package com.maths;

import java.util.ArrayList;
import java.util.Collections;

/**
 * Class for calculating the Fast Fourier Transform (FFT) of a discrete signal using the Cooley-Tukey algorithm.
 *
 * @author Ioannis Karavitsis
 * @version 1.0
 * */
public class FFT
{
    /**
     * This class represents a complex number and has methods for basic operations.
     *
     * More info:
     * https://introcs.cs.princeton.edu/java/32class/Complex.java.html
     * */
    static class Complex
    {
        private double real, img;

        /**
         * Default Constructor.
         * Creates the complex number 0.
         * */
        public Complex()
        {
            real = 0;
            img = 0;
        }

        /**
         * Constructor. Creates a complex number.
         *
         * @param r The real part of the number.
         * @param i The imaginary part of the number.
         * */
        public Complex(double r, double i)
        {
            real = r;
            img = i;
        }

        /**
         * Returns the real part of the complex number.
         *
         * @return The real part of the complex number.
         * */
        public double getReal()
        {
            return real;
        }

        /**
         * Returns the imaginary part of the complex number.
         *
         * @return The imaginary part of the complex number.
         * */
        public double getImaginary()
        {
            return img;
        }

        /**
         * Adds this complex number to another.
         *
         * @param z The number to be added.
         * @return The sum.
         * */
        public Complex add(Complex z)
        {
            Complex temp = new Complex();
            temp.real = this.real + z.real;
            temp.img = this.img + z.img;
            return temp;
        }

        /**
         * Subtracts a number from this complex number.
         *
         * @param z The number to be subtracted.
         * @return The difference.
         * */
        public Complex subtract(Complex z)
        {
            Complex temp = new Complex();
            temp.real = this.real - z.real;
            temp.img = this.img - z.img;
            return temp;
        }

        /**
         * Multiplies this complex number by another.
         *
         * @param z The number to be multiplied.
         * @return The product.
         * */
        public Complex multiply(Complex z)
        {
            Complex temp = new Complex();
            temp.real = this.real*z.real - this.img*z.img;
            temp.img = this.real*z.img + this.img*z.real;
            return temp;
        }

        /**
         * Multiplies this complex number by a scalar.
         *
         * @param n The real number to be multiplied.
         * @return The product.
         * */
        public Complex multiply(double n)
        {
            Complex temp = new Complex();
            temp.real = this.real * n;
            temp.img = this.img * n;
            return temp;
        }

        /**
         * Finds the conjugate of this complex number.
         *
         * @return The conjugate.
         * */
        public Complex conjugate()
        {
            Complex temp = new Complex();
            temp.real = this.real;
            temp.img  = -this.img;
            return temp;
        }

        /**
         * Finds the magnitude of the complex number.
         *
         * @return The magnitude.
         * */
        public double abs()
        {
            return Math.hypot(this.real, this.img);
        }

        /**
         * Divides this complex number by another.
         *
         * @param z The divisor.
         * @return The quotient.
         * */
        public Complex divide(Complex z)
        {
            Complex temp = new Complex();
            temp.real = (this.real*z.real + this.img*z.img) / (z.abs()*z.abs());
            temp.img = (this.img*z.real - this.real*z.img) / (z.abs()*z.abs());
            return temp;
        }

        /**
         * Divides this complex number by a scalar.
         *
         * @param n The divisor which is a real number.
         * @return The quotient.
         * */
        public Complex divide(double n)
        {
            Complex temp = new Complex();
            temp.real = this.real / n;
            temp.img = this.img / n;
            return temp;
        }
    }

    /**
     * Iterative In-Place Radix-2 Cooley-Tukey Fast Fourier Transform Algorithm with Bit-Reversal.
     * The size of the input signal must be a power of 2. If it isn't then it is padded with zeros and the output FFT will be bigger than the input signal.
     *
     * More info:
     * https://www.algorithm-archive.org/contents/cooley_tukey/cooley_tukey.html
     * https://www.geeksforgeeks.org/iterative-fast-fourier-transformation-polynomial-multiplication/
     * https://en.wikipedia.org/wiki/Cooley%E2%80%93Tukey_FFT_algorithm
     * https://cp-algorithms.com/algebra/fft.html
     *
     * @param x The discrete signal which is then converted to the FFT or the IFFT of signal x.
     * @param inverse True if you want to find the inverse FFT.
     * */
    public static void fft(ArrayList x, boolean inverse)
    {
        /* Pad the signal with zeros if necessary */
        paddingPowerOfTwo(x);
        int N = x.size();

        /* Find the log2(N) */
        int log2N = 0;
        while((1