NAG Library Routine Document

Integer, Intent (In)	::	b
Integer, Intent (Inout)	::	ifail
Integer, Intent (Out)	::	pn
Real (Kind=nag_wp), Intent (In)	::	mrcomm(20,b)
Real (Kind=nag_wp), Intent (Out)	::	xmean, xsd, xskew, xkurt, xmin, xmax, rcomm(*)

C Header Interface

#include <nagmk26.h>

void	g01auf_ (const Integer b, const double mrcomm[], Integer pn, double xmean, double xsd, double xskew, double xkurt, double xmin, double xmax, double rcomm[], Integer *ifail)

3

Description

Assume a dataset containing

n

observations, denoted by

x = \{x_{i} : i = 1, 2, \dots, n\}

and a set of weights,

w = \{w_{i} : i = 1, 2, \dots, n\}

, has been split into

b

blocks, and each block summarised via a call to g01atf. Then g01auf takes the

b

communication arrays returned by g01atf and returns the mean (

\bar{x}

), standard deviation (

s_{2}

), coefficients of skewness (

s_{3}

) and kurtosis (

s_{4}

), and the maximum and minimum values for the whole dataset.

For a definition of

\bar{x}, s_{2}, s_{3}

and

s_{4}

see Section 3 in g01atf.

4

References

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

5

Arguments

1: $b$ – IntegerInput: On entry: $b$ , the number of blocks the full dataset was split into.

Constraint: $b \geq 1$ .
2: $mrcomm (20, b)$ – Real (Kind=nag_wp) arrayCommunication Array: On entry: the $j$ th column of mrcomm must contain the information returned in rcomm from one of the runs of g01atf.
3: $pn$ – IntegerOutput: On exit: the number of valid observations, that is the number of observations with $w_{i} > 0$ , for $i = 1, 2, \dots, n$ .
4: $xmean$ – Real (Kind=nag_wp)Output: On exit: $\bar{x}$ , the mean.
5: $xsd$ – Real (Kind=nag_wp)Output: On exit: $s_{2}$ , the standard deviation.
6: $xskew$ – Real (Kind=nag_wp)Output: On exit: $s_{3}$ , the coefficient of skewness.
7: $xkurt$ – Real (Kind=nag_wp)Output: On exit: $s_{4}$ , the coefficient of kurtosis.
8: $xmin$ – Real (Kind=nag_wp)Output: On exit: the smallest value.
9: $xmax$ – Real (Kind=nag_wp)Output: On exit: the largest value.
10: $rcomm (*)$ – Real (Kind=nag_wp) arrayCommunication Array: Note: the dimension of the array rcomm must be at least $20$ .

On exit: an amalgamation of the information held in mrcomm. This is in the same format as rcomm from g01atf.
11: $ifail$ – IntegerInput/Output: On entry: ifail must be set to $0$ , $- 1 or 1$ . 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 $- 1 or 1$ 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 $- 1 or 1$ 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:

$ifail = 11$: On entry, $b = 〈value〉$ .
Constraint: $b \geq 1$ .

$ifail = 21$: On entry, mrcomm is not in the expected format.

$ifail = 31$: On entry, the number of valid observations is zero.

$ifail = 51$: On exit we were unable to calculate xskew or xkurt. A value of $0$ has been returned.

$ifail = 52$: On exit we were unable to calculate xsd, xskew or xkurt. A value of $0$ has been returned.

$ifail = - 99$: 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.

$ifail = - 399$: 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.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

Not applicable.

8

Parallelism and Performance

g01auf is not threaded in any implementation.

9

Further Comments

The order that the

b

communication arrays are stored in mrcomm is arbitrary. Different orders can lead to slightly different results due to numerical accuracy of floating-point calculations.

Both g01auf and g01atf consolidate results from multiple summaries. Whereas the former can only be used to combine summaries calculated sequentially, the latter combines summaries calculated in an arbitrary order allowing, for example, summaries calculated on different processing units to be combined.

10

Example

This example summarises some simulated data. The data is supplied in three blocks, the first consisting of

21

observations, the second

51

observations and the last

28

observations. Summaries are produced for each block of data separately and then an overall summary is produced.

NAG Library Routine Document

g01auf (summary_onevar_combine)

▸▿ 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

1

Purpose

2

Specification