🧮 CSharpNumerics

A comprehensive numerical library for scientific computing, mathematical analysis, and iterative processes in C#. NuGet Package

---

✨ Features

• 🔢 Numerical extensions (Factorial, derivatives, integrals, root finding, etc.)
• 📈 Vectors, matrices, and complex numbers
• 🌊 Vector fields (Gradient, Divergence, Curl, Laplacian)
• 🧠 Complex and real function analysis
• 🔬 Fourier, Laplace, and Monte Carlo transforms
• 📉 Differential equation solvers (Runge–Kutta, Trapezoidal, etc.)
• 📊 Statistics and regression tools
• 🔗 Full integration with LINQ and extension methods

---

📘 Numeric Extensions

Factorial

int result = 5.Factorial(); // 120

Root Finding (Newton–Raphson)

Func<double, double> func = x => Math.Pow(x, 2) - 4;
double root = func.NewtonRaphson(); // 2

---

Derivative

Func<double, double> f = x => Math.Pow(x, 2);
Func<double, double> g = x => 4 * x - 3;
var result = f.Derivate(g, 1);

Supports Chain, Product, and Quotient rules via:

var result = f.Derivate(g, Numerics.Enums.DerivateOperator.Product);

Multiple variables:

Func<double[], double> func = vars => vars[0] * vars[1];
var dfdx = func.Derivate(new double[] { 2, 3 }, index: 0);

Or with vectors:

Func<Vector, double> func = v => v.x * v.y;
var dfdx = func.Derivate(new Vector(2, 3, 0), Cartesian.X);

Derivate series:

Func<double, double> displacement = t => 9.81 * Math.Pow(t, 2) / 2;
var velocity = displacement.GetSeries(0, 10, 1000).Derivate();

---

∫ Integrals

Trapezoidal rule:

Func<double, double> f = x => Math.Sin(x);
double integral = f.Integrate(0, Math.PI);

Integrate a series or timeseries:

List<TimeSerie> ts = ...;
double total = ts.Integrate();

Monte Carlo Integration

Func<(double x, double y), double> func = p => p.x * p.y;
double result = func.Integrate((0, 1), (0, 1));

---

🧩 Complex Numbers

var a = new ComplexNumber(3, 2);
var b = new ComplexNumber(5, 3);

var sum = a + b;
var product = a * b;
var power = a.Pow(2); // 5 + 12i

Exponential:

new ComplexNumber(0, Math.PI).Exponential(); // -1

---

🧭 Vector

var a = new Vector(5, 3, 0);
var b = new Vector(2, 6, 0);

var dot = a.Dot(b);
var cross = a.Cross(b);

From spherical coordinates:

var v = Vector.FromSphericalCoordinates(radius, inclination, azimuth);

---

🧮 Matrix

var A = new Matrix(new double[,] { { 1, 3, 7 }, { 5, 2, 9 } });
var transpose = A.Transpose();
var det = A.Determinant();
var inv = A.Inverse();

Arithmetic:

var B = new Matrix(new double[,] { { 2, 5, 1 }, { 4, 3, 7 } });
var sum = A + B;
var product = A * B;

With vector:

var x = new Vector(2, 1, 3);
var y = A * x;

---

🌐 Vector Field

Gradient

Func<Vector, double> f = p => Math.Pow(p.x, 2) * Math.Pow(p.y, 3);
var grad = f.Gradient((1, -2, 0));

Divergence

var field = new VectorField(p => Math.Sin(p.x * p.y),
                            p => Math.Cos(p.x * p.y),
                            p => Math.Exp(p.z));

double div = field.Divergence((1, 2, 2));

Curl

var field = new VectorField(p => p.y, p => -p.x, p => 0);
var curl = field.Curl((1, 4, 2));

---

⚙️ Transform

FFT

Func<double, double> f = t => Math.Exp(-t * t / 0.02);
var freq = f.FastFouriertransform(-0.5, 0.5, 100)
             .ToFrequencyResolution(100);

Laplace Transform

double result = f.LaplaceTransform(2.0);

---

📐 Differential Equations

Runge–Kutta (RK4)

Func<(double t, double y), double> f = v => Math.Tan(v.y) + 1;
var result = f.RungeKutta(1, 1.1, 0.025, 1);

Linear Systems

var result = A.LinearSystemSolver(b);
var eigenValues = A.EigenValues();

---

📊 Statistics

var noise = new Random().GenerateNoise(4);
double median = ts.Median(p => p.Value);
double std = ts.StandardDeviation(p => p.Value);

Regression:

var (slope, intercept, corr) = serie.LinearRegression(p => (p.Index, p.Value));
var expFunc = serie.ExponentialRegression(p => (p.Index, p.Value));

K-nearest neighbors:

var data = new List<(double x, double y, int c)> { (7,7,0), (7,4,0), (3,4,1), (1,4,1) };
int classification = data.KnearestNeighbors(p => (p.x, p.y, p.c), (3,7), 3);

---

📎 Tips

• All methods are available as extension methods — just using Numerics.Extensions.
• You can export data with .Save(path) for CSV visualization.
• Works with LINQ pipelines for composable scientific workflows.

---

🧠 Example: Full Workflow

Func<double, double> func = x => Math.Sin(x);
var integral = func.Integrate(0, Math.PI);
var derivative = func.Derivate(Math.PI / 4);
var fft = func.FastFouriertransform(-1, 1, 100);

---

🧾 License

MIT License © 2025 — CSharpNumerics