Integer, Intent (In)	::	nxeval, nyeval, iopts(*)
Integer, Intent (Inout)	::	ifail
Real (Kind=nag_wp), Intent (In)	::	xevalm(nxeval), yevalm(nyeval), coefs(), opts()
Real (Kind=nag_wp), Intent (Out)	::	fevalm(nxeval,nyeval)

C Header Interface

#include <nag.h>

void	e02jff_ (const Integer nxeval, const Integer nyeval, const double xevalm[], const double yevalm[], const double coefs[], double fevalm[], const Integer iopts[], const double opts[], Integer *ifail)

The routine may be called by the names e02jff or nagf_fit_dim2_spline_ts_evalm.

3 Description

e02jff calculates values on a rectangular mesh of a bivariate spline computed by e02jdf. The points in the mesh are defined by

x

coordinates (

x_{i}

), for

i = 1, 2, \dots, n_{x}

, and

y

coordinates (

y_{j}

), for

j = 1, 2, \dots, n_{y}

. This routine is derived from the TSFIT package of O. Davydov and F. Zeilfelder.

4 References

Davydov O, Morandi R and Sestini A (2006) Local hybrid approximation for scattered data fitting with bivariate splines Comput. Aided Geom. Design 23 703–721

Davydov O, Sestini A and Morandi R (2005) Local RBF approximation for scattered data fitting with bivariate splines Trends and Applications in Constructive Approximation M. G. de Bruin, D. H. Mache, and J. Szabados, Eds ISNM Vol. 151 Birkhauser 91–102

Davydov O and Zeilfelder F (2004) Scattered data fitting by direct extension of local polynomials to bivariate splines Advances in Comp. Math. 21 223–271

Farin G and Hansford D (2000) The Essentials of CAGD Natic, MA: A K Peters, Ltd.

5 Arguments

1: $nxeval$ – Integer Input: On entry: $n_{x}$ , the number of values in the $x$ direction forming the mesh on which the spline is to be evaluated.

Constraint: $nxeval \geq 1$ .
2: $nyeval$ – Integer Input: On entry: $n_{y}$ , the number of values in the $y$ direction forming the mesh on which the spline is to be evaluated.

Constraint: $nyeval \geq 1$ .
3: $xevalm (nxeval)$ – Real (Kind=nag_wp) array Input: On entry: the $(x_{i})$ values forming the mesh on which the spline is to be evaluated.

Constraint: for all $i$ , $xevalm (i)$ must lie inside, or on the boundary of, the spline's bounding box as determined by e02jdf.
4: $yevalm (nyeval)$ – Real (Kind=nag_wp) array Input: On entry: the $(y_{j})$ values forming the mesh on which the spline is to be evaluated.

Constraint: for all $j$ , $yevalm (j)$ must lie inside, or on the boundary of, the spline's bounding box as determined by e02jdf.
5: $coefs (*)$ – Real (Kind=nag_wp) array Communication Array: Note: the dimension of this array is dictated by the requirements of associated functions that must have been previously called. This array must be the same array passed as argument coefs in the previous call to e02jdf.

On entry: the computed spline coefficients as output from e02jdf.
6: $fevalm (nxeval, nyeval)$ – Real (Kind=nag_wp) array Output: On exit: if $ifail = 0$ on exit $fevalm (i, j)$ contains the computed spline value at $(x_{i}, y_{j})$ .
7: $iopts (*)$ – Integer array Communication Array: Note: the dimension of this array is dictated by the requirements of associated functions that must have been previously called. This array must be the same array passed as argument iopts in the previous call to e02zkf.

On entry: the contents of the array must not have been modified either directly or indirectly, by a call to e02zkf, between calls to e02jdf and e02jff.
8: $opts (*)$ – Real (Kind=nag_wp) array Communication Array: Note: the dimension of this array is dictated by the requirements of associated functions that must have been previously called. This array must be the same array passed as argument opts in the previous call to e02zkf.

On entry: the contents of the array must not have been modified either directly or indirectly, by a call to e02zkf, between calls to e02jdf and e02jff.
9: $ifail$ – Integer Input/Output: On entry: ifail must be set to $0$ , $−1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $−1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $−1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. 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:

$ifail = 6$: On entry, $nxeval = ⟨ value ⟩$ .
Constraint: $nxeval \geq 1$ .

$ifail = 7$: On entry, $nyeval = ⟨ value ⟩$ .
Constraint: $nyeval \geq 1$ .

$ifail = 9$: Option arrays are not initialized or are corrupted.

$ifail = 10$: The fitting routine has not been called, or the array of coefficients has been corrupted.

$ifail = 13$: On entry, $xevalm (⟨ value ⟩) = ⟨ value ⟩$ was outside the bounding box.
Constraint: $⟨ value ⟩ \leq xevalm (i) \leq ⟨ value ⟩$ for all $i$ .

$ifail = 14$: On entry, $yevalm (⟨ value ⟩) = ⟨ value ⟩$ was outside the bounding box.
Constraint: $⟨ value ⟩ \leq yevalm (j) \leq ⟨ value ⟩$ for all $j$ .

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.