ChebyshevND

Fast multidimensional Chebyshev interpolation in Python, using DCTs to compute coefficients, Numba-accelerated Clenshaw recursions for evaluation, and structured coefficient pruning for compression.

For smooth functions, Chebyshev interpolation converges spectrally: the error decays exponentially with the number of nodes per axis. ChebyshevND turns a tensor grid of function samples into an interpolant that can be evaluated anywhere in the domain at close to machine precision — with built-in error estimates that come free from the coefficient decay.

Installation

pip install chebyshevnd

Requires Python ≥ 3.10; numpy, scipy, and numba are installed automatically.

Quickstart

Sample your function at Chebyshev nodes, build the interpolant from the values, evaluate anywhere:

import numpy as np
from chebyshevnd import ChebyshevInterpolant1D, chebyshev_nodes

f = lambda x: 1.0 / (1.0 + 25 * x**2)   # Runge function
a, b = -1.0, 1.0

x_nodes = chebyshev_nodes(100, a, b)
interp = ChebyshevInterpolant1D(f(x_nodes), a, b)

interp.evaluate(0.3)                     # a float
interp.evaluate(np.linspace(a, b, 50))   # an array
interp.relative_error()                  # a-posteriori error estimate

The example notebooks below walk through each dimension, including convergence, coefficient decay, pruning, and precomputation timings.

Examples

Reference

Citation

The techniques implemented in this package were derived and developed for:

H. Khalvati, P. Lynch, O. Burke, L. Speri, M. van de Meent, and Z. Nasipak, Systematic errors in fast relativistic waveforms for Extreme Mass Ratio Inspirals, Phys. Rev. D 113, 084042 (2026), arXiv:2509.08875.

If this package contributes to your research, please cite that paper — machine-readable citation metadata is in the repository’s CITATION.cff.