signal (version 0.5)

pchip: Piecewise cubic hermite interpolation

Description

Piecewise cubic hermite interpolation.

Usage

pchip(x, y, xi = NULL)

Arguments

x,y

vectors giving the coordinates of the points to be interpolated. x must be strictly monotonic (either increasing or decreasing).

xi

points at which to interpolate.

Value

• Normally, the interpolated signal, an array of length(xi). if xi == NULL, a list of class pp, a piecewise polynomial representation with the following elements:
• x
  breaks between intervals.
• P
  a matrix with n times d rows and k columns. The ith row of P, P[i,], contains the coefficients for the polynomial over the ith interval, ordered from highest to lowest. There must be one row for each interval in x.
• n
  number of intervals (length(x) - 1).
• k
  polynomial order.
• d
  number of polynomials.

Details

In contrast to spline, pchip preserves the monotonicity of x and y.

References

Fritsch, F. N. and Carlson, R. E., "Monotone Piecewise Cubic Interpolation," SIAM Journal of Numerical Analysis, vol. 17, pp.238-246, 1980. Octave Forge http://octave.sf.net

See Also

approx, spline, interp1

Examples

xf = linspace(0,11,500); yf = sin(2*pi*xf/5)
xp = c(0:10); yp = sin(2*pi*xp/5)
pch  = pchip(xp, yp, xf)
plot(xp, yp, xlim=c(0,11))
lines(xf, pch, col = "orange")