Fourier_Transform__Test | C# Online Compiler

Fourier_Transform__Test by the-anonymous-guy

using System;
using System.Numerics;
using System.Drawing;
using System.Drawing.Imaging;
using System.IO;
using System.Windows.Forms;

namespace Fourier_Transform__Test
{
	public enum Direction
	{
		Forward = 1,
		Backward = -1
	}

	;
	public class Tools
	{
		public static int Pow2(int power)
		{
			return ((power >= 0) && (power <= 30)) ? (1 << power) : 0;
		}

		public static int Log2(int x)
		{
			if (x <= 65536)
			{
				if (x <= 256)
				{
					if (x <= 16)
					{
						if (x <= 4)
						{
							if (x <= 2)
							{
								if (x <= 1)
									return 0;
								return 1;
							}

							return 2;
						}

						if (x <= 8)
							return 3;
						return 4;
					}

					if (x <= 64)
					{
						if (x <= 32)
							return 5;
						return 6;
					}

					if (x <= 128)
						return 7;
					return 8;
				}

				if (x <= 4096)
				{
					if (x <= 1024)
					{
						if (x <= 512)
							return 9;
						return 10;
					}

					if (x <= 2048)
						return 11;
					return 12;
				}

				if (x <= 16384)
				{
					if (x <= 8192)
						return 13;
					return 14;
				}

				if (x <= 32768)
					return 15;
				return 16;
			}

			if (x <= 16777216)
			{
				if (x <= 1048576)
				{
					if (x <= 262144)
					{
						if (x <= 131072)
							return 17;
						return 18;
					}

					if (x <= 524288)
						return 19;
					return 20;
				}

				if (x <= 4194304)
				{
					if (x <= 2097152)
						return 21;
					return 22;
				}

				if (x <= 8388608)
					return 23;
				return 24;
			}

			if (x <= 268435456)
			{
				if (x <= 67108864)
				{
					if (x <= 33554432)
						return 25;
					return 26;
				}

				if (x <= 134217728)
					return 27;
				return 28;
			}

			if (x <= 1073741824)
			{
				if (x <= 536870912)
					return 29;
				return 30;
			}

			return 31;
		}

		public static bool IsPowerOf2(int x)
		{
			return (x > 0) ? ((x & (x - 1)) == 0) : false;
		}
	}

	public static class FourierTransform
	{
		private static void FastFourierTransform1d(Complex[] data, Direction direction)
		{
			int n = data.Length;
			int m = Tools.Log2(n);
			// reorder data first
			ReorderData(data);
			// compute FFT
			int tn = 1, tm;
			for (int k = 1; k <= m; k++)
			{
				Complex[] rotation = FourierTransform.GetComplexRotation(k, direction);
				tm = tn;
				tn <<= 1;
				for (int i = 0; i < tm; i++)
				{
					Complex t = rotation[i];
					for (int even = i; even < n; even += tn)
					{
						int odd = even + tm;
						Complex ce = data[even];
						Complex co = data[odd];
						double tr = co.Real * t.Real - co.Imaginary * t.Imaginary;
						double ti = co.Real * t.Imaginary + co.Imaginary * t.Real;
						data[even] += new Complex(tr, ti);
						data[odd] = new Complex(ce.Real - tr, ce.Imaginary - ti);
					}
				}
			}

			if (direction == Direction.Forward)
			{
				for (int i = 0; i < data.Length; i++)
					data[i] /= (double)n;
			}
		}

		public static void FastFourierTransform2d(Complex[, ] data, Direction direction)
		{
			int k = data.GetLength(0);
			int n = data.GetLength(1);
			// check data size
			if (!Tools.IsPowerOf2(k) || !Tools.IsPowerOf2(n))
				throw new ArgumentException("The matrix rows and columns must be a power of 2.");
			if (k < minLength || k > maxLength || n < minLength || n > maxLength)
				throw new ArgumentException("Incorrect cInputFft length.");
			// process rows
			var row = new Complex[n];
			for (int i = 0; i < k; i++)
			{
				// copy row
				for (int j = 0; j < row.Length; j++)
					row[j] = data[i, j];
				// transform it
				FourierTransform.FastFourierTransform1d(row, direction);
				// copy back
				for (int j = 0; j < row.Length; j++)
					data[i, j] = row[j];
			}

			// process columns
			var col = new Complex[k];
			for (int j = 0; j < n; j++)
			{
				// copy column
				for (int i = 0; i < k; i++)
					col[i] = data[i, j];
				// transform it
				FourierTransform.FastFourierTransform1d(col, direction);
				// copy back
				for (int i = 0; i < k; i++)
					data[i, j] = col[i];
			}
		}

#region Private Region
		private const int minLength = 2;
		private const int maxLength = 16384;
		private const int minBits = 1;
		private const int maxBits = 14;
		private static int[][] reversedBits = new int[maxBits][];
		private static Complex[, ][] complexRotation = new Complex[maxBits, 2][];
		// Get array, indicating which data members should be swapped before FFT
		private static int[] GetReversedBits(int numberOfBits)
		{
			if ((numberOfBits < minBits) || (numberOfBits > maxBits))
				throw new ArgumentOutOfRangeException();
			// check if the array is already calculated
			if (reversedBits[numberOfBits - 1] == null)
			{
				int n = Tools.Pow2(numberOfBits);
				int[] rBits = new int[n];
				// calculate the array
				for (int i = 0; i < n; i++)
				{
					int oldBits = i;
					int newBits = 0;
					for (int j = 0; j < numberOfBits; j++)
					{
						newBits = (newBits << 1) | (oldBits & 1);
						oldBits = (oldBits >> 1);
					}

					rBits[i] = newBits;
				}

				reversedBits[numberOfBits - 1] = rBits;
			}

			return reversedBits[numberOfBits - 1];
		}

		// Get rotation of complex number
		private static Complex[] GetComplexRotation(int numberOfBits, Direction direction)
		{
			int directionIndex = (direction == Direction.Forward) ? 0 : 1;
			// check if the array is already calculated
			if (complexRotation[numberOfBits - 1, directionIndex] == null)
			{
				int n = 1 << (numberOfBits - 1);
				double uR = 1.0;
				double uI = 0.0;
				double angle = System.Math.PI / n * (int)direction;
				double wR = System.Math.Cos(angle);
				double wI = System.Math.Sin(angle);
				double t;
				Complex[] rotation = new Complex[n];
				for (int i = 0; i < n; i++)
				{
					rotation[i] = new Complex(uR, uI);
					t = uR * wI + uI * wR;
					uR = uR * wR - uI * wI;
					uI = t;
				}

				complexRotation[numberOfBits - 1, directionIndex] = rotation;
			}

			return complexRotation[numberOfBits - 1, directionIndex];
		}

		// Reorder data for FFT using
		private static void ReorderData(Complex[] data)
		{
			int len = data.Length;
			// check data length
			if ((len < minLength) || (len > maxLength) || (!Tools.IsPowerOf2(len)))
				throw new ArgumentException("Incorrect cInputFft length.");
			int[] rBits = GetReversedBits(Tools.Log2(len));
			for (int i = 0; i < len; i++)
			{
				int s = rBits[i];
				if (s > i)
				{
					Complex t = data[i];
					data[i] = data[s];
					data[s] = t;
				}
			}
		}
#endregion
	}

	public class FourierImageOperation
	{
		public static Complex[, ] FastFourierTransform2d(Complex[, ] image)
		{
			Complex[, ] comp = (Complex[, ])image.Clone();
			int Width = comp.GetLength(0);
			int Height = comp.GetLength(1);
			for (int y = 0; y < Height; y++)
			{
				for (int x = 0; x < Width; x++)
				{
					if (((x + y) & 0x1) != 0)
					{
						comp[x, y] *= -1;
					}
				}
			}

			FourierTransform.FastFourierTransform2d(comp, Direction.Forward);
			return comp;
		}

		public static Complex[, ] InverseFourierTransform2d(Complex[, ] image)
		{
			int Width = image.GetLength(0);
			int Height = image.GetLength(1);
			FourierTransform.FastFourierTransform2d(image, Direction.Backward);
			for (int y = 0; y < Height; y++)
			{
				for (int x = 0; x < Width; x++)
				{
					if (((x + y) & 0x1) != 0)
					{
						image[x, y] *= -1;
					}
				}
			}

			return image;
		}
	}

	public partial class MainForm : Form
	{
		string path = @"lena.png";
		public MainForm()
		{
			InitializeComponent();
		}

		private void loadImageButton_Click(object sender, EventArgs e)
		{
			Bitmap bitmap = Bitmap.FromFile(path) as Bitmap;
			originalImagePictureBox.Image = bitmap as Image;
		}

		private void grayscaleButton_Click(object sender, EventArgs e)
		{
			Bitmap originalImage = originalImagePictureBox.Image as Bitmap;
			Bitmap grayscale = Grayscale.ToGrayscale(originalImage);
			grayscaleImagePictureBox.Image = grayscale as Image;
		}

		private void fftButton_Click(object sender, EventArgs e)
		{
			Bitmap grayscale = grayscaleImagePictureBox.Image as Bitmap;
			Complex[, ] cGrayscale = ImageDataConverter.ToComplex(grayscale);
			Complex[, ] cFFt = FourierImageOperation.FastFourierTransform2d(cGrayscale);
			fftPictureBox.Image = ImageDataConverter.ToBitmap(cFFt, true);
		}

		private void ifftButton_Click(object sender, EventArgs e)
		{
			Bitmap fftImage = fftPictureBox.Image as Bitmap;
			Complex[, ] image = ImageDataConverter.ToComplex(fftImage);
			Complex[, ] cGrayscale = FourierImageOperation.InverseFourierTransform2d(image);
			ifftPictureBox.Image = ImageDataConverter.ToBitmap(image, false);
		}
	}
}

​x
 
using System;
using System.Numerics;
using System.Drawing;
using System.Drawing.Imaging;
using System.IO;
using System.Windows.Forms;
​
namespace Fourier_Transform__Test
{
    public enum Direction
    {
        Forward = 1,
        Backward = -1
    }
​
    ;
    public class Tools
    {
        public static int Pow2(int power)
        {
            return ((power >= 0) && (power <= 30)) ? (1 << power) : 0;
        }
​
        public static int Log2(int x)
        {
            if (x <= 65536)
            {
                if (x <= 256)
                {
                    if (x <= 16)
                    {
                        if (x <= 4)
                        {
                            if (x <= 2)
                            {
                                if (x <= 1)
                                    return 0;
                                return 1;
                            }
​
                            return 2;
                        }
​
                        if (x <= 8)
                            return 3;
                        return 4;
                    }
​
                    if (x <= 64)
                    {
                        if (x <= 32)
                            return 5;
                        return 6;
                    }
​
                    if (x <= 128)
                        return 7;
                    return 8;
                }
​
                if (x <= 4096)
                {
                    if (x <= 1024)
                    {
                        if (x <= 512)
                            return 9;
                        return 10;
                    }
​
                    if (x <= 2048)
                        return 11;
                    return 12;
                }
​
                if (x <= 16384)
                {
                    if (x <= 8192)
                        return 13;
                    return 14;
                }
​
                if (x <= 32768)
                    return 15;
                return 16;
            }
​
            if (x <= 16777216)
            {
                if (x <= 1048576)
                {
                    if (x <= 262144)
                    {
                        if (x <= 131072)
                            return 17;
                        return 18;
                    }
​
                    if (x <= 524288)
                        return 19;
                    return 20;
                }
​
                if (x <= 4194304)
                {
                    if (x <= 2097152)
                        return 21;
                    return 22;
                }
​
                if (x <= 8388608)
                    return 23;
                return 24;
            }
​
            if (x <= 268435456)
            {
                if (x <= 67108864)
                {
                    if (x <= 33554432)
                        return 25;
                    return 26;
                }
​
                if (x <= 134217728)
                    return 27;
                return 28;
            }
​
            if (x <= 1073741824)
            {
                if (x <= 536870912)
                    return 29;
                return 30;
            }
​
            return 31;
        }
​
        public static bool IsPowerOf2(int x)
        {
            return (x > 0) ? ((x & (x - 1)) == 0) : false;
        }
    }
​
    public static class FourierTransform
    {
        private static void FastFourierTransform1d(Complex[] data, Direction direction)
        {
            int n = data.Length;
            int m = Tools.Log2(n);
            // reorder data first
            ReorderData(data);
            // compute FFT
            int tn = 1, tm;
            for (int k = 1; k <= m; k++)
            {
                Complex[] rotation = FourierTransform.GetComplexRotation(k, direction);
                tm = tn;
                tn <<= 1;
                for (int i = 0; i < tm; i++)
                {
                    Complex t = rotation[i];
                    for (int even = i; even < n; even += tn)
                    {
                        int odd = even + tm;
                        Complex ce = data[even];
                        Complex co = data[odd];
                        double tr = co.Real * t.Real - co.Imaginary * t.Imaginary;
                        double ti = co.Real * t.Imaginary + co.Imaginary * t.Real;
                        data[even] += new Complex(tr, ti);
                        data[odd] = new Complex(ce.Real - tr, ce.Imaginary - ti);
                    }
                }
            }
​
            if (direction == Direction.Forward)
            {
                for (int i = 0; i < data.Length; i++)
                    data[i] /= (double)n;
            }
        }
​
        public static void FastFourierTransform2d(Complex[, ] data, Direction direction)
        {
            int k = data.GetLength(0);
            int n = data.GetLength(1);
            // check data size
            if (!Tools.IsPowerOf2(k) || !Tools.IsPowerOf2(n))
                throw new ArgumentException("The matrix rows and columns must be a power of 2.");
            if (k < minLength || k > maxLength || n < minLength || n > maxLength)
                throw new ArgumentException("Incorrect cInputFft length.");
            // process rows
            var row = new Complex[n];
            for (int i = 0; i < k; i++)
            {
                // copy row
                for (int j = 0; j < row.Length; j++)
                    row[j] = data[i, j];
                // transform it
                FourierTransform.FastFourierTransform1d(row, direction);
                // copy back
                for (int j = 0; j < row.Length; j++)
                    data[i, j] = row[j];
            }
​
            // process columns
            var col = new Complex[k];
            for (int j = 0; j < n; j++)
            {
                // copy column
                for (int i = 0; i < k; i++)
                    col[i] = data[i, j];
                // transform it
                FourierTransform.FastFourierTransform1d(col, direction);
                // copy back
                for (int i = 0; i < k; i++)
                    data[i, j] = col[i];
            }
        }
​
#region Private Region
        private const int minLength = 2;
        private const int maxLength = 16384;
        private const int minBits = 1;
        private const int maxBits = 14;
        private static int[][] reversedBits = new int[maxBits][];
        private static Complex[, ][] complexRotation = new Complex[maxBits, 2][];
        // Get array, indicating which data members should be swapped before FFT
        private static int[] GetReversedBits(int numberOfBits)
        {
            if ((numberOfBits < minBits) || (numberOfBits > maxBits))
                throw new ArgumentOutOfRangeException();
            // check if the array is already calculated
            if (reversedBits[numberOfBits - 1] == null)
            {
                int n = Tools.Pow2(numberOfBits);
                int[] rBits = new int[n];
                // calculate the array
                for (int i = 0; i < n; i++)
                {
                    int oldBits = i;
                    int newBits = 0;
                    for (int j = 0; j < numberOfBits; j++)
                    {
                        newBits = (newBits << 1) | (oldBits & 1);
                        oldBits = (oldBits >> 1);
                    }
​
                    rBits[i] = newBits;
                }
​
                reversedBits[numberOfBits - 1] = rBits;
            }
​
            return reversedBits[numberOfBits - 1];
        }
​
        // Get rotation of complex number
        private static Complex[] GetComplexRotation(int numberOfBits, Direction direction)
        {
            int directionIndex = (direction == Direction.Forward) ? 0 : 1;
            // check if the array is already calculated
            if (complexRotation[numberOfBits - 1, directionIndex] == null)
            {
                int n = 1 << (numberOfBits - 1);
                double uR = 1.0;
                double uI = 0.0;
                double angle = System.Math.PI / n * (int)direction;
                double wR = System.Math.Cos(angle);
                double wI = System.Math.Sin(angle);
                double t;
                Complex[] rotation = new Complex[n];
                for (int i = 0; i < n; i++)
                {
                    rotation[i] = new Complex(uR, uI);
                    t = uR * wI + uI * wR;
                    uR = uR * wR - uI * wI;
                    uI = t;
                }
​
                complexRotation[numberOfBits - 1, directionIndex] = rotation;
            }
​
            return complexRotation[numberOfBits - 1, directionIndex];
        }
​
        // Reorder data for FFT using
        private static void ReorderData(Complex[] data)
        {
            int len = data.Length;
            // check data length
            if ((len < minLength) || (len > maxLength) || (!Tools.IsPowerOf2(len)))
                throw new ArgumentException("Incorrect cInputFft length.");
            int[] rBits = GetReversedBits(Tools.Log2(len));
            for (int i = 0; i < len; i++)
            {
                int s = rBits[i];
                if (s > i)
                {
                    Complex t = data[i];
                    data[i] = data[s];
                    data[s] = t;
                }
            }
        }
#endregion
    }
​
    public class FourierImageOperation
    {
        public static Complex[, ] FastFourierTransform2d(Complex[, ] image)
        {
            Complex[, ] comp = (Complex[, ])image.Clone();
            int Width = comp.GetLength(0);
            int Height = comp.GetLength(1);
            for (int y = 0; y < Height; y++)
            {
                for (int x = 0; x < Width; x++)
                {
                    if (((x + y) & 0x1) != 0)
                    {
                        comp[x, y] *= -1;
                    }
                }
            }
​
            FourierTransform.FastFourierTransform2d(comp, Direction.Forward);
            return comp;
        }
​
        public static Complex[, ] InverseFourierTransform2d(Complex[, ] image)
        {
            int Width = image.GetLength(0);
            int Height = image.GetLength(1);
            FourierTransform.FastFourierTransform2d(image, Direction.Backward);
            for (int y = 0; y < Height; y++)
            {
                for (int x = 0; x < Width; x++)
                {
                    if (((x + y) & 0x1) != 0)
                    {
                        image[x, y] *= -1;
                    }
                }
            }
​
            return image;
        }
    }
​
    public partial class MainForm : Form
    {
        string path = @"lena.png";
        public MainForm()
        {
            InitializeComponent();
        }
​
        private void loadImageButton_Click(object sender, EventArgs e)
        {
            Bitmap bitmap = Bitmap.FromFile(path) as Bitmap;
            originalImagePictureBox.Image = bitmap as Image;
        }
​
        private void grayscaleButton_Click(object sender, EventArgs e)
        {
            Bitmap originalImage = originalImagePictureBox.Image as Bitmap;
            Bitmap grayscale = Grayscale.ToGrayscale(originalImage);
            grayscaleImagePictureBox.Image = grayscale as Image;
        }
​
        private void fftButton_Click(object sender, EventArgs e)
        {
            Bitmap grayscale = grayscaleImagePictureBox.Image as Bitmap;
            Complex[, ] cGrayscale = ImageDataConverter.ToComplex(grayscale);
            Complex[, ] cFFt = FourierImageOperation.FastFourierTransform2d(cGrayscale);
            fftPictureBox.Image = ImageDataConverter.ToBitmap(cFFt, true);
        }
​
        private void ifftButton_Click(object sender, EventArgs e)
        {
            Bitmap fftImage = fftPictureBox.Image as Bitmap;
            Complex[, ] image = ImageDataConverter.ToComplex(fftImage);
            Complex[, ] cGrayscale = FourierImageOperation.InverseFourierTransform2d(image);
            ifftPictureBox.Image = ImageDataConverter.ToBitmap(image, false);
        }
    }
}

1 - Customers Before

CustomerID	Code	Name
1	Code_0	Customer_0
2	Code_1	Customer_1
3	Code_2	Customer_2
4	Code_3	Customer_3
5	Code_4	Customer_4

2 - Customers After

CustomerID	Code	Name
1	Code_0	Customer_0
2	Code_1	Customer_1
3	Code_2	Customer_2_Z
4	Code_3	Customer_3_Z
5	Code_4	Customer_4_Z

Cached Result
Last Run:	7:06:18 pm
Compile:	0.045s
Execute:	1.68s
Memory:	80.35Mb
CPU:	1.725s

1 - Customers Before

2 - Customers After

View IL Code