ChebyshevSharp

Multi-dimensional Chebyshev tensor interpolation with analytical derivatives for .NET.

ChebyshevSharp builds fast, reusable polynomial surrogates for smooth multi-dimensional functions. Use it when direct model evaluations are expensive but repeated values, derivatives, integrals, roots, or optimizers are needed inside .NET applications.

Key Features

  • Multi-dimensional Chebyshev interpolation with spectral convergence
  • Analytical derivatives via spectral differentiation matrices
  • Vectorized evaluation routing N-D tensor contractions through BLAS (via BlasSharp.OpenBlas)
  • Piecewise Chebyshev splines with user-specified knots at singularities
  • Sliding technique for high-dimensional approximation
  • Tensor Train decomposition for 5+ dimensional functions
  • Chebyshev algebra — combine interpolants via +, -, *, /
  • Spectral calculus — integration, rootfinding, and optimization
  • Targets .NET 8 and .NET 10

Installation

dotnet add package ChebyshevSharp

Quick Start

using ChebyshevSharp;

// Define a function to interpolate
double MyFunction(double[] x, object? data) => Math.Sin(x[0]) + Math.Sin(x[1]);

// Build a 2D Chebyshev interpolant
var cheb = new ChebyshevApproximation(
    function: MyFunction,
    numDimensions: 2,
    domain: new[] { new[] { -1.0, 1.0 }, new[] { -1.0, 1.0 } },
    nNodes: new[] { 11, 11 }
);
cheb.Build();

// Evaluate at a point
double value = cheb.VectorizedEval(new[] { 0.5, 0.3 }, new[] { 0, 0 });

// Compute partial derivative df/dx1
double dfdx = cheb.VectorizedEval(new[] { 0.5, 0.3 }, new[] { 1, 0 });

Where to Go Next

Path Start here
Build your first interpolant Getting Started
Choose an approximation family Which Class Should I Use?
Understand the numerical assumptions Mathematical Concepts
Improve accuracy or handle kinks Error-Driven Construction, then Piecewise Chebyshev Interpolation
Work in higher dimensions Sliding Technique or Tensor Train Interpolation
Use saved or external function values Serialization & Construction and Pre-computed Values
Validate or contribute changes Testing & Validation, Support & Reporting, and Contributing
Check mathematical sources Citations
Check release history Release Notes

API Reference

See the API documentation for full class and method reference, auto-generated from XML documentation comments.

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