Monotonic interpolating splines

Perform cubic spline monotonic interpolation of given data points, returning either a list of points obtained by the interpolation or a function performing the interpolation. The splines are constrained to be monotonically increasing (i.e., the slope is never negative).

Usage

cm.spline(x, y = NULL, n = 3 * length(x), xmin = min(x), xmax = max(x), ...)

cm.splinefun(x, y = NULL, ...)

Arguments

x, y

vectors giving the coordinates of the points to be interpolated. Alternatively a single plotting structure can be specified: see xy.coords.

n

interpolation takes place at n equally spaced points spanning the interval [xmin, xmax].

xmin

left-hand endpoint of the interpolation interval.

xmax

right-hand endpoint of the interpolation interval.

...

Other arguments are ignored.

Value

cm.spline

returns a list containing components x and y which give the ordinates where interpolation took place and the interpolated values.

cm.splinefun

returns a function which will perform cubic spline interpolation of the given data points. This is often more useful than spline.

Details

These are simply wrappers to the splinefun function family from the stats package.

References

Forsythe, G. E., Malcolm, M. A. and Moler, C. B. (1977) Computer Methods for Mathematical Computations. Hyman (1983) SIAM J. Sci. Stat. Comput. 4(4):645-654. Dougherty, Edelman and Hyman 1989 Mathematics of Computation, 52: 471-494.

Author

Rob J Hyndman

Examples

x <- seq(0,4,l=20)
y <- sort(rnorm(20))
plot(x,y)
lines(spline(x, y, n = 201), col = 2) # Not necessarily monotonic
lines(cm.spline(x, y, n = 201), col = 3) # Monotonic