nlstac: Non-Gradient Separable Nonlinear Least Squares Fitting

Facultad de Ciencias, Universidad de Extremadura

jfernandck@alumnos.unex.es

Departmento de Matemáticas para la Economía y la Empresa, Universidad de Valencia

rabesua@uv.es

Facultad de Ciencias, Universidad de Extremadura

arias@unex.es

Facultad de Ciencias, Universidad de Extremadura

coco@unex.es

Abstract

A new package for nonlinear least squares fitting is introduced in this paper. This package implements a recently developed algorithm that, for certain types of nonlinear curve fitting, reduces the number of nonlinear parameters to be fitted. One notable feature of this method is the absence of initialization which is typically necessary for nonlinear fitting gradient-based algorithms. Instead, just some bounds for the nonlinear parameters are required. Even though convergence for this method is guaranteed for exponential decay using the max-norm, the algorithm exhibits remarkable robustness, and its use has been extended to a wide range of functions using the Euclidean norm. Furthermore, this data-fitting package can also serve as a valuable resource for providing accurate initial parameters to other algorithms that rely on them.

Arora, Rajesh Kumar. 2015. Optimization. Algorithms and Applications. Taylor & Francis Group, LLC.

Bates, Douglas, Katharine M. Mullen, John C. Nash, and Ravi Varadhan. 2014. Minqa: Derivative-Free Optimization Algorithms by Quadratic Approximation. https://CRAN.R-project.org/package=minqa.

Bendtsen., Claus. 2022. Pso: Particle Swarm Optimization. https://CRAN.R-project.org/package=pso.

Björck. 1996. Numerical Methods for Least Squares Problems. 1st ed. United States of America: Society for Industrial; Applied Mathematics. https://doi.org/10.1137/1.9781611971484.

Christoffersen, Benjamin. 2022. Psqn: Partially Separable Quasi-Newton. https://CRAN.R-project.org/package=psqn.

Conceicao, Eduardo L. T. 2022. DEoptimR: Differential Evolution Optimization in Pure r. https://CRAN.R-project.org/package=DEoptimR.

Coppola, Antonio, Brandon Stewart, and Naoaki Okazaki. 2022. Lbfgs: Limited-Memory BFGS Optimization. https://CRAN.R-project.org/package=lbfgs.

Corporation, Microsoft, and Steve Weston. 2022. doParallel: Foreach Parallel Adaptor for the ’Parallel’ Package. https://CRAN.R-project.org/package=doParallel.

Golub, G. H., and Victor Pereyra. 1973. “The Differentiation of Pseudo-Inverses and Nonlinear Least Squares Problems Whose Variables Separate.” SIAM Journal on Numerical Analysis 10 (April): 413–32. https://doi.org/10.1137/0710036.

Golub, Gene, and Victor Pereyra. 2003. “Separable Nonlinear Least Squares: The Variable Projection Method and Its Applications.” Inverse Problems 19 (January): R1–R26(1).

Microsoft, and Steve Weston. 2022. Foreach: Provides Foreach Looping Construct. https://CRAN.R-project.org/package=foreach.

Mullen, Katharine M., and Ivo H. M. van Stokkum. 2007. “TIMP: An r Package for Modeling Multi-Way Spectroscopic Measurements.” Journal of Statistical Software 18 (3). https://doi.org/10.18637/jss.v018.i03.

Nash, John C, and Duncan Murdoch. 2023. Nlsr: Functions for Nonlinear Least Squares Solutions - Updated 2022. https://CRAN.R-project.org/package=nlsr.

Nocedal, Jorge, and Stephen J. Wright. 2006. Numerical Optimization. Second. New York, NY, USA: Springer.

Pruim, Randall, Daniel Kaplan, and Nicholas Horton. 2022. mosaicData: Project MOSAIC Data Sets. https://CRAN.R-project.org/package=mosaicData.

R Core Team. 2021. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.

Rhinehart, R Russell. 2016. Nonlinear Regression Modeling for Engineering Applications: Modeling, Model Validation, and Enabling Design of Experiments. John Wiley & Sons.

Scrucca, Luca. 2013. “GA: A Package for Genetic Algorithms in R.” Journal of Statistical Software 53 (4): 1–37. https://doi.org/10.18637/jss.v053.i04.

Torvisco, J. A. F., M. R. Arias, and Javier Cabello Sánchez. 2018. “A New Algorithm to Fit Exponential Decays Without Initial Guess.” Filomat 32 (January): 4233–48. https://doi.org/10.2298/FIL1812233T.

Vega Yon, George, and Enyelbert Muñoz. 2017. ABCoptim: An Implementation of the Artificial Bee Colony (ABC) Algorithm. https://github.com/gvegayon/ABCoptim.

Wickham, Hadley. 2016. Ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York. https://ggplot2.tidyverse.org.

Wilson, Martin. 2021. “Spant: An r Package for Magnetic Resonance Spectroscopy Analysis.” Journal of Open Source Software 6 (67): 3646. https://doi.org/10.21105/joss.03646.

Xiang, Yang, Sylvain Gubian, Brian Suomela, and Julia Hoeng. 2013. “Generalized Simulated Annealing for Efficient GlobalOptimization: The GenSA Package for r.” The R Journal 5/1. https://journal.r-project.org.

Xu, Huan, Feng Ding, and Erfu Yang. 2019. “Modeling a Nonlinear Process Using the Exponential Autoregressive Time Series Model.” Nonlinear Dynamics 95 (February). https://doi.org/10.1007/s11071-018-4677-0.