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MathExtended

Pure C# MathLibrary.

Legal information and credits

MathExtended is project by Ales Hotko and was first released in 2020. It's licensed under the MIT license.

[TOC]

Libraries

Common

Common

Complex Numbers

Matrices

Creating

Square Matrix

//Create square matrix of size 3x3
Matrix matrix = new Matrix(3);

Matrix of any size

//Create matrix of any size (i.e. 5x3)
Matrix matrix = new Matrix(5, 3);

Zero Matrix

Matrix zero = Matrix.Zero(rows, cols);
//..or..
Matrix zeroSquare = Matrix.Zero(size);
Identity Matrix
Matrix identity = Matrix.Identity(size);

Populating the matrix

//Populate Matrix
matrix[1, 1] = 5.0;
matrix[1, 2] = 5.0;
matrix[1, 3] = 5.0;
//...or populate with random values between -5.0 and 10.0
matrix.Randomize(-5,0, 10.0);
//..or with random values between 0 and 1
matrix.Randomize();

Math operations

Matrix a = new Matrix(3, 3);
Matrix b = new Matrix(3, 3);

Addition

Matrix sum = a + b;
//..or..
a.Add(b);

Subtraction

Matrix diff = a - b;
//..or..
a.Add(b);

Multiplication

//multiplication with scalar
Matrix product = a * 3.0;
//..or..
a.Multiply(3.0);
//multiplication with another matrix
Matrix product = a * b;
//..or..
a.Multiply(b);

Hadamard Product

a.HadamardProduct(b);

Inversion

Matrix inverse = !a;
//..or..
a.Inverse();

Transposition

Matrix r = new Matrix(5, 4);
r.Transpose();

Mapping elements with a function

Matrix r = new Matrix(5, 4);
r.Map(Math.Sin); //Apply Sine function to every matrix element
//or own function
public double MyFunction(double param)
{
	return param * 42.0;
}

//[...]
r.Map(MyFunction);
//[...]

Comparing the matrices

//Equality
if(a == b) {}
//..or..
if(a != b) {}
//..or..
if(a > b) {}
//..or..
if(a < b) {}
//..or..
if(a >= b) {}
//..or..
if(a <= b) {}

Creating Transformation Matrices

Rotation

//2D
Matrix rotation2D = Matrix.Rotation2D(angleInDegrees);
//3D around X, Y or Z axis
Matrix rotation3D = Matrix.Rotation3DX(angleInDegrees);
Matrix rotation3D = Matrix.Rotation3DY(angleInDegrees);
Matrix rotation3D = Matrix.Rotation3DZ(angleInDegrees);

Scaling

Matrix scaling = Matrix.Scaling(factorX, factorY, factorZ);

Translation

Matrix translation = Matrix.Translation(moveX, moveY, moveZ);

Fractions

Creation

//fraction can be created with numerator and denominator as parameters:
Fraction fraction = new Fraction(2, 5);
Console.WriteLine($"Fraction = {fraction.ToString()}");
//Output:
//Fraction = 2/5

//...or only by numerator part (in this case denominator is 1):
Fraction fraction = new Fraction(2);
Console.WriteLine($"Fraction = {fraction.ToString()}");
//Output:
//Fraction = 2/1

//...or from string in format "numerator/denominator":
Fraction fraction = new Fraction("1/5");
Console.WriteLine($"Fraction = {fraction.ToString()}");
//Output:
//Fraction = 1/5

//...or from decimal value with accuracy:
Fraction fraction = new Fraction(0.3333, 0.01);
Console.WriteLine($"Fraction = {fraction.ToString()}");
//Output:
//Fraction = 1/3

//...or from decimal value with default accuracy:
Fraction fraction = new Fraction(0.3333);
Console.WriteLine($"Fraction = {fraction.ToString()}");
//Output:
//Fraction = 3333/10000

Assigning the value

Value can be initially assigned at creation, as seen in previous section. If value needs to be assigned afterwards afterwards, there are several possible ways.

//...or by using numerator and denominator properties:
fraction.Numerator = 3;
fraction.Denominator = 7;
Console.WriteLine($"Fraction = {fraction.ToString()}");
//Output:
//Fraction = 3/7

//...or by using .AsDouble property:
fraction.AsDouble = 0.5;
Console.WriteLine($"Fraction = {fraction.ToString()}, AsDouble = {fraction.AsDouble}");
//Output:
//Fraction = 1/2, AsDouble = 0.5

//...or by using .AsFloat property:
fraction.AsFloat = 0.5f;
Console.WriteLine($"Fraction = {fraction.ToString()}, AsFloat = {fraction.AsFloat}");
//Output:
//Fraction = 1/2, AsFloat = 0.5

Available Mathematical Operations

Addition

//addition of two fractions
var fractionOne = new Fraction(1, 5);
var fractionTwo = new Fraction(2, 5);
var result = fractionOne + fractionTwo;
Console.WriteLine($"Fraction = {result.ToString()}, reduced fraction = {result.Reduced().ToString()}");
//Output:
//Fraction = 15/25, reduced fraction = 3/5

//addition of fraction and number
result = fractionOne + 3;
Console.WriteLine($"Fraction = {result.ToString()}, reduced fraction = {result.Reduced().ToString()}");
//Output:
//Fraction = 16/5, reduced fraction = 16/5

//addition of fraction and a decimal number
result = fractionOne + 0.5;
Console.WriteLine($"Fraction = {result.ToString()}, reduced fraction = {result.Reduced().ToString()}");
//Output:
//Fraction = 7/10, reduced fraction = 7/10

Subtraction

//subtraction of two fractions
var fractionOne = new Fraction(1, 5);
var fractionTwo = new Fraction(2, 5);
var result = fractionOne - fractionTwo;
Console.WriteLine($"Fraction = {result.ToString()}, reduced fraction = {result.Reduced().ToString()}");
//Output:
//Fraction = -1/5, reduced fraction = -1/5

//subtraction of fraction and number
result = fractionOne - 3;
Console.WriteLine($"Fraction = {result.ToString()}, reduced fraction = {result.Reduced().ToString()}");
//Output:
//Fraction = -14/5, reduced fraction = -14/5

//subtraction of fraction and a decimal number
result = fractionOne - 0.5;
Console.WriteLine($"Fraction = {result.ToString()}, reduced fraction = {result.Reduced().ToString()}");
//Output:
//Fraction = -3/10, reduced fraction = -3/10

Multiplication

//multiplication of two fractions
var fractionOne = new Fraction(1, 5);
var fractionTwo = new Fraction(2, 5);
var result = fractionOne * fractionTwo;
Console.WriteLine($"Fraction = {result.ToString()}, reduced fraction = {result.Reduced().ToString()}");
//Output:
//Fraction = 2/25, reduced fraction = 2/25

//multiplication of fraction and number
result = fractionOne * 3;
Console.WriteLine($"Fraction = {result.ToString()}, reduced fraction = {result.Reduced().ToString()}");
//Output:
//Fraction = 3/5, reduced fraction = 3/5

//multiplication of fraction and a decimal number
result = fractionOne * 0.5;
Console.WriteLine($"Fraction = {result.ToString()}, reduced fraction = {result.Reduced().ToString()}");
//Output:
//Fraction = 1/10, reduced fraction = 1/10

Division

//division of two fractions
var fractionOne = new Fraction(1, 5);
var fractionTwo = new Fraction(2, 5);
var result = fractionOne / fractionTwo;
Console.WriteLine($"Fraction = {result.ToString()}, reduced fraction = {result.Reduced().ToString()}");
//Output:
//Fraction = 5/10, reduced fraction = 1/2

//division of fraction and number
result = fractionOne / 3;
Console.WriteLine($"Fraction = {result.ToString()}, reduced fraction = {result.Reduced().ToString()}");
//Output:
//Fraction = 1/15, reduced fraction = 1/15

//division of fraction and a decimal number
result = fractionOne / 0.5;
Console.WriteLine($"Fraction = {result.ToString()}, reduced fraction = {result.Reduced().ToString()}");
//Output:
//Fraction = 2/5, reduced fraction = 2/5

Other operations

Reduce

var fraction = new Fraction(3, 15);
Console.WriteLine($"Fraction = {fraction.ToString()}");
fraction.Reduce();
Console.WriteLine($"Fraction reduced = {fraction.ToString()}");
//Output:
//Fraction = 3/15
//Fraction reduced = 1/5

Inverse

fraction = new Fraction(3, 15);
Console.WriteLine($"Fraction = {fraction.ToString()}");
fraction.Inverse();
Console.WriteLine($"Fraction inversed = {fraction.ToString()}");
fraction.Reduce();
Console.WriteLine($"Fraction inversed and reduced = {fraction.ToString()}");
//Output:
//Fraction = 3/15
//Fraction inversed = 15/3
//Fraction inversed and reduced = 5/1

Continued Fractions

Also support for continued fractions is added. Continued fraction can be assigned at fraction creation or assigned at runtime.

//...
public static class ContinuedFractions
{
    public static readonly string e = "[2;1,2,1,1,4,1,1,6,1,1,8,1,1,10,1,1,12,1,1,14,1,1,16,1,1,18,1,1,20,1,1,22,1,1,24,1,1,26,1,1,28,1,1,30,1,1,32,1,1,34,1,1,36,1,1,38,1,1,40,1,1,42,1,1,44,1,1,46,1,1,48,1,1,50,1,1,52,1,1,54,1,1,56,1,1,58,1,1,60,1,1,62,1,1,64,1,1,66]";
    public static readonly string Pi = "[3;7,15,1,292,1,1,1,2,1,3,1,14,2,1,1,2,2,2,2,1,84,2,1,1,15,3,13,1,4,2,6,6,99,1,2,2,6,3,5,1,1,6,8,1,7,1,2,3,7,1,2,1,1,12,1,1,1,3,1,1,8,1,1,2,1,6,1,1,5,2,2,3,1,2,4,4,16,1,161,45,1,22,1,2,2,1,4,1,2,24,1,2,1,3,1,2,1]";
    public static readonly string Phi = "[1;1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]";
    public static readonly string Sqrt2 = "[1;2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2]";
    public static readonly string Sqrt3 = "[1;1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2,1,2]";
}
//...

fraction = new Fraction(ContinuedFractions.e);
Console.WriteLine($"Fraction (e) = {fraction.ToString()}, AsDouble = {fraction.AsDouble}, AsContinuedFraction = {fraction.AsContinuedFraction}");
//Output:
//Fraction (e) = 1264/465, AsDouble = 2,71827956989247, AsContinuedFraction = [2;1,2,1,1,4,1,1,6]

fraction = new Fraction(ContinuedFractions.Pi);
Console.WriteLine($"Fraction (Pi) = {fraction.ToString()}, AsDouble = {fraction.AsDouble}, AsContinuedFraction = {fraction.AsContinuedFraction}");
//Output:
//Fraction (Pi) = 355/113, AsDouble = 3,14159292035398, AsContinuedFraction = [3;7,16]

fraction = new Fraction(Math.PI);
Console.WriteLine($"Fraction (Math.Pi) = {fraction.ToString()}, AsDouble = {fraction.AsDouble}, AsContinuedFraction = {fraction.AsContinuedFraction}");
//Output:
//Fraction (Math.Pi) = 355/113, AsDouble = 3,14159292035398, AsContinuedFraction = [3;7,16]

fraction = new Fraction(ContinuedFractions.Phi);
Console.WriteLine($"Fraction (Phi) = {fraction.ToString()}, AsDouble = {fraction.AsDouble}, AsContinuedFraction = {fraction.AsContinuedFraction}");
//Output:
//Fraction (Phi) = 377/233, AsDouble = 1,61802575107296, AsContinuedFraction = [1;1,1,1,1,1,1,1,1,1,1,2]

fraction = new Fraction(ContinuedFractions.Sqrt2);
Console.WriteLine($"Fraction (Sqrt2) = {fraction.ToString()}, AsDouble = {fraction.AsDouble}, AsContinuedFraction = {fraction.AsContinuedFraction}");
//Output:
//Fraction (Sqrt2) = 577/408, AsDouble = 1,41421568627451, AsContinuedFraction = [1;2,2,2,2,2,2,2]

fraction = new Fraction(ContinuedFractions.Sqrt3);
Console.WriteLine($"Fraction (Sqrt3) = {fraction.ToString()}, AsDouble = {fraction.AsDouble}, AsContinuedFraction = {fraction.AsContinuedFraction}");
//Output:
//Fraction (Sqrt3) = 362/209, AsDouble = 1,73205741626794, AsContinuedFraction = [1;1,2,1,2,1,2,1,3]

fraction = new Fraction("[2;1,4,3]");
Console.WriteLine($"Fraction (45/16) = {fraction.ToString()}, AsDouble = {fraction.AsDouble}, AsContinuedFraction = {fraction.AsContinuedFraction}");
//Output:
//Fraction (45/16) = 45/16, AsDouble = 2,8125, AsContinuedFraction = [2;1,4,3]

Output

For output of resulting fraction method ToString() can be used, which results in a string, representing the fraction.

fraction = new Fraction(3, 15);
Console.WriteLine($"Fraction = {fraction.ToString()}");
//Output:
//Fraction = 3/15

Display Modifiers (Options)

Several modifiers can be used. They are sent to ToString() method as parameter. Modifiers are in DisplayOptions enum, described below:

[Flags]
public enum DisplayOptions
{
    /// <summary>Default display of fraction (e.g. 2/5 or 31/7)</summary>
    None = 0,
    /// <summary>Show improper fractions (e.g. 7/5) as mixed number (1 2/5)</summary>
    ImproperFractionAsMixedNumber = 1,
    /// <summary>Use unicode superscript and subscript set instead of standard ACSII set for numbers in fraction.</summary>
    UseUnicodeCharacters = 2
}

//...
private static void OutputFractionWithModifiers(Fraction fraction)
{
    var builder = new StringBuilder();
    builder.Append("Fraction = ").Append(fraction.ToString());
    builder.Append(", as mixed number = ").Append(fraction.ToString(Fraction.DisplayOptions.ImproperFractionAsMixedNumber));
    builder.Append(", with Unicode characters = ").Append(fraction.ToString(Fraction.DisplayOptions.UseUnicodeCharacters));
    builder.Append(", all modifiers = ").Append(fraction.ToString(Fraction.DisplayOptions.ImproperFractionAsMixedNumber | Fraction.DisplayOptions.UseUnicodeCharacters));
    Console.WriteLine(builder.ToString());
}
//...

//examples of different output options
fraction = new Fraction(10, 5);
OutputFractionWithModifiers(fraction);
fraction = new Fraction(11, 5);
OutputFractionWithModifiers(fraction);
fraction = new Fraction(3, 5);
OutputFractionWithModifiers(fraction);
fraction = new Fraction(15, -15);
OutputFractionWithModifiers(fraction);
fraction = new Fraction(11, 175);
OutputFractionWithModifiers(fraction);
fraction = new Fraction(113, 11);
OutputFractionWithModifiers(fraction);
//Output (in image):

foo

Easings

Usage

var easings = new EasingFunctions();

//quadratic
var easedInOutQuad = easings.EaseInOutQuad(x);

//cubic
var easedInOutCubic = easings.EaseInOutCubic(x);

//quartic
var easedInOutQuart = easings.EaseInOutQuart(x);

//quintic
var easedInOutQuint = easings.EaseInOutQuint(x);

var easedInOutBounce = easings.EaseInOutBounce(x);
var easedInOutElastic = easings.EaseInOutElastic(x);
var easedInOutExpo = easings.EaseInOutExpo(x);
var easedInOutCirc = easings.EaseInOutCirc(x);
var easedInOutBack = easings.EaseInOutBack(x);
var easedInOutSine = easings.EaseInOutSine(x);

Statistics

Interpolations

Usage

using MathExtended.Interpolations;

var interpolation = new Interpolation();
interpolation.Add(1, 2);
interpolation.Add(5, 8);
interpolation.Add(7.7, 5);
interpolation.Add(10, 15);
interpolation.Add(11, 11.3);

//Linear interpolation
double interpolatedValueLinear = interpolation.Linear(3.5);
//...or...
interpolation.Linear();
double interpolatedValueLinear = interpolation.Interpolate(3.5);

//Spline interpolation
double interpolatedValue = interpolation.Spline(3.5);
//...or...
interpolation.Spline();
double interpolatedValue = interpolation.Interpolate(3.5);	

//Cosine interpolation
double interpolatedValue = interpolation.Cosine(3.5);
//...or...
interpolation.Cosine();
double interpolatedValue = interpolation.Interpolate(3.5);

Random

Pure C# RANMAR Random Number Generator Algorithm Library.

Original ©:

RANMAR pseudo-random number generator This random number generator originally appeared in "Toward a Universal Random Number Generator" by George Marsaglia and Arif Zaman. Florida State University Report: FSU-SCRI-87-50 (1987) It was later modified by F. James and published in "A Review of Pseudo- random Number Generators" THIS IS THE BEST KNOWN RANDOM NUMBER GENERATOR AVAILABLE. (However, a newly discovered technique can yield a period of 10^600. But that is still in the development stage.) It passes ALL of the tests for random number generators and has a period of 2^144, is completely portable (gives bit identical results on all machines with at least 24-bit mantissas in the floating point representation). The algorithm is a combination of a Fibonacci sequence (with lags of 97 and 33, and operation "subtraction plus one, modulo one") and an "arithmetic sequence" (using subtraction).

C language version was written by Jim Butler, and was based on a FORTRAN program posted by David LaSalle of Florida State University. Adapted for Delphi by Anton Zhuchkov ([email protected]) in February, 2002. Converted into a class by Primoz Gabrijelcic ([email protected]) in November, 2002. (Url: https://github.com/gabr42/GpDelphiUnits/blob/master/src/GpRandomGen.pas)

Adapted for C# by Ales Hotko (https://github.com/ahotko) in May, 2020 (from Delphi (gabr42) and C (Url: https://www.pell.portland.or.us/~orc/Code/Misc/random.c))

Usage

int factor = 4096 * 4096;
var ranmar = new Ranmar(1802, 9373);

//To validate RANMAR generator, use the following procedure (described in original source):
// - set Seed1 to 1802
// - set Seed2 to 9373
// - Generate 20000 random numbers
// - next 6 generated numbers multiplied by 4096*4096 must be:
//   6533892, 14220222, 7275067, 6172232, 8354498, 10633180

for (int i = 0; i < 20006; i++)
{
    int generatedNumber = ranmar.Next(factor);
    if (i < 20000) continue;
    Console.WriteLine($"{i + 1}. {generatedNumber}");
}

//Output:
//20001. 6533892
//20002. 14220222
//20003. 7275067
//20004. 6172232
//20005. 8354498
//20006. 10633180

Also double can be generated:

Console.WriteLine($"Double = {ranmar.NextDouble()}");

//Output:
//Double = 0,339674651622772

Regressions

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