Module smooth_basis 

Basis-penalized smoothing with continuous derivative penalties.

This module implements smooth.basis from R’s fda package. Unlike the discrete difference penalty used in P-splines (basis.rs), this uses continuous derivative penalties: min ||y - Φc||² + λ·∫(Lf)² dt.

Key capabilities:

• smooth_basis — Penalized least squares with continuous roughness penalty
• smooth_basis_gcv — GCV-optimal smoothing parameter selection
• bspline_penalty_matrix / fourier_penalty_matrix — Roughness penalty matrices

Structs

BasisNbasisCvConfig

Configuration for cross-validation-based basis selection.

BasisNbasisCvResult

Result of nbasis selection.

FdPar

Functional data parameter object (basis + penalty specification).

SmoothBasisGcvConfig

Configuration for GCV-based smoothing parameter selection.

SmoothBasisResult

Result of basis-penalized smoothing.

Enums

BasisCriterion

Criterion for nbasis selection.

BasisType

Basis type for penalized smoothing.

Functions

basis_nbasis_cv

Select the optimal number of basis functions using multiple criteria (R’s fdata2basis_cv).

basis_nbasis_cv_with_config

Select the optimal number of basis functions using a config struct.

bspline_penalty_matrix

Compute the roughness penalty matrix for B-splines via numerical quadrature.

fourier_penalty_matrix

Compute the roughness penalty matrix for a Fourier basis.

smooth_basis

Perform basis-penalized smoothing.

smooth_basis_gcv

Perform basis-penalized smoothing with GCV-optimal lambda.

smooth_basis_gcv_with_config

Perform basis-penalized smoothing with GCV-optimal lambda using a config struct.