splines2
The R package splines2 is intended to be a user-friendly supplement to the base package splines.
Features
The package splines2 (version 0.4.5) provides functions to construct basis matrices of
- B-splines
- M-splines
- I-splines
- convex splines (C-splines)
- periodic M-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 v0.3.0, 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 for reference as follows:
library(microbenchmark)
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]]), 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,
times = 1e3,
unit = "relative"
)Unit: relative
expr min lq mean median uq max neval cld
splines::bs 3.6436 3.5392 3.5667 3.4591 3.4965 1.2118 1000 c
splines::splineDesign 2.2156 2.1265 2.1414 2.0520 2.1235 1.0717 1000 b
splines2::bSpline 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1000 a
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,
times = 1e3,
unit = "relative"
)Unit: relative
expr min lq mean median uq max neval cld
splines::splineDesign 2.6213 2.4951 2.4608 2.4362 2.4634 1.1087 1000 b
splines2::dbs 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1000 a
The splines package does not contain an implementation for integrals
of B-splines. Thus, we performed a comparison with package ibs
(version r packageVersion("ibs")), 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,
times = 1e3,
unit = "relative"
)Unit: relative
expr min lq mean median uq max neval cld
ibs::ibs 9.2171 8.2285 6.5033 9.5655 9.4491 18.632 1000 b
splines2::ibs 1.0000 1.0000 1.0000 1.0000 1.0000 1.000 1000 a
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::naturalSpline() 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::naturalSpline" = naturalSpline(
x, knots = internal_knots, intercept = TRUE,
Boundary.knots = boundary_knots
),
times = 1e3,
unit = "relative"
)Unit: relative
expr min lq mean median uq max neval cld
splines::ns 5.1898 4.9857 4.7973 4.736 4.5995 1.6821 1000 b
splines2::naturalSpline 1.0000 1.0000 1.0000 1.000 1.0000 1.0000 1000 a
The function mSpline() produces periodic spline basis functions (based
on M-splines) when periodic = TRUE is specified. The
splines::periodicSpline() returns a periodic interpolation spline
(based on B-splines) instead of basis matrix. Thus, we performed a
comparison with package pbs (version r packageVersion("pbs")),
where the function pbs::pbs() produces a basis matrix of periodic
B-spline by using splines::spline.des() (a wrapper function of
splines::splineDesign()).
microbenchmark(
"pbs::pbs" = pbs::pbs(x, knots = internal_knots, degree = degree,
intercept = TRUE, periodic = TRUE,
Boundary.knots = boundary_knots),
"splines2::mSpline" = mSpline(
x, knots = internal_knots, degree = degree, intercept = TRUE,
Boundary.knots = boundary_knots, periodic = TRUE
),
times = 1e3,
unit = "relative"
)Unit: relative
expr min lq mean median uq max neval cld
pbs::pbs 3.3766 3.229 3.1478 3.1355 3.1166 1.4485 1000 b
splines2::mSpline 1.0000 1.000 1.0000 1.0000 1.0000 1.0000 1000 a
Session Information for Benchmarks
sessionInfo()R version 4.1.0 (2021-05-18)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Arch Linux
Matrix products: default
BLAS: /usr/lib/libopenblasp-r0.3.17.so
LAPACK: /usr/lib/liblapack.so.3.10.0
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
attached base packages:
[1] splines stats graphics grDevices utils datasets methods base
other attached packages:
[1] splines2_0.4.5 microbenchmark_1.4-7
loaded via a namespace (and not attached):
[1] Rcpp_1.0.7 mvtnorm_1.1-2 lattice_0.20-44 codetools_0.2-18 ibs_1.4
[6] zoo_1.8-9 digest_0.6.27 MASS_7.3-54 grid_4.1.0 magrittr_2.0.1
[11] evaluate_0.14 rlang_0.4.11 stringi_1.7.3 multcomp_1.4-17 Matrix_1.3-4
[16] sandwich_3.0-1 rmarkdown_2.10 TH.data_1.0-10 tools_4.1.0 stringr_1.4.0
[21] survival_3.2-11 xfun_0.25 yaml_2.2.1 compiler_4.1.0 pbs_1.1
[26] htmltools_0.5.1.1 knitr_1.33