded result of the division operation.
complex	divdown (const complex &, const real &) throw ()
	Returns the downward rounded result of the division operation.
complex	divdown (const real &, const complex &) throw ()
	Returns the downward rounded result of the division operation.
complex	divn (const complex &, const complex &)
	Returns the nearest rounded result of the division operation.
complex	divup (const complex &, const complex &)
	Returns the upward rounded result of the operation.
complex	divup (const complex &, const real &) throw ()
	Returns the upward rounded result of the division operation.
complex	divup (const real &, const complex &) throw ()
	Returns the upward rounded result of the division operation.
real &	Im (complex &a)
	Returns the imaginary part of the complex value.
real	Im (const complex &a)
	Returns the imaginary part of the complex value.
complex	multdown (const complex &, const complex &) throw ()
	Returns the downward rounded result of the multiplication operation.
complex	multdown (const complex &, const real &) throw ()
	Returns the downward rounded result of the multiplication operation.
complex	multdown (const real &, const complex &) throw ()
	Returns the downward rounded result of the multiplication operation.
complex	multup (const complex &, const complex &) throw ()
	Returns the upward rounded result of the multiplication operation.
complex	multup (const complex &, const real &) throw ()
	Returns the upward rounded result of the multiplication operation.
complex	multup (const real &, const complex &) throw ()
	Returns the upward rounded result of the multiplication operation.
bool	operator! (const complex &a) throw ()
	Implementation of standard negation operation.
bool	operator!= (const complex &a, const complex &b) throw ()
	Implementation of standard negated equality operation.
bool	operator!= (const complex &a, const real &b) throw ()
	Implementation of standard negated equality operation.
bool	operator!= (const real &a, const complex &b) throw ()
	Implementation of standard negated equality operation.
bool	operator!= (const complex &a, const dotprecision &b) throw ()
	Implementation of standard negated equality operation.
bool	operator!= (const dotprecision &a, const complex &b) throw ()
	Implementation of standard negated equality operation.
complex	operator* (const complex &, const complex &) throw ()
	Implementation of standard algebraic multiplication operation.
complex	operator* (const complex &, const real &) throw ()
	Implementation of standard algebraic multiplication operation.
complex	operator* (const real &, const complex &) throw ()
	Implementation of standard algebraic multiplication operation.
complex &	operator*= (complex &, const complex &) throw ()
	Implementation of standard algebraic multiplication and allocation operation.
complex &	operator*= (complex &, const real &) throw ()
	Implementation of standard algebraic multiplication and allocation operation.
complex	operator+ (const complex &) throw ()
	Implementation of standard algebraic positive sign operation.
complex	operator+ (const complex &, const complex &) throw ()
	Implementation of standard algebraic addition operation.
complex	operator+ (const complex &, const real &) throw ()
	Implementation of standard algebraic addition operation.
complex	operator+ (const real &, const complex &) throw ()
	Implementation of standard algebraic addition operation.
complex &	operator+= (complex &, const complex &) throw ()
	Implementation of standard algebraic addition and allocation operation.
complex &	operator+= (complex &, const real &) throw ()
	Implementation of standard algebraic addition and allocation operation.
complex	operator- (const complex &) throw ()
	Implementation of standard algebraic negative sign operation.
complex	operator- (const complex &, const complex &) throw ()
	Implementation of standard algebraic subtraction operation.
complex	operator- (const complex &, const real &) throw ()
	Implementation of standard algebraic subtraction operation.
complex	operator- (const real &, const complex &) throw ()
	Implementation of standard algebraic subtraction operation.
complex &	operator-= (complex &, const complex &) throw ()
	Implementation of standard algebraic subtraction and allocation operation.
complex &	operator-= (complex &, const real &) throw ()
	Implementation of standard algebraic subtraction and allocation operation.
complex	operator/ (const complex &, const complex &) throw ()
	Implementation of standard algebraic division operation.
complex	operator/ (const complex &, const real &) throw ()
	Implementation of standard algebraic division operation.
complex	operator/ (const real &, const complex &) throw ()
	Implementation of standard algebraic division operation.
complex &	operator/= (complex &, const complex &) throw ()
	Implementation of standard algebraic division and allocation operation.
complex &	operator/= (complex &, const real &) throw ()
	Implementation of standard algebraic division and allocation operation.
std::ostream &	operator<< (std::ostream &, const complex &) throw ()
	Implementation of standard output method.
std::string &	operator<< (std::string &, const complex &) throw ()
	Implementation of standard output method.
bool	operator== (const complex &a, const complex &b) throw ()
	Implementation of standard equality operation.
bool	operator== (const complex &a, const real &b) throw ()
	Implementation of standard equality operation.
bool	operator== (const real &a, const complex &b) throw ()
	Implementation of standard equality operation.
bool	operator== (const complex &a, const dotprecision &b) throw ()
	Implementation of standard equality operation.
bool	operator== (const dotprecision &a, const complex &b) throw ()
	Implementation of standard equality operation.
std::istream &	operator>> (std::istream &, complex &) throw ()
	Implementation of standard input method.
std::string &	operator>> (std::string &, complex &) throw ()
	Implementation of standard input method.
void	operator>> (const char *, complex &) throw ()
	Implementation of standard input method.
void	operator>> (const std::string &, complex &) throw ()
	Implementation of standard input method.
real &	Re (complex &a)
	Returns the real part of the complex value.
real	Re (const complex &a)
	Returns the real part of the complex value.
complex &	SetIm (complex &a, const real &b)
	Sets the imaginary part of a complex value.
complex &	SetRe (complex &a, const real &b)
	Sets the real part of a complex value.
complex	subdown (const complex &, const complex &) throw ()
	Returns the downward rounded result of the subtraction operation.
complex	subdown (const complex &, const real &) throw ()
	Returns the downward rounded result of the subtraction operation.
complex	subdown (const real &, const complex &) throw ()
	Returns the downward rounded result of the subtraction operation.
complex	subup (const complex &, const complex &) throw ()
	Returns the upward rounded result of the subtraction operation.
complex	subup (const complex &, const real &) throw ()
	Returns the upward rounded result of the subtraction operation.
complex	subup (const real &, const complex &) throw ()
	Returns the upward rounded result of the subtraction operation.

Detailed Description

The Scalar Type complex.

The data type complex is used to store complex numbers $z = x + i y \in C$ , where $ x $ denotes the real part, $ y $ denotes the imaginary part of $ z $ , and $ i $ denotes the imaginary unit $\sqrt{-1}$ .