NAG Library Routine Document

E01SBF

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

9 Example

1 Purpose

E01SBF evaluates at a given point the two-dimensional interpolant function computed by E01SAF.

2 Specification

SUBROUTINE E01SBF (	M, X, Y, F, TRIANG, GRADS, PX, PY, PF, IFAIL)
INTEGER	M, TRIANG(7*M), IFAIL
*double precision*	X(M), Y(M), F(M), GRADS(2,M), PX, PY, PF

3 Description

E01SBF takes as input the parameters defining the interpolant Fx,y of a set of scattered data points xr,yr,fr, for r=1,2,…,m, as computed by E01SAF, and evaluates the interpolant at the point px,py.

If px,py is equal to xr,yr for some value of r, the returned value will be equal to fr.

If px,py is not equal to xr,yr for any r, the derivatives in GRADS will be used to compute the interpolant. A triangle is sought which contains the point px,py, and the vertices of the triangle along with the partial derivatives and fr values at the vertices are used to compute the value Fpx,py. If the point px,py lies outside the triangulation defined by the input parameters, the returned value is obtained by extrapolation. In this case, the interpolating function F is extended linearly beyond the triangulation boundary. The method is described in more detail in Renka and Cline (1984) and the code is derived from Renka (1984).

E01SBF must only be called after a call to E01SAF.

4 References

Renka R L (1984) Algorithm 624: Triangulation and interpolation of arbitrarily distributed points in the plane ACM Trans. Math. Software 10 440–442

Renka R L and Cline A K (1984) A triangle-based C1 interpolation method Rocky Mountain J. Math. 14 223–237

5 Parameters

1: M – INTEGERInput
2: X(M) – double precision arrayInput
3: Y(M) – double precision arrayInput
4: F(M) – double precision arrayInput
5: TRIANG(7×M) – INTEGER arrayInput
6: GRADS(2,M) – double precision arrayInput: On entry: M, X, Y, F, TRIANG and GRADS must be unchanged from the previous call of E01SAF.
7: PX – double precisionInput
8: PY – double precisionInput: On entry: the point px,py at which the interpolant is to be evaluated.
9: PF – double precisionOutput: On exit: the value of the interpolant evaluated at the point px,py.
10: 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.

On exit: IFAIL=0 unless the routine detects an error (see Section 6).
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.