PyChebyshev¶

Fast multi-dimensional Chebyshev tensor interpolation with analytical derivatives.

PyChebyshev builds a Chebyshev interpolant of any smooth function in up to N dimensions, then evaluates it and its derivatives in microseconds using vectorized NumPy operations. Four classes cover different use cases:

ChebyshevApproximation — full tensor interpolation with analytical derivatives (up to ~5 dimensions)
ChebyshevSpline — piecewise Chebyshev interpolation with knots at known singularities (kinks, discontinuities)
ChebyshevTT — Tensor Train format via TT-Cross for 5+ dimensions
ChebyshevSlider — additive decomposition for separable high-dimensional functions

Key Features¶

Spectral accuracy — exponential error decay as node count increases
Chebyshev Splines — piecewise interpolation at kinks restores spectral convergence for non-smooth functions
Arithmetic operators — combine interpolants via +, -, *, / for portfolio-level proxies
Extrusion & slicing — add or fix dimensions to combine interpolants across different risk-factor sets
Pre-computed values — generate nodes first, evaluate externally, load values later (nodes() + from_values())
Integration, rootfinding & optimization — spectral calculus directly on interpolants, no re-evaluation needed
Analytical derivatives — via spectral differentiation matrices (no finite differences)
Tensor Train — TT-Cross builds from O(d·n·r²) evaluations instead of O(n^d)
Fast evaluation — ~0.065 ms per query (price), ~0.29 ms for price + 5 Greeks
Save & load — persist built interpolants to disk; rebuild-free deployment
Pure Python — NumPy + SciPy only, no compiled extensions needed

Quick Example¶

import math
from pychebyshev import ChebyshevApproximation

# Define any smooth function
def my_func(x, _):
    return math.sin(x[0]) * math.exp(-x[1])

# Build interpolant
cheb = ChebyshevApproximation(
    my_func,
    num_dimensions=2,
    domain=[[-1, 1], [0, 2]],
    n_nodes=[15, 15],
)
cheb.build()

# Evaluate
value = cheb.vectorized_eval([0.5, 1.0], [0, 0])

# First derivative with respect to x[0]
dfdx = cheb.vectorized_eval([0.5, 1.0], [1, 0])

Installation¶

pip install pychebyshev

Performance¶

Method	Price Error	Greek Error	Build Time	Query Time
Chebyshev Barycentric	0.000%	1.980%	~0.35s	~0.065ms
Chebyshev TT	0.014%	0.029%	~0.35s	~0.004ms
MoCaX Standard (C++)	0.000%	1.980%	~1.04s	~0.47ms
FDM	0.803%	2.234%	N/A	~500ms

Based on 5D Black-Scholes tests with 11 nodes per dimension. TT uses ~7,400 function evaluations (vs 161,051 for full tensor methods). See Benchmarks for detailed comparisons including MoCaX TT.