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Posted 19 Sep 2012
Licenced CPOL

Yet Another Math Parser (YAMP)

, 30 Sep 2012
Constructing a fast math parser using Reflection to do numerics like Matlab.
YAMP
YAMPCompare
LLMathParser
MathFormula
MathParser
MathParserNet
Exceptions
MathParserTK
YAMPCompare.pidb
YAMPConsole
YAMPConsole.pidb
Exceptions
Expressions
Functions
ArgumentFunctions
LinearAlgebra
LogicFunctions
Spectroscopy
StandardFunctions
Trigonometric
Interfaces
Numerics
Decompositions
Integration
Interpolations
ODE
Optimization
Others
Solvers
Operators
AssigmentOperators
BinaryOperators
DotOperators
LogicOperators
UnaryOperators
Values
YAMP.csproj.user
YAMP.pidb
YAMP.csproj.user
YAMP.pidb
using System;
using YAMP;

namespace YAMP.Numerics
{
    public class FFT
    {
        private FFT()
        {
        }

        public static MatrixValue fft(MatrixValue x)
        {
            var length = x.Length;

            if (length == 1) 
                return x.Clone();

            // Cooley-Tukey FFT
            if (length % 2 != 0) 
                throw new MatrixFormatException("length != 2^n");

            // even fft
            var even = new MatrixValue(length / 2, 1);

            for (int k = 1; k <= even.Length; k++)
                even[k] = x[2 * k];
            
            var q = fft(even);

            // odd fft;
            var odd = even; 

            for (int k = 1; k <= odd.Length; k++)
                odd[k] = x[2 * k - 1];

            var r = fft(odd);

            // combine
            var y = new MatrixValue(length, 1);

            for (int k = 1; k <= odd.Length; k++)
            {
                var value = -2 * (k - 1) * Math.PI / length;
                var wk = new ScalarValue(Math.Cos(value), Math.Sin(value));
                y[k] = q[k] + (wk * r[k]);
                y[k + odd.Length] = q[k] - (wk * r[k]);
            }

            return y;
        }

        public static MatrixValue ifft(MatrixValue x)
        {
            var length = x.Length;

            // Cooley-Tukey FFT
            if (length % 2 != 0)
                throw new MatrixFormatException("length != 2^n");

            var y = new MatrixValue(length, 1);

            //conjugate
            for (int i = 1; i <= length; i++)
                y[i] = x[i].Conjugate();

            // compute forward FFT
            y = fft(y);

            // take conjugate again and divide by N
            for (int i = 1; i <= length; i++)
                y[i] = y[i].Conjugate() / (double)length;

            return y;
        }

        public static MatrixValue fft2d(MatrixValue input)
        {
            var output = input.Clone();

            // Rows first:
            var x = new MatrixValue(output.DimensionY, 1);

            for (int h = 1; h <= output.DimensionX; h++)
            {
                for (int i = 1; i <= output.DimensionY; i++)
                    x[i] = output[i, h];
                
                x = fft(x);

                for (int i = 1; i <= output.DimensionY; i++)
                    output[i, h] = x[i];
            }

            //Columns last
            var y = new MatrixValue(output.DimensionX, 1);

            for (int h = 0; h < output.DimensionY; h++)
            {
                for (int i = 1; i <= output.DimensionX; i++)
                    y[i] = output[h, i];

                y = fft(y);

                for (int i = 1; i <= output.DimensionX; i++)
                    output[h, i] = y[i];
            }

            return output;
        }

        public static MatrixValue ifft2d(MatrixValue input)
        {
            var output = input.Clone();

            // Rows first:
            var x = new MatrixValue(output.DimensionY, 1);

            for (int h = 1; h <= output.DimensionX; h++)
            {
                for (int i = 1; i <= output.DimensionY; i++)
                    x[i] = output[i, h];
                
                x = ifft(x);

                for (int i = 1; i <= output.DimensionY; i++)
                    output[i, h] = x[i];
            }

            //Columns last
            var y = new MatrixValue(output.DimensionX, 1);

            for (int h = 1; h <= output.DimensionY; h++)
            {
                for (int i = 1; i <= output.DimensionX; i++)
                    y[i] = output[h, i];
                
                y = ifft(y);

                for (int i = 1; i <= output.DimensionX; i++)
                    output[h, i] = y[i];
            }

            return output;
        }
    }
}

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About the Author

Florian Rappl
Chief Technology Officer
Germany Germany
Florian lives in Munich, Germany. He started his programming career with Perl. After programming C/C++ for some years he discovered his favorite programming language C#. He did work at Siemens as a programmer until he decided to study Physics.

During his studies he worked as an IT consultant for various companies. After graduating with a PhD in theoretical particle Physics he is working as a senior technical consultant in the field of home automation and IoT.

Florian has been giving lectures in C#, HTML5 with CSS3 and JavaScript, software design, and other topics. He is regularly giving talks at user groups, conferences, and companies. He is actively contributing to open-source projects. Florian is the maintainer of AngleSharp, a completely managed browser engine.

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