package edu.princeton.cs.algs4.ch60;
import edu.princeton.cs.introcs.*;
/*************************************************************************
* Compilation: javac Complex.java
* Execution: java Complex
*
* Data type for complex numbers.
*
* The data type is "immutable" so once you create and initialize
* a Complex object, you cannot change it. The "final" keyword
* when declaring re and im enforces this rule, making it a
* compile-time error to change the .re or .im fields after
* they've been initialized.
*
* % java Complex
* a = 5.0 + 6.0i
* b = -3.0 + 4.0i
* Re(a) = 5.0
* Im(a) = 6.0
* b + a = 2.0 + 10.0i
* a - b = 8.0 + 2.0i
* a * b = -39.0 + 2.0i
* b * a = -39.0 + 2.0i
* a / b = 0.36 - 1.52i
* (a / b) * b = 5.0 + 6.0i
* conj(a) = 5.0 - 6.0i
* |a| = 7.810249675906654
* tan(a) = -6.685231390246571E-6 + 1.0000103108981198i
*
*************************************************************************/
public class Complex {
private final double re; // the real part
private final double im; // the imaginary part
// create a new object with the given real and imaginary parts
public Complex(double real, double imag) {
re = real;
im = imag;
}
// return a string representation of the invoking Complex object
public String toString() {
if (im == 0) return re + "";
if (re == 0) return im + "i";
if (im < 0) return re + " - " + (-im) + "i";
return re + " + " + im + "i";
}
// return abs/modulus/magnitude and angle/phase/argument
public double abs() { return Math.hypot(re, im); } // Math.sqrt(re*re + im*im)
public double phase() { return Math.atan2(im, re); } // between -pi and pi
// return a new Complex object whose value is (this + b)
public Complex plus(Complex b) {
Complex a = this; // invoking object
double real = a.re + b.re;
double imag = a.im + b.im;
return new Complex(real, imag);
}
// return a new Complex object whose value is (this - b)
public Complex minus(Complex b) {
Complex a = this;
double real = a.re - b.re;
double imag = a.im - b.im;
return new Complex(real, imag);
}
// return a new Complex object whose value is (this * b)
public Complex times(Complex b) {
Complex a = this;
double real = a.re * b.re - a.im * b.im;
double imag = a.re * b.im + a.im * b.re;
return new Complex(real, imag);
}
// scalar multiplication
// return a new object whose value is (this * alpha)
public Complex times(double alpha) {
return new Complex(alpha * re, alpha * im);
}
// return a new Complex object whose value is the conjugate of this
public Complex conjugate() { return new Complex(re, -im); }
// return a new Complex object whose value is the reciprocal of this
public Complex reciprocal() {
double scale = re*re + im*im;
return new Complex(re / scale, -im / scale);
}
// return the real or imaginary part
public double re() { return re; }
public double im() { return im; }
// return a / b
public Complex divides(Complex b) {
Complex a = this;
return a.times(b.reciprocal());
}
// return a new Complex object whose value is the complex exponential of this
public Complex exp() {
return new Complex(Math.exp(re) * Math.cos(im), Math.exp(re) * Math.sin(im));
}
// return a new Complex object whose value is the complex sine of this
public Complex sin() {
return new Complex(Math.sin(re) * Math.cosh(im), Math.cos(re) * Math.sinh(im));
}
// return a new Complex object whose value is the complex cosine of this
public Complex cos() {
return new Complex(Math.cos(re) * Math.cosh(im), -Math.sin(re) * Math.sinh(im));
}
// return a new Complex object whose value is the complex tangent of this
public Complex tan() {
return sin().divides(cos());
}
// a static version of plus
public static Complex plus(Complex a, Complex b) {
double real = a.re + b.re;
double imag = a.im + b.im;
Complex sum = new Complex(real, imag);
return sum;
}
// sample client for testing
public static void main(String[] args) {
Complex a = new Complex(5.0, 6.0);
Complex b = new Complex(-3.0, 4.0);
StdOut.println("a = " + a);
StdOut.println("b = " + b);
StdOut.println("Re(a) = " + a.re());
StdOut.println("Im(a) = " + a.im());
StdOut.println("b + a = " + b.plus(a));
StdOut.println("a - b = " + a.minus(b));
StdOut.println("a * b = " + a.times(b));
StdOut.println("b * a = " + b.times(a));
StdOut.println("a / b = " + a.divides(b));
StdOut.println("(a / b) * b = " + a.divides(b).times(b));
StdOut.println("conj(a) = " + a.conjugate());
StdOut.println("|a| = " + a.abs());
StdOut.println("tan(a) = " + a.tan());
}
}
/*************************************************************************
* Copyright 2002-2012, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4-package.jar, which accompanies the textbook
*
* Algorithms, 4th edition by Robert Sedgewick and Kevin Wayne,
* Addison-Wesley Professional, 2011, ISBN 0-321-57351-X.
* http://algs4.cs.princeton.edu
*
*
* algs4-package.jar is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* algs4-package.jar is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
* You should have received a copy of the GNU General Public License
* along with algs4-package.jar. If not, see http://www.gnu.org/licenses.
*************************************************************************/