# mrts: Multi-Resolution Thin-plate Spline Basis Functions In autoFRK: Automatic Fixed Rank Kriging

## Description

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.

## Usage

 `1` ```mrts(knot, k, x = NULL) ```

## 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`.

## 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`.

## Author(s)

ShengLi Tzeng and Hsin-Cheng Huang.

## References

Tzeng, S., & Huang, H. C. (2018). Resolution Adaptive Fixed Rank Kriging. Technometrics, https://doi.org/10.1080/00401706.2017.1345701.

`predict.mrts`
 ```1 2 3 4 5 6``` ```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()} ```