demography (version 1.11)

cm.spline: Monotonic interpolating splines

Description

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.splinefun(x, y = NULL, method = "fmm", gulim=0)
cm.spline(x, y = NULL, n = 3*length(x), method = "fmm",
       xmin = min(x), xmax = max(x), gulim=0)

Arguments

x,y

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

method

specifies the type of spline to be used. Possible values are fmm, natural and periodic.

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.

gulim

if gulim!=0 then it is taken as the upper limit on the gradient, and interpolant is gradient limited rather than monotonic.

Value

• spline
  returns a list containing components x and y which give the ordinates where interpolation took place and the interpolated values.
• splinefun
  returns a function which will perform cubic spline interpolation of the given data points. This is often more useful than spline.

Details

Results are identical to splinefun except that Hyman Filtering is used to produce co-monotonic interpolation.

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.

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