Package website: release | development
The R package splines2 is intended to be a user-friendly supplementary package to the base package splines.
The package splines2 provides functions to construct basis matrices of
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.
You can install the released version from CRAN.
install.packages("splines2")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")The Online document provides a reference for all functions and contains the following vignettes:
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 100Similarly, 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 100The 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 100The 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 100The 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 100sessionInfo()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