edu.princeton.cs.algs4.Complex Maven / Gradle / Ivy
/******************************************************************************
* Compilation: javac Complex.java
* Execution: java Complex
* Dependencies: StdOut.java
*
* 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
*
******************************************************************************/
package edu.princeton.cs.algs4;
/**
* The {@code Complex} class represents a complex number.
* Complex numbers are immutable: their values cannot be changed after they
* are created.
* It includes methods for addition, subtraction, multiplication, division,
* conjugation, and other common functions on complex numbers.
*
* For additional documentation, see Section 9.9 of
* Algorithms, 4th Edition by Robert Sedgewick and Kevin Wayne.
*
* @author Robert Sedgewick
* @author Kevin Wayne
*/
public class Complex {
private final double re; // the real part
private final double im; // the imaginary part
/**
* Initializes a complex number from the specified real and imaginary parts.
*
* @param real the real part
* @param imag the imaginary part
*/
public Complex(double real, double imag) {
re = real;
im = imag;
}
/**
* Returns a string representation of this complex number.
*
* @return a string representation of this complex number,
* of the form 34 - 56i.
*/
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";
}
/**
* Returns the absolute value of this complex number.
* This quantity is also known as the modulus or magnitude.
*
* @return the absolute value of this complex number
*/
public double abs() {
return Math.hypot(re, im);
}
/**
* Returns the phase of this complex number.
* This quantity is also known as the angle or argument.
*
* @return the phase of this complex number, a real number between -pi and pi
*/
public double phase() {
return Math.atan2(im, re);
}
/**
* Returns the sum of this complex number and the specified complex number.
*
* @param that the other complex number
* @return the complex number whose value is {@code (this + that)}
*/
public Complex plus(Complex that) {
double real = this.re + that.re;
double imag = this.im + that.im;
return new Complex(real, imag);
}
/**
* Returns the result of subtracting the specified complex number from
* this complex number.
*
* @param that the other complex number
* @return the complex number whose value is {@code (this - that)}
*/
public Complex minus(Complex that) {
double real = this.re - that.re;
double imag = this.im - that.im;
return new Complex(real, imag);
}
/**
* Returns the product of this complex number and the specified complex number.
*
* @param that the other complex number
* @return the complex number whose value is {@code (this * that)}
*/
public Complex times(Complex that) {
double real = this.re * that.re - this.im * that.im;
double imag = this.re * that.im + this.im * that.re;
return new Complex(real, imag);
}
/**
* Returns the product of this complex number and the specified scalar.
*
* @param alpha the scalar
* @return the complex number whose value is {@code (alpha * this)}
*/
public Complex scale(double alpha) {
return new Complex(alpha * re, alpha * im);
}
/**
* Returns the product of this complex number and the specified scalar.
*
* @param alpha the scalar
* @return the complex number whose value is {@code (alpha * this)}
* @deprecated Replaced by {@link #scale(double)}.
*/
@Deprecated
public Complex times(double alpha) {
return new Complex(alpha * re, alpha * im);
}
/**
* Returns the complex conjugate of this complex number.
*
* @return the complex conjugate of this complex number
*/
public Complex conjugate() {
return new Complex(re, -im);
}
/**
* Returns the reciprocal of this complex number.
*
* @return the complex number whose value is {@code (1 / this)}
*/
public Complex reciprocal() {
double scale = re*re + im*im;
return new Complex(re / scale, -im / scale);
}
/**
* Returns the real part of this complex number.
*
* @return the real part of this complex number
*/
public double re() {
return re;
}
/**
* Returns the imaginary part of this complex number.
*
* @return the imaginary part of this complex number
*/
public double im() {
return im;
}
/**
* Returns the result of dividing the specified complex number into
* this complex number.
*
* @param that the other complex number
* @return the complex number whose value is {@code (this / that)}
*/
public Complex divides(Complex that) {
return this.times(that.reciprocal());
}
/**
* Returns the complex exponential of this complex number.
*
* @return the complex exponential of this complex number
*/
public Complex exp() {
return new Complex(Math.exp(re) * Math.cos(im), Math.exp(re) * Math.sin(im));
}
/**
* Returns the complex sine of this complex number.
*
* @return the complex sine of this complex number
*/
public Complex sin() {
return new Complex(Math.sin(re) * Math.cosh(im), Math.cos(re) * Math.sinh(im));
}
/**
* Returns the complex cosine of this complex number.
*
* @return the complex cosine of this complex number
*/
public Complex cos() {
return new Complex(Math.cos(re) * Math.cosh(im), -Math.sin(re) * Math.sinh(im));
}
/**
* Returns the complex tangent of this complex number.
*
* @return the complex tangent of this complex number
*/
public Complex tan() {
return sin().divides(cos());
}
/**
* Unit tests the {@code Complex} data type.
*
* @param args the command-line arguments
*/
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 2002-2018, Robert Sedgewick and Kevin Wayne.
*
* This file is part of algs4.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.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.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.jar. If not, see http://www.gnu.org/licenses.
******************************************************************************/