package jhplot.math;

import java.io.Serializable;
import java.lang.Math;

/**
 * Complex implements a complex number and defines complex arithmetic and
 * mathematical functions Last Updated February 27, 2001 Copyright 1997-2001
 * 
 * @version 1.0
 * @author Andrew G. Bennett, S.Chekanov
 */
public class Complex extends Object implements Cloneable, Serializable {

	/**
	 * 
	 */
	private static final long serialVersionUID = 1L;
	private double x, y;


	
	/**
	 * Constructs the complex number z = u + i*v
	 * 
	 * @param u
	 *            Real part
	 * @param v
	 *            Imaginary part
	 */
	public Complex(double u, double v) {
		x = u;
		y = v;
	}

	/**
	 * Real part of this Complex number (the x-coordinate in rectangular
	 * coordinates).
	 * 
	 * @return Re[z] where z is this Complex number.
	 */
	public double real() {
		return x;
	}

	/**
	 * Imaginary part of this Complex number (the y-coordinate in rectangular
	 * coordinates).
	 * 
	 * @return Im[z] where z is this Complex number.
	 */
	public double imag() {
		return y;
	}

	/**
	 * Modulus of this Complex number (the distance from the origin in polar
	 * coordinates).
	 * 
	 * @return |z| where z is this Complex number.
	 */
	public double mod() {
		if (x != 0 || y != 0) {
			return Math.sqrt(x * x + y * y);
		} else {
			return 0d;
		}
	}

	/**
	 * Argument of this Complex number (the angle in radians with the x-axis in
	 * polar coordinates).
	 * 
	 * @return arg(z) where z is this Complex number.
	 */
	public double arg() {
		return Math.atan2(y, x);
	}

	/**
	 * Complex conjugate of this Complex number (the conjugate of x+i*y is
	 * x-i*y).
	 * 
	 * @return z-bar where z is this Complex number.
	 */
	public Complex conj() {
		return new Complex(x, -y);
	}

	/**
	 * Addition of Complex numbers (doesn't change this Complex number). 

	 * (x+i*y) + (s+i*t) = (x+s)+i*(y+t).
	 * 
	 * @param w
	 *            is the number to add.
	 * @return z+w where z is this Complex number.
	 */
	public Complex plus(Complex w) {
		return new Complex(x + w.real(), y + w.imag());
	}

	/**
	 * Subtraction of Complex numbers (doesn't change this Complex number). 

	 * (x+i*y) - (s+i*t) = (x-s)+i*(y-t).
	 * 
	 * @param w
	 *            is the number to subtract.
	 * @return z-w where z is this Complex number.
	 */
	public Complex minus(Complex w) {
		return new Complex(x - w.real(), y - w.imag());
	}


	/**
	 * Subtraction from real part
	 * 
	 * @param w real value for subtraction
	 */
	public Complex minusReal(double w) {
		return new Complex(x - w, y);
	}
	
	
	
	
	/**
	 * Complex multiplication (doesn't change this Complex number).
	 * 
	 * @param w
	 *            is the number to multiply by.
	 * @return z*w where z is this Complex number.
	 */
	public Complex times(Complex w) {
		return new Complex(x * w.real() - y * w.imag(), x * w.imag() + y
				* w.real());
	}

	 /**
     * Returns this complex multiplied by the specified factor.
     *
     * @param  k the factor multiplier.
     * @return this * k.
     */
    public Complex times(double k) {
        this.x = x * k;
        this.y = y * k;
        return this;
    }

    /**
     * Returns this complex divided by the specified factor.
     *
     * @param  k the factor divisor.
     * @return this / k.
     */
    public Complex divide(double k) {
        this.x = x / k;
        this.y = y / k;
        return this;
    }

	
	/**
	 * Division of Complex numbers (doesn't change this Complex number). 

	 * (x+i*y)/(s+i*t) = ((x*s+y*t) + i*(y*s-y*t)) / (s^2+t^2)
	 * 
	 * @param w
	 *            is the number to divide by
	 * @return new Complex number z/w where z is this Complex number
	 */
	public Complex div(Complex w) {
		double den = Math.pow(w.mod(), 2);
		return new Complex((x * w.real() + y * w.imag()) / den,
				(y * w.real() - x * w.imag()) / den);
	}

	/**
	 * Complex exponential (doesn't change this Complex number).
	 * 
	 * @return exp(z) where z is this Complex number.
	 */
	public Complex exp() {
		return new Complex(Math.exp(x) * Math.cos(y), Math.exp(x) * Math.sin(y));
	}

	/**
	 * Principal branch of the Complex logarithm of this Complex number.
	 * (doesn't change this Complex number). The principal branch is the branch
	 * with -pi < arg <= pi.
	 * 
	 * @return log(z) where z is this Complex number.
	 */
	public Complex log() {
		return new Complex(Math.log(this.mod()), this.arg());
	}

	/**
	 * Complex square root (doesn't change this complex number). Computes the
	 * principal branch of the square root, which is the value with 0 <= arg <
	 * pi.
	 * 
	 * @return sqrt(z) where z is this Complex number.
	 */
	public Complex sqrt() {
		double r = Math.sqrt(this.mod());
		double theta = this.arg() / 2;
		return new Complex(r * Math.cos(theta), r * Math.sin(theta));
	}

	
	
	
	/**
	 * Real cosh function (used to compute complex trig functions)
	 * @param theta
	 */
	
	private double cosh(double theta) {
		return (Math.exp(theta) + Math.exp(-theta)) / 2;
	}

	
	
	/**
	 * Real sinh function (used to compute complex trig functions)
	 * @param theta
	 */
	private double sinh(double theta) {
		return (Math.exp(theta) - Math.exp(-theta)) / 2;
	}

	/**
	 * Sine of this Complex number (doesn't change this Complex number). 

	 * sin(z) = (exp(i*z)-exp(-i*z))/(2*i).
	 * 
	 * @return sin(z) where z is this Complex number.
	 */
	public Complex sin() {
		return new Complex(cosh(y) * Math.sin(x), sinh(y) * Math.cos(x));
	}

	/**
	 * Cosine of this Complex number (doesn't change this Complex number). 

	 * cos(z) = (exp(i*z)+exp(-i*z))/ 2.
	 * 
	 * @return cos(z) where z is this Complex number.
	 */
	public Complex cos() {
		return new Complex(cosh(y) * Math.cos(x), -sinh(y) * Math.sin(x));
	}

	/**
	 * Hyperbolic sine of this Complex number (doesn't change this Complex
	 * number). 

	 * sinh(z) = (exp(z)-exp(-z))/2.
	 * 
	 * @return sinh(z) where z is this Complex number.
	 */
	public Complex sinh() {
		return new Complex(sinh(x) * Math.cos(y), cosh(x) * Math.sin(y));
	}

	/**
	 * Hyperbolic cosine of this Complex number (doesn't change this Complex
	 * number). 

	 * cosh(z) = (exp(z) + exp(-z)) / 2.
	 * 
	 * @return cosh(z) where z is this Complex number.
	 */
	public Complex cosh() {
		return new Complex(cosh(x) * Math.cos(y), sinh(x) * Math.sin(y));
	}

	/**
	 * Tangent of this Complex number (doesn't change this Complex number). 

	 * tan(z) = sin(z)/cos(z).
	 * 
	 * @return tan(z) where z is this Complex number.
	 */
	public Complex tan() {
		return (this.sin()).div(this.cos());
	}

	/**
	 * Negative of this complex number (chs stands for change sign). This
	 * produces a new Complex number and doesn't change this Complex number. 

	 * -(x+i*y) = -x-i*y.
	 * 
	 * @return -z where z is this Complex number.
	 */
	public Complex chs() {
		return new Complex(-x, -y);
	}

	public Object clone() {
		try {
			return super.clone();
		} catch (CloneNotSupportedException e) {
			throw new InternalError(e.toString());
		}
	}

	/**
	 * String representation of this Complex number.
	 * 
	 * @return x+i*y, x-i*y, x, or i*y as appropriate.
	 */
	public String toString() {
		if (x != 0 && y > 0) {
			return x + " + " + y + "i";
		}
		if (x != 0 && y < 0) {
			return x + " - " + (-y) + "i";
		}
		if (y == 0) {
			return String.valueOf(x);
		}
		if (x == 0) {
			return y + "i";
		}
		// shouldn't get here (unless Inf or NaN)
		return x + " + i*" + y;

	}
}