Integer, Intent (In)	::	px, py, m, npoint, nadres
Integer, Intent (Inout)	::	ifail
Integer, Intent (Out)	::	point(npoint), adres(nadres)
Real (Kind=nag_wp), Intent (In)	::	lamda(px), mu(py), x(m), y(m)

C Header Interface

#include <nag.h>

void	e02zaf_ (const Integer px, const Integer py, const double lamda[], const double mu[], const Integer m, const double x[], const double y[], Integer point[], const Integer npoint, Integer adres[], const Integer nadres, Integer ifail)

The routine may be called by the names e02zaf or nagf_fit_dim2_spline_sort.

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

lamda (i)

, for

i = 5, 6, \dots, px - 4

and

mu (j)

, for

j = 5, 6, \dots, 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

(px - 7) \times (py - 7)

4 References

None.

5 Arguments

1: $px$ – Integer Input

2: $py$ – Integer Input

On entry: px and py must specify eight more than the number of intercepts on the

x

axis and

y

axis, respectively.

Constraint:

px \geq 8

and

py \geq 8

3: $lamda (px)$ – Real (Kind=nag_wp) array Input

On entry:

lamda (5)

lamda (px - 4)

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) array Input

On entry:

mu (5)

mu (py - 4)

must contain, in nondecreasing order, the intercepts on the

y

axis of the sides of the panels parallel to the

x

axis.

5: $m$ – Integer Input

On entry: the number

m

of data points.

6: $x (m)$ – Real (Kind=nag_wp) array Input

7: $y (m)$ – Real (Kind=nag_wp) array Input

On entry: the coordinates of the

r

th data point

(x_{r}, y_{r})

, for

r = 1, 2, \dots, m

8: $point (npoint)$ – Integer array Output

On exit: for

i = 1, 2, \dots, npoint

point (m + i) = I1

is the index of the first point in panel

i

point (I1) = I2

is the index of the second point in panel

i

and so on.

point (In) = 0

indicates that

x (In), y (In)

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: $npoint$ – Integer Input

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

Constraint:

npoint \geq m + (px - 7) \times (py - 7)

10: $adres (nadres)$ – Integer array Workspace

11: $nadres$ – Integer Input

On entry: the value

(px - 7) \times (py - 7)

, the number of panels into which the

(x, y)

plane is divided.

12: $ifail$ – Integer Input/Output

On entry: ifail must be set to

0

−1

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

1

is recommended. If message printing is undesirable, then the value

1

is recommended. Otherwise, the value

0

is recommended. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit:

ifail = 0

unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

−1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: On entry, $I = ⟨ value ⟩$ , $lamda (I) = ⟨ value ⟩$ and $lamda (I - 1) = ⟨ value ⟩$ .
Constraint: $lamda (I) \geq lamda (I - 1)$ .

On entry, $I = ⟨ value ⟩$ , $mu (I) = ⟨ value ⟩$ and $mu (I - 1) = ⟨ value ⟩$ .
Constraint: $mu (I) \geq mu (I - 1)$ .

$ifail = 2$: On entry, $m = ⟨ value ⟩$ .
Constraint: $m > 0$ .

On entry, $nadres = ⟨ value ⟩$ , $px = ⟨ value ⟩$ and $py = ⟨ value ⟩$ .
Constraint: $nadres = (px - 7) \times (py - 7)$ .

On entry, $npoint = ⟨ value ⟩$ , $m = ⟨ value ⟩$ , $px = ⟨ value ⟩$ and $py = ⟨ value ⟩$ .
Constraint: $npoint \geq m + (px - 7) \times (py - 7)$ .

On entry, $px = ⟨ value ⟩$ .
Constraint: $px \geq 8$ .

On entry, $py = ⟨ value ⟩$ .
Constraint: $py \geq 8$ .

$ifail = - 99$: 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.

$ifail = - 399$: 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.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.

e02zaf is not threaded in any implementation.

9 Further Comments

The time taken is approximately proportional to

m \times \log (npoint)

This subroutine was written to sort two-dimensional data in the manner required by routine e02daf. The first

9

arguments of e02zaf are the same as the arguments in e02daf which have the same name.

10 Example

This example reads in data points and the intercepts of the panel sides on the

x

and

y

axes; it calls e02zaf to set up the index array point; and finally it prints the data points in panel order.

e02za: FL CL CPP AD PY MB

NAG FL Interfacee02zaf (dim2_​spline_​sort)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG FL Interface
e02zaf (dim2_spline_sort)