/*  ComplexDemo.java
 *  M.Lampton uCB SSL 2009, 2015
 *  Demonstrates a simple internal Complex class
 */


public class ComplexDemo
{
    // Exercise methods in Complex class and its Utilities, defined below

    public static void main ( String args[] ) 
    {

        System.out.println("\nComplex number demo");

        // Set up two complex numbers .....

        Complex cA = new Complex( 1.0, 2.0 );
        Complex cB = new Complex( 3.0, 4.0 );

        System.out.println("Complex number cA = " + cA.toString() );
        System.out.println("Complex number cB = " + cB.toString() );

        // demonstrate results

        Complex cC = C.cAdd(cA, cB); 
        System.out.println("Sum = "+ cC.toString()); 
      
        Complex cD = C.cSub(cA, cB); 
        System.out.println("Diff= "+ cD.toString()); 
      
        Complex cE = C.cMul(cA, cB); 
        System.out.println("Mul = "+ cE.toString()); 
      
        Complex cF = C.cDiv(cA, cB); 
        System.out.println("Div = "+ cF.toString()); 
        
        Complex cG = C.cMul(cF, cB); 
        System.out.println("Mul = "+ cG.toString()); 
      
        double d = C.dAbs(cB); 
        System.out.println("Abs = " + d); 
      
        Complex cH = C.cConj(cA); 
        System.out.println("Conj= " + cH.toString());
      
        Complex cI = C.cSqrt(cA); 
        System.out.println("Sqrt= "+ cI.toString()); 
      
        Complex cJ = C.cMul(cI, cI); 
        System.out.println("S*S = " + cJ.toString()); 
      
        Complex cK = C.cExp(cA); 
        System.out.println("Exp = "+ cK.toString()); 
      
        Complex cL = C.cLog(cK); 
        System.out.println("Log = "+ cL.toString()); 
        
        Complex cM = C.cExp(C.cAdd(C.cLog(cA), C.cLog(cB))); 
        System.out.println("Mul the hard way = "+cM.toString()); 
        
        Complex cN = C.cExp(C.cScale(C.cLog(cA), 0.5)); 
        System.out.println("Sqrt the hard way = "+cN.toString());
        
        // demonstrate accessibility of internal parts
      
        cA.i = 133.0;
        System.out.println("cA imaginary part is changed to 133: "+ cA.toString()); 
    }
}


class Complex // defines a complex number
{
    protected double r, i;   // allows co-classes to access contents

    public Complex( double gr, double gi ) // constructor
    {
       r = gr;
       i = gi;
    }

    public String toString()     // method that classes usually offer
    {
        String s = (i>=0) ? "+" : "";
        return r + s + i + "i";
    }
}    
    

class C   // static utilities for complex arithmetic
{
    public static double dAbs(Complex c)
    {
        return Math.sqrt(c.r*c.r + c.i*c.i);
    }
    
    public static Complex cScale(Complex c, double s)
    {
        return new Complex(s*c.r, s*c.i); 
    }

    public static Complex cNeg(Complex c) 
    {
        return new Complex(-c.r, -c.i);
    }
    
    public static Complex cConj(Complex c)
    {
        return new Complex(c.r, -c.i); 
    }

    public static Complex cAdd(Complex cA,  Complex cB) 
    {
        return new Complex(cA.r+cB.r, cA.i+cB.i);
    }

    public static Complex cSub(Complex cA,  Complex cB) 
    {
        return new Complex(cA.r-cB.r, cA.i-cB.i);
    }

    public static Complex cMul(Complex cA,  Complex cB) 
    {
        return new Complex(cA.r*cB.r - cA.i*cB.i, 
                           cA.i*cB.r + cA.r*cB.i);
    }
    
    public static Complex cDiv(Complex a,  Complex b) 
    {
        double numr = a.r*b.r + a.i*b.i; 
        double numi = a.i*b.r - a.r*b.i; 
        double denom = b.r*b.r + b.i*b.i; 
        return new Complex(numr/denom, numi/denom);
    }
        
    public static Complex cSqrt(Complex c)
    {
        double abs = dAbs(c); 
        double rootr = Math.sqrt(abs + c.r);
        double rooti = Math.sqrt(abs - c.r); 
        double sign = (c.i < 0) ? -1.0 : 1.0; 
        double coef = Math.sqrt(0.5); 
        return new Complex(coef*rootr, coef*sign*rooti); 
    }
     
    public static Complex cCirc(double t)
    {
        return new Complex(Math.cos(t), Math.sin(t));
    }
     
    public static Complex cExp(Complex c)
    {
        double coef = Math.exp(c.r); 
        return new Complex(coef*Math.cos(c.i), coef*Math.sin(c.i)); 
    }
    
    public static Complex cLog(Complex c)
    {
        return new Complex(Math.log(dAbs(c)), Math.atan2(c.i, c.r)); 
    }
}