complex (3C++std) - Tru64 UNIX
Standard C++ LibraryCopyright 1996, Rogue Wave Software, Inc.
NAME
complex - C++ complex number library
This page describes ANSI complex class. If you would like information on
the pre-ANSI complex package, use the command:
man 3C++ complex or man complex.3C++
SPECIALIZATIONS
complex <float>
complex <double>
complex <long double>
SYNOPSIS
#include <complex>
template <class T>
class complex ;
class complex<float>;
class complex<double>;
class complex<long double>;
DESCRIPTION
complex<T> is a class that supports complex numbers. A complex number has a
real part and an imaginary part. The complex class supports equality,
comparison and basic arithmetic operations. In addition, mathematical
functions such as exponents, logarithms, powers, and square roots are also
available.
INTERFACE
template <class T>
class complex {
public:
typedef T value_type;
complex (T = 0 , T = 0);
template <class X> complex
(const complex<X>&);
T real () const;
T imag () const;
complex<T>& operator= (const T&);
complex<T>& operator+=(const T&);
complex<T>& operator-=(const T&);
complex<T>& operator*=(const T&);
complex<T>& operator/=(const T&);
template <class X>
complex<T>& operator= (const complex<X>&);
template <class X>
complex<T>& operator+= (const complex<X>&);
template <class X>
complex<T>& operator-= (const complex<X>&);
template <class X>
complex<T>& operator*= (const complex<X>&);
template <class X>
complex<T>& operator/= (const complex<X>&);
};
// Non-member Operators
template<class T>
complex<T> operator+ (const complex<T>&, const complex<T>&);
template<class T>
complex<T> operator+ (const complex<T>&, T);
template<class T>
complex<T> operator+ (T, const complex<T>&);
template<class T>
complex<T> operator- (const complex<T>&, const complex<T>&);
template<class T>
complex<T> operator- (const complex<T>&, T);
template<classT>
complex<T> operator- (T, const complex<T>&);
template<class T>
complex<T> operator* (const complex<T>&, const complex<T>&);
template<class T>
complex<T> operator* (const complex<T>&, T);
template<class T>
complex<T> operator* (T, const complex<T>&);
template<class T>
complex<T> operator/ (const complex<T>&, const complex<T>&);
template<class T>
complex<T> operator/ (const complex<T>&, T);
template<class T>
complex<T> operator/ (T, const complex<T>&);
template<class T>
complex<T> operator+ (const complex<T>&);
template<class T>
complex<T> operator- (const complex<T>&);
template<class T>
bool operator== (const complex<T>&, const complex<T>&);
template<class T>
bool operator== (const complex<T>&, T);
template<class T>
bool operator== (T, const complex<T>&);
template<class T>
bool operator!= (const complex<T>&, const complex<T>&);
template<class T>
bool operator!= (const complex<T>&, T);
template<class T>
bool operator!= (T, const complex<T>&);
template <class X>
istream& operator>> (istream&, complex<X>&);
template <class X>
ostream& operator<< (ostream&, const complex<X>&);
// Values
template<class T> T real (const complex<T>&);
template<class T> T imag (const complex<T>&);
template<class T> T abs (const complex<T>&);
template<class T> T arg (const complex<T>&);
template<class T> T norm (const complex<T>&);
template<class T> complex<T> conj (const complex<T>&);
template<class T> complex<T> polar (T, T);
// Transcendentals
template<class T> complex<T> cos (const complex<T>&);
template<class T> complex<T> cosh (const complex<T>&);
template<class T> complex<T> exp (const complex<T>&);
template<class T> complex<T> log (const complex<T>&);
template<class T> complex<T> log10 (const complex<T>&);
template<class T> complex<T> pow (const complex<T>&, int);
template<class T> complex<T> pow (const complex<T>&, T);
template<class T> complex<T> pow (const complex<T>&,
const complex<T>&);
template<class T> complex<T> pow (T, const complex<T>&);
template<class T> complex<T> sin (const complex<T>&);
template<class T> complex<T> sinh (const complex<T>&);
template<class T> complex<T> sqrt (const complex<T>&);
template<class T> complex<T> tan (const complex<T>&);
template<class T> complex<T> tanh (const complex<T>&);
CONSTRUCTORS
complex
(const T& re_arg = 0, const T& im_arg = 0);
Constructs an object of class complex, initializing re_arg to the real
part and im_arg to the imaginary part.
ASSIGNMENT OPERATORS
template <class X> complex
(const complex<X>&);
Copy constructor. Constructs a complex number from another complex
number.
complex<T>& operator=(const T& v);
Assigns v to the real part of itself, setting the imaginary part to 0.
complex<T>& operator+=(const T& v);
Adds v to the real part of itself, then returns the result.
complex<T>& operator-=(const T& v);
Subtracts v from the real part of itself, then returns the result.
complex<T>& operator*=(const T& v);
Multiplies v by the real part of itself, then returns the result.
complex<T>& operator/=(const T& v);
Divides v by the real part of itself, then returns the result.
template <class X>
complex<T>
operator=(const complex<X>& c);
Assigns c to itself.
template <class X>
complex<T>
operator+=(const complex<X>& c);
Adds c to itself, then returns the result.
template <class X>
complex<T>
operator-=(const complex<X>& c);
Subtracts c from itself, then returns the result.
template <class X>
complex<T>
operator*=(const complex<X>& c);
Multiplies itself by c then returns the result.
template <class X>
complex<T>
operator/=(const complex<X>& c);
Divides itself by c, then returns the result.
MEMBER FUNCTIONS
T
imag() const;
Returns the imaginary part of the complex number.
T
real() const;
Returns the real part of the complex number.
NON-MEMBER OPERATORS
template<class T> complex<T>
operator+(const complex<T>& lhs,const complex<T>& rhs);
template<class T> complex<T>
operator+(const complex<T>& lhs, T rhs);
template<class T> complex<T>
operator+(T lhs, const complex<T>& rhs);
Returns the sum of lhs and rhs.
template<class T> complex<T>
operator-(const complex<T>& lhs,const complex<T>& rhs);
template<class T> complex<T>
operator-(const complex<T>& lhs, T rhs);
operator-(T lhs, const complex<T>& rhs);
Returns the difference of lhs and rhs.
template<class T> complex<T>
operator*(const complex<T>& lhs,const complex<T>& rhs);
template<class T> complex<T>
operator*(const complex<T>& lhs, T rhs);
template<class T> complex<T>
operator* (T lhs, const complex<T>& rhs);
Returns the product of lhs and rhs.
template<class T> complex<T>
operator/(const complex<T>& lhs,const complex<T>& rhs);
template<class T> complex<T>
operator/(const complex<T>& lhs, T rhs);
template<class T> complex<T>
operator/(T lhs, const complex<T>& rhs);
Returns the quotient of lhs divided by rhs.
template<class T> complex<T>
operator+(const complex<T>& rhs);
Returns rhs.
template<class T> complex<T>
operator-(const complex<T>& lhs);
Returns complex<T>(-lhs.real(), -lhs.imag()).
template<class T> bool
operator==(const complex<T>& x, const complex<T>& y);
Returns true if the real and imaginary parts of x and y are equal.
template<class T> bool
operator==(const complex<T>& x, T y);
Returns true if y is equal to the real part of x and the imaginary part
of x is equal to 0.
template<class T> bool
operator==(T x, const complex<T>& y);
Returns true if x is equal to the real part of y and the imaginary part
of y is equal to 0.
template<class T> bool
operator!=(const complex<T>& x, const complex<T>& y);
Returns true if either the real or the imaginary part of x and y are not
equal.
template<class T> bool
operator!=(const complex<T>& x, T y);
Returns true if y is not equal to the real part of x or the imaginary
part of x is not equal to 0.
template<class T> bool
operator!=(T x, const complex<T>& y);
Returns true if x is not equal to the real part of y or the imaginary
part of y is not equal to 0.
template <class X> istream&
operator>>(istream& is, complex<X>& x);
Reads a complex number x into the input stream is. x may be of the form
u, (u), or (u,v) where u is the real part and v is the imaginary part.
If bad input is encountered, the ios::badbit flag is set.
template <class X> ostream&
operator<<(ostream& os, const complex<X>& x);
Returns os << "(" << x.real() << "," << x.imag() << ")".
NON-MEMBER FUNCTIONS
template<class T> T
abs(const complex<T>& c);
Returns the absolute value or magnitude of c (the square root of the
norm).
template<class T> complex<T>
conj(const complex<T>& c);
Returns the conjugate of c.
template<class T> complex<T>
cos(const complex<T>& c);
Returns the cosine of c.
template<class T> complex<T>
cosh(const complex<T>& c);
Returns the hyperbolic cosine of c.
template<class T> complex<T>
exp(const complex<T>& x);
Returns e raised to the x power.
template<class T> T
imag(const complex<T>& c) const;
Returns the imaginary part of c.
template<class T> complex<T>
log(const complex<T>& x);
Returns the natural logarithm of x. This function returns the complex
value whose phase angle is greater than -pi and less than pi.
template<class T> complex<T>
log10(const complex<T>& x);
Returns the logarithm base 10 of x.
template<class T> T
norm(const complex<T>& c);
Returns the squared magnitude of c. (The sum of the squares of the real
and imaginary parts.)
template<class T> complex<T>
polar(const T& m, const T& a);
Returns the complex value of a complex number whose magnitude is m and
phase angle is a, measured in radians.
template<class T> complex<T>
pow(const complex<T>& x, int y);
template<class T> complex<T>
pow(const complex<T>& x, T y);
template<class T> complex<T>
pow(const complex<T>& x, const complex<T>& y);
template<class T> complex<T>
pow(T x, const complex<T>& y);
Returns x raised to the y power.
template<class T> T
real(const complex<T>& c);
Returns the real part of c.
template<class T> complex<T>
sin(const complex<T>& c);
Returns the sine of c.
template<class T> complex<T>
sinh(const complex<T>& c);
Returns the hyperbolic sine of c.
template<class T> complex<T>
sqrt(const complex<T>& x);
Returns the square root of x. This function returns the complex value
whose phase angle is greater than -pi/2 and less than or equal to
template<class T> complex<T>
tan(const complex<T>& x);
Returns the tangent of x.
template<class T> complex<T>
tanh(const complex<T>& x);
Returns the hyperbolic tangent of x.
EXAMPLE
//
// complex.cpp
//
#include <complex>
#include <iostream.h>
int main()
{
complex<double> a(1.2, 3.4);
complex<double> b(-9.8, -7.6);
a += b;
a /= sin(b) * cos(a);
b *= log(a) + pow(b, a);
cout << "a = " << a << ", b = " << b << endl;
return 0;
}
Output :
a = (1.42804e-06,-0.0002873), b = (58.2199,69.7354)
WARNINGS
On compilers that don't support member function templates, the arithmetic
operators will not work on any arbitrary type. (They will work only on
float, double and long doubles.) You also will only be able to perform
binary arithmetic on types that are the same.
Compilers that don't support non-converting constructors will permit unsafe
downcasts (i.e., long double to double, double to float, long double to
float).
STANDARDS CONFORMANCE
ANSI X3J16/ISO WG21 Joint C++ Committee
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