/******************************************************************************
 * This program demonstrates the Complex Number class.
 * 
 * Copyright © 2021 Richard Lesh.  All rights reserved.
 *****************************************************************************/

import org.pureprogrammer.Utils;

public class ComplexNumberClass {

    static class Complex {
// Internal representation for a complex number is two doubles
        private double real = 0.0;
        private double imaginary = 0.0;

// Constructor
        public Complex(double r, double i) {
            real = r;
            imaginary = i;
        }

        public Complex add(final Complex x) {
            return new Complex(real + x.real, imaginary + x.imaginary);
        }

        public Complex sub(final Complex x) {
            return new Complex(real - x.real, imaginary - x.imaginary);
        }

        public Complex mul(final Complex x) {
            return new Complex(real * x.real - imaginary * x.imaginary, real * x.imaginary + imaginary * x.real);
        }

        public Complex recip() {
            final double MAG_SQUARED = real * real + imaginary * imaginary;
            return new Complex(real / MAG_SQUARED, -imaginary / MAG_SQUARED);
        }

        public Complex div(final Complex x) {
            return this.mul(x.recip());
        }

        public double abs() {
            final double MAG_SQUARED = real * real + imaginary * imaginary;
            return Math.sqrt(MAG_SQUARED);
        }

        public double phase() {
            final double MAGNITUDE = this.abs();
            if (real < 0. && imaginary == 0.) {
                return Math.PI;
            }
            return 2. * Math.atan(imaginary / (MAGNITUDE + real));
        }

        public Complex csqrt() {
            final double MAG = this.abs();
            final double r = Math.sqrt((real + MAG) / 2.);
            double i = Math.sqrt((-real + MAG) / 2.);
            i *= ((imaginary > 0) ? 1 : ((imaginary < 0) ? -1 : 0));
            return new Complex(r, i);
        }

        public Complex cexp() {
            final double MAG = Math.exp(real);
            return new Complex(MAG * Math.cos(imaginary), MAG * Math.sin(imaginary));
        }

        public Complex clog() {
            final double MAG = this.abs();
            return new Complex(Math.log(MAG), phase());
        }

        public String toString() {
            if (real == 0.0) {
                return Utils.join("", String.valueOf(imaginary), "i");
            } else if (imaginary == 0.0) {
                return String.valueOf(real);
            } else if (imaginary < 0) {
                return Utils.join("", String.valueOf(real), String.valueOf(imaginary), "i");
            } else {
                return Utils.join("", String.valueOf(real), "+", String.valueOf(imaginary), "i");
            }
        }
    }

    public static void main(String[] args) {
        Complex a = new Complex(1., 1.);
        Complex b = new Complex(3., 4.);
        System.out.println(Utils.join("", "a: ", a.toString()));
        System.out.println(Utils.join("", "b: ", b.toString()));
        System.out.println(Utils.join("", "a + b: ", a.add(b).toString()));
        System.out.println(Utils.join("", "a - b: ", a.sub(b).toString()));
        System.out.println(Utils.join("", "a * b: ", a.mul(b).toString()));
        System.out.println(Utils.join("", "1 / a: ", a.recip().toString()));
        System.out.println(Utils.join("", "1 / b: ", b.recip().toString()));
        System.out.println(Utils.join("", "a / b: ", a.div(b).toString()));
        System.out.println(Utils.join("", "|a|: ", a.abs()));
        System.out.println(Utils.join("", "|b|: ", b.abs()));
        System.out.println(Utils.join("", "φ(a): ", a.phase()));
        System.out.println(Utils.join("", "φ(b): ", b.phase()));
        System.out.println(Utils.join("", "sqrt(a): ", a.csqrt().toString()));
        System.out.println(Utils.join("", "sqrt(b): ", b.csqrt().toString()));
        System.out.println(Utils.join("", "exp(a): ", a.cexp().toString()));
        System.out.println(Utils.join("", "exp(b): ", b.cexp().toString()));
        System.out.println(Utils.join("", "ln(a): ", a.clog().toString()));
        System.out.println(Utils.join("", "ln(b): ", b.clog().toString()));
    }
}