plectrum

Complex.java (6016B)

---

 package be.tarsos.dsp.util;
 
 
 
 /**
  * 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
  * @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;
     
 }       
 }