NAG Library Routine Document

E01BFF

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: $M \geq 1$ .
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: $PF (i)$ contains the value of the interpolant evaluated at the point $PX (i)$ , for $i = 1, 2, \dots, m$ .
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

- 1

, explanatory error messages are output on the current error message unit (as defined by X04AAF).

Errors or warnings detected by the routine:

$IFAIL = 1$

On entry,

N < 2

$IFAIL = 2$: The values of $X (r)$ , for $r = 1, 2, \dots, N$ , are not in strictly increasing order.

$IFAIL = 3$

On entry,

M < 1

$IFAIL = 4$: At least one of the points $PX (i)$ , for $i = 1, 2, \dots, M$ , lies outside the interval [ $X (1), X (N)$ ], 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

[X (r - 1), X (r)]

). 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.

NAG Library Routine DocumentE01BFF

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

9 Example

9.1 Program Text

9.2 Program Data

9.3 Program Results

NAG Library Routine Document

E01BFF