R Under development (unstable) (2024-02-14 r85901 ucrt) -- "Unsuffered Consequences"
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> library(cpr)
> require(splines)
Loading required package: splines
> 
> ################################################################################
> # derivatives are as expected
> e <- new.env()
> with(e, {
+   f0 <- function(x) {
+     #(x + 2) * (x - 1) * (x - 3)
+     x^3 - 2 * x^2 - 5 * x + 6
+   }
+   f1 <- function(x) {
+     3 * x^2 - 4 * x - 5
+   }
+   f2 <- function(x) {
+     6 * x - 4
+   }
+ 
+   x <- sort(runif(n = 100, min = -3, max = 5))
+   bknots = c(-3, 5)
+   bmat <- bsplines(x, bknots = bknots)
+   theta <- coef(lm(f0(x) ~ bsplines(x, bknots = bknots) + 0) )
+ 
+   baseD1 <- splines::spline.des(c(-3, -3, -3, -3, 5, 5, 5, 5), x, derivs = rep(1, length(x)))$design
+   cprD1 <- bsplineD(x, bknots = bknots, derivative = 1L)
+ 
+   baseD2 <- splines::spline.des(c(-3, -3, -3, -3, 5, 5, 5, 5), x, derivs = rep(2, length(x)))$design
+   cprD2 <- bsplineD(x, bknots = bknots, derivative = 2L)
+ 
+   # verify that I can get cubic correct
+   stopifnot(isTRUE(all.equal(f0(x), as.numeric(bmat %*% theta))))
+ 
+   # verify that I can get the first derivative correct -- this is different from
+   # base R in that, by my construction, the derivative at the boundardy knots
+   # should be NA, as the k-fold knots should result in no differentiability at
+   # these points.
+   stopifnot(isTRUE(all.equal(f1(x), as.numeric(cprD1 %*% theta))))
+ 
+   # verify that I can get the second derivative correct
+   stopifnot(isTRUE(all.equal(f2(x), as.numeric(cprD2 %*% theta))))
+ 
+   if (interactive()) {
+     par(mfrow = c(1, 3))
+     plot(x, f0(x), type = "l")
+     points(x, bmat %*% theta, pch = 2, col = 'blue')
+ 
+     plot(x, f1(x), type = "l")
+     points(x, baseD1 %*% theta, pch = 16, col = 'red', cex = 0.7)
+     points(x, cprD1 %*% theta, pch = 2, col = 'blue')
+ 
+     plot(x, f2(x), type = "l")
+     points(x, baseD2 %*% theta, pch = 16, col = 'red', cex = 0.7)
+     points(x, cprD2 %*% theta, pch = 2, col = 'blue')
+   }
+ 
+   # another set of tests
+   xvec <- seq(-1, 5, length = 100)
+   iknots <- c(-0.8, 0.2, 2.3, 2.5)
+ 
+   xi <- sort(c(rep(range(xvec), 4), iknots))
+ 
+   baseD1 <- spline.des(xi, xvec, derivs = rep(1, length(xvec)))$design
+   baseD2 <- spline.des(xi, xvec, derivs = rep(2, length(xvec)))$design
+ 
+   cprD1 <- bsplineD(xvec, iknots = iknots, derivative = 1L)
+   cprD2 <- bsplineD(xvec, iknots = iknots, derivative = 2L)
+ 
+   stopifnot(isTRUE(
+                    all.equal(
+                              cprD1[-100, ]
+                              ,
+                              baseD1[-100, ]
+                    )
+                    ))
+   stopifnot(isTRUE( all.equal(cprD2[-100, ], baseD2[-100, ])))
+ 
+   x <- tryCatch(bsplineD(xvec, derivative = 1.5), error = function(e) {e})
+   stopifnot(identical(class(x), c("simpleError", "error", "condition")))
+   stopifnot(identical(x$message, "Only first and second derivatives are supported"))
+ 
+   x <- tryCatch(bsplineD(xvec, derivative = 3), error = function(e) {e})
+   stopifnot(identical(class(x), c("simpleError", "error", "condition")))
+   stopifnot(identical(x$message, "Only first and second derivatives are supported"))
+ 
+   x <- tryCatch(bsplineD(xvec, order = 2, derivative = 2), error = function(e) {e})
+   stopifnot(identical(class(x), c("simpleError", "error", "condition")))
+   stopifnot(identical(x$message, "(order - 2) <= 0"))
+ })
> 
> ################################################################################
> # verify that order is an integer of at least 2
> e <- new.env()
> with(e, {
+   xvec    <- runif(n = 100, min = -1, max = 5)
+   bknots  <- c(-1, 5)
+   bmat    <- tryCatch(bsplines(xvec, bknots = bknots, order = 1), error = function(e) e)
+   bmatD1  <- tryCatch(bsplineD(xvec, bknots = bknots, order = 1, derivative = 1L), error = function(e) e)
+   bmatD2  <- tryCatch(bsplineD(xvec, bknots = bknots, order = 1, derivative = 2L), error = function(e) e)
+ 
+   stopifnot(inherits(bmat, "simpleError"))
+   stopifnot(inherits(bmatD1, "simpleError"))
+   stopifnot(inherits(bmatD2, "simpleError"))
+ 
+   stopifnot(identical(bmat$message, "order needs to be an integer value >= 2."))
+   stopifnot(identical(bmatD1$message, "order needs to be an integer value >= 2."))
+   stopifnot(identical(bmatD2$message, "order needs to be an integer value >= 2."))
+ 
+   bmat <- tryCatch(bsplines(xvec, bknots = bknots, order = 1.9), error = function(e) e)
+   stopifnot(inherits(bmat, "simpleError"))
+   stopifnot(identical(bmat$message, "order needs to be an integer value >= 2."))
+ 
+   bmat <- tryCatch(bsplines(xvec, bknots = bknots, order = 2.9), error = function(e) e)
+   stopifnot(inherits(bmat, "cpr_bs"))
+   stopifnot(identical(attr(bmat, "order"), 2))
+ 
+ })
> 
> ################################################################################
> # attributes of bsplineD
> e <- new.env()
> with(e, {
+   xvec <- runif(n = 100, min = -1, max = 5)
+   iknots <- c(-0.8, 0.2, 2.3, 2.5)
+   bknots <- c(-1.2, 5.2)
+ 
+   bmatD1 <- tryCatch(bsplineD(xvec, iknots = iknots, bknots = bknots, derivative = 1L), error = function(e) e)
+   bmatD2 <- tryCatch(bsplineD(xvec, iknots = iknots, bknots = bknots, derivative = 2L), error = function(e) e)
+ 
+   stopifnot(inherits(bmatD1, "cpr_bsD1"))
+   stopifnot(inherits(bmatD2, "cpr_bsD2"))
+ 
+   stopifnot(identical(
+       names(attributes(bmatD1))
+       ,
+       c("dim", "order", "df", "iknots", "bknots", "xi", "xi_star", "derivative", "class")
+     )
+   )
+ 
+   stopifnot(identical(
+       names(attributes(bmatD2))
+       ,
+       c("dim", "order", "df", "iknots", "bknots", "xi", "xi_star", "derivative", "class")
+     )
+   )
+ 
+   stopifnot(identical(attr(bmatD1, "dim"), c(100L, 8L)))
+   stopifnot(identical(attr(bmatD2, "dim"), c(100L, 8L)))
+ 
+   stopifnot(identical(attr(bmatD1, "order"), 4))
+   stopifnot(identical(attr(bmatD2, "order"), 4))
+ 
+   stopifnot(identical(attr(bmatD1, "df"), 4 + length(iknots)))
+   stopifnot(identical(attr(bmatD2, "df"), 4 + length(iknots)))
+ 
+   stopifnot(identical(attr(bmatD1, "iknots"), iknots))
+   stopifnot(identical(attr(bmatD2, "iknots"), iknots))
+ 
+   stopifnot(identical(attr(bmatD1, "bknots"), bknots))
+   stopifnot(identical(attr(bmatD2, "bknots"), bknots))
+ 
+   stopifnot(identical(attr(bmatD1, "xi"), sort(c(rep(bknots, 4), iknots))))
+   stopifnot(identical(attr(bmatD2, "xi"), sort(c(rep(bknots, 4), iknots))))
+ 
+   stopifnot(identical(attr(bmatD1, "derivative"), 1L))
+   stopifnot(identical(attr(bmatD2, "derivative"), 2L))
+ 
+ })
> 
> ################################################################################
> ##                                End of File                                 ##
> ################################################################################
> 
> proc.time()
   user  system elapsed 
   0.25    0.10    0.34