NAG Library Routine Document

e02zaf (dim2_spline_sort)

1

Purpose

2

Specification

3

Description

A set of $m$ data points with rectangular Cartesian coordinates $x_r,y_r$ are sorted into panels defined by lines parallel to the $y$ and $x$ axes. The intercepts of these lines on the $x$ and $y$ axes are given in $\mathbf{lamda}\left(\mathit{i}\right)$, for $\mathit{i}=5,6,\dots ,\mathbf{px}-4$ and $\mathbf{mu}\left(\mathit{j}\right)$, for $\mathit{j}=5,6,\dots ,\mathbf{py}-4$, respectively. The subroutine orders the data so that all points in a panel occur before data in succeeding panels, where the panels are numbered from bottom to top and then left to right, with the usual arrangement of axes, as shown in the diagram. Within a panel the points maintain their original order.

Figure 1

4

References

5

Arguments

1:     $\mathbf{px}$ – IntegerInput

2:     $\mathbf{py}$ – IntegerInput

On entry: px and py must specify eight more than the number of intercepts on the $x$ axis and $y$ axis, respectively.

Constraint: $\mathbf{px}\ge 8$ and $\mathbf{py}\ge 8$.

3:     $\mathbf{lamda}\left(\mathbf{px}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: $\mathbf{lamda}\left(5\right)$ to $\mathbf{lamda}\left(\mathbf{px}-4\right)$ must contain, in nondecreasing order, the intercepts on the $x$ axis of the sides of the panels parallel to the $y$ axis.

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

On entry: $\mathbf{mu}\left(5\right)$ to $\mathbf{mu}\left(\mathbf{py}-4\right)$ must contain, in nondecreasing order, the intercepts on the $y$ axis of the sides of the panels parallel to the $x$ axis.

5:     $\mathbf{m}$ – IntegerInput

On entry: the number $m$ of data points.

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

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

On entry: the coordinates of the $\mathit{r}$th data point $\left(x_{\mathit{r}},y_{\mathit{r}}\right)$, for $\mathit{r}=1,2,\dots ,m$.

8:     $\mathbf{point}\left(\mathbf{npoint}\right)$ – Integer arrayOutput

On exit: for $i=1,2,\dots ,\mathbf{npoint}$, $\mathbf{point}\left(m+i\right)=\mathrm{I1}$ is the index of the first point in panel $i$, $\mathbf{point}\left(\mathrm{I1}\right)=\mathrm{I2}$ is the index of the second point in panel $i$ and so on.

$\mathbf{point}\left(\mathrm{In}\right)=0$ indicates that $\mathbf{x}\left(\mathrm{In}\right),\mathbf{y}\left(\mathrm{In}\right)$ was the last point in the panel.

The coordinates of points in panel $i$ can be accessed in turn by means of the following instructions:

in = m + i
10 in = point(in)
If (in.eq. 0) Goto 20
xi = x(in)
yi = y(in)
.
.
.
Goto 10
20 ...

9:     $\mathbf{npoint}$ – IntegerInput

On entry: the dimension of the array point as declared in the (sub)program from which e02zaf is called.

Constraint: $\mathbf{npoint}\ge \mathbf{m}+\left(\mathbf{px}-7\right)\times \left(\mathbf{py}-7\right)$.

10:   $\mathbf{adres}\left(\mathbf{nadres}\right)$ – Integer arrayWorkspace

11:   $\mathbf{nadres}$ – IntegerInput

On entry: the value $\left(\mathbf{px}-7\right)\times \left(\mathbf{py}-7\right)$, the number of panels into which the $\left(x,y\right)$ plane is divided.

12:   $\mathbf{ifail}$ – 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, $\mathit{I}=〈\mathit{\text{value}}〉$, $\mathbf{lamda}\left(\mathit{I}\right)=〈\mathit{\text{value}}〉$ and $\mathbf{lamda}\left(\mathit{I}-1\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{lamda}\left(\mathit{I}\right)\ge \mathbf{lamda}\left(\mathit{I}-1\right)$.

On entry, $\mathit{I}=〈\mathit{\text{value}}〉$, $\mathbf{mu}\left(\mathit{I}\right)=〈\mathit{\text{value}}〉$ and $\mathbf{mu}\left(\mathit{I}-1\right)=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{mu}\left(\mathit{I}\right)\ge \mathbf{mu}\left(\mathit{I}-1\right)$.

$\mathbf{ifail}=2$

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}>0$.

On entry, $\mathbf{nadres}=〈\mathit{\text{value}}〉$, $\mathbf{px}=〈\mathit{\text{value}}〉$ and $\mathbf{py}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{nadres}=\left(\mathbf{px}-7\right)\times \left(\mathbf{py}-7\right)$.

On entry, $\mathbf{npoint}=〈\mathit{\text{value}}〉$, $\mathbf{m}=〈\mathit{\text{value}}〉$, $\mathbf{px}=〈\mathit{\text{value}}〉$ and $\mathbf{py}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{npoint}\ge \mathbf{m}+\left(\mathbf{px}-7\right)\times \left(\mathbf{py}-7\right)$.

On entry, $\mathbf{px}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{px}\ge 8$.

On entry, $\mathbf{py}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{py}\ge 8$.

$\mathbf{ifail}=-99$

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

10

Example

10.1

Program Text

Program Text (e02zafe.f90)

10.2

Program Data

Program Data (e02zafe.d)

10.3

Program Results

Program Results (e02zafe.r)