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Introduction

This R package implements Lagrangian multiplier smoothing splines, which reformulate smoothing splines through constrained optimization. This approach provides direct access to predictor-response relationships through interpretable coefficients, unlike other formulations that require post-fitting algebraic manipulation.

Installation

devtools::install_github("matthewlouisdavisBioStat/lgspline")

Citation

If you use this package in your research, please cite:

Davis, M. (2025). Lagrangian Multiplier Smoothing Splines. https://github.com/matthewlouisdavisBioStat/lgspline/

Contact

For questions or feedback, please open an issue on GitHub.

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Version

Install

install.packages('lgspline')

Version

0.2.0

License

MIT + file LICENSE

Issues

Pull Requests

Stars

Forks

Repository

https://github.com/matthewlouisdavisBioStat/lgspline

Maintainer

Matthew Davis

Last Published

April 24th, 2025

Functions in lgspline (0.2.0)

Compute Matrix Square Root Derivative

Create One-Hot Encoded Matrix

create_block_diagonal

Create Block Diagonal Matrix

compute_gram_block_diagonal

Compute Gram Matrix for Block Diagonal Structure

BFGS Implementation for REML Parameter Estimation

compute_trace_UGXX_wrapper

Calculate Trace of Matrix Product \(\text{trace}(\textbf{X}\textbf{U}\textbf{G}\textbf{X}^{T})\)

compute_dW_dlambda_wrapper

Compute Derivative of Penalty Matrix G with Respect to Lambda (Wrapper)

compute_dG_dlambda

Compute Derivative of Penalty Matrix G with Respect to Lambda

damped_newton_r

Damped Newton-Raphson Parameter Optimization

generate_posterior

Generate Posterior Samples from Fitted Lagrangian Multiplier Smoothing Spline

compute_dG_u_dlambda_xy

Compute Derivative of \(\textbf{U}\textbf{G}\textbf{X}^{T}\textbf{y}\) with Respect to Lambda

get_2ndDerivPenalty

Compute Integrated Squared Second Derivative Penalty Matrix for Smoothing Splines

Find Extremum of Fitted Lagrangian Multiplier Smoothing Spline

Find Neighboring Cluster Partitions Using Midpoint Distance Criterion

Efficiently Construct U Matrix

Get Centers for Partitioning

get_2ndDerivPenalty_wrapper

Wrapper for Smoothing Spline Penalty Computation

lgspline-package

Lagrangian Multiplier Smoothing Splines

Compute Leave-One-Out Cross-Validated predictions for Gaussian Response/Identity Link under Constraint.

lgspline-methods

lgspline: Lagrangian Multiplier Smoothing Splines

efficient_matrix_mult

Efficient Matrix Multiplication

get_polynomial_expansions

Generate Design Matrix with Polynomial and Interaction Terms

knot_expand_list

Expand Matrix into Partition Lists Based on Knot Boundaries

Efficient Matrix Multiplication Operator

get_interaction_patterns

Generate Interaction Variable Patterns

Generate Grid Indices Without expand.grid()

Get Constrained GLM Coefficient Estimates

Compute Gram Matrix

Matrix Inversion with Fallback Methods

Test if Vector is Binary

Compute Log-Likelihood for Weibull Accelerated Failure Time Model

make_constraint_matrix

Create Smoothing Spline Constraint Matrix

matmult_block_diagonal

Multiply Block Diagonal Matrices in Parallel

Calculate Matrix Inverse Square Root

Calculate Matrix Square Root

make_partitions

Create Data Partitions Using Clustering

make_derivative_matrix

Compute First and Second Derivative Matrices

Fit Lagrangian Multiplier Smoothing Splines

Low-Level Fitting for Lagrangian Smoothing Splines

Left-Multiply a List of Block-Diagonal Matrices by U

Compute Newton-Raphson Parameter Update with Numerical Stabilization

Plot Method for Lagrangian Multiplier Smoothing Spline Models

Compute softplus transform

Standardize Vector to Z-Scores

summary.lgspline

Summary method for lgspline Objects

take_derivative

Calculate Derivatives of Polynomial Terms

predict.lgspline

Predict Method for Fitted Lagrangian Multiplier Smoothing Spline

Print Method for lgspline Objects

print.summary.lgspline

Print Method for lgspline Object Summaries

vectorproduct_block_diagonal

Vector-Matrix Multiplication for Block Diagonal Matrices

wald_univariate

Univariate Wald Tests and Confidence Intervals for Lagrangian Multiplier Smoothing Splines

Log-Prior Distribution Evaluation for lgspline Models

take_interaction_2ndderivative

Calculate Second Derivatives of Interaction Terms

Tune Smoothing and Ridge Penalties via Generalized Cross Validation

weibull_dispersion_function

Estimate Weibull Dispersion for Accelerated Failure Time Model

Weibull Family for Survival Model Specification

unconstrained_fit_default

Unconstrained Generalized Linear Model Estimation

weibull_qp_score_function

Compute gradient of log-likelihood of Weibull accelerated failure model without penalization

weibull_shur_correction

Correction for the Variance-Covariance Matrix for Uncertainty in Scale

weibull_glm_weight_function

Weibull GLM Weight Function for Constructing Information Matrix

Estimate Scale for Weibull Accelerated Failure Time Model

unconstrained_fit_weibull

Unconstrained Weibull Accelerated Failure Time Model Estimation

collapse_block_diagonal

Collapse Matrix List into a Single Block-Diagonal Matrix

Efficient Matrix Multiplication of G and A Matrices

compute_G_eigen

Compute Eigenvalues and Related Matrices for G

Finite-difference Gradient Computer

Lagrangian Multiplier Smoothing Splines: Mathematical Details

Extract model coefficients

AGAmult_wrapper

Efficient Matrix Multiplication for \(\textbf{A}^{T}\textbf{G}\textbf{A}\)

compute_GhalfXy_temp_wrapper

Compute Component \(\textbf{G}^{1/2}\textbf{A}(\textbf{A}^{T}\textbf{G}\textbf{A})^{-1}\textbf{A}^{T}\textbf{G}\textbf{X}^{T}\textbf{y}\)

Matrix Inversion using Armadillo

Construct Smoothing Spline Penalty Matrix