The R package splines2 provides functions to construct basis matrix of
In addition to the R interface, splines2 also provides a C++ header-only library integrated with Rcpp, which allows construction of spline basis matrix directly in C++ with the help of Rcpp and RcppArmadillo. So it can also be treated as one of the Rcpp* packages. A toy example package that uses the C++ interface is available here.
You can install the released version from CRAN.
The latest version of package is under development at GitHub. If it is able to pass the building check by Travis CI, one may install it by
Online document provides reference for all functions and contains the following vignettes:
Since v0.3.0, the implementation of the main functions has been rewritten in C++ with the help of the Rcpp and RcppArmadillo package. The computational performance has thus been boosted.
Some benchmarks with the splines package (version 4.0.1) are provided for reference as follows:
library(microbenchmark)
library(splines)
library(splines2)
x <- seq.int(0, 1, 0.001)
degree <- 3
ord <- degree + 1
knots <- seq.int(0.1, 0.9, 0.1)
b_knots <- range(x)
all_knots <- sort(c(knots, rep(b_knots, ord)))
## check equivalency of outputs
my_check <- function(values) {
all(sapply(values[- 1], function(x) {
all.equal(unclass(values[[1]]), x, check.attributes = FALSE)
}))
}For B-splines, function splines2::bSpline() provides equivalent results with splines::bs() and splines::splineDesign(), and is about 3x faster than bs() and 2x faster than splineDesign().
## B-splines
microbenchmark(
"splines::bs" = bs(x, knots = knots, degree = degree,
intercept = TRUE, Boundary.knots = b_knots),
"splines::splineDesign" = splineDesign(x, knots = all_knots, ord = ord),
"splines2::bSpline" = bSpline(x, knots = knots, degree = degree,
intercept = TRUE, Boundary.knots = b_knots),
check = my_check,
times = 1e3
)Unit: microseconds
expr min lq mean median uq max neval cld
splines::bs 335.703 353.810 387.53 362.81 381.259 3015.9 1000 c
splines::splineDesign 204.151 213.133 244.16 216.05 226.820 2342.8 1000 b
splines2::bSpline 84.866 91.677 108.45 95.46 99.399 2149.9 1000 a Similarly, for derivatives of B-splines, splines2::dbs() provides equivalent results with splines::splineDesign(), and is more than 2x faster.
## Derivatives of B-splines
derivs <- 2
microbenchmark(
"splines::splineDesign" = splineDesign(x, knots = all_knots,
ord = ord, derivs = derivs),
"splines2::dbs" = dbs(x, derivs = derivs, knots = knots, degree = degree,
intercept = TRUE, Boundary.knots = b_knots),
check = my_check,
times = 1e3
)Unit: microseconds
expr min lq mean median uq max neval cld
splines::splineDesign 274.066 285.540 330.04 295.3 327.12 4143.4 1000 b
splines2::dbs 88.085 94.344 127.73 99.0 107.18 2639.1 1000 a The splines package does not provide function producing integrals of B-splines. So we instead performed a comparison with package ibs (version 1.4), where the function ibs::ibs() was also implemented in Rcpp.
## integrals of B-splines
set.seed(123)
coef_sp <- rnorm(length(all_knots) - ord)
microbenchmark(
"ibs::ibs" = ibs::ibs(x, knots = all_knots, ord = ord, coef = coef_sp),
"splines2::ibs" = as.numeric(
splines2::ibs(x, knots = knots, degree = degree,
intercept = TRUE, Boundary.knots = b_knots) %*% coef_sp
),
check = my_check,
times = 1e3
)Unit: microseconds
expr min lq mean median uq max neval cld
ibs::ibs 2445.25 2666.93 3259.59 3213.59 3342.26 113446.1 1000 b
splines2::ibs 264.84 319.18 363.78 338.62 360.94 2826.4 1000 a The function ibs::ibs() returns the integrated B-splines instead of the integrals of spline bases. So we applied the same coefficients to the bases from splines2::ibs() for equivalent results, which was still much faster than ibs::ibs().