Derivkit documentation

Contents:

DerivKit is a robust Python toolkit for stable numerical derivatives, built for scientific computing, cosmology, and any domain requiring accurate gradients or higher-order expansions.

It provides:

  • Adaptive polynomial fitting that excludes noisy points based on residuals,

  • High-order finite differences for accurate stencil-based derivatives,

  • A simple API for comparing both approaches side by side.

Detailed documentation of the toolkit’s modules can be found in the sidebar.

Installation

pip install derivkit

Quick Start

from derivkit import DerivativeKit

def simple_function(x):
    return x**2 + x

dk = DerivativeKit(
  function=simple_function,
  central_value=1.0,
  derivative_order=1
)
print("Adaptive:", dk.adaptive.compute())
print("Finite Difference:", dk.finite.compute())

Adaptive Fit Example

Below is a visual example of the derivkit.adaptive_fit module estimating the first derivative of a nonlinear function in the presence of noise. The method selectively discards outlier points before fitting a polynomial, resulting in a robust and smooth estimate.

_images/adaptive_fit_with_noise_order1_demo_func.png

Citation

If you use derivkit in your research, please cite it as follows:

@software{sarcevic2025derivkit,
  author       = {Nikolina Šarčević and Matthijs van der Wild},
  title        = {derivkit: A Python Toolkit for Numerical Derivatives},
  year         = {2025},
  publisher    = {GitHub},
  journal      = {GitHub Repository},
  howpublished = {\url{https://github.com/nikosarcevic/derivkit}},
  note         = {If you use this software, please cite this entry.}

License

MIT License © 2025 Niko Šarčević, Matthijs van der Wild