NAG Library Routine Document

E01THF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     M – INTEGERInput

2:     X(M) – REAL (KIND=nag_wp) arrayInput

3:     Y(M) – REAL (KIND=nag_wp) arrayInput

4:     Z(M) – REAL (KIND=nag_wp) arrayInput

5:     F(M) – REAL (KIND=nag_wp) arrayInput

On entry: M, X, Y, Z and F must be the same values as were supplied in the preceding call to E01TGF.

6:     IQ(LIQ) – INTEGER arrayInput

On entry: must be unchanged from the value returned from a previous call to E01TGF.

7:     LIQ – INTEGERInput

On entry: the dimension of the array IQ as declared in the (sub)program from which E01THF is called.

Constraint: $\mathbf{LIQ}\ge 2\times \mathbf{M}+1$.

8:     RQ(LRQ) – REAL (KIND=nag_wp) arrayInput

On entry: must be unchanged from the value returned from a previous call to E01TGF.

9:     LRQ – INTEGERInput

On entry: the dimension of the array RQ as declared in the (sub)program from which E01THF is called.

Constraint: $\mathbf{LRQ}\ge 10\times \mathbf{M}+7$.

10:   N – INTEGERInput

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

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

11:   U(N) – REAL (KIND=nag_wp) arrayInput

12:   V(N) – REAL (KIND=nag_wp) arrayInput

13:   W(N) – REAL (KIND=nag_wp) arrayInput

On entry: $\mathbf{U}\left(\mathit{i}\right)$, $\mathbf{V}\left(\mathit{i}\right)$, $\mathbf{W}\left(\mathit{i}\right)$ must be set to the evaluation point $\left(u_{\mathit{i}},v_{\mathit{i}},w_{\mathit{i}}\right)$, for $\mathit{i}=1,2,\dots ,n$.

14:   Q(N) – REAL (KIND=nag_wp) arrayOutput

On exit: $\mathbf{Q}\left(\mathit{i}\right)$ contains the value of the interpolant at $\left(u_{\mathit{i}},v_{\mathit{i}},w_{\mathit{i}}\right)$, 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 the largest machine representable number (see X02ALF), and E01THF returns with $\mathbf{IFAIL}=\mathbf{3}$.

15:   QX(N) – REAL (KIND=nag_wp) arrayOutput

16:   QY(N) – REAL (KIND=nag_wp) arrayOutput

17:   QZ(N) – REAL (KIND=nag_wp) arrayOutput

On exit: $\mathbf{QX}\left(\mathit{i}\right)$, $\mathbf{QY}\left(\mathit{i}\right)$, $\mathbf{QZ}\left(\mathit{i}\right)$ contains the value of the partial derivatives of the interpolant $Q\left(x,y,z\right)$ at $\left(u_{\mathit{i}},v_{\mathit{i}},w_{\mathit{i}}\right)$, 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 QX, QY and QZ are set to the largest machine representable number (see X02ALF), and E01THF returns with $\mathbf{IFAIL}=\mathbf{3}$.

18:   IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction 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 parameter, 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,	$\mathbf{M}<10$,
or	$\mathbf{LIQ}<2\times \mathbf{M}+1$,
or	$\mathbf{LRQ}<10\times \mathbf{M}+7$,
or	$\mathbf{N}<1$.

$\mathbf{IFAIL}=2$

Values supplied in IQ or RQ appear to be invalid. Check that these arrays have not been corrupted between the calls to E01TGF and E01THF.

$\mathbf{IFAIL}=3$

At least one evaluation point lies outside the region of definition of the interpolant. At all such points the corresponding values in Q, QX, QY and QZ have been set to the largest machine representable number (see X02ALF).

7  Accuracy

8  Further Comments

9  Example