##
## R package splines2 by Wenjie Wang and Jun Yan
## Copyright (C) 2016-2024
##
## This file is part of the R package splines2.
##
## The R package splines2 is free software: You can redistribute it and/or
## modify it under the terms of the GNU General Public License as published by
## the Free Software Foundation, either version 3 of the License, or any later
## version (at your option). See the GNU General Public License at
## <https://www.gnu.org/licenses/> for details.
##
## The R package splines2 is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
##
##' C-Spline Basis for Polynomial Splines
##'
##' Generates the convex regression spline (called C-spline) basis matrix by
##' integrating I-spline basis for a polynomial spline or the corresponding
##' derivatives.
##'
##' It is an implementation of the closed-form C-spline basis derived from the
##' recursion formula of I-splines and M-splines. The function \code{csp()} is
##' an alias of to encourage the use in a model formula.
##'
##' @inheritParams bSpline
##'
##' @param degree The degree of C-spline defined to be the degree of the
##' associated M-spline instead of actual polynomial degree. For example,
##' C-spline basis of degree 2 is defined as the scaled double integral of
##' associated M-spline basis of degree 2.
##' @param intercept If \code{TRUE} by default, all of the spline basis
##' functions are returned. Notice that when using C-Spline for
##' shape-restricted regression, \code{intercept = TRUE} should be set even
##' when an intercept term is considered additional to the spline basis in
##' the model.
##' @param derivs A nonnegative integer specifying the order of derivatives of
##' C-splines. The default value is \code{0L} for C-spline basis functions.
##' @param scale A logical value indicating if scaling C-splines is required. If
##' \code{TRUE} by default, each C-spline basis is scaled to have unit
##' height at right boundary knot. The corresponding I-spline and M-spline
##' produced by \code{deriv} methods will be scaled to the same extent.
##'
##' @inherit iSpline return
##'
##' @references
##'
##' Meyer, M. C. (2008). Inference using shape-restricted regression splines.
##' \emph{The Annals of Applied Statistics}, 2(3), 1013--1033.
##'
##' @example inst/examples/ex-cSpline.R
##'
##' @seealso
##' \code{\link{iSpline}} for I-splines;
##' \code{\link{mSpline}} for M-splines.
##'
##' @export
cSpline <- function(x, df = NULL, knots = NULL, degree = 3L,
intercept = TRUE, Boundary.knots = NULL,
derivs = 0L, scale = TRUE,
warn.outside = getOption("splines2.warn.outside", TRUE),
...)
{
## check inputs
if ((derivs <- as.integer(derivs)) < 0) {
stop("The 'derivs' must be a nonnegative integer.")
}
if ((degree <- as.integer(degree)) < 0)
stop("The 'degree' must be a nonnegative integer.")
if (is.null(df)) {
df <- 0L
} else {
df <- as.integer(df)
if (df < 0) {
stop("The 'df' must be a nonnegative integer.")
}
}
knots <- null2num0(knots)
Boundary.knots <- null2num0(Boundary.knots)
## take care of possible NA's in `x`
nax <- is.na(x)
if (all(nax)) {
stop("The 'x' cannot be all NA's!")
}
## remove NA's in x
xx <- if (nas <- any(nax)) {
x[! nax]
} else {
x
}
out <- if (scale) {
rcpp_cSpline(
x = xx,
df = df,
degree = degree,
internal_knots = knots,
boundary_knots = Boundary.knots,
complete_basis = intercept,
derivs = derivs
)
} else {
if (derivs == 0) {
rcpp_iSpline(
x = xx,
df = df,
degree = degree,
internal_knots = knots,
boundary_knots = Boundary.knots,
complete_basis = intercept,
derivs = 0,
integral = TRUE
)
} else {
rcpp_iSpline(
x = xx,
df = df,
degree = degree,
internal_knots = knots,
boundary_knots = Boundary.knots,
complete_basis = intercept,
derivs = derivs - 1,
integral = FALSE
)
}
}
## throw warning if any x is outside of the boundary
b_knots <- attr(out, "Boundary.knots")
if (warn.outside && any((xx < b_knots[1L]) | (xx > b_knots[2L]))) {
warning(wrapMessages(
"Some 'x' values beyond boundary knots",
"may cause ill-conditioned basis functions."
))
}
## keep NA's as is
if (nas) {
nmat <- matrix(NA, length(nax), ncol(out))
nmat[! nax, ] <- out
saved_attr <- attributes(out)
saved_attr$dim[1] <- length(nax)
out <- nmat
attributes(out) <- saved_attr
attr(out, "x") <- x
}
## add dimnames for consistency
name_x <- names(x)
if (! is.null(name_x)) {
row.names(out) <- name_x
}
## add class
if (scale || derivs == 0) {
## add "scale" to attributes for predict(), etc.
attr(out, "scale") <- scale
class(out) <- c("CSpline", "splines2", "matrix")
} else if (derivs == 1) {
class(out) <- c("ISpline", "splines2", "matrix")
} else {
class(out) <- c("MSpline", "splines2", "matrix")
}
## return
out
}
##' @rdname cSpline
##' @export
csp <- cSpline
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