Regression Spline Functions and Classes.
splines2
Package website: release | development
The R package splines2 is intended to be a user-friendly supplementary package to the base package splines.
Features
The package splines2 provides functions to construct basis matrices of
- B-splines
- M-splines
- I-splines
- convex splines (C-splines)
- periodic splines
- natural cubic splines
- generalized Bernstein polynomials
- their integrals (except C-splines) and derivatives of given order by closed-form recursive formulas
In addition to the R interface, splines2 provides a C++ header-only library integrated with Rcpp, which allows the construction of spline basis functions directly in C++ with the help of Rcpp and RcppArmadillo. Thus, it can also be treated as one of the Rcpp* packages. A toy example package that uses the C++ interface is available here.
Installation of CRAN Version
You can install the released version from CRAN.
install.packages("splines2")
Development
The latest version of the package is under development at GitHub. If it is able to pass the automated package checks, one may install it by
if (! require(remotes)) install.packages("remotes")
remotes::install_github("wenjie2wang/splines2", upgrade = "never")
Getting Started
The Online document provides a reference for all functions and contains the following vignettes:
Performance
Since version 0.3.0, the implementation of the main functions has been rewritten in C++ with the help of the Rcpp and RcppArmadillo packages. The computational performance has thus been boosted and comparable with the function splines::splineDesign().
Some quick micro-benchmarks are provided below for reference.
library(microbenchmark)
options(microbenchmark.unit="relative")
library(splines)
library(splines2)
set.seed(123)
x <- runif(1e3)
degree <- 3
ord <- degree + 1
internal_knots <- seq.int(0.1, 0.9, 0.1)
boundary_knots <- c(0, 1)
all_knots <- sort(c(internal_knots, rep(boundary_knots, ord)))
## check equivalency of outputs
my_check <- function(values) {
all(sapply(values[- 1], function(x) {
all.equal(unclass(values[[1]]), unclass(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() for this example.
## B-splines
microbenchmark(
"splines::bs" = bs(x, knots = internal_knots, degree = degree,
intercept = TRUE, Boundary.knots = boundary_knots),
"splines::splineDesign" = splineDesign(x, knots = all_knots, ord = ord),
"splines2::bSpline" = bSpline(
x, knots = internal_knots, degree = degree,
intercept = TRUE, Boundary.knots = boundary_knots
),
check = my_check
)
Unit: relative
expr min lq mean median uq max neval
splines::bs 3.7488 3.4227 2.9600 3.2924 2.6877 1.9122 100
splines::splineDesign 2.2028 1.9788 2.0333 2.1305 1.8288 8.2016 100
splines2::bSpline 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 100
Similarly, for derivatives of B-splines, splines2::dbs() provides equivalent results with splines::splineDesign(), and is about 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 = internal_knots,
degree = degree, intercept = TRUE,
Boundary.knots = boundary_knots),
check = my_check
)
Unit: relative
expr min lq mean median uq max neval
splines::splineDesign 2.6498 2.4535 2.193 2.2861 2.1459 1.558 100
splines2::dbs 1.0000 1.0000 1.000 1.0000 1.0000 1.000 100
The splines package does not contain an implementation for integrals of B-splines. Thus, we 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 = internal_knots, degree = degree,
intercept = TRUE, Boundary.knots = boundary_knots) %*%
coef_sp
),
check = my_check
)
Unit: relative
expr min lq mean median uq max neval
ibs::ibs 24.306 21.108 22.016 21.621 21.342 26.533 100
splines2::ibs 1.000 1.000 1.000 1.000 1.000 1.000 100
The function ibs::ibs() returns the integrated B-splines instead of the integrals of spline basis functions. Thus, we applied the same coefficients to the basis functions from splines2::ibs() for equivalent results, which was still much faster than ibs::ibs().
For natural cubic splines (based on B-splines), splines::ns() uses the QR decomposition to find the null space of the second derivatives of B-spline basis functions at boundary knots, while splines2::nsp() utilizes the closed-form null space derived from the second derivatives of cubic B-splines, which produces nonnegative basis functions (within boundary) and is more computationally efficient.
microbenchmark(
"splines::ns" = ns(x, knots = internal_knots, intercept = TRUE,
Boundary.knots = boundary_knots),
"splines2::nsp" = nsp(
x, knots = internal_knots, intercept = TRUE,
Boundary.knots = boundary_knots
)
)
Unit: relative
expr min lq mean median uq max neval
splines::ns 4.9751 4.7263 4.6571 4.4456 4.8987 5.274 100
splines2::nsp 1.0000 1.0000 1.0000 1.0000 1.0000 1.000 100
The functions bSpline() and mSpline() produce periodic spline basis functions based on B-splines and M-splines, respectively, when periodic = TRUE is specified. The splines::periodicSpline() returns a periodic interpolation spline (based on B-splines) instead of basis matrix. We performed a comparison with package pbs (version 1.1), where the function pbs::pbs() produces a basis matrix of periodic B-spline by using splines::spline.des().
microbenchmark(
"pbs::pbs" = pbs::pbs(x, knots = internal_knots, degree = degree,
intercept = TRUE, periodic = TRUE,
Boundary.knots = boundary_knots),
"splines2::bSpline" = bSpline(
x, knots = internal_knots, degree = degree, intercept = TRUE,
Boundary.knots = boundary_knots, periodic = TRUE
),
"splines2::mSpline" = mSpline(
x, knots = internal_knots, degree = degree, intercept = TRUE,
Boundary.knots = boundary_knots, periodic = TRUE
)
)
Unit: relative
expr min lq mean median uq max neval
pbs::pbs 4.0864 3.9469 3.34075 3.8658 3.6311 1.23830 100
splines2::bSpline 1.0000 1.0000 1.00000 1.0000 1.0000 1.00000 100
splines2::mSpline 1.1598 1.1350 0.95918 1.1516 1.1169 0.12212 100
Session Information for Benchmarks
sessionInfo()
R version 4.4.0 (2024-04-24)
Platform: x86_64-pc-linux-gnu
Running under: Arch Linux
Matrix products: default
BLAS/LAPACK: /usr/lib/libopenblas.so.0.3; LAPACK version 3.12.0
locale:
[1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C LC_TIME=en_US.UTF-8
[4] LC_COLLATE=en_US.UTF-8 LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
[7] LC_PAPER=en_US.UTF-8 LC_NAME=C LC_ADDRESS=C
[10] LC_TELEPHONE=C LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
time zone: America/New_York
tzcode source: system (glibc)
attached base packages:
[1] splines stats graphics grDevices utils datasets methods base
other attached packages:
[1] splines2_0.5.2 microbenchmark_1.4.10
loaded via a namespace (and not attached):
[1] digest_0.6.35 codetools_0.2-20 ibs_1.4 fastmap_1.1.1 xfun_0.43
[6] pbs_1.1 knitr_1.46 htmltools_0.5.8.1 rmarkdown_2.26 cli_3.6.2
[11] compiler_4.4.0 tools_4.4.0 evaluate_0.23 Rcpp_1.0.12 yaml_2.3.8
[16] rlang_1.1.3