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Usage:

Examples

usingMathNet.Numerics;usingSystem;usingSystem.Linq;usingМатКлассы;usingComplex=МатКлассы.Number.Complex;usingRational=МатКлассы.Number.Rational;

Complex numbers

vara=newComplex(1);a.Show();// 1varb=newComplex(2.5,1.5);b.Show();// 2,5 + 1,5ib.Conjugate.Show();// 2,5 - 1,5ib.Re.Show();// 2,5b.Im.Show();// 1,5b.Abs.Show();// 2,9154759474226504b.Arg.Show();// 0,5404195002705842varc=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 + 23,649577072514752ic.Round(4).Show();// 21,0996 + 23,6496ic.Swap.Show();// 23,649577072514752 + 21,099555214728547ic.Pow(3.5).Show();// -175884,94745749474 + 34459,051603806576inewCVectors(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 + 2iComplex.ToComplex("-1 + 2,346e-5i").Show();// -1 + 2,346e-5i

Rational numbers

vara=newRational(2123343454656);a.Show();// 2123343454656varb=newRational(455,15);b.Show();// 91/3b.ShowMixed();// 30 + 1/3(a+b).IntPart.Show();// 2123343454686b.FracPart.Show();// 1/3varc=newRational(22.16);c.Show();// 554/25Rational.ToRational(-12.46572).Show();// -311643/25000(b+c).ShowMixed();// 52 + 37/75(a/3213443+b*c).ShowMixed();// 661441 + 40262377/241008225

2D Points

varp1=newPoint(1,4);p1.Show();// (1 , 4)Point.Add(p1,3).Show();// (4 , 7)Point.Add(p1,-1,-3).Show();// (0 , 1)Point.Eudistance(newPoint(0.4,-2),newPoint(1,1)).Show();// 3,059411708155671vargen=Expendator.ThreadSafeRandomGen(100);varpoints=Enumerable.Range(0,10).Select(s=>newPoint(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(varpinpoints)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

vargen=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(inti=0;i<5;i++){vard=gen.NextDouble()*50;$"{f1(d)} =={f2(d)}".Show();}//2,1254805141764708 == 2,1254805141764708//1,8237614071831993 == 1,8237614071831991//0,9607774340933849 == 0,9607774340933849//1,8366859282256982 == 1,8366859282256982//1,3013656833866554 == 1,3013656833866554Func<Complex,Complex>c1=ParserComplex.GetDelegate("Re(z)*Im(z) + sh(z)*I + sin(z)/100");Func<Complex,Complex>c2= z=>z.Re*z.Im+Complex.Sh(z)*Complex.I+Complex.Sin(z)/100;for(inti=0;i<5;i++){vard=newComplex(gen.NextDouble()*50,gen.NextDouble()*10);$"{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

varv=newVectors(5);v.Show();// (       0       0       0       0       0       )v=newVectors(5,1.0);v.Show();// (       1       1       1       1       1       )v=newVectors(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=newVectors(newdouble[]{1,2,3,-3,-2,-1,0});v.Show();// (       1       2       3       -3      -2      -1      0       )v[6].Show();// 0v.EuqlidNorm.Show();// 0,7559289460184545v.Normalize(0,1).Show();// (       0,6666666666666666      0,8333333333333333      1       0       0,16666666666666666     0,3333333333333333     0,5      )v.Range.Show();// 6v.SubVector(4).Show();// (       1       2       3       -3      )v.Average.Show();// 1,7142857142857142v.Contain(3).Show();// Truev.Normalize(-0.5,0.5).ToRationalStringTab().Show();// (       1/6     1/3     1/2     -1/2    -1/3    -1/6    0       )varp=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();// 5,970744096674025Vectors.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

varv1=newVectors(1,2,3,4,5);varv2=newVectors(0,3,4,3,-5);varc=newCVectors(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)varb=newCVectors(newComplex[]{newComplex(1,2),newComplex(4,5),newComplex(4.4,0),newComplex(),newComplex(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

varmat=newSqMatrix(newdouble[,]{{1,-5},{-40,0.632}});mat.PrintMatrix();//  1      -5//- 40     0,632vari=SqMatrix.I(mat.RowCount);i.PrintMatrix();//1       0//0       1varmat2=mat+i*40;mat2.PrintMatrix();//41      -5//-40     40,632varinv=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();// 0,9999999999999999mat.Solve(newVectors(4.0,-5)).Show();// (       0,11271618313871837     -0,7774567633722562     )

Random numbers

RandomNumbers.SetSeed(0);RandomNumbers.NextDouble.Show();// 0,7262432699679598RandomNumbers.NextDouble2(min:40,max:50).Show();// 48,173253595909685RandomNumbers.NextNumber().Show();// 1649316166

Double nets

voidshow(NetOnDoublen)=>newVectors(n.Array).Show();varnet=newNetOnDouble(begin:-1,end:1,count:8);// like numpy.linspaseshow(net);// (       -1      -0,7142857142857143     -0,4285714285714286     -0,1428571428571429     0,1428571428571428      0,4285714285714284      0,7142857142857142      1       )net=newNetOnDouble(begin:-1,end:1,step:0.3);// like numpy.arangeshow(net);// (       -1      -0,7    -0,4    -0,10000000000000009    0,19999999999999996     0,5     0,7999999999999998      )varnet2=newNetOnDouble(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);doubleintegral=FuncMethods.DefInteg.GaussKronrod.GaussKronrodSum(freal,a:-3,b:3,n:61,count:5);integral.Show();// -9,992366179186035Complexinteg=FuncMethods.DefInteg.GaussKronrod.GaussKronrodSum(  z=>(Math.Exp(-z.Abs)+Complex.Sin(z+Complex.I))/(1+z*z/5),a:newComplex(-1,-4.3),b:3+Complex.I*2,n:61,count:10);integ.Show();// -3,325142834912312 + 10,22008333462534i

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);varf_Memoized=newMemoize<double,double>(f,capacity:10,concurrencyLevel:1).Value;vart=DateTime.Now;voidshow_time(){(DateTime.Now-t).Ticks.Show();t=DateTime.Now;}f_Memoized(2).Show();// 0,16961762375804412show_time();// 842753f_Memoized(2.5).Show();// 0,05506678006050927show_time();// 8179f_Memoized(3).Show();// 0,013923062412768037show_time();// 7991f_Memoized(2.5).Show();// 0,05506678006050927show_time();// 1442// not only real functions!Func<(double,Complex,bool),(int,int)>c= tuple=>{varx=tuple.Item1;varz=tuple.Item2;varb=tuple.Item3;if(b)return((int)(x+z.Re),(int)(x+z.Im));elsereturn(0,0);};varc_tmp=newMemoize<(double,Complex,bool),(int,int)>(c,100,4).Value;Func<double,Complex,bool,(int,int)>c_Memoized=(doublex,Complexz,boolb)=>c_tmp((x,z,b));

Polynoms

// create by coefsvarpol=newPolynom(newdouble[]{1,2,3,4,5});pol.Show();// 5x^4 + 4x^3 + 3x^2 + 2x^1 + 1// create by head coef and rootspol=newPolynom(aN:2,-1,0,1,2);pol.Show();// 2x^4 + -4x^3 + -2x^2 + 4x^1 + -0varpoints=newPoint[]{newPoint(1,2),newPoint(3,4),newPoint(5,7)};// interpolation polynompol=newPolynom(points);pol.Show();// 0,125x^2 + 0,5x^1 + 1,375pol.Value(1).Show();// 2pol.Value(3).Show();// 4pol.Value(5).Show();// 7// interpolation polynompol=newPolynom(x=>Math.Sin(x)+x,n:6,a:-1,b:1);foreach(varvalinnewNetOnDouble(-1,1,12).Array)$"pol ={pol.Value(val)}   f ={Math.Sin(val)+val}".Show();//pol = -1,841470984807902   f = -1,8414709848078965//pol = -1,5480795026639842   f = -1,548086037891892//pol = -1,230639272195443   f = -1,230638423911926//pol = -0,8936010083785814   f = -0,8935994224990154//pol = -0,5420855146782465   f = -0,5420861802628714//pol = -0,18169222919395844   f = -0,1816930144179611//pol = 0,18169222919395842   f = 0,1816930144179611//pol = 0,5420855146782463   f = 0,5420861802628714//pol = 0,8936010083785806   f = 0,8935994224990154//pol = 1,2306392721954413   f = 1,230638423911926//pol = 1,5480795026639818   f = 1,5480860378918924//pol = 1,8414709848078967   f = 1,8414709848078965// operationsvarpol1=newPolynom(newdouble[]{1,2,3,4,5});varpol2=newPolynom(newdouble[]{2.2,3});pol1.Show();// 5x^4 + 4x^3 + 3x^2 + 2x^1 + 1pol2.Show();// 3x^1 + 2,2pol2.ShowRational();// (3x^1) + 11/5(pol1*pol2).Show();// 15x^5 + 23x^4 + 17,8x^3 + 12,600000000000001x^2 + 7,4x^1 + 2,2(pol1/2+pol2*2.8-4.66).Show();// 2,5x^4 + 2x^3 + 1,5x^2 + 9,399999999999999x^1 + 2vara=pol1/pol2;varb=pol1%pol2;$"{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);$"{pol1-1.5} =={a*pol2+b}".Show();// 5x^4 + 4x^3 + 3x^2 + 2x^1 + -0,5 == 5x^4 + 4x^3 + 3x^2 + 2x^1 + -0,5// derivative(pol1|2).Show();// 60x^2 + 24x^1 + 6pol2.Value(pol1).Show();//pol2.Value(newSqMatrix(newdouble[,]{{1,2},{3,4}})).PrintMatrix();//5,2     6//9       14,2// integration$"{pol1.S(-3,2)} =={FuncMethods.DefInteg.GaussKronrod.MySimpleGaussKronrod(pol1.Value,-3,2,n:15)}".Show();// 245 == 244,99999999999997

Swarm algorithm

doublerastr(doublev)=>v*v-10*Math.Cos(2*Math.PI*v);doubleshvel(doublev)=>-v*Math.Sin(Math.Sqrt(v.Abs()));

// 1D functionsvar(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// u can write -func to find the maximum of functionvar(argmin2, _)=BeeHiveAlgorithm.GetGlobalMin((Pointp)=>-shvel(p.x)-shvel(p.y),minimum:newPoint(-150,-150),maximum:newPoint(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((Pointp)=>-shvel(p.x)-shvel(p.y)+RandomNumbers.NextDouble2(-1,1),minimum:newPoint(-150,-150),maximum:newPoint(150,150),eps:1e-15,countpoints:500,maxiter:200);argmin2.Show();// (124,97163349762559 , 126,79389473050833)

// u can use 3D+ functionsvar(argmin3, _)=BeeHiveAlgorithm.GetGlobalMin((Vectorsv)=>Math.Sin(v[0]).Abs()*rastr(v[1])*shvel(v[2]).Abs()+shvel(v[3]),minimum:newVectors(-100,-100,-100,-50),maximum:newVectors(100,50,50,50),eps:1e-15,countpoints:500,maxiter:500);argmin3.Show();// (       48,37734238244593       0,09753305930644274     -60,919505648780614     46,69636117760092       )