11# Math Classes in CSharp
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23[ ![ NuGet version] ( https://buildstats.info/nuget/MathClassesDmPa )] ( https://www.nuget.org/packages/MathClassesDmPa/ )
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35## About
6+
47Set of simple mathematical classes in C# including
8+
59* Vectors (with complex cases)
610* Matrixes (not only square)
711* Polynoms (including intergation and derivatives)
@@ -15,17 +19,29 @@ Set of simple mathematical classes in C# including
1519* Net functions methods
1620* Function optimization (including swarm algorithm for 1/2/n dimentions)
1721* Function values memorising (memoize) for parallel/non-parallel cases
22+
1823I'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.
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1925There are .NET Framework version and newest supported .NET Core (named MathClassesLibrary) copy with few upgrading.
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2027See some examples of using and results [ here] ( https://github.com/PasaOpasen/Old_Math_CSharpCpp_Projects ) or [ here] ( https://github.com/PasaOpasen/Search-for-defects-in-plates )
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2129## How to download
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2231Downloading in VS:
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2333![ 1] ( https://github.com/PasaOpasen/MathClasses/blob/master/gifs/download.gif )
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2435## Usage:
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2537![ 1] ( https://github.com/PasaOpasen/MathClasses/blob/master/gifs/usage.gif )
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2639## Examples
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2741Below you can see examples of using most used classes of this library.
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2843Firstly load the objects and set aliases:
44+
2945``` csharp
3046using MathNet .Numerics ;
3147using System ;
@@ -34,133 +50,208 @@ using МатКлассы;
3450using Complex = МатКлассы.Number .Complex ;
3551using Rational = МатКлассы.Number .Rational ;
3652```
53+
3754### Complex numbers
55+
3856``` csharp
39- var a = new Complex (1 );
40- a .Show (); // 1
41- var b = new Complex (2 . 5 , 1 . 5 );
42- b .Show (); // 2,5 + 1,5i
43- b .Conjugate .Show (); // 2,5 - 1,5i
44- b .Re .Show (); // 2,5
45- b .Im .Show (); // 1,5
46- b .Abs .Show (); // 2,9154759474226504
47- b .Arg .Show (); // 0,5404195002705842
48- var c = a / b + 3 + 5 . 6 + a * b +
49- Complex .Cos (b ) + Complex .Sin (a + b ) + Complex .Ch (a * b * b ) +
50- Complex .Ln (b ) + Complex .Exp (a ) + Complex .Expi (10 );
51- c .Show (); // 21,099555214728547 + 23,649577072514752i
52- c .Round (4 ).Show (); // 21,0996 + 23,6496i
53- c .Swap .Show (); // 23,649577072514752 + 21,099555214728547i
54- c .Pow (3 . 5 ).Show (); // -175884,94745749474 + 34459,051603806576i
55- 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)
56- Complex .ToComplex (" 1+2i" Show (); // 1 + 2i
57- Complex .ToComplex (" -1 + 2,346e-5i" Show (); // -1 + 2,346e-5i
57+ var a = new Complex (1 );
58+ a .Show (); // 1
59+
60+ var b = new Complex (2 . 5 , 1 . 5 );
61+ b .Show (); // 2,5 + 1,5i
62+ b .Conjugate .Show (); // 2,5 - 1,5i
63+ b .Re .Show (); // 2,5
64+ b .Im .Show (); // 1,5
65+ b .Abs .Show (); // 2,9154759474226504
66+ b .Arg .Show (); // 0,5404195002705842
67+
68+
69+ var c = a / b + 3 + 5 . 6 + a * b +
70+ Complex .Cos (b ) + Complex .Sin (a + b ) + Complex .Ch (a * b * b ) +
71+ Complex .Ln (b ) + Complex .Exp (a ) + Complex .Expi (10 );
72+ c .Show (); // 21,099555214728547 + 23,649577072514752i
73+ c .Round (4 ).Show (); // 21,0996 + 23,6496i
74+
75+ c .Swap .Show (); // 23,649577072514752 + 21,099555214728547i
76+ c .Pow (3 . 5 ).Show (); // -175884,94745749474 + 34459,051603806576i
77+
78+ 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)
79+
80+ Complex .ToComplex (" 1+2i" Show (); // 1 + 2i
81+ Complex .ToComplex (" -1 + 2,346e-5i" Show (); // -1 + 2,346e-5i
5882```
83+
5984### Rational numbers
85+
6086``` csharp
6187var a = new Rational (2123343454656 );
62- a .Show (); // 2123343454656
63- var b = new Rational (455 , 15 );
64- b .Show (); // 91/3
65- b .ShowMixed (); // 30 + 1/3
66- a + b ).IntPart .Show (); // 2123343454686
67- b .FracPart .Show (); // 1/3
68- var c = new Rational (22 . 16 );
69- c .Show (); // 554/25
70- Rational .ToRational (- 12 . 46572 ).Show (); // -311643/25000
71- b + c ).ShowMixed (); // 52 + 37/75
72- a / 3213443 + b * c ).ShowMixed (); // 661441 + 40262377/241008225
88+ a .Show (); // 2123343454656
89+
90+ var b = new Rational (455 , 15 );
91+ b .Show (); // 91/3
92+ b .ShowMixed (); // 30 + 1/3
93+
94+ (a + b ).IntPart .Show (); // 2123343454686
95+ b .FracPart .Show (); // 1/3
96+
97+ var c = new Rational (22 . 16 );
98+ c .Show (); // 554/25
99+
100+ Rational .ToRational (- 12 . 46572 ).Show (); // -311643/25000
101+
102+ (b + c ).ShowMixed (); // 52 + 37/75
103+
104+ (a / 3213443 + b * c ).ShowMixed (); // 661441 + 40262377/241008225
73105```
106+
74107### 2D Points
108+
75109``` csharp
76110var p1 = new Point (1 , 4 );
77111p1 .Show (); // (1 , 4)
78- Point .Add (p1 , 3 ).Show (); // (4 , 7)
79- Point .Add (p1 , - 1 , - 3 ).Show (); // (0 , 1)
80- Point .Eudistance (new Point (0 . 4 , - 2 ), new Point (1 , 1 )).Show (); // 3,059411708155671
81- var gen = Expendator .ThreadSafeRandomGen (100 );
82- var points = Enumerable .Range (0 , 10 ).Select (s => new Point (gen .NextDouble (), gen .NextDouble ())).ToArray ();
83- Point .Center (points ).Show (); // (0,6655678990602344 , 0,531635367093438)
84- points = Point .Points (x => Math .Sin (x ) + 2 * Math .Round (x ), n : 10 , a : - 0 . 2 , b : 0 . 2 );
85- foreach (var p in points )
86- Console .WriteLine (p );
87- // (0, 6655678990602344, 0, 531635367093438)
88- // (-0, 2, -0, 19866933079506122)
89- // (-0, 16, -0, 15931820661424598)
90- // (-0, 12000000000000001, -0, 11971220728891938)
91- // (-0, 08000000000000002, -0, 07991469396917271)
92- // (-0, 04000000000000001, -0, 03998933418663417)
93- // (0, 0)
94- // (0, 03999999999999998, 0, 03998933418663414)
95- // (0, 08000000000000002, 0, 07991469396917271)
96- // (0, 12, 0, 11971220728891936)
97- // (0, 15999999999999998, 0, 15931820661424595)
98- // (0, 2, 0, 19866933079506122)
112+
113+ Point .Add (p1 , 3 ).Show (); // (4 , 7)
114+ Point .Add (p1 , - 1 , - 3 ).Show (); // (0 , 1)
115+
116+ Point .Eudistance (new Point (0 . 4 , - 2 ), new Point (1 , 1 )).Show (); // 3,059411708155671
117+
118+ var gen = Expendator .ThreadSafeRandomGen (100 );
119+
120+ var points = Enumerable .Range (0 , 10 ).Select (s => new Point (gen .NextDouble (), gen .NextDouble ())).ToArray ();
121+
122+ Point .Center (points ).Show (); // (0,6655678990602344 , 0,531635367093438)
123+
124+ points = Point .Points (x => Math .Sin (x ) + 2 * Math .Round (x ), n : 10 , a : - 0 . 2 , b : 0 . 2 );
125+
126+ foreach (var p in points )
127+ Console .WriteLine (p );
128+
129+ // (0, 6655678990602344, 0, 531635367093438)
130+ // (-0, 2, -0, 19866933079506122)
131+ // (-0, 16, -0, 15931820661424598)
132+ // (-0, 12000000000000001, -0, 11971220728891938)
133+ // (-0, 08000000000000002, -0, 07991469396917271)
134+ // (-0, 04000000000000001, -0, 03998933418663417)
135+ // (0, 0)
136+ // (0, 03999999999999998, 0, 03998933418663414)
137+ // (0, 08000000000000002, 0, 07991469396917271)
138+ // (0, 12, 0, 11971220728891936)
139+ // (0, 15999999999999998, 0, 15931820661424595)
140+ // (0, 2, 0, 19866933079506122)
99141```
142+
100143### Function parser
144+
101145``` csharp
102- var gen = Expendator .ThreadSafeRandomGen (1 );
103- Func < double , double > f1 = Parser .GetDelegate (" cos(x)+sin(x/2+4,6)*exp(-sqr(x))+abs(x)^0,05"
104- 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 );
105- for (int i = 0 ; i < 5 ; i ++ )
106- {
107- var d = gen .NextDouble () * 50 ;
108- $" {f1 (d )} == {f2 (d )}" Show ();
109- }
110- // 2,1254805141764708 == 2,1254805141764708
111- // 1,8237614071831993 == 1,8237614071831991
112- // 0,9607774340933849 == 0,9607774340933849
113- // 1,8366859282256982 == 1,8366859282256982
114- // 1,3013656833866554 == 1,3013656833866554
115- Func < Complex , Complex > c1 = ParserComplex .GetDelegate (" Re(z)*Im(z) + sh(z)*I + sin(z)/100"
116- Func < Complex , Complex > c2 = z => z .Re * z .Im + Complex .Sh (z ) * Complex .I + Complex .Sin (z ) / 100 ;
117- for (int i = 0 ; i < 5 ; i ++ )
118- {
119- var d = new Complex (gen .NextDouble () * 50 , gen .NextDouble () * 10 );
120- $" {c1 (d )} == {c2 (d )}" Show ();
121- }
122- // 485696399,00749403 - 1151202339,537752i == 485696398,8506223 - 1151202339,7349265i
123- // - 1,328008130324937E+20 + 8,291419281824573E+19i == -1,328008130324937E+20 + 8,291419281824573E+19i
124- // - 12609203585138,465 + 42821192159972,99i == -12609203585138,78 + 42821192159972,99i
125- // 7270,488386388151 - 121362,61308893963i == 7270,344179063162 - 121362,52416901031i
126- // - 7,964336745137357E+20 + 1,3345594600169975E+21i == -7,964336745137357E+20 + 1,3345594600169975E+21i
146+
147+ var gen = Expendator .ThreadSafeRandomGen (1 );
148+
149+ Func < double , double > f1 = Parser .GetDelegate (" cos(x)+sin(x/2+4,6)*exp(-sqr(x))+abs(x)^0,05"
150+ 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 );
151+
152+ for (int i = 0 ; i < 5 ; i ++ )
153+ {
154+ var d = gen .NextDouble () * 50 ;
155+ $" {f1 (d )} == {f2 (d )}" Show ();
156+ }
157+ // 2,1254805141764708 == 2,1254805141764708
158+ // 1,8237614071831993 == 1,8237614071831991
159+ // 0,9607774340933849 == 0,9607774340933849
160+ // 1,8366859282256982 == 1,8366859282256982
161+ // 1,3013656833866554 == 1,3013656833866554
162+
163+ Func < Complex , Complex > c1 = ParserComplex .GetDelegate (" Re(z)*Im(z) + sh(z)*I + sin(z)/100"
164+ Func < Complex , Complex > c2 = z => z .Re * z .Im + Complex .Sh (z ) * Complex .I + Complex .Sin (z ) / 100 ;
165+
166+ for (int i = 0 ; i < 5 ; i ++ )
167+ {
168+ var d = new Complex (gen .NextDouble () * 50 , gen .NextDouble () * 10 );
169+
170+ $" {c1 (d )} == {c2 (d )}" Show ();
171+ }
172+
173+ // 485696399,00749403 - 1151202339,537752i == 485696398,8506223 - 1151202339,7349265i
174+ // - 1,328008130324937E+20 + 8,291419281824573E+19i == -1,328008130324937E+20 + 8,291419281824573E+19i
175+ // - 12609203585138,465 + 42821192159972,99i == -12609203585138,78 + 42821192159972,99i
176+ // 7270,488386388151 - 121362,61308893963i == 7270,344179063162 - 121362,52416901031i
177+ // - 7,964336745137357E+20 + 1,3345594600169975E+21i == -7,964336745137357E+20 + 1,3345594600169975E+21i
178+
127179```
128180### Real vectors
181+
129182``` csharp
130- var v = new Vectors (5 );
131- v .Show (); // ( 0 0 0 0 0 )
132- v = new Vectors (5 , 1 . 0 );
133- v .Show (); // ( 1 1 1 1 1 )
134- v = new Vectors (1 , 2 , 3 , 4 , 5 , 6 , 7 , 9 . 5 , - 2 , 3 );
135- v .Show (); // ( 1 2 3 4 5 6 7 9,5 -2 3 )
136- v = new Vectors (new double [] { 1 , 2 , 3 ,- 3 ,- 2 ,- 1 ,0 });
137- v .Show (); // ( 1 2 3 -3 -2 -1 0 )
138- v [6 ].Show (); // 0
139- v .EuqlidNorm .Show (); // 0,7559289460184545
140- v .Normalize (0 , 1 ).Show (); // ( 0,6666666666666666 0,8333333333333333 1 0 0,16666666666666666 0,3333333333333333 0,5 )
141- v .Range .Show (); // 6
142- v .SubVector (4 ).Show (); // ( 1 2 3 -3 )
143- v .Average .Show (); // 1,7142857142857142
144- v .Contain (3 ).Show (); // True
145- v .Normalize (- 0 . 5 , 0 . 5 ).ToRationalStringTab ().Show (); // ( 1/6 1/3 1/2 -1/2 -1/3 -1/6 0 )
146- var p = Vectors .Create (dim : 7 , min : 0 , max : 2 );
147- p .Show (); // ( 1,4585359040647745 1,7510524201206863 1,4706563879735768 0,45403700647875667 0,022686069831252098 1,9943826524540782 0,3851787596940994 )
148- Vectors .Mix (v , p ).Show ();
149- // ( 1 1,4585359040647745 2 1,7510524201206863 3 1,4706563879735768 -3 0,45403700647875667 -2 0,022686069831252098 -1 1,9943826524540782 0 0,3851787596940994 )
150- v + p ).Show (); // ( 2,4585359040647745 3,7510524201206863 4,470656387973577 -2,5459629935212433 -1,977313930168748 0,9943826524540782 0,3851787596940994 )
151- v * p ).Show (); // 5,970744096674025
152- Vectors .CompMult (v , p ).Show (); // ( 1,4585359040647745 3,5021048402413726 4,41196916392073 -1,36211101943627 -0,045372139662504196 -1,9943826524540782 0 )
153- 2 . 4 * v .AbsVector - p / 2 ).Sort .BinaryApproxSearch (1 . 5 ).Show (); // 1,4028086737729608
183+ var v = new Vectors (5 );
184+ v .Show (); // ( 0 0 0 0 0 )
185+
186+ v = new Vectors (5 , 1 . 0 );
187+ v .Show (); // ( 1 1 1 1 1 )
188+
189+ v = new Vectors (1 , 2 , 3 , 4 , 5 , 6 , 7 , 9 . 5 , - 2 , 3 );
190+ v .Show (); // ( 1 2 3 4 5 6 7 9,5 -2 3 )
191+
192+ v = new Vectors (new double [] { 1 , 2 , 3 ,- 3 ,- 2 ,- 1 ,0 });
193+ v .Show (); // ( 1 2 3 -3 -2 -1 0 )
194+
195+
196+ v [6 ].Show (); // 0
197+
198+ v .EuqlidNorm .Show (); // 0,7559289460184545
199+
200+ v .Normalize (0 , 1 ).Show (); // ( 0,6666666666666666 0,8333333333333333 1 0 0,16666666666666666 0,3333333333333333 0,5 )
201+
202+ v .Range .Show (); // 6
203+
204+ v .SubVector (4 ).Show (); // ( 1 2 3 -3 )
205+
206+ v .Average .Show (); // 1,7142857142857142
207+
208+ v .Contain (3 ).Show (); // True
209+
210+ v .Normalize (- 0 . 5 , 0 . 5 ).ToRationalStringTab ().Show (); // ( 1/6 1/3 1/2 -1/2 -1/3 -1/6 0 )
211+
212+ var p = Vectors .Create (dim : 7 , min : 0 , max : 2 );
213+ p .Show (); // ( 1,4585359040647745 1,7510524201206863 1,4706563879735768 0,45403700647875667 0,022686069831252098 1,9943826524540782 0,3851787596940994 )
214+
215+ Vectors .Mix (v , p ).Show ();
216+ // ( 1 1,4585359040647745 2 1,7510524201206863 3 1,4706563879735768 -3 0,45403700647875667 -2 0,022686069831252098 -1 1,9943826524540782 0 0,3851787596940994 )
217+
218+ (v + p ).Show (); // ( 2,4585359040647745 3,7510524201206863 4,470656387973577 -2,5459629935212433 -1,977313930168748 0,9943826524540782 0,3851787596940994 )
219+ v * p ).Show (); // 5,970744096674025
220+ Vectors .CompMult (v , p ).Show (); // ( 1,4585359040647745 3,5021048402413726 4,41196916392073 -1,36211101943627 -0,045372139662504196 -1,9943826524540782 0 )
221+
222+ (2 . 4 * v .AbsVector - p / 2 ).Sort .BinaryApproxSearch (1 . 5 ).Show (); // 1,4028086737729608
223+
154224```
225+
155226### Complex vectors
227+
156228``` csharp
157- var v1 = new Vectors (1 , 2 , 3 , 4 , 5 );
158- var v2 = new Vectors (0 , 3 , 4 , 3 , - 5 );
159- var c = new CVectors (R : v1 , I : v2 );
160- c .Show (); // (1 2 + 3i 3 + 4i 4 + 3i 5 - 5i)
161- c .Re .Show (); // ( 1 2 3 4 5 )
162- c .Normalize .Show (); // (0,1414213562373095 0,282842712474619 + 0,42426406871192845i 0,42426406871192845 + 0,565685424949238i 0,565685424949238 + 0,42426406871192845i 0,7071067811865475 - 0,7071067811865475i)
163- c .Conjugate .Show (); // (1 2 - 3i 3 - 4i 4 - 3i 5 + 5i)
164- 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 ) });
165- (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)
229+ var v1 = new Vectors (1 , 2 , 3 , 4 , 5 );
230+ var v2 = new Vectors (0 , 3 , 4 , 3 , - 5 );
231+
232+ var c = new CVectors (R : v1 , I : v2 );
233+
234+ c .Show (); // (1 2 + 3i 3 + 4i 4 + 3i 5 - 5i)
235+ c .Re .Show (); // ( 1 2 3 4 5 )
236+ c .Normalize .Show (); // (0,1414213562373095 0,282842712474619 + 0,42426406871192845i 0,42426406871192845 + 0,565685424949238i 0,565685424949238 + 0,42426406871192845i 0,7071067811865475 - 0,7071067811865475i)
237+ c .Conjugate .Show (); // (1 2 - 3i 3 - 4i 4 - 3i 5 + 5i)
238+
239+ 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 ) });
240+
241+ (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)
242+
166243```
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