`package be.tarsos.dsp.util;/** * Complex implements a complex number and defines complexarithmetic and mathematical functionsLast Updated February 27, 2001Copyright 1997-2001@version 1.0@author Andrew G. Bennett * @author joren * */public class Complex {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). <br>(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). <br>(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());}/** 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());}/** Division of Complex numbers (doesn't change this Complex number). <br>(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)private double cosh(double theta) { return (Math.exp(theta)+Math.exp(-theta))/2;}// Real sinh function (used to compute complex trig functions)private double sinh(double theta) { return (Math.exp(theta)-Math.exp(-theta))/2;}/** Sine of this Complex number (doesn't change this Complex number). <br>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). <br>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). <br>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). <br>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). <br>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. <br>-(x+i*y) = -x-i*y. @return -z where z is this Complex number.*/public Complex chs() { return new Complex(-x,-y);}/** 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; } }`