E01BFF (PDF version)
E01 Chapter Contents
E01 Chapter Introduction
NAG Library Manual

NAG Library Routine Document


Note:  before using this routine, please read the Users' Note for your implementation to check the interpretation of bold italicised terms and other implementation-dependent details.

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

E01BFF evaluates a piecewise cubic Hermite interpolant at a set of points.

2  Specification

REAL (KIND=nag_wp)  X(N), F(N), D(N), PX(M), PF(M)

3  Description

E01BFF evaluates a piecewise cubic Hermite interpolant, as computed by E01BEF, at the points PXi, for i=1,2,,m. If any point lies outside the interval from X1 to XN, a value is extrapolated from the nearest extreme cubic, and a warning is returned.
The routine is derived from routine PCHFE in Fritsch (1982).

4  References

Fritsch F N (1982) PCHIP final specifications Report UCID-30194 Lawrence Livermore National Laboratory

5  Parameters

1:     N – INTEGERInput
2:     X(N) – REAL (KIND=nag_wp) arrayInput
3:     F(N) – REAL (KIND=nag_wp) arrayInput
4:     D(N) – REAL (KIND=nag_wp) arrayInput
On entry: N, X, F and D must be unchanged from the previous call of E01BEF.
5:     M – INTEGERInput
On entry: m, the number of points at which the interpolant is to be evaluated.
Constraint: M1.
6:     PX(M) – REAL (KIND=nag_wp) arrayInput
On entry: the m values of x at which the interpolant is to be evaluated.
7:     PF(M) – REAL (KIND=nag_wp) arrayOutput
On exit: PFi contains the value of the interpolant evaluated at the point PXi, for i=1,2,,m.
8:     IFAIL – INTEGERInput/Output
On entry: IFAIL must be set to 0, -1​ or ​1. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value -1​ or ​1 is recommended. If the output of error messages is undesirable, then the value 1 is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is 0. When the value -1​ or ​1 is used it is essential to test the value of IFAIL on exit.
On exit: IFAIL=0 unless the routine detects an error or a warning has been flagged (see Section 6).

6  Error Indicators and Warnings

If on entry IFAIL=0 or -1, explanatory error messages are output on the current error message unit (as defined by X04AAF).
Errors or warnings detected by the routine:
On entry,N<2.
The values of Xr, for r=1,2,,N, are not in strictly increasing order.
On entry,M<1.
At least one of the points PXi, for i=1,2,,M, lies outside the interval [X1,XN], and extrapolation was performed at all such points. Values computed at such points may be very unreliable.

7  Accuracy

The computational errors in the array PF should be negligible in most practical situations.

8  Further Comments

The time taken by E01BFF is approximately proportional to the number of evaluation points, m. The evaluation will be most efficient if the elements of PX are in nondecreasing order (or, more generally, if they are grouped in increasing order of the intervals Xr-1,Xr). A single call of E01BFF with m>1 is more efficient than several calls with m=1.

9  Example

This example reads in values of N, X, F and D, and then calls E01BFF to evaluate the interpolant at equally spaced points.

9.1  Program Text

Program Text (e01bffe.f90)

9.2  Program Data

Program Data (e01bffe.d)

9.3  Program Results

Program Results (e01bffe.r)

E01BFF (PDF version)
E01 Chapter Contents
E01 Chapter Introduction
NAG Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012