Integer, Intent (In)	::	n
Integer, Intent (Inout)	::	ifail
Integer, Intent (Out)	::	nord, iwrk(n)
Real (Kind=nag_wp), Intent (In)	::	x(n), y(n), wt(*)
Real (Kind=nag_wp), Intent (Out)	::	xord(n), yord(n), wtord(n), rss
Character (1), Intent (In)	::	weight

C Header Interface

#include <nag.h>

void	g10zaf_ (const char weight, const Integer n, const double x[], const double y[], const double wt[], Integer nord, double xord[], double yord[], double wtord[], double rss, Integer iwrk[], Integer *ifail, const Charlen length_weight)

The routine may be called by the names g10zaf or nagf_smooth_data_order.

3 Description

Given a set of observations

(x_{i}, y_{i})

, for

i = 1, 2, \dots, n

, with corresponding weights

w_{i}

, g10zaf rearranges the observations so that the

x_{i}

are in ascending order.

For any equal

x_{i}

in the ordered set, say

x_{j} = x_{j + 1} = \dots = x_{j + k}

, a single observation

x_{j}

is returned with a corresponding

y^{'}

and

w^{'}

, calculated as

w^{'} = \sum_{l = 0}^{k} w_{i + l}

and

y^{'} = \frac{\sum_{l = 0}^{k} w_{i + l} y_{i + l}}{w^{'}} .

Observations with zero weight are ignored. If no weights are supplied by you, then unit weights are assumed; that is

w_{i} = 1

, for

i = 1, 2, \dots, n

In addition, the within group sum of squares is computed for the tied observations using West's algorithm (see West (1979)).

4 References

Draper N R and Smith H (1985) Applied Regression Analysis (2nd Edition) Wiley

West D H D (1979) Updating mean and variance estimates: An improved method Comm. ACM 22 532–555

5 Arguments

1: $weight$ – Character(1) Input

On entry: indicates whether user-defined weights are to be used.

If $weight ='W'$ , user-defined weights are to be used and must be supplied in wt.
If $weight ='U'$ , the data is treated as unweighted.

Constraint:

weight ='W'

'U'

2: $n$ – Integer Input

On entry:

n

, the number of observations.

Constraint:

n \geq 1

3: $x (n)$ – Real (Kind=nag_wp) array Input

On entry: the values,

x_{i}

, for

i = 1, 2, \dots, n

4: $y (n)$ – Real (Kind=nag_wp) array Input

On entry: the values

y_{i}

, for

i = 1, 2, \dots, n

5: $wt (*)$ – Real (Kind=nag_wp) array Input

Note: the dimension of the array wt must be at least

n

weight ='W'

On entry: if

weight ='W'

, wt must contain the

n

weights. Otherwise wt is not referenced and unit weights are assumed.

Constraints:

if $weight ='W'$ , $wt (i) \geq 0.0$ , for $i = 1, 2, \dots, n$ ;
if $weight ='W'$ , $\sum_{i = 1}^{n} wt (i) > 0$ .

6: $nord$ – Integer Output

On exit: the number of distinct observations.

7: $xord (n)$ – Real (Kind=nag_wp) array Output

On exit: the first nord elements contain the ordered and distinct

x_{i}

8: $yord (n)$ – Real (Kind=nag_wp) array Output

On exit: the first nord elements contain the values

y^{'}

corresponding to the values in xord.

9: $wtord (n)$ – Real (Kind=nag_wp) array Output

On exit: the first nord elements contain the values

w^{'}

corresponding to the values of xord and yord.

10: $rss$ – Real (Kind=nag_wp) Output

On exit: the within group sum of squares for tied observations.

11: $iwrk (n)$ – Integer array Workspace

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, $n = ⟨ value ⟩$ .
Constraint: $n \geq 1$ .

On entry, $weight = ⟨ value ⟩$ .
Constraint: $weight ='W'$ or $'U'$ .

$ifail = 2$: On entry, all weights are zero.

On entry, $i = ⟨ value ⟩$ and $wt (i) = ⟨ value ⟩$ .
Constraint: $wt (i) \geq 0.0$ .

$ifail = - 99$: 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

For a discussion on the accuracy of the algorithm for computing mean and variance see West (1979).

8 Parallelism and Performance

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

g10zaf is not threaded in any implementation.

9 Further Comments

g10zaf may be used to compute the pure error sum of squares in simple linear regression along with g02daf; see Draper and Smith (1985).

10 Example

A set of unweighted observations are input and g10zaf used to produce a set of strictly increasing weighted observations.

g10za: FL CL CPP AD PY MB

NAG FL Interfaceg10zaf (data_​order)

▸▿ 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
g10zaf (data_order)