nag_monotonic_interpolant (e01bec) computes a monotonicity-preserving piecewise cubic Hermite interpolant to a set of data points.
nag_monotonic_interpolant (e01bec) estimates first derivatives at the set of data points
, for
, which determine a piecewise cubic Hermite interpolant to the data, that preserves monotonicity over ranges where the data points are monotonic. If the data points are only piecewise monotonic, the interpolant will have an extremum at each point where monotonicity switches direction. The estimates of the derivatives are computed by a formula due to Brodlie, which is described in
Fritsch and Butland (1984), with suitable changes at the boundary points.
The algorithm is derived from routine PCHIM in
Fritsch (1982).
Values of the computed interpolant can subsequently be computed by calling
nag_monotonic_evaluate (e01bfc).
Fritsch F N and Butland J (1984) A method for constructing local monotone piecewise cubic interpolants SIAM J. Sci. Statist. Comput. 5 300–304
The computational errors in the array
d should be negligible in most practical situations.
Not applicable.
The time taken by nag_monotonic_interpolant (e01bec) is approximately proportional to .
The values of the computed interpolant at the points
, for
, may be obtained in the real array
pf, of length at least
, by the call:
e01bfc (n, x, f, d, m, px, pf, &fail)
where
n,
x and
f are the input arguments to nag_monotonic_interpolant (e01bec) and
d is the output argument from nag_monotonic_interpolant (e01bec).
This example program reads in a set of data points, calls nag_monotonic_interpolant (e01bec) to compute a piecewise monotonic interpolant, and then calls
nag_monotonic_evaluate (e01bfc) to evaluate the interpolant at equally spaced points.