pracma (version 1.8.6)

pchip: Hermitean Interpolation Polynomials

Description

Piecewise Cubic Hermitean Interpolation Polynomials.

Usage

pchip(xi, yi, x)
pchipfun(xi, yi)

Arguments

xi, yi

x- and y-coordinates of supporting nodes.

x

x-coordinates of interpolation points.

Value

• Values of interpolated data at points x.

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.

References

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

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))
fp <- pchipfun(x, y)
fp(seq(1, 6, by = 0.5))

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")