RadialBasis.R
RadialBasis <- function(d, M, dimension, derivative=0) {
# compute the exponent for a thin-plate spline
# based on smoothness and dimension
p <- 2 * M - dimension
if (p <= 0) {
stop("M too small for thin plates spline, need: 2m-d >0")
}
if( (p-1 <0) & (derivative >0) ) {
stop("M is too small for derivatives, need: 2m-d < 1")}
if( derivative==0){
if (dimension%%2 == 0) {
# factor of 2 from the log term
ifelse(d > 1e-14, radbas.constant(M, dimension) *
(d^p) * log(d), 0)}
else {
radbas.constant(M, dimension) * (d^p)}}
## find derivative
else{
if (dimension%%2 == 0) {
# factor of 2 from the log term
ifelse(d > 1e-14,
radbas.constant(M, dimension) * (d^(p-1))* (p* log(d) +1) , 0)}
else {
con<- radbas.constant(M, dimension)*p
con * (d^(p-1))}}
##### should not get here!
}