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la4j - Linear Algebra for Java

, 14 Nov 2011 CPOL
Elegant and pure Java matrix library
package la4j.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 
 */
public class Complex extends Object{
    
    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;
    }
    
    public boolean equals(Object obj) {
        Complex cn = (Complex)obj;
        if(cn.x == this.x && cn.y == this.y)
            return true;
        else
            return false;
    }
}

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About the Author

Vladimir Kostyukov
Software Developer Intel
Russian Federation Russian Federation
I've received a Master's Degree in Computer Science at the IT Faculty of Altai State Technical University, Russia.
 
Currently, I am Software Engineer at Intel Corporation.
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