compute_Lambda: Construct Smoothing Spline Penalty Matrix

In lgspline: Lagrangian Multiplier Smoothing Splines for Smooth Function Estimation

Construct Smoothing Spline Penalty Matrix

Description

Builds penalty matrix combining smoothing spline and ridge penalties with optional predictor/partition-specific components. Handles custom penalties and scaling.

Usage

compute_Lambda(
  custom_penalty_mat,
  L1,
  wiggle_penalty,
  flat_ridge_penalty,
  K,
  nc,
  unique_penalty_per_predictor,
  unique_penalty_per_partition,
  penalty_vec,
  colnm_expansions,
  just_Lambda = TRUE
)

Arguments

custom_penalty_mat	Matrix; optional custom ridge penalty structure
L1	Matrix; integrated squared second derivative penalty (\textbf{L}_1)
wiggle_penalty, flat_ridge_penalty	Numeric; smoothing and ridge penalty parameters
K	Integer; number of interior knots (K)
nc	Integer; number of basis columns per partition
unique_penalty_per_predictor, unique_penalty_per_partition	Logical; enable predictor/partition-specific penalties
penalty_vec	Named numeric; custom penalty values for predictors/partitions
colnm_expansions	Character; column names for linking penalties to predictors
just_Lambda	Logical; return only combined penalty matrix (\boldsymbol{\Lambda})

Value

List containing:

• Lambda - Combined nc \times nc penalty matrix (\boldsymbol{\Lambda})

• L1 - Smoothing spline penalty matrix (\textbf{L}_1)

• L2 - Ridge penalty matrix (\textbf{L}_2)

• L_predictor_list - List of predictor-specific penalty matrices (\textbf{L}_\text{predictor\_list})

• L_partition_list - List of partition-specific penalty matrices (\textbf{L}_\text{partition\_list})

If just_Lambda=TRUE and no partition penalties, returns only Lambda matrix \boldsymbol{\Lambda}.

lgspline documentation built on June 8, 2025, 10:45 a.m.