Compute cubic B-spline basis functions for the given wavenumbers.

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).

Usage

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

Arguments

V

a vector of wavenumbers, \(\Delta \tilde{\nu}\).

n.b

the number of basis functions to use.

pen

the smoothing penalty hyperparameter.

prec

a constant scale factor.

Value

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.

References

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.

See also

sparseMatrix