StapletonMathPackage 1.3.3

StapletonMathPackage

StapletonMathPackage is a C# numerical methods library providing tools for linear algebra, optimization, root-finding, interpolation, and ODE solving. It is pretty old, and I mostly started it as a wrapper around other math packages because I wanted to stick with double arrays in my program rather than specialized matrix classes. This version wraps around Math.Numerics for many of the linear algebra operations.

Licensed under the MIT License.

Features

Linear Algebra

• Matrix and vector operations (MatrixMath, VectorMath)
• Determinant, trace, inverse, transpose
• Eigenvalues & eigenvectors (general & 3×3 symmetric closed form)
• Gaussian elimination, LU, banded solvers
• Utilities for stacking, extracting, reshaping, swapping rows/columns

Calculus

• Numerical integration: trapezoid, Romberg
• Double integration
• Vector and matrix-valued integrands

Root Finding

• Newton-Raphson solvers:
  • With Jacobian supplied
  • With numerical tangent
  • With local secant updates
  • With initial slope
• Regula Falsi (False Position) method

Interpolation

• Cubic spline interpolation with derivatives
• Tridiagonal solver for spline coefficients

Optimization

• Genetic Algorithm framework:
  • Chromosome representation
  • Mutation & perturbation
  • Tournament-based crossover & population evolution
  • Multicore evaluation via ThreadLocal<Random>

ODE System Solvers

• Matrix exponential (Taylor, Padé, scaling & squaring)
• Constant step matrix exponential integration
• Variable coefficient systems
• Non-homogeneous systems with forcing functions

Installation

Install via NuGet:

dotnet add package StapletonMathPackage

Or in Visual Studio:

PM> Install-Package StapletonMathPackage

Usage Examples

Matrix Operations

using RandomMath;

double[,] A = { { 1, 2 }, { 3, 4 } };
double[,] B = { { 5, 6 }, { 7, 8 } };

double[,] C = MatrixMath.Multiply(A, B);
double detA = MatrixMath.Determinant(A);

Cubic Spline Interpolation

using RandomMath.CubicSplineFit;

var xs = new double[] { 0, 1, 2, 3 };
var ys = new double[] { 0, 1, 0, 1 };

var spline = new CubicSplineFit(xs, ys);

double dy = 0, d2y = 0;
double yInterp = spline.Interpolate(1.5, ref dy, ref d2y);

Genetic Algorithm

using RandomMath.GeneticAlgorithm;

public class SphereFunction : IOptimize {
    public int nX => 3;
    public double Eval(double[] X) => X.Sum(x => x*x);
    public IOptimize DeepCopy() => new SphereFunction();
}

var ga = new GeneticAlgorithm(new SphereFunction());
ga.Run();
Console.WriteLine($"Best fitness: {ga.Best.Fitness}");

Newton-Raphson (Jacobian supplied)

using RandomMath.NewtonRaphson;

public class SimpleFunc : IMatrixFunctionAndDerivative {
    public double[] Eval(double[] X) => new[] { X[0]*X[0] - 2 };
    public double[,] DEval(double[] X) => new double[,] { { 2*X[0] } };
}

var solver = new NewtonRaphsonJacobian(
    new double[] { 0 },    // target y
    new double[] { 1.0 },  // initial guess
    new SimpleFunc(),
    1e-10, 50
);
solver.Solve();
Console.WriteLine($"Root ≈ {solver.X[0]}");

Matrix Exponential ODE Solve

using RandomMath.ODESystemSolver;

double[,] A = { { 0, 1 }, { -1, 0 } };
var mexp = new MatrixExponential(A, 1.0);
var expAx = mexp.Solve(1.0); // exp(A*1.0)

Documentation

• All public APIs include XML comments visible in IntelliSense.
• Example usage included in this README.
• For advanced methods (ODE solvers, GA tuning), see source files in RandomMath.* namespaces.

Contributing

Contributions are welcome!
Please open an issue or submit a PR with improvements, bug fixes, or new numerical routines.

Guidelines:

• Follow existing naming conventions.
• Provide XML documentation for new public APIs.
• Add unit tests where possible.

License

This project is licensed under the MIT License — see the LICENSE file for details.