Hermitean Interpolation Polynomials

Piecewise Cubic Hermitean Interpolation Polynomials.

pchip(xi, yi, x)

pchipfun(xi, yi)

Arguments

xi, yi

x- and y-coordinates of supporting nodes.

x

x-coordinates of interpolation points.

Details

pchip is a `shape-preserving' piecewise cubic Hermite polynomial approach that apptempts to determine slopes such that function values do not overshoot data values. pchipfun is a wrapper around pchip and returns a function. Both pchip and the function returned by pchipfun are vectorized.

xi and yi must be vectors of the same length greater or equal 3 (for cubic interpolation to be possible), and xi must be sorted. pchip can be applied to points outside [min(xi), max(xi)], but the result does not make much sense outside this interval.

Value

Values of interpolated data at points x.

References

Moler, C. (2004). Numerical Computing with Matlab. Revised Reprint, SIAM.

Author

Copyright of the Matlab version from Cleve Moler in his book “Numerical Computing with Matlab”, Chapter 3 on Interpolation. R Version by Hans W. Borchers, 2011.

See also

interp1

Examples

x <- c(1, 2, 3, 4, 5, 6)
y <- c(16, 18, 21, 17, 15, 12)
pchip(x, y, seq(1, 6, by = 0.5))
#>  [1] 16.00000 16.88750 18.00000 19.80000 21.00000 19.33333 17.00000 15.96667
#>  [9] 15.00000 13.63750 12.00000
fp <- pchipfun(x, y)
fp(seq(1, 6, by = 0.5))
#>  [1] 16.00000 16.88750 18.00000 19.80000 21.00000 19.33333 17.00000 15.96667
#>  [9] 15.00000 13.63750 12.00000

if (FALSE) { # \dontrun{
plot(x, y, col="red", xlim=c(0,7), ylim=c(10,22),
     main = "Spline and 'pchip' Interpolation")
grid()

xs <- seq(1, 6, len=51)
ys <- interp1(x, y, xs, "spline")
lines(xs, ys, col="cyan")
yp <- pchip(x, y, xs)
lines(xs, yp, col = "magenta")} # }