001package algs12;
002import stdlib.*;
003/* ***********************************************************************
004 *  Compilation:  javac Complex.java
005 *  Execution:    java Complex
006 *
007 *  Data type for complex numbers.
008 *
009 *  The data type is "immutable" so once you create and initialize
010 *  a Complex object, you cannot change it. The "final" keyword
011 *  when declaring re and im enforces this rule, making it a
012 *  compile-time error to change the .re or .im fields after
013 *  they've been initialized.
014 *
015 *  % java Complex
016 *  a            = 5.0 + 6.0i
017 *  b            = -3.0 + 4.0i
018 *  Re(a)        = 5.0
019 *  Im(a)        = 6.0
020 *  b + a        = 2.0 + 10.0i
021 *  a - b        = 8.0 + 2.0i
022 *  a * b        = -39.0 + 2.0i
023 *  b * a        = -39.0 + 2.0i
024 *  a / b        = 0.36 - 1.52i
025 *  (a / b) * b  = 5.0 + 6.0i
026 *  conj(a)      = 5.0 - 6.0i
027 *  |a|          = 7.810249675906654
028 *  tan(a)       = -6.685231390246571E-6 + 1.0000103108981198i
029 *
030 *************************************************************************/
031
032public class Complex {
033        private final double re;   // the real part
034        private final double im;   // the imaginary part
035
036        // create a new object with the given real and imaginary parts
037        public Complex(double real, double imag) {
038                re = real;
039                im = imag;
040        }
041
042        // return a string representation of the invoking Complex object
043        public String toString() {
044                if (im == 0) return re + "";
045                if (re == 0) return im + "i";
046                if (im <  0) return re + " - " + (-im) + "i";
047                return re + " + " + im + "i";
048        }
049
050        // return abs/modulus/magnitude and angle/phase/argument
051        public double abs()   { return Math.hypot(re, im); }  // Math.sqrt(re*re + im*im)
052        public double phase() { return Math.atan2(im, re); }  // between -pi and pi
053
054        // return a new Complex object whose value is (this + b)
055        public Complex plus(Complex b) {
056                Complex a = this;             // invoking object
057                double real = a.re + b.re;
058                double imag = a.im + b.im;
059                return new Complex(real, imag);
060        }
061
062        // return a new Complex object whose value is (this - b)
063        public Complex minus(Complex b) {
064                Complex a = this;
065                double real = a.re - b.re;
066                double imag = a.im - b.im;
067                return new Complex(real, imag);
068        }
069
070        // return a new Complex object whose value is (this * b)
071        public Complex times(Complex b) {
072                Complex a = this;
073                double real = a.re * b.re - a.im * b.im;
074                double imag = a.re * b.im + a.im * b.re;
075                return new Complex(real, imag);
076        }
077
078        // scalar multiplication
079        // return a new object whose value is (this * alpha)
080        public Complex times(double alpha) {
081                return new Complex(alpha * re, alpha * im);
082        }
083
084        // return a new Complex object whose value is the conjugate of this
085        public Complex conjugate() {  return new Complex(re, -im); }
086
087        // return a new Complex object whose value is the reciprocal of this
088        public Complex reciprocal() {
089                double scale = re*re + im*im;
090                return new Complex(re / scale, -im / scale);
091        }
092
093        // return the real or imaginary part
094        public double re() { return re; }
095        public double im() { return im; }
096
097        // return a / b
098        public Complex divides(Complex b) {
099                Complex a = this;
100                return a.times(b.reciprocal());
101        }
102
103        // return a new Complex object whose value is the complex exponential of this
104        public Complex exp() {
105                return new Complex(Math.exp(re) * Math.cos(im), Math.exp(re) * Math.sin(im));
106        }
107
108        // return a new Complex object whose value is the complex sine of this
109        public Complex sin() {
110                return new Complex(Math.sin(re) * Math.cosh(im), Math.cos(re) * Math.sinh(im));
111        }
112
113        // return a new Complex object whose value is the complex cosine of this
114        public Complex cos() {
115                return new Complex(Math.cos(re) * Math.cosh(im), -Math.sin(re) * Math.sinh(im));
116        }
117
118        // return a new Complex object whose value is the complex tangent of this
119        public Complex tan() {
120                return sin().divides(cos());
121        }
122
123
124
125        // a static version of plus
126        public static Complex plus(Complex a, Complex b) {
127                double real = a.re + b.re;
128                double imag = a.im + b.im;
129                Complex sum = new Complex(real, imag);
130                return sum;
131        }
132
133
134
135        // sample client for testing
136        public static void main(String[] args) {
137                Complex a = new Complex(5.0, 6.0);
138                Complex b = new Complex(-3.0, 4.0);
139
140                StdOut.println("a            = " + a);
141                StdOut.println("b            = " + b);
142                StdOut.println("Re(a)        = " + a.re());
143                StdOut.println("Im(a)        = " + a.im());
144                StdOut.println("b + a        = " + b.plus(a));
145                StdOut.println("a - b        = " + a.minus(b));
146                StdOut.println("a * b        = " + a.times(b));
147                StdOut.println("b * a        = " + b.times(a));
148                StdOut.println("a / b        = " + a.divides(b));
149                StdOut.println("(a / b) * b  = " + a.divides(b).times(b));
150                StdOut.println("conj(a)      = " + a.conjugate());
151                StdOut.println("|a|          = " + a.abs());
152                StdOut.println("tan(a)       = " + a.tan());
153        }
154
155}