package com.github.davidmoten.ar;

/*************************************************************************
 * 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
	@Override
	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);

		System.out.println("a            = " + a);
		System.out.println("b            = " + b);
		System.out.println("Re(a)        = " + a.re());
		System.out.println("Im(a)        = " + a.im());
		System.out.println("b + a        = " + b.plus(a));
		System.out.println("a - b        = " + a.minus(b));
		System.out.println("a * b        = " + a.times(b));
		System.out.println("b * a        = " + b.times(a));
		System.out.println("a / b        = " + a.divides(b));
		System.out.println("(a / b) * b  = " + a.divides(b).times(b));
		System.out.println("conj(a)      = " + a.conjugate());
		System.out.println("|a|          = " + a.abs());
		System.out.println("tan(a)       = " + a.tan());
	}

}

@@ -3895,24 +3895,212 @@
 rn sum;%0A%09%7D%0A%0A
+%09public static Complex%5B%5D toComplex(double%5B%5D x) %7B%0A%09%09Complex%5B%5D result = new Complex%5Bx.length%5D;%0A%09%09for (int i = 0; i %3C x.length; i++)%0A%09%09%09result%5Bi%5D = new Complex(x%5Bi%5D, 0);%0A%09%09return result;%0A%09%7D%0A%0A
 %09// sample c

add tests