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Math Classes for .NET

NuGet version Join the chat at https://gitter.im/MathClasses/community

About

Set of simple mathematical classes in C# including

  • Vectors (with complex cases)
  • Matrixes (not only square)
  • Polynoms (including intergation and derivatives)
  • Systems of linear equations
  • Integrals methods (including Gauss-Kronrod)
  • Complex numbers, complex vectors, matrixes and methods for complex functions
  • Rational numbers
  • Graphs
  • Methods for solving simple differential equations
  • Function approximation/interpolation
  • Net functions methods
  • Function optimization (including swarm algorithm for 1/2/n dimentions)
  • Function values memorising (memoize) for parallel/non-parallel cases

I've been creating this library since 2017 for my university homework and firts job. Writing it I was practicing my C# skills from C# 3.0 to C# 7.1, getting coding experience.

There are .NET Framework version and newest supported .NET Core (named MathClassesLibrary) copy with few upgrading.

See some examples of using and results here or here

How to download

Downloading in VS:

1

Usage:

1

Examples

Below you can see examples of using most used classes of this library.

Firstly load the objects and set aliases:

using MathNet.Numerics;
using System;
using System.Linq;
using МатКлассы;
using Complex = МатКлассы.Number.Complex;
using Rational = МатКлассы.Number.Rational;

Complex numbers

var a = new Complex(1);
a.Show(); // 1

var b = new Complex(2.5, 1.5);
b.Show(); // 2,5 + 1,5i
b.Conjugate.Show(); // 2,5 - 1,5i
b.Re.Show(); // 2,5
b.Im.Show(); // 1,5
b.Abs.Show(); // 2,9154759474226504
b.Arg.Show(); // 0,5404195002705842


var c = a / b + 3 + 5.6 + a * b +
Complex.Cos(b) + Complex.Sin(a + b) + Complex.Ch(a * b * b) +
Complex.Ln(b) + Complex.Exp(a) + Complex.Expi(10);
c.Show(); // 21,099555214728547 + 23,649577072514752i
c.Round(4).Show(); // 21,0996 + 23,6496i

c.Swap.Show(); // 23,649577072514752 + 21,099555214728547i
c.Pow(3.5).Show(); // -175884,94745749474 + 34459,051603806576i

new CVectors(Complex.Radical(a + b + b * b, 7)).Show(); // (1,4101632808375018 + 0,1774107754735756i   0,7405170949635271 + 1,2131238576267886i   -0,4867535672138724 + 1,3353299317700824i   -1,3474888653159458 + 0,4520053315239409i   -1,1935375640715047 - 0,771688502588176i   -0,14082813335184957 - 1,4142851546746704i   1,0179277541521443 - 0,9918962391315406i)

Complex.ToComplex("1+2i").Show(); // 1 + 2i
Complex.ToComplex("-1 + 2,346e-5i").Show(); // -1 + 2,346e-5i

Rational numbers

var a = new Rational(2123343454656);
a.Show(); // 2123343454656

var b = new Rational(455, 15);
b.Show(); // 91/3
b.ShowMixed(); // 30 + 1/3

(a + b).IntPart.Show(); // 2123343454686
b.FracPart.Show(); // 1/3

var c = new Rational(22.16);
c.Show(); // 554/25

Rational.ToRational(-12.46572).Show(); // -311643/25000

(b + c).ShowMixed(); // 52 + 37/75

(a / 3213443 + b * c).ShowMixed(); // 661441 + 40262377/241008225

2D Points

var p1 = new Point(1, 4);
p1.Show(); // (1 , 4)

Point.Add(p1, 3).Show(); // (4 , 7)
Point.Add(p1, -1, -3).Show(); // (0 , 1)

Point.Eudistance(new Point(0.4, -2), new Point(1, 1)).Show(); // 3,059411708155671

var gen = Expendator.ThreadSafeRandomGen(100);

var points = Enumerable.Range(0, 10).Select(s => new Point(gen.NextDouble(), gen.NextDouble())).ToArray();

Point.Center(points).Show(); // (0,6655678990602344 , 0,531635367093438) 

points = Point.Points(x => Math.Sin(x) + 2 * Math.Round(x), n: 10, a: -0.2, b: 0.2);

foreach (var p in points)
  Console.WriteLine(p);

//(0, 6655678990602344, 0, 531635367093438)
//(-0, 2, -0, 19866933079506122)
//(-0, 16, -0, 15931820661424598)
//(-0, 12000000000000001, -0, 11971220728891938)
//(-0, 08000000000000002, -0, 07991469396917271)
//(-0, 04000000000000001, -0, 03998933418663417)
//(0, 0)
//(0, 03999999999999998, 0, 03998933418663414)
//(0, 08000000000000002, 0, 07991469396917271)
//(0, 12, 0, 11971220728891936)
//(0, 15999999999999998, 0, 15931820661424595)
//(0, 2, 0, 19866933079506122)

Function parser

var gen = Expendator.ThreadSafeRandomGen(1);

Func<double, double> f1 = Parser.GetDelegate("cos(x)+sin(x/2+4,6)*exp(-sqr(x))+abs(x)^0,05");
Func<double, double> f2 = x => Math.Cos(x) + Math.Sin(x / 2 + 4.6) * Math.Exp(-x * x) + Math.Pow(Math.Abs(x), 0.05);

for (int i = 0; i < 5; i++)
{
  var d = gen.NextDouble() * 50;
  $"{f1(d)} == {f2(d)}".Show();
}
//2,1254805141764708 == 2,1254805141764708
//1,8237614071831993 == 1,8237614071831991
//0,9607774340933849 == 0,9607774340933849
//1,8366859282256982 == 1,8366859282256982
//1,3013656833866554 == 1,3013656833866554

Func<Complex, Complex> c1 = ParserComplex.GetDelegate("Re(z)*Im(z) + sh(z)*I + sin(z)/100");
Func<Complex, Complex> c2 = z => z.Re * z.Im + Complex.Sh(z) * Complex.I + Complex.Sin(z) / 100;

for (int i = 0; i < 5; i++)
{
  var d = new Complex(gen.NextDouble() * 50, gen.NextDouble() * 10);

  $"{c1(d)} == {c2(d)}".Show();
}

// 485696399,00749403 - 1151202339,537752i == 485696398,8506223 - 1151202339,7349265i
//- 1,328008130324937E+20 + 8,291419281824573E+19i == -1,328008130324937E+20 + 8,291419281824573E+19i
// - 12609203585138,465 + 42821192159972,99i == -12609203585138,78 + 42821192159972,99i
//7270,488386388151 - 121362,61308893963i == 7270,344179063162 - 121362,52416901031i
//- 7,964336745137357E+20 + 1,3345594600169975E+21i == -7,964336745137357E+20 + 1,3345594600169975E+21i

Real vectors

var v = new Vectors(5);
v.Show(); // (       0       0       0       0       0       )

v = new Vectors(5, 1.0);
v.Show(); // (       1       1       1       1       1       )

v = new Vectors(1, 2, 3, 4, 5, 6, 7, 9.5, -2, 3);
v.Show(); // (       1       2       3       4       5       6       7       9,5     -2      3       )

v = new Vectors(new double[] { 1, 2, 3,-3,-2,-1,0 });
v.Show(); // (       1       2       3       -3      -2      -1      0       )


v[6].Show(); // 0

v.EuqlidNorm.Show(); // 0,7559289460184545

v.Normalize(0, 1).Show(); // (       0,6666666666666666      0,8333333333333333      1       0       0,16666666666666666     0,3333333333333333     0,5      )

v.Range.Show(); // 6

v.SubVector(4).Show(); // (       1       2       3       -3      )

v.Average.Show(); // 1,7142857142857142

v.Contain(3).Show(); // True

v.Normalize(-0.5, 0.5).ToRationalStringTab().Show(); // (       1/6     1/3     1/2     -1/2    -1/3    -1/6    0       )

var p = Vectors.Create(dim: 7, min: 0, max: 2);
p.Show(); // (       1,4585359040647745      1,7510524201206863      1,4706563879735768      0,45403700647875667     0,022686069831252098    1,9943826524540782      0,3851787596940994      )

Vectors.Mix(v, p).Show(); 
// (       1       1,4585359040647745      2       1,7510524201206863      3       1,4706563879735768      -3      0,45403700647875667      -2      0,022686069831252098    -1      1,9943826524540782      0       0,3851787596940994      )
(v + p).Show(); // (       2,4585359040647745      3,7510524201206863      4,470656387973577       -2,5459629935212433     -1,977313930168748      0,9943826524540782      0,3851787596940994      )
(v * p).Show(); // 5,970744096674025
Vectors.CompMult(v, p).Show(); // (       1,4585359040647745      3,5021048402413726      4,41196916392073        -1,36211101943627       -0,045372139662504196   -1,9943826524540782     0       )

(2.4*v.AbsVector - p/2).Sort.BinaryApproxSearch(1.5).Show(); // 1,4028086737729608

Complex vectors

var v1 = new Vectors(1, 2, 3, 4, 5);
var v2 = new Vectors(0, 3, 4, 3, -5);

var c = new CVectors(R: v1, I: v2);

c.Show(); // (1    2 + 3i   3 + 4i   4 + 3i   5 - 5i)
c.Re.Show(); // (       1       2       3       4       5       )
c.Normalize.Show(); // (0,1414213562373095    0,282842712474619 + 0,42426406871192845i   0,42426406871192845 + 0,565685424949238i   0,565685424949238 + 0,42426406871192845i   0,7071067811865475 - 0,7071067811865475i)
c.Conjugate.Show(); // (1    2 - 3i   3 - 4i   4 - 3i   5 + 5i)

var b = new CVectors(new Complex[] { new Complex(1, 2), new Complex(4, 5), new Complex(4.4, 0), new Complex(), new Complex(4.5) });

(c/5 + b*(0.2-Complex.I)).Show(); // (2,4000000000000004 - 0,6i   6,2 - 2,4i   1,48 - 3,6000000000000005i   0,8 + 0,6i   1,9 - 5,5i)

Square matrixes

var mat = new SqMatrix(new double[,] { { 1, -5 }, { -40, 0.632 } });

mat.PrintMatrix();
//  1      -5
//- 40     0,632

var i = SqMatrix.I(mat.RowCount);

i.PrintMatrix();
//1       0
//0       1

var mat2 = mat + i * 40;

mat2.PrintMatrix();
//41      -5
//-40     40,632

var inv = mat.Invertion;
inv.PrintMatrix();
//-0,003170017254524297   -0,02507925043136311
//-0,20063400345090485 - 0,0050158500862726215

(inv * mat).PrintMatrix();
//1       0
//2,7755575615628914E-17  0,9999999999999999


(inv * mat).Track.Show(); // 2


(inv * mat).CubeNorm.Show(); // 1

(inv * mat).Det.Show(); // 0,9999999999999999

mat.Solve(new Vectors(4.0, -5)).Show(); // (       0,11271618313871837     -0,7774567633722562     )

There are also complex square matrixes, real nonsquare matrixes, real systems of linear equations and complex systems of linear equations.

Random numbers

RandomNumbers.SetSeed(0);

RandomNumbers.NextDouble.Show(); // 0,7262432699679598

RandomNumbers.NextDouble2(min: 40, max: 50).Show(); // 48,173253595909685

RandomNumbers.NextNumber().Show(); // 1649316166

Double nets

void show(NetOnDouble n) => new Vectors(n.Array).Show();

var net = new NetOnDouble(begin: -1, end: 1, count: 8); // like numpy.linspase

show(net); // (       -1      -0,7142857142857143     -0,4285714285714286     -0,1428571428571429     0,1428571428571428      0,4285714285714284      0,7142857142857142      1       )

net = new NetOnDouble(begin: -1, end: 1, step: 0.3); // like numpy.arange

show(net); // (       -1      -0,7    -0,4    -0,10000000000000009    0,19999999999999996     0,5     0,7999999999999998      )

var net2 = new NetOnDouble(net, newCount: 5);

show(net2); // (       -1      -0,6    -0,19999999999999996    0,20000000000000018     0,6000000000000001      )

Integration

Func<double, double> freal = x => (x-4 + Math.Sin(x*10)) / (1 + x * x);

double integral = FuncMethods.DefInteg.GaussKronrod.GaussKronrodSum(freal, a: -3, b: 3, n: 61, count: 5);

integral.Show(); // -9,992366179186035

Complex integ = FuncMethods.DefInteg.GaussKronrod.GaussKronrodSum(
  z => (Math.Exp(-z.Abs) + Complex.Sin(z + Complex.I)) / (1 + z * z / 5), 
  a: new Complex(-1,-4.3), b: 3+Complex.I*2, n: 61, count: 10);

integ.Show(); // -3,325142834912312 + 10,22008333462534i

This class also supports improper integrals, double integrals and Monte-Carlo methods (for vector-functions too).

Memoization

Func<double, double> f = t => 
  FuncMethods.DefInteg.GaussKronrod.GaussKronrodSum(x=>Math.Exp(-(x-t).Sqr()-x*x), a: -20, b: 10, n: 61, count: 12);

var f_Memoized = new Memoize<double,double>(f, capacity: 10, concurrencyLevel: 1).Value;

var t = DateTime.Now;
void show_time()
{
  (DateTime.Now-t).Ticks.Show();
  t = DateTime.Now;
}

f_Memoized(2).Show(); // 0,16961762375804412

show_time(); // 842753

f_Memoized(2.5).Show(); // 0,05506678006050927

show_time(); // 8179

f_Memoized(3).Show(); // 0,013923062412768037

show_time(); // 7991

f_Memoized(2.5).Show(); // 0,05506678006050927

show_time(); // 1442



// not only real functions!

Func<(double, Complex, bool), (int, int)> c = tuple =>
{
  var x = tuple.Item1;
  var z = tuple.Item2;
  var b = tuple.Item3;

  if (b)
    return ((int)(x + z.Re), (int)(x + z.Im));
  else
    return (0, 0);
};

var c_tmp = new Memoize<(double, Complex, bool), (int, int)>(c, 100, 4).Value;

Func<double, Complex, bool,(int,int)> c_Memoized = (double x, Complex z, bool b) => c_tmp((x, z, b));

There are threadsafe and nonthreadsafe implementations.

Polynoms

// create by coefs
var pol = new Polynom(new double[] { 1, 2, 3, 4, 5 });
pol.Show(); // 5x^4 + 4x^3 + 3x^2 + 2x^1 + 1

// create by head coef and roots
pol = new Polynom(aN: 2, -1, 0, 1, 2);
pol.Show(); // 2x^4 + -4x^3 + -2x^2 + 4x^1 + -0


var points = new Point[] { new Point(1, 2), new Point(3, 4), new Point(5, 7) };
// interpolation polynom
pol = new Polynom(points);

pol.Show(); // 0,125x^2 + 0,5x^1 + 1,375
pol.Value(1).Show(); // 2
pol.Value(3).Show(); // 4
pol.Value(5).Show(); // 7


// interpolation polynom
pol = new Polynom(x => Math.Sin(x) + x, n: 6, a: -1, b: 1);

foreach (var val in new NetOnDouble(-1, 1, 12).Array)
  $"pol = {pol.Value(val)}   f = {Math.Sin(val)+val}".Show();

//pol = -1,841470984807902   f = -1,8414709848078965
//pol = -1,5480795026639842   f = -1,548086037891892
//pol = -1,230639272195443   f = -1,230638423911926
//pol = -0,8936010083785814   f = -0,8935994224990154
//pol = -0,5420855146782465   f = -0,5420861802628714
//pol = -0,18169222919395844   f = -0,1816930144179611
//pol = 0,18169222919395842   f = 0,1816930144179611
//pol = 0,5420855146782463   f = 0,5420861802628714
//pol = 0,8936010083785806   f = 0,8935994224990154
//pol = 1,2306392721954413   f = 1,230638423911926
//pol = 1,5480795026639818   f = 1,5480860378918924
//pol = 1,8414709848078967   f = 1,8414709848078965

// operations

var pol1 = new Polynom(new double[] { 1, 2, 3, 4, 5 });
var pol2 = new Polynom(new double[] { 2.2, 3 });

pol1.Show(); // 5x^4 + 4x^3 + 3x^2 + 2x^1 + 1
pol2.Show(); // 3x^1 + 2,2
pol2.ShowRational(); // (3x^1) + 11/5

(pol1 * pol2).Show(); // 15x^5 + 23x^4 + 17,8x^3 + 12,600000000000001x^2 + 7,4x^1 + 2,2

(pol1 / 2 + pol2 * 2.8-4.66).Show(); // 2,5x^4 + 2x^3 + 1,5x^2 + 9,399999999999999x^1 + 2

var a = pol1 / pol2;
var b = pol1 % pol2;

$"{pol1} == {a*pol2+b}".Show(); // 5x^4 + 4x^3 + 3x^2 + 2x^1 + 1 == 5x^4 + 4x^3 + 3x^2 + 2x^1 + 1

(a, b) = Polynom.Division(pol1 - 1.5, pol2);
$"{pol1-1.5} == {a * pol2 + b}".Show(); // 5x^4 + 4x^3 + 3x^2 + 2x^1 + -0,5 == 5x^4 + 4x^3 + 3x^2 + 2x^1 + -0,5

// derivative
(pol1 | 2).Show(); // 60x^2 + 24x^1 + 6



pol2.Value(pol1).Show(); // 

pol2.Value(new SqMatrix(new double[,] { { 1, 2 }, { 3, 4 } })).PrintMatrix();

//5,2     6
//9       14,2


// integration

$"{pol1.S(-3,2)} == {FuncMethods.DefInteg.GaussKronrod.MySimpleGaussKronrod(pol1.Value,-3,2,n:15)}".Show();

// 245 == 244,99999999999997

There are also splines and rational interpolation.

Swarm algorithm

double rastr(double v) => v * v - 10 * Math.Cos(2 * Math.PI * v);
double shvel(double v) => -v * Math.Sin(Math.Sqrt(v.Abs()));

1 1

Use swarm algorithm to find global minimum of 1D-functions:

// 1D functions

var (argmin, min) = BeeHiveAlgorithm.GetGlobalMin(rastr, minimum: -5, maximum: 5,eps:1e-15, countpoints: 100, maxiter: 100);

$"min = {min}, argmin = {argmin}".Show(); // min = -9,973897874017823, argmin = 0,011472797486931086


(argmin, min) = BeeHiveAlgorithm.GetGlobalMin(shvel, minimum: -150, maximum: 150, eps: 1e-15, countpoints: 100, maxiter: 100);

$"min = {min}, argmin = {argmin}".Show(); // min = -122,45163537317933, argmin = -126,64228803478181

2D-functions

// 2D functions

// u can write -func to find the maximum of function
var (argmin2, _) = BeeHiveAlgorithm.GetGlobalMin((Point p) => -shvel(p.x) - shvel(p.y), 
  minimum: new Point(-150, -150), maximum: new Point(150, 150), eps: 1e-15, countpoints: 300, maxiter: 200);

argmin2.Show(); // (125,85246982052922 , 133,86488312389702)


// u don't need only smooth functions!
(argmin2, _) = BeeHiveAlgorithm.GetGlobalMin((Point p) => -shvel(p.x) - shvel(p.y)+RandomNumbers.NextDouble2(-1,1), 
  minimum: new Point(-150, -150), maximum: new Point(150, 150), eps: 1e-15, countpoints: 500, maxiter: 200);

argmin2.Show(); // (124,97163349762559 , 126,79389473050833)

1

And more than 2D functions:

// u can use 3D+ functions

var (argmin3, _) = BeeHiveAlgorithm.GetGlobalMin((Vectors v) => Math.Sin(v[0]).Abs()*rastr(v[1])*shvel(v[2]).Abs()+shvel(v[3]),
  minimum: new Vectors(-100, -100, -100, -50),
  maximum: new Vectors(100, 50, 50, 50),
  eps: 1e-15,
  countpoints: 500,
  maxiter: 500);

argmin3.Show(); // (       48,37734238244593       0,09753305930644274     -60,919505648780614     46,69636117760092       )

This class also contains the bee colony method.