# [R] Non-monotonic spline using splinefun(method = "monoH.FC")

Tim Heaton t.heaton at sheffield.ac.uk
Mon Feb 15 16:59:46 CET 2010

```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
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)

```