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.
E01SHF takes as input the interpolant Qx,y of a set of scattered data points xr,yr,fr, for r=1,2,…,m, as computed by E01SGF,
and evaluates the interpolant and its first partial derivatives at the set of points ui,vi, for i=1,2,…,n.
E01SHF must only be called after a call to
E01SGF.
This routine is derived from the routine QS2GRD described by Renka (1988).
4 References
Renka R J (1988) Algorithm 660: QSHEP2D: Quadratic Shepard method for bivariate interpolation of scattered data ACM Trans. Math. Software14 149–150
On exit: the values of the interpolant at ui,vi, for i=1,2,…,n. If any of these evaluation points lie outside the region of definition of the interpolant the corresponding entries in Q are set to the largest machine representable number (see X02ALF), and E01SHF returns with IFAIL=3.
On exit: the values of the partial derivatives of the interpolant Qx,y at ui,vi, for i=1,2,…,n. If any of these evaluation points lie outside the region of definition of the interpolant, the corresponding entries in QX and QY are set to the largest machine representable number (see X02ALF), and E01SHF returns with IFAIL=3.
15: 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.
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:
IFAIL=1
On entry,
M<6,
or
LIQ<2×M+1,
or
LRQ<6×M+5,
or
N<1.
IFAIL=2
Values supplied in IQ or RQ appear to be invalid. Check that these arrays have not been corrupted between the calls to
E01SGF and E01SHF.
IFAIL=3
At least one evaluation point lies outside the region of definition of the interpolant. At all such points the corresponding values in
Q, QX and QY have been set to the largest machine representable number (see X02ALF).
7 Accuracy
Computational errors should be negligible in most practical situations.
8 Further Comments
The time taken for a call to E01SHF will depend in general on the distribution of the data points. If X and Y are approximately uniformly distributed, then the time taken should be only On. At worst Omn time will be required.