/*
* Encog(tm) Core v3.4 - Java Version
* http://www.heatonresearch.com/encog/
* https://github.com/encog/encog-java-core
* Copyright 2008-2016 Heaton Research, Inc.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*
* For more information on Heaton Research copyrights, licenses
* and trademarks visit:
* http://www.heatonresearch.com/copyright
*/
package org.encog.mathutil;
/**
* A complex number class. This class is based on source code by
*
* Andrew G. Bennett, Department of Mathematics
* Kansas State University
*
* The original version can be found here:
*
* http://www.math.ksu.edu/~bennett/jomacg/c.html
*
*/
public class ComplexNumber {
/**
* The real part.
*/
private final double x;
/**
* The imaginary part.
*/
private final double y;
/**
Constructs the complex number z = u + i*v
@param u Real part
@param v Imaginary part
*/
public ComplexNumber(double u, double v) {
x = u;
y = v;
}
/**
* Create a complex number from another complex number.
* @param other The other complex number.
*/
public ComplexNumber(ComplexNumber other) {
this.x = other.getReal();
this.y = other.getImaginary();
}
/**
Real part of this Complex number
(the x-coordinate in rectangular coordinates).
@return Re[z] where z is this Complex number.
*/
public double getReal() {
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 getImaginary() {
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 ComplexNumber conj() {
return new ComplexNumber(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 ComplexNumber plus(ComplexNumber w) {
return new ComplexNumber(x + w.getReal(), y + w.getImaginary());
}
/**
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 ComplexNumber minus(ComplexNumber w) {
return new ComplexNumber(x - w.getReal(), y - w.getImaginary());
}
/**
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 ComplexNumber times(ComplexNumber w) {
return new ComplexNumber(x * w.getReal() - y * w.getImaginary(), x * w.getImaginary() + y
* w.getReal());
}
/**
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 ComplexNumber div(ComplexNumber w) {
double den = Math.pow(w.mod(), 2);
return new ComplexNumber((x * w.getReal() + y * w.getImaginary()) / den, (y
* w.getReal() - x * w.getImaginary())
/ den);
}
/**
Complex exponential (doesn't change this Complex number).
@return exp(z) where z is this Complex number.
*/
public ComplexNumber exp() {
return new ComplexNumber(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 ComplexNumber log() {
return new ComplexNumber(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 ComplexNumber sqrt() {
double r = Math.sqrt(this.mod());
double theta = this.arg() / 2;
return new ComplexNumber(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 ComplexNumber sin() {
return new ComplexNumber(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 ComplexNumber cos() {
return new ComplexNumber(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 ComplexNumber sinh() {
return new ComplexNumber(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 ComplexNumber cosh() {
return new ComplexNumber(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 ComplexNumber 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 ComplexNumber chs() {
return new ComplexNumber(-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;
}
}