DComplex

Module:  Essential Math    Group:  DComplex class

Does not inherit

• Local Index
• Synopsis
• Description
• Public Constructors
• Public Member Operators
• Global Operators
• Related Global Functions

Members

DComplex() operator*=()

operator+=() operator-=()

operator/=()

Non-Members

abs() arg() conj() cos() cosh() exp()

imag() log() norm() operator!=() operator>>() operator<<()

operator*() operator+() operator-() operator/() operator==() polar()

pow() real() sin() sinh() sqrt()

#include <rw/dcomplex.h>
DComplex a;

Please note that the Related Global Functions for DComplex are defined at the end of this entry, rather than in Part III.

DComplex()

Unadorned constructor. The real and imaginary parts are initialized to 0.

DComplex(double r);

Constructs a complex number with real part equal to r and imaginary part equal to 0.

DComplex(double r, double i);

Constructs a complex number with real part equal to r and imaginary part equal to i.

void     operator+=(DComplex);
void     operator-=(DComplex);
void     operator*=(DComplex);
void     operator/=(DComplex);

Performs the indicated operation, but the operations are defined for complex numbers. For example,

a += b,

where a and b are complex numbers, implies:

Re(a) replaced by: Re(a) + Re(b);
Im(a) replaced by: Im(a) + Im(b).

DComplex   operator-(DComplex);
DComplex   operator+(DComplex, DComplex);
DComplex   operator-(DComplex, DComplex);
DComplex   operator*(DComplex, DComplex);
DComplex   operator/(DComplex, DComplex);
DComplex   operator+(double, DComplex);
DComplex   operator+(DComplex, double);
DComplex   operator-(double, DComplex);
DComplex   operator-(DComplex, double);
DComplex   operator*(DComplex, double);
DComplex   operator*(double, DComplex);

Performs the indicated operation, but the operations are defined for complex numbers. Note that some of these operators involve type double.

int   operator==(DComplex a, DComplex b);
int   operator!=(DComplex a, DComplex b);

Tests for equality or inequality. For operator== to return 1, both Re(a) == Re(b) and Im(a) == Im(b) must be true. If either expression is false, then operator!= returns 1.

ostream&  operator<<(ostream& s, DComplex a);

Writes a complex number a to ostream s in the form:

( Re(a), Im(a) )

istream&  operator>>(istream& s, DComplex& a);

Reads a complex number from istream s in any of the following forms:

u

( u )

or:

( u, v )

where u is the real part and v is the imaginary part of the number.

double
real(const DComplex& a);
double
imag(const DComplex& a);

Returns the real or imaginary part of a complex number as a double precision number.

double
abs(DComplex);
double
norm(DComplex);

Returns the absolute value or the norm of a complex number as a double precision number: [norm(a) = abs(a)2].

double
arg(DComplex);

Returns the argument in radians of a complex number as a double precision number.

DComplex
conj(DComplex a);

Returns the complex conjugate of a complex number.

DComplex
polar(double r, double t);

For arguments r and t, where complex number a = re^it, returns a complex number in Cartesian form.

DComplex   
cos(DComplex);
DComplex   
cosh(DComplex);
DComplex   
exp(DComplex);
DComplex   
log(DComplex);
DComplex   
pow(double, DComplex);
DComplex   
pow(DComplex, int);
DComplex   
pow(DComplex, double);
DComplex   
pow(DComplex, DComplex);
DComplex   
sin(DComplex);
DComplex   
sinh(DComplex);
DComplex   
sqrt(DComplex);

Analogous to the standard C functions, except that they are defined as complex functions, taking arguments of type DComplex and returning type DComplex. For multivalued functions such as log or sqrt, the principal value is returned. Note that several instances of pow are defined, with different argument types.

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