complex.h

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//-------------------------------------------------------------------------
// Complex Numbers
// Revision :   $Rev$
// Last changed : $Date$
//
// Author       : Seungtaik Oh
// Last Update  : 19 JUL 2011
//-------------------------------------------------------------------------
#ifndef COMPLEX_
#define COMPLEX_

#include <iostream>
#include <cmath>

const double PI = 3.141592653589793238462643383279502884197169399375105820974944592308;
const double TWO_PI = 2.0*PI;

class Complex
{
public:
    Complex() : a(0.0), b(0.0) {}
    Complex( double ta, double tb ) : a(ta), b(tb) {}
    Complex( const Complex& p )
    {
        a = p.a;
        b = p.b;
    }
   
    double mag2() const  { return a*a+b*b; }
    double mag()  const  { return sqrt(a*a+b*b); }

    double arg() const
    {
        double r = mag();
        double theta = acos( a/r );

        if( sin(theta)-b/r < 10e-6 )    
            return theta;
        else 
            return 2.0*PI-theta;
    }

    void euler( double& r, double& theta )
    {
        r = mag();
        theta = arg();
    }

    Complex conj() const {    return Complex(a, -b); }

    // arithmetic
    const Complex& operator= (const Complex& p )
    {
        a = p.a;
        b = p.b;

        return *this;
    }

    const Complex& operator+= (const Complex& p )
    {
        a += p.a;
        b += p.b;

        return *this; 
    }

    const Complex& operator-= (const Complex& p)
    {
        a -= p.a;
        b -= p.b;

        return *this;
    }

    const Complex& operator*= (const double k)
    {
        a *= k;
        b *= k;

        return *this;
    }

    const Complex& operator*= (const Complex& p)
    {
        const double ta = a;
        const double tb = b;

        a = ta*p.a-tb*p.b;
        b = ta*p.b+tb*p.a;

        return *this;
    }

    const Complex& operator/= (const double k)
    {
        a /= k;
        b /= k;

        return *this;
    }

    friend const Complex operator+ ( const Complex& p, const Complex& q)
    {
        return Complex(p) += q;
    }

    friend const Complex operator- ( const Complex& p, const Complex& q )
    {
        return Complex(p) -= q;
    }

    friend const Complex operator* ( const double k, const Complex& p )
    {
        return Complex(p) *= k;
    }

    friend const Complex operator* ( const Complex& p, const double k )
    {
        return Complex(p) *= k;
    }

    friend const Complex operator* ( const Complex& p, const Complex& q )
    {
        return Complex( p.a*q.a-p.b*q.b, p.a*q.b+p.b*q.a );
    }

    friend const Complex operator/ ( const Complex& p, const Complex& q )
    {
        return Complex((1.0/q.mag2())*(p*q.conj()));
    }

    // stream
    friend std::ostream& operator << ( std::ostream& os, const Complex& p )
    {
        os << "(" << p.a << ", " << p.b << ")";
        return os;
    }

public:
    double a, b;
};


#endif