Hi, In my version of R, the stats package splinefun code for fitting a Fritsch and Carlson monotonic spline does not appear to guarantee a monotonic result. If two adjoining sections both have over/undershoot the way the resulting adjustment of alpha and beta is performed can give modified values which still do not satisfy the required constraints. I do not think this is due to finite precision arithmetic. Is this a known bug? Have had a look through the bug database but couldn't find anything.
Below is an example created to demonstrate this, ############################################### # Create the following data # This is created so that their are two adjoining sections which have to be adjusted x <- 1:8 y <- c(-12, -10, 3.5, 4.45, 4.5, 140, 142, 142) # Now run the splinefun() function FailMonSpline <- splinefun(x, y, method = "mono") # In theory this should be monotonic increasing but the required conditions are not satisfied # Check values of alpha and beta for this curve m <- FailMonSpline(x, deriv = 1) nx <- length(x) n1 <- nx - 1L dy <- y[-1] - y[-nx] dx <- x[-1] - x[-nx] Sx <- dy/dx alpha <- m[-nx]/Sx beta <- m[-1]/Sx a2b3 <- 2 * alpha + beta - 3 ab23 <- alpha + 2 * beta - 3 ok <- (a2b3 > 0 & ab23 > 0) ok <- ok & (alpha * (a2b3 + ab23) < a2b3^2) # If the curve is monotonic then all ok should be FALSE however this is not the case ok # Alternatively can easily seen to be non-monotonic by plotting the region between 4 and 5 t <- seq(4,5, length = 200) plot(t, FailMonSpline(t), type = "l") ######################################################## The version of R I am running is platform x86_64-suse-linux-gnu arch x86_64 os linux-gnu system x86_64, linux-gnu status major 2 minor 8.1 year 2008 month 12 day 22 svn rev 47281 language R version.string R version 2.8.1 (2008-12-22) ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
