getBsplineBasis: Compute cubic B-spline basis functions for the given...
In serrsBayes: Bayesian Modelling of Raman Spectroscopy

Description Usage Arguments Value References See Also

This function computes penalised cubic B-splines using the method proposed by Eilers & Marx (1996). The spline coefficients can be computed efficiently using sparse matrix algebra, as described in Sect. 2.3.3 of Green & Silverman (1994) and Appendix B of Ruppert, Wand & Carroll (2003).

1	getBsplineBasis(V, n.b, pen, prec = 1e-08)

`V`	a `vector` of wavenumbers, Δ \tilde{ν}.
`n.b`	the number of basis functions to use.
`pen`	the smoothing penalty hyperparameter.
`prec`	a constant scale factor.

a list containing:

basis: A dense nwl by n.b matrix containing the values of the basis functions.
precision: A sparse n.b by n.b dsCMatrix, the inverse of the prior covariance.
distance: The distance between each knot (cm^{-1}).
knots: The knot locations.

Eilers, PHC & Marx, BD (1996) "Flexible smoothing with B-splines and penalties," Statist. Sci. 11(2): 89–121, doi: 10.1214/ss/1038425655

Green, PJ & Silverman, BW (1994) "Nonparametric Regression and Generalized Linear Models: a roughness penalty approach" Chapman & Hall, Boca Raton, FL, pp. 11–21.

Ruppert, D; Wand, MP & Carroll, RJ (2003) "Semiparametric Regression" CUP, Cambridge, UK, pp. 336–340.

sparseMatrix

serrsBayes documentation built on June 28, 2021, 5:14 p.m.