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Yet Another Math Parser (YAMP)

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

namespace YAMP
{
	public class MatrixValue : Value
	{
		ScalarValue[,] _values;
		
		int capacityX;
		int dimX;
		
		public int DimensionX
		{
			get { return dimX; }
		}
		
		int capacityY;
		int dimY;
		
		public int DimensionY
		{
			get { return dimY; }
		}
		
		public int Length
		{
			get { return dimY * dimX; }
		}
		
		public MatrixValue ()
		{
			dimX = 0;
			dimY = 0;
			capacityX = 32;
			capacityY = 32;
			_values = new ScalarValue[capacityX, capacityY];
			
			for(int i = 0; i < capacityX; i++)
				for(int j = 0; j < capacityY; j++)
					_values[i, j] = new ScalarValue();
		}
		
		public MatrixValue(int rows, int cols) : this()
		{
			if(rows > 0 && cols > 0)
				this[rows, cols] = new ScalarValue();
		}

        public MatrixValue(double[][] values, int rows, int cols) : this(rows, cols)
        {
            for (var j = 0; j < rows; j++)
                for (var i = 0; i < cols; i++)
                    _values[i, j].Value = values[j][i];
        }

        public static MatrixValue Create(Value value)
		{
			if(value is MatrixValue)
				return value as MatrixValue;
			else if(value is ScalarValue)
			{
				var m = new MatrixValue();
				m[1, 1] = value as ScalarValue;
				return m;
			}
			
			throw new ArgumentException("matrix");
		}

        public static MatrixValue One(int dimension)
        {
            var m = new MatrixValue(dimension, dimension);

            for (var i = 1; i <= dimension; i++)
                m[i, i] = new ScalarValue(1.0);

            return m;
        }

        public static MatrixValue Ones(int rows, int cols)
        {
            var m = new MatrixValue(rows, cols);

            for (var j = 1; j <= rows; j++)
                for (var i = 1; i <= cols; i++)
                    m[j, i] = new ScalarValue(1.0);

            return m;
        }

        public MatrixValue Clone()
        {
            var m = new MatrixValue();
			m._values = _values.Clone() as ScalarValue[,];
			m.dimX = dimX;
			m.dimY = dimY;
            return m;
        }
		
		public MatrixValue AddColumn(Value value)
		{
			if(value is MatrixValue)
			{
				var t = value as MatrixValue;				
				int j, i = 1;
				
				for(var k = 1; k <= t.DimensionY; k++)
				{
					j = DimensionX + 1;
					
					for(var l = 1; l <= t.DimensionX; l++)
						this[i, j++] = t[k, l];
					
					i++;
				}
				
				return this;
			}
			else if(value is ScalarValue)
			{
				var t = value as ScalarValue;
				this[1, DimensionX + 1] = t;
				return this;
			}
			
			throw new OperationNotSupportedException(",", value);
		}
		
		public MatrixValue AddRow(Value value)
		{
			if(value is MatrixValue)
			{
				var t = value as MatrixValue;				
				int j, i = DimensionY + 1;
				
				for(var k = 1; k <= t.DimensionY; k++)
				{
					j = 1;
					
					for(var l = 1; l <= t.DimensionX; l++)
						this[i, j++] = t[k, l];
					
					i++;
				}
				
				return this;
			}
			else if(value is ScalarValue)
			{
				var t = value as ScalarValue;
				this[DimensionY + 1, 1] = t;
				return this;
			}
			
			throw new OperationNotSupportedException(";", value);
		}
	
		public override Value Add (Value right)
		{
			if(right is MatrixValue)
			{
				var r = right as MatrixValue;
				
				if(r.DimensionX != DimensionX)
					throw new DimensionException(DimensionX, r.DimensionX);
				
				if(r.DimensionY != DimensionY)
					throw new DimensionException(DimensionY, r.DimensionY);
				
                var m = new MatrixValue(DimensionY, DimensionX);
				
				for(var j = 1; j <= DimensionY; j++)
					for(var i = 1; i <= DimensionX; i++)
						m[j, i] = this[j, i].Add(r[j, i]) as ScalarValue;				
				
				return m;
			}
            else if (right is ScalarValue)
            {
                var m = new MatrixValue(DimensionY, DimensionX);

				for(var j = 1; j <= DimensionY; j++)
					for(var i = 1; i <= DimensionX; i++)
						m[j, i] = this[j, i].Add(right) as ScalarValue;

                return m;
            }
			
			throw new OperationNotSupportedException("+", right);
		}
		
		public override Value Power (Value exponent)
		{
            if (DimensionX != DimensionY)
                throw new DimensionException(DimensionX, DimensionY);

            if (exponent is ScalarValue)
            {
                if (DimensionX == 1)
                    return this[1, 1].Power(exponent);

                var exp = exponent as ScalarValue;
                
                if(exp.ImaginaryValue != 0.0 || Math.Floor(exp.Value) != exp.Value)
                    throw new OperationNotSupportedException("^", exponent);

                var eye = MatrixValue.One(DimensionX);
                var multiplier = this;
                var count = (int)Math.Abs(exp.Value);

                if (exp.Value < 0)
                    multiplier = this.Inverse();

                for (var i = 0; i < count; i++)
                    eye = eye.Multiply(multiplier) as MatrixValue;

                return eye;
            }

            throw new OperationNotSupportedException("^", exponent);
		}
		
		public override Value Subtract (Value right)
		{
			if(right is MatrixValue)
			{
				var r = right as MatrixValue;
				
				if(r.DimensionX != DimensionX)
					throw new DimensionException(DimensionX, r.DimensionX);
				
				if(r.DimensionY != DimensionY)
					throw new DimensionException(DimensionY, r.DimensionY);
				
                var m = new MatrixValue(DimensionY, DimensionX);
				
				for(var j = 1; j <= DimensionY; j++)
					for(var i = 1; i <= DimensionX; i++)
						m[j, i] = this[j, i].Subtract(r[j, i]) as ScalarValue;				
				
				return m;
			}
            else if (right is ScalarValue)
            {
                var m = new MatrixValue(DimensionY, DimensionX);

				for(var j = 1; j <= DimensionY; j++)
					for(var i = 1; i <= DimensionX; i++)
						m[j, i] = this[j, i].Subtract(right) as ScalarValue;

                return m;
            }
			
			throw new OperationNotSupportedException("-", right);
		}

		public override Value Multiply (Value right)
		{	
			if(right is MatrixValue)
			{
				var A = this;
				var B = right as MatrixValue;
				
				if(A.DimensionX != B.DimensionY)
					throw new DimensionException(A.DimensionX, B.DimensionY);
				
				var M = new MatrixValue(A.DimensionY, B.DimensionX);
				
				for(var j = 1; j <= B.DimensionX; j++)
				{					
					for(var i = 1; i <= A.DimensionY; i++)
					{						
						for(var k = 1; k <= A.DimensionX; k++)
							M[i, j] = M[i, j].Add(A[i, k].Multiply(B[k, j])) as ScalarValue;
						
						if(A.DimensionY == B.DimensionX && A.DimensionY == 1)
							return M[1, 1];
					}
				}
				
				return M;
			}
			else if(right is ScalarValue)
			{
                var A = new MatrixValue(DimensionY, DimensionX);

				for(var i = 1; i <= DimensionX; i++)
					for(var j = 1; j <= DimensionY; j++)
						A[j, i] = this[j, i].Multiply(right) as ScalarValue;

                return A;
			}
			
			throw new OperationNotSupportedException("*", right);
		}

		public override Value Divide (Value denominator)
		{
			if(denominator is ScalarValue)
			{
                var m = new MatrixValue(DimensionY, DimensionX);
				
				for(var j = 1; j <= DimensionY; j++)
					for(var i = 1; i <= DimensionX; i++)
						m[j, i] = this[j, i].Divide(denominator) as ScalarValue;
				
				return m;
			}
			else if (denominator is MatrixValue)
			{
				var Q = denominator as MatrixValue;
				
				if(DimensionX != Q.DimensionX)
					throw new DimensionException(DimensionX, Q.DimensionX);
				
				return this.Multiply(Q.Inverse());
			}
			
			throw new OperationNotSupportedException("/", denominator);
		}
		
		public override byte[] Serialize ()
		{
			var ms = new System.IO.MemoryStream();
			var dy = BitConverter.GetBytes(dimY);
			ms.Write(dy, 0, dy.Length);
			var dx = BitConverter.GetBytes(dimX);
			ms.Write(dx, 0, dx.Length);

			for(var i = 1; i <= dimX; i++)
			{
				for(var j = 1; j <= dimY; j++)
				{
					var buffer = this[j, i].Serialize();
					ms.Write(buffer, 0, buffer.Length);
				}
			}

			var content = ms.ToArray();
			ms.Close();
			ms.Dispose();
			return content;
		}

		public override Value Deserialize (byte[] content)
		{
			var dy = BitConverter.ToInt32 (content, 0);
			var dx = BitConverter.ToInt32 (content, 4);
			var pos = 8;

			for(var i = 1; i <= dx; i++)
			{
				for(var j = 1; j <= dy; j++)
				{
					var re = BitConverter.ToDouble(content, pos);
					var im = BitConverter.ToDouble(content, pos + 8);
					this[j, i] = new ScalarValue(re, im);
					pos += 16;
				}
			}

			return this;
		}
		
		public MatrixValue Inverse()
		{
			var target = One(DimensionX);

			if(DimensionX != DimensionY || DimensionX < 32)
			{
				var lu = new YAMP.Numerics.LUDecomposition(this);
				return lu.Solve(target);
			}

			var qr = new YAMP.Numerics.QRDecomposition(this);
			return qr.Solve(target);
		}
		
		public override string ToString ()
		{			
			var sb = new StringBuilder();
			
			for(var j = 1; j <= DimensionY; j++)
			{
				for(var i = 1; i <= DimensionX; i++)
				{
					sb.Append(this[j, i].ToString());
					
					if(i < DimensionX)
						sb.Append("\t");
				}
				
				if(j < DimensionY)
					sb.AppendLine();
			}
			
			return sb.ToString();
		}
		
		void Resize()
		{
			int newX = capacityX;
			int newY = capacityY;
			
			if(DimensionX > newX)
				newX = DimensionX * 2;
			
			if(DimensionY > newY)
				newY = DimensionY * 2;
			
			var tmp = new ScalarValue[newX, newY];
			
			for(int i = 0; i < newX; i++)
			{
				for(int j = 0; j < newY; j++)
				{
					if(i < capacityX && j < capacityY)
						tmp[i, j] = _values[i, j];
					else
						tmp[i, j] = new ScalarValue();
				}
			}
			
			_values = tmp;
			capacityX = newX;
			capacityY = newY;
		}
							
		public ScalarValue this[int j, int i]
		{
			get
			{
				if(i > DimensionX || i < 1 || j > DimensionY || j < 1)
					throw new ArgumentOutOfRangeException("Access in Matrix out of bounds.");
									
				return _values[i - 1, j - 1];
			}
			set
			{
				if(i < 1 || j < 1)
					throw new ArgumentOutOfRangeException("Access in Matrix out of bounds.");
				
				if(i > DimensionX)
					dimX = i;
				
				if(j > DimensionY)
					dimY = j;
				
				if(DimensionX > capacityX || DimensionY > capacityY)
					Resize();
									
				_values[i - 1, j - 1] = value;
			}
		}
		
		public ScalarValue this[int i]
		{
			get
			{
				if(i > Length || i < 1)
					throw new ArgumentOutOfRangeException("Access in Matrix out of bounds.");
				
				var row = (i - 1) % DimensionY + 1;
				var col = (i - 1) / DimensionY + 1;
				return this[row, col];
			}
			set
			{
				if(i < 1)
					throw new ArgumentOutOfRangeException("Access in Matrix out of bounds.");

                var row = (i - 1) % DimensionY + 1;
                var col = (i - 1) / DimensionY + 1;
				this[row, col] = value;
			}
		}
		
		public MatrixValue GetRowVector(int j)
		{
			var m = new MatrixValue(1, DimensionX);
			
			for(var i = 1; i <= DimensionX; i++)
				m[1, i] = this[j, i].Clone();
			
			return m;
		}
		
		public MatrixValue GetColumnVector(int i)
		{
			var m = new MatrixValue(DimensionY, 1);
			
			for(var j = 1; j <= DimensionY; j++)
				m[j, 1] = this[j, i].Clone();
			
			return m;
		}

        public MatrixValue Adjungate()
        {
            var m = new MatrixValue(dimX, dimY);

            for (var i = 1; i <= DimensionY; i++)
                for (var j = 1; j <= DimensionX; j++)
                    m[j, i] = this[i, j].Conjugate();

            return m;
        }
		
		public MatrixValue Transpose()
		{
			var m = new MatrixValue(dimX, dimY);
			
			for(var i = 1; i <= DimensionY; i++)
				for(var j = 1; j <= DimensionX; j++)
					m[j, i] = this[i, j];
			
			return m;
		}
		
		public ScalarValue Abs()
		{
			var sum = 0.0;
			
			foreach(var p in _values)
			{
				sum += (p.Value * p.Value + p.ImaginaryValue * p.ImaginaryValue);
			}
			
			return new ScalarValue(Math.Sqrt(sum));
		}

        public ScalarValue Trace()
        {
            var sum = new ScalarValue();
            var n = Math.Min(DimensionX, DimensionY);

            for(var i = 1; i <= n; i++)
            {
                sum = sum + this[n, n];
            }

            return sum;
        }
		
		public ScalarValue Det()
		{
			if(DimensionX == DimensionY)
			{
                var n = DimensionX;

				if(n == 1)
					return this[1, 1];
                else if (n == 2)
                    return this[1, 1] * this[2, 2] - this[1, 2] * this[2, 1];
                else if (n == 3)
                {
                    return  this[1, 1] * (this[2, 2] * this[3, 3] - this[2, 3] * this[3, 2]) +
                            this[1, 2] * (this[2, 3] * this[3, 1] - this[2, 1] * this[3, 3]) +
                            this[1, 3] * (this[2, 1] * this[3, 2] - this[2, 2] * this[3, 1]);
                }
                else if (n == 4)
                {
                    return  this[1, 1] * (this[2, 2] * (this[3, 3] * this[4, 4] - this[3, 4] * this[4, 3]) + this[2, 3] * (this[3, 4] * this[4, 2] - this[3, 2] * this[4, 4]) + this[2, 4] * (this[3, 2] * this[4, 3] - this[3, 3] * this[4, 2])) -
                            this[1, 2] * (this[2, 1] * (this[3, 3] * this[4, 4] - this[3, 4] * this[4, 3]) + this[2, 3] * (this[3, 4] * this[4, 1] - this[3, 1] * this[4, 4]) + this[2, 4] * (this[3, 1] * this[4, 3] - this[3, 3] * this[4, 1])) +
                            this[1, 3] * (this[2, 1] * (this[3, 2] * this[4, 4] - this[3, 4] * this[4, 2]) + this[2, 2] * (this[3, 4] * this[4, 1] - this[3, 1] * this[4, 4]) + this[2, 4] * (this[3, 1] * this[4, 2] - this[3, 2] * this[4, 1])) -
                            this[1, 4] * (this[2, 1] * (this[3, 2] * this[4, 3] - this[3, 3] * this[4, 2]) + this[2, 2] * (this[3, 3] * this[4, 1] - this[3, 1] * this[4, 3]) + this[2, 3] * (this[3, 1] * this[4, 2] - this[3, 2] * this[4, 1]));
                }
                
                return ComputeDet();
			}
			
			return new ScalarValue();
		}

        public ScalarValue ComputeDet()
        {
            var lu = new YAMP.Numerics.LUDecomposition(this);
            return new ScalarValue(lu.Determinant());
        }

		public override int GetHashCode ()
		{
			return dimX + dimY;
		}

		public override bool Equals (object obj)
		{
			if(obj is MatrixValue)
			{
				var m = obj as MatrixValue;

				if(m.DimensionX != DimensionX)
					return false;

				if(m.DimensionY != DimensionY)
					return false;

				for(var i = 1; i <= DimensionX; i++)
					for(var j = 1; j <= DimensionY; j++)
						if(!this[j, i].Equals(m[j, i]))
						   return false;

				return true;
			}
			else if(DimensionX == 1 && DimensionY == 1)
				return this[1, 1].Equals(obj);

			return false;
		}

        public double[][] GetRealArray()
        {
            var array = new double[DimensionY][];

            for (var j = 0; j < DimensionY; j++)
            {
                array[j] = new double[DimensionX];

                for (var i = 0; i < DimensionX; i++)
                    array[j][i] = _values[i, j].Value;
            }

            return array;
        }

        public MatrixValue SubMatrix(int dy, int dimy, int dx, int dimx)
        {
            var X = new MatrixValue(dimy - dy, dimx - dx);

            for (int j = dy + 1; j <= dimy; j++)
                for (int i = dx + 1; i <= dimx; i++)
                    X[j - dy, i - dx] = this[j, i].Clone();

            return X;
        }

        public MatrixValue SubMatrix(int[] y, int dx, int dimx)
        {
            var X = new MatrixValue(y.Length, dimx - dx);

            for (int j = 1; j <= y.Length; j++)
                for (int i = dx + 1; i <= dimx; i++)
                    X[j, i - dx] = this[y[j - 1], i].Clone();

            return X;
        }
    }
}

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About the Author

Florian Rappl
Chief Technology Officer
Germany Germany
Florian is from Regensburg, 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.
 
Florian is also giving lectures in C#, HTML5 with CSS3 and JavaScript, and other topics. Having graduated from University with a Master's degree in theoretical physics he is currently busy doing his PhD in the field of High Performance Computing.
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