smoothcon

smoothcon constructs JAX-native basis matrices and quadratic penalties for smooth terms. Arrays and construction parameters go in, and an immutable Smooth object comes out.

Relationship to mgcv

Much of smoothcon's numerical implementation is a Python/JAX adaptation of algorithms from Simon N. Wood's GPL-licensed R package mgcv. Development and regression testing are pinned to mgcv 1.9-4.

smoothcon is licensed under GPL-3.0-or-later. See the third-party notices for detailed source provenance, copyright notices, and academic citations.

Installation

pip install smoothcon

With uv, use uv add smoothcon instead.

Quick start

import jax.numpy as jnp
import smoothcon

x = jnp.linspace(0.0, 1.0, 100)
smooth = smoothcon.pspline(x, k=20, degree=3, penalty_order=2)

basis = smooth.basis(x)
penalty = smooth.penalty

smooth.basis(values) evaluates the design matrix, smooth.penalty contains the coefficient penalty, and smooth.rank records its numerical rank. The basis can be evaluated inside JAX transformations such as jax.jit.

Smooth families

• P-splines and integrated-derivative B-splines
• cyclic P-splines and cyclic cubic splines
• natural cubic regression splines
• thin-plate regression splines
• fixed-range Gaussian-process smooths
• Markov random fields

Transformations

Transformations return new Smooth objects, so their order remains explicit:

nonlinear = (
    smooth.constrain("constant_and_linear", values=x)
    .scale_penalty(values=x)
    .diagonalize_penalty(values=x)
)

See the API reference for all constructors and the deviations from mgcv for numerical compatibility notes.