C Programming on the IBM PC (C Programmers Reference Guide Series)
|
|
The complex Class
The header <complex> defines the complex class, which represents complex numbers. It also defines a series of functions and operators that operate on objects of type complex.
The template specification for complex is shown here:
template <class T> class complex
Here, T specifies the type used to store the components of a complex number. There are three predefined specializations of complex:
class complex<float> class complex<double> class complex<long double>
The complex class has the following constructors:
complex(const T &real = T( ), const T = &imaginary = T( )); complex(const complex &ob); template <class T1> complex(const complex<T1> &ob);
The first constructs a complex object with a real component of real and an imaginary component of imaginary. These values default to zero if not specified. The second creates a copy of ob. The third creates a complex object from ob.
The following operations are defined for complex objects:
| + | – | * | / |
| – = | += | /= | *= |
| = | == | != |
The nonassignment operators are overloaded three ways: once for operations involving a complex object on the left and a scalar object on the right, again for operations involving a scalar on the left and a complex object on the right, and finally for operations involving two complex objects. For example, the following types of operations are allowed:
complex_ob + scalar scalar + complex_ob complex_ob + complex_ob
Operations involving scalar quantities affect only the real component.
Two member functions are defined for complex: real( ) and imag( ). They are shown here:
T real( ) const; T imag( ) const;
The real( ) function returns the real component of the invoking object and imag( ) returns the imaginary component. The following functions are also defined for complex objects:
| Function | Description |
|---|---|
| template <class T> T abs(const complex<T> &ob); | Returns the absolute value of ob |
| template <class T> T arg(const complex<T> &ob); | Returns the phase angle of ob |
| template <class T> complex<T> conj(const complex<T> &ob); | Returns the conjugate of ob |
| template <class T> complex<T> cos(const complex<T> &ob); | Returns the cosine of ob |
| template <class T> complex<T> cosh(const complex<T> &ob); | Returns the hyperbolic cosine of ob |
| template <class T> complex<T> exp(const complex<T> &ob); | Returns the eob |
| template <class T> T imag(const complex<T> &ob); | Returns the imaginary component of ob |
| template <class T> complex<T> log(const complex<T> &ob); | Returns the natural logarithm of ob |
| template <class T> complex<T> log10(const complex<T> &ob); | Returns the base 10 logarithm of ob |
| template <class T> T norm(const complex<T> &ob); | Returns the magnitude of ob squared |
| template <class T> complex<T> polar(const T &v, const T &theta=0); | Returns a complex number that has the magnitude specified by v and a phase angle of theta |
| template <class T> complex<T> pow(const complex<T> &b, int e); | Returns be |
| template <class T> complex<T> pow(const complex<T> &b, const T &e); | Returns be |
| template <class T> complex<T> pow(const complex<T> &b, const complex<T> &e); | Returns be |
| template <class T> complex<T> pow(const T &b, const complex<T> &e); | Returns be |
| template <class T> T real(const complex<T> &ob); | Returns the real component of ob |
| template <class T> complex<T> sin(const complex<T> &ob); | Returns the sine of ob |
| template <class T> complex<T> sinh(const complex<T> &ob); | Returns the hyperbolic sine of ob |
| template <class T> complex<T> sqrt(const complex<T> &ob); | Returns the square root of ob |
| template <class T> complex<T> tan(const complex<T> &ob); | Returns the tangent of ob |
| template <class T> complex<T> tanh(const complex<T> &ob); | Returns the hyperbolic tangent of ob |
|
|