Multi-Resolution Thin-plate Spline Basis Functions

This function generates multi-resolution thin-plate spline basis functions. The basis functions are (descendingly) ordered in terms of their degrees of smoothness with a higher-order function corresponding to larger-scale features and a lower-order one corresponding to smaller-scale details. They are useful in the spatio-temporal random effects model.

mrts(knot, k, x = NULL, maxknot = 5000)

Arguments

knot: m by d matrix (d<=3) for m locations of d-dimensional knots as in ordinary splines. Missing values are not allowed.
k: the number (<=m) of basis functions.
x: n by d matrix of coordinates corresponding to n locations where the values of basis functions to be evaluated. Default is NULL, which uses the m by d matrix in knot.
maxknot: maximum number of knots to be used in generating basis functions. If maxknot < m, a deterministic subset selection of knots will be used. For using all knots, set maxknot>=m.

Value

An mrts object is generated. If x=NULL (default) it returns an m by k matrix of k basis function taken values at knots. With x given, it returns n by k matrix for basis functions taken values at x.

References

Tzeng, S., & Huang, H. C. (2018). Resolution Adaptive Fixed Rank Kriging. Technometrics, https://doi.org/10.1080/00401706.2017.1345701.
Tzeng, S., & Huang, H. C. (2015). Multi-Resolution Spatial Random-Effects Models for Irregularly Spaced Data. arXiv preprint arXiv:1504.05659.
Nychka D, Hammerling D, Sain S, Lenssen N (2016). “LatticeKrig: Multiresolution Kriging Based on Markov Random Fields.” doi:10.5065/D6HD7T1R https://doi.org/10.5065/D6HD7T1R, R package version 8.4, https://github.com/NCAR/LatticeKrig.

Author

ShengLi Tzeng, Hsin-Cheng Huang and Wen-Ting Wang.

Examples

originalPar <- par(no.readonly = TRUE)
knot <- seq(0, 1, l = 30)
b <- mrts(knot, 30)
x0 <- seq(0, 1, l = 200)
bx <- predict(b, x0)
par(mfrow = c(5, 6), mar = c(0, 0, 0, 0))
for (i in 1:30) {
  plot(bx[, i], type = "l", axes = FALSE)
  box()
}

par(originalPar)