NAG FL Interface
e01znf (dimn_​scat_​shep_​eval)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{d}$ – Integer Input

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

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

2: $\mathbf{m}$ – Integer Input

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

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

3: $\mathbf{x}(\mathbf{d},\mathbf{m})$ – Real (Kind=nag_wp) array Input

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

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) array Input

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 array Input

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

6: $\mathbf{rq}(*)$ – Real (Kind=nag_wp) array Input

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

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

7: $\mathbf{n}$ – Integer Input

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

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

8: $\mathbf{xe}(\mathbf{d},\mathbf{n})$ – Real (Kind=nag_wp) array Input

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

On entry: $\mathbf{xe}(1:\mathbf{d},\mathit{j})$ 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) array Output

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: $\mathbf{qx}(\mathbf{d},\mathbf{n})$ – Real (Kind=nag_wp) array Output

On exit: $\mathbf{qx}(i,j)$ 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: $\mathbf{ifail}$ – 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 $-\mathbf{1}$ 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, $((\mathbf{d}+1)\times (\mathbf{d}+2)/2)\times \mathbf{m}+2\times \mathbf{d}+1$ 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: $\mathbf{m}\ge (\mathbf{d}+1)\times (\mathbf{d}+2)/2+2$.

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 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

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.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

9.1 Internal Changes

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results