I’m attempting to model car speed data using B-spline basis functions and compute the associated roughness penalty matrix. I’m using the fda package in R to create B-spline basis functions and the getbasispenalty function to compute the roughness penalty matrix.

The problem arises when I’m computing the roughness penalty matrix K1. Upon careful examination, I suspect that the issue may be due to some misconfiguration of the B-spline basis functions. While I’ve ensured that the range of the data and the B-spline basis functions are consistent, I’m still encountering this problem.

Code snippet

# 0. Data
library(fields)
library(fda)
library(car)
library(numDeriv)

x1 <- cars$speed          # Speeds of cars
y1 <- cars$dist           # Stopping distances of cars   
range(x1); range(y1)
N1 <- length(y1)
###

# p1
rg <- c(3,26)
m1 <- 4             # Order of splines
bp <- c(sort(x1))   # Break points/knots
bf <- fda::create.bspline.basis(
  rangeval = rg, norder = m1, breaks = bp)

# class(bf);names(bf);bf$names
nb <- bf$nbasis     # Number of basis functions

plot(bf, lwd = 2, col = 1:nb,
     main = "B-spline basis functions")
points(x1, rep(0, N1), pch = 20, cex = 1.5, col = "red")

# p2 
nb <- bf$nbasis            # nb = m1 + length(bp) - 2
plot(bf, lwd = 2, col = 1:nb,
     main = "B-spline basis functions")

# p3
F1 <- fda::eval.basis(x1,bf)     # dim(F1)
fields::image.plot((t(F1[, nb:1])),
                   main = "B-spline basis data matrix")

# p4
L1 <- int2Lfd(2) # The 2nd-order differential operator d^2 / dx^2

# p5
fields::image.plot((t(K1[,nb:1])),
                   main = "Roughness penalty matrix")
K1 <- getbasispenalty(bf, L1)  # dim(K1) = nb x nb

getbasispenalty(bf, L1) issues

Error in knotmult > rng[1] && knotmult < rng[2] :
‘length = 13’ in coercion to ‘logical(1)’

If anyone has any insights, ideas, or suggestions regarding this issue, I would greatly appreciate your help.