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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;

namespace YAMP
{
	public class ScalarValue : Value
	{
		const double epsilon = 1e-12;
		
		double _real;
		double _imag;
		
		public ScalarValue () : this(0.0, 0.0)
		{
		}

		public ScalarValue(bool boolean) : this(boolean ? 1.0 : 0.0, 0.0)
		{
		}
		
		public ScalarValue(double real) : this(real, 0.0)
		{
		}
		
		public ScalarValue(ScalarValue value) : this(value._real, value._imag)
		{
		}
		
		public ScalarValue(double real, double imag)
		{
			_real = real;
			_imag = imag;
		}

		public int IntValue
		{
			get { return (int)_real; } 
		}
		
		public double Value 
		{
			get { return _real; }
			set { _real = value; }
		}
		
		public double ImaginaryValue 
		{
			get { return _imag; }
			set { _imag = value; }
		}
		
		public ScalarValue Clone()
		{
			return new ScalarValue(this);
		}
		
		public static ScalarValue I
		{
			get { return new ScalarValue(0.0, 1.0); }
		}
		
		public ScalarValue Abs()
		{
			return new ScalarValue(abs());
		}

        public ScalarValue AbsSquare()
        {
            return new ScalarValue(_real * _real + _imag * _imag);
        }
		
		public ScalarValue Conjugate()
		{
			return new ScalarValue(_real, -_imag);
		}
		
		public override Value Add (Value right)
		{
			if(right is ScalarValue)
			{
				var r = right as ScalarValue;
                var re = _real + r._real;
                var im = _imag + r._imag;
                return new ScalarValue(re, im);
            }
            else if (right is MatrixValue)
            {
                var r = right as MatrixValue;
                return r.Add(this);
            }
			else if(right is StringValue)
			{
				var t = new StringValue(this.ToString());
				return t.Add(right);
			}
			
			throw new OperationNotSupportedException("+", right);
		}
		
		public override Value Subtract (Value right)
		{
			if(right is ScalarValue)
			{
				var r = right as ScalarValue;
                var re = _real - r._real;
                var im = _imag - r._imag;
                return new ScalarValue(re, im);
            }
            else if (right is MatrixValue)
            {
				var r = right as MatrixValue;
				var m = new MatrixValue(r.DimensionY, r.DimensionX);
				
				for(var j = 1; j <= r.DimensionY; j++)
					for(var i = 1; i <= r.DimensionX; i++)
						m[j, i] = this.Subtract(r[j, i]) as ScalarValue;
				
				return m;
            }
			
			throw new OperationNotSupportedException("-", right);
		}
		
		public override Value Multiply (Value right)
		{
			if(right is ScalarValue)
			{
				var r = right as ScalarValue;
				var re = _real * r._real - _imag * r._imag;
				var im = _real * r._imag + _imag * r._real;
                return new ScalarValue(re, im);
			}
            else if (right is MatrixValue)
            {
                var r = right as MatrixValue;
                return r.Multiply(this);
            }
			
			throw new OperationNotSupportedException("*", right);
		}
		
		public override Value Divide (Value right)
		{
			if(right is ScalarValue)
			{
				var r = (right as ScalarValue).Conjugate();
                var q = r._real * r._real + r._imag * r._imag;
                var re = (_real * r._real - _imag * r._imag) / q;
                var im = (_real * r._imag + _imag * r._real) / q;
				return new ScalarValue(re, im);
			}
			else if(right is MatrixValue)
			{
				var inv = (right as MatrixValue).Inverse();
				return this.Multiply(inv);
			}
			
			throw new OperationNotSupportedException("/", right);
		}
		
		public override Value Power (Value exponent)
		{
            if(exponent is ScalarValue)
			{
                if (Value == 0.0 && ImaginaryValue == 0.0)
                    return new ScalarValue();

                var exp = exponent as ScalarValue;
                var theta = _real == 0.0 ? Math.PI / 2 * Math.Sign(ImaginaryValue) : Math.Atan2(_imag, _real);
                var L = _real / Math.Cos(theta);
                var phi = Ln() * exp._imag;
                var R = (I.Multiply(phi) as ScalarValue).Exp();
                var alpha = _real == 0.0 ? 1.0 : Math.Pow(Math.Abs(L), exp._real);
                var beta = theta * exp._real;
                var _cos = Math.Cos(beta);
                var _sin = Math.Sin(beta);
                var re = alpha * (_cos * R._real - _sin * R._imag);
                var im = alpha * (_cos * R._imag + _sin * R._real);

                if (L < 0)
                    return new ScalarValue(-im, re);
                
                return new ScalarValue(re, im);
			}
			else if(exponent is MatrixValue)
			{
				var b = exponent as MatrixValue;
				var m = new MatrixValue(b.DimensionY, b.DimensionX);

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

				return m;
			}
			
			throw new OperationNotSupportedException("^", exponent);
		}
		
		public override byte[] Serialize ()
		{
			var re = BitConverter.GetBytes(_real);
			var im = BitConverter.GetBytes(_imag);
			var ov = new byte[re.Length + im.Length];
			re.CopyTo(ov, 0);
			im.CopyTo(ov, re.Length);
			return ov;
		}

		public override Value Deserialize (byte[] content)
		{
			_real = BitConverter.ToDouble(content, 0);
			_imag = BitConverter.ToDouble(content, 8);
			return this;
		}

        public ScalarValue Sqrt()
        {
            return Power(new ScalarValue(0.5)) as ScalarValue;
        }
		
		public ScalarValue Cos()
		{
			var re = Math.Cos(_real) * Math.Cosh(_imag);
			var im = -Math.Sin(_real) * Math.Sinh(_imag);
			return new ScalarValue(re, im);
		}
		
		public ScalarValue Sin()
		{
			var re = Math.Sin(_real) * Math.Cosh(_imag);
			var im = Math.Cos(_real) * Math.Sinh(_imag);
			return new ScalarValue(re, im);
		}
		
		public ScalarValue Exp()
		{
			var f = Math.Exp(_real);
			var re = f * Math.Cos(_imag);
			var im = f * Math.Sin(_imag);
			return new ScalarValue(re, im);
		}
		
		public ScalarValue Ln()
		{
			var re = Math.Log(abs());
			var im = arg();
			return new ScalarValue(re, im);
		}
		
		public ScalarValue Log()
		{
			var re = Math.Log(abs(), 10.0);
			var im = arg();
			return new ScalarValue(re, im);
		}

		public ScalarValue IsInt ()
		{
			return new ScalarValue((double)IntValue == Value && ImaginaryValue == 0.0);
		}

		public ScalarValue IsPrime ()
		{
            if (IsInt().Value == 1)
            {
                var k = IntValue;

                if ((k & 1) == 0)
                    return new ScalarValue(false);

                var sqrt = (int)Math.Sqrt(Value);

                for (var i = 3; i < sqrt; i += 2)
                    if (k % i == 0)
                        return new ScalarValue(false);

                return new ScalarValue(true);
            }

			return new ScalarValue(false);
		}
		
		public ScalarValue Faculty()
		{
            var re = faculty(_real);
            var im = faculty(_imag);

            if (_imag == 0.0)
                im = 0.0;
            else if (_real == 0.0 && _imag != 0.0)
                re = 0.0;

			return new ScalarValue(re, im);
		}
		
		double faculty(double r)
		{
			var k = (int)Math.Abs(r);
			var value = r < 0 ? -1.0 : 1.0;
			
			while(k > 1)
			{
				value *= k;
				k--;
			}
			
			return value;
        }

        double abs()
        {
            return Math.Sqrt(_real * _real + _imag * _imag);
        }

        double arg()
        {
            return Math.Atan2(_imag, _real);
        }
		
		public override string ToString ()
		{
			//TODO
			if(Math.Abs(_imag) < epsilon)
				return string.Format(Tokens.NumberFormat, "{0}", Math.Abs (Value) < epsilon ? 0.0 : Math.Round(Value, 4));
			else if(Math.Abs(_real) < epsilon)
				return string.Format(Tokens.NumberFormat, "{0}i", Math.Round(ImaginaryValue, 4));
			
			return string.Format (Tokens.NumberFormat, "{0}{2}{1}i", Math.Round(Value, 4), Math.Round(ImaginaryValue, 4), ImaginaryValue < 0.0 ? string.Empty : "+");
		}
		
		public override bool Equals (object obj)
		{
			if(obj is ScalarValue)
			{
				var sv = obj as ScalarValue;
				return sv._real == _real && sv._imag == _imag;
			}
			
			if(obj is double && _imag == 0.0)
				return (double)obj == _real;
			
			return false;
		}
		
		public override int GetHashCode ()
		{
			return (_real + _imag).GetHashCode();
        }

        public static ScalarValue operator +(ScalarValue a, ScalarValue b)
        {
            return a.Add(b) as ScalarValue;
        }

        public static ScalarValue operator +(ScalarValue a, double b)
        {
            return new ScalarValue(a._real + b, a._imag);
        }

        public static ScalarValue operator +(double b, ScalarValue a)
        {
            return a + b;
        }

        public static ScalarValue operator -(ScalarValue a, ScalarValue b)
        {
            return a.Subtract(b) as ScalarValue;
        }

        public static ScalarValue operator -(ScalarValue a, double b)
        {
            return new ScalarValue(a._real - b, a._imag);
        }

        public static ScalarValue operator -(double b, ScalarValue a)
        {
            return new ScalarValue(b - a._real, a._imag);
        }

        public static ScalarValue operator *(ScalarValue a, ScalarValue b)
        {
            return a.Multiply(b) as ScalarValue;
        }

        public static ScalarValue operator *(double b, ScalarValue a)
        {
            return a * b;
        }

		public static ScalarValue operator <(ScalarValue l, ScalarValue r)
		{
			if(l.ImaginaryValue == 0.0 && r.ImaginaryValue == 0)
			{
				if(l._real < r._real)
					return new ScalarValue(true);
			}
			else if(l.abs() < r.abs ())
				return new ScalarValue(true);

			return new ScalarValue(false);
		}
		
		public static ScalarValue operator >(ScalarValue l, ScalarValue r)
		{
			if(l.ImaginaryValue == 0.0 && r.ImaginaryValue == 0)
			{
				if(l._real > r._real)
					return new ScalarValue(true);
			}
			else if(l.abs() > r.abs ())
				return new ScalarValue(true);
			
			return new ScalarValue(false);
        }

        public static ScalarValue operator <=(ScalarValue l, ScalarValue r)
        {
            if (l.ImaginaryValue == 0.0 && r.ImaginaryValue == 0)
            {
                if (l._real <= r._real)
                    return new ScalarValue(true);
            }
            else if (l.abs() <= r.abs())
                return new ScalarValue(true);

            return new ScalarValue(false);
        }

        public static ScalarValue operator >=(ScalarValue l, ScalarValue r)
        {
            if (l.ImaginaryValue == 0.0 && r.ImaginaryValue == 0)
            {
                if (l._real >= r._real)
                    return new ScalarValue(true);
            }
            else if (l.abs() >= r.abs())
                return new ScalarValue(true);

            return new ScalarValue(false);
        }
		
		public static ScalarValue operator ==(ScalarValue l, ScalarValue r)
		{
			if(Math.Abs (l.ImaginaryValue - r.ImaginaryValue) > epsilon)
				return new ScalarValue(false);

			if(Math.Abs(l.Value - r.Value) > epsilon)
				return new ScalarValue(false);
			
			return new ScalarValue(true);
		}
		
		public static ScalarValue operator !=(ScalarValue l, ScalarValue r)
		{
			if(Math.Abs (l.ImaginaryValue - r.ImaginaryValue) > epsilon)
				return new ScalarValue(true);
			
			if(Math.Abs(l.Value - r.Value) > epsilon)
				return new ScalarValue(true);
			
			return new ScalarValue(false);
		}

        public static ScalarValue operator *(ScalarValue a, double b)
        {
            return new ScalarValue(a._real * b, a._imag * b);
        }

        public static ScalarValue operator /(ScalarValue a, ScalarValue b)
        {
            return a.Divide(b) as ScalarValue;
        }

        public static ScalarValue operator /(double b, ScalarValue a)
        {
            return new ScalarValue(b, 0.0) / a;
        }

        public static ScalarValue operator /(ScalarValue a, double b)
        {
            return new ScalarValue(a._real / b, a._imag / b);
        }

        public static ScalarValue operator -(ScalarValue a)
        {
            return new ScalarValue(-a._real, -a._imag);
        }
    }
}

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About the Author

Florian Rappl
Architect
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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