NAG Library Routine Document

E02ZAF

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

A data point lying exactly on one or more panel sides is taken to be in the highest-numbered panel adjacent to the point. The subroutine does not physically rearrange the data, but provides the array POINT which contains a linked list for each panel, pointing to the data in that panel. The total number of panels is $\left(\mathbf{PX}-7\right)\times \left(\mathbf{PY}-7\right)$.

4  References

5  Parameters

1:     PX – INTEGERInput

2:     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:     LAMDA(PX) – 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:     MU(PY) – 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:     M – INTEGERInput

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

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

7:     Y(M) – 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:     POINT(NPOINT) – 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:     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:   ADRES(NADRES) – INTEGER arrayWorkspace

11:   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:   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

$\mathbf{IFAIL}=1$

The intercepts in the array LAMDA, or in the array MU, are not in nondecreasing order.

$\mathbf{IFAIL}=2$

On entry,	$\mathbf{PX}<8$,
or	$\mathbf{PY}<8$,
or	$\mathbf{M}\le 0$,
or	$\mathbf{NADRES}\ne \left(\mathbf{PX}-7\right)\times \left(\mathbf{PY}-7\right)$,
or	$\mathbf{NPOINT}<\mathbf{M}+\left(\mathbf{PX}-7\right)\times \left(\mathbf{PY}-7\right)$.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (e02zafe.f90)

9.2  Program Data

Program Data (e02zafe.d)

9.3  Program Results

Program Results (e02zafe.r)