NAG Library Routine Document

e01znf  (dimn_scat_shep_eval)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{d}$ – IntegerInput

On entry: must be the same value supplied for argument d in the preceding call to e01zmf.

Constraint: $\mathbf{d}\ge 2$.

2:     $\mathbf{m}$ – IntegerInput

On entry: must be the same value supplied for argument m in the preceding call to e01zmf.

Constraint: $\mathbf{m}\ge \left(\mathbf{d}+1\right)\times \left(\mathbf{d}+2\right)/2+2$.

3:     $\mathbf{x}\left(\mathbf{d},\mathbf{m}\right)$ – Real (Kind=nag_wp) arrayInput

Note: the $i$th ordinate of the point $x_j$ is stored in $\mathbf{x}\left(i,j\right)$.

On entry: must be the same array supplied as argument x in the preceding call to e01zmf. It must remain unchanged between calls.

4:     $\mathbf{f}\left(\mathbf{m}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: must be the same array supplied as argument f in the preceding call to e01zmf. It must remain unchanged between calls.

5:     $\mathbf{iq}\left(2\times \mathbf{m}+1\right)$ – Integer arrayInput

On entry: must be the same array returned as argument iq in the preceding call to e01zmf. It must remain unchanged between calls.

6:     $\mathbf{rq}\left(*\right)$ – Real (Kind=nag_wp) arrayInput

Note: the dimension of the array rq must be at least $\left(\left(\mathbf{d}+1\right)\times \left(\mathbf{d}+2\right)/2\right)\times \mathbf{m}+2\times \mathbf{d}+1$.

On entry: must be the same array returned as argument rq in the preceding call to e01zmf. It must remain unchanged between calls.

7:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of evaluation points.

Constraint: $\mathbf{n}\ge 1$.

8:     $\mathbf{xe}\left(\mathbf{d},\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayInput

Note: the $i$th ordinate of the point $x_j$ is stored in $\mathbf{xe}\left(i,j\right)$.

On entry: $\mathbf{xe}\left(1:\mathbf{d},\mathit{j}\right)$ must be set to the evaluation point ${\mathbf{x}}_{\mathit{j}}$, for $\mathit{j}=1,2,\dots ,n$.

9:     $\mathbf{q}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: $\mathbf{q}\left(\mathit{i}\right)$ contains the value of the interpolant, at ${\mathbf{x}}_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$. If any of these evaluation points lie outside the region of definition of the interpolant the corresponding entries in q are set to an extrapolated approximation, and e01znf returns with $\mathbf{ifail}=\mathbf{3}$.

10:   $\mathbf{qx}\left(\mathbf{d},\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: $\mathbf{qx}\left(i,j\right)$ contains the value of the partial derivatives with respect to the $i$th independent variable (dimension) of the interpolant $Q\left(\mathbf{x}\right)$ at ${\mathbf{x}}_{\mathit{j}}$, for $\mathit{j}=1,2,\dots ,n$, and for each of the partial derivatives $i=1,2,\dots ,d$. If any of these evaluation points lie outside the region of definition of the interpolant, the corresponding entries in qx are set to extrapolated approximations to the partial derivatives, and e01znf returns with $\mathbf{ifail}=\mathbf{3}$.

11:   $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6

Error Indicators and Warnings

$\mathbf{ifail}=1$

On entry, $\mathbf{d}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{d}\ge 2$.

On entry, $\left(\left(\mathbf{d}+1\right)\times \left(\mathbf{d}+2\right)/2\right)\times \mathbf{m}+2\times \mathbf{d}+1$ exceeds the largest machine integer.
$\mathbf{d}=〈\mathit{\text{value}}〉$ and $\mathbf{m}=〈\mathit{\text{value}}〉$.

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$ and $\mathbf{d}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}\ge \left(\mathbf{d}+1\right)\times \left(\mathbf{d}+2\right)/2+2$.

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 1$.

$\mathbf{ifail}=2$

On entry, values in iq appear to be invalid. Check that iq has not been corrupted between calls to e01zmf and e01znf.

On entry, values in rq appear to be invalid. Check that rq has not been corrupted between calls to e01zmf and e01znf.

$\mathbf{ifail}=3$

On entry, at least one evaluation point lies outside the region of definition of the interpolant. At such points the corresponding values in q and qx contain extrapolated approximations. Points should be evaluated one by one to identify extrapolated values.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

9.1

Internal Changes

10

Example

10.1

Program Text

Program Text (e01znfe.f90)

10.2

Program Data

Program Data (e01znfe.d)

10.3

Program Results

Program Results (e01znfe.r)