void	g01auc (Integer b, const double mrcomm[], Integer pn, double xmean, double xsd, double xskew, double xkurt, double xmin, double xmax, double rcomm[], NagError fail)

The function may be called by the names: g01auc, nag_stat_summary_onevar_combine or nag_summary_stats_onevar_combine.

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 g01atc. Then g01auc takes the

b

communication arrays returned by g01atc 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 g01atc.

4 References

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

5 Arguments

1: $b$ – Integer Input

On entry:

b

, the number of blocks the full dataset was split into.

Constraint:

b \geq 1

2: $mrcomm [20 \times b]$ – const double Communication Array

Note: where

MRCOMM (i, j)

appears in this document, it refers to the array element

mrcomm [(j - 1) \times 20 + i - 1]

On entry: the

j

th column of MRCOMM must contain the information returned in rcomm from one of the runs of g01atc.

3: $pn$ – Integer * Output

On exit: the number of valid observations, that is the number of observations with

w_{i} > 0

, for

i = 1, 2, \dots, n

4: $xmean$ – double * Output

On exit:

\bar{x}

, the mean.

5: $xsd$ – double * Output

On exit:

s_{2}

, the standard deviation.

6: $xskew$ – double * Output

On exit:

s_{3}

, the coefficient of skewness.

7: $xkurt$ – double * Output

On exit:

s_{4}

, the coefficient of kurtosis.

8: $xmin$ – double * Output

On exit: the smallest value.

9: $xmax$ – double * Output

On exit: the largest value.

10: $rcomm [\dim]$ – double Communication Array

Note: the dimension, dim, of the array rcomm must be at least

$20$ , when $rcomm is not NULL$ .

On exit: an amalgamation of the information held in mrcomm. This is in the same format as rcomm from g01atc.

If rcomm is NULL, rcomm is not referenced.

11: $fail$ – NagError * Input/Output

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM: On entry, argument $⟨ value ⟩$ had an illegal value.
NE_CASES_ONE: On exit we were unable to calculate xsd, xskew or xkurt. A value of $0$ has been returned.
NE_CASES_ZERO: On entry, the number of valid observations is zero.
NE_ILLEGAL_COMM: On entry, mrcomm is not in the expected format.
NE_INT: On entry, $b = ⟨ value ⟩$ .
Constraint: $b \geq 1$ .
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NE_ZERO_VARIANCE: On exit we were unable to calculate xskew or xkurt. A value of $0$ has been returned.

7 Accuracy

Not applicable.

8 Parallelism and Performance

g01auc 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 g01auc and g01atc 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.

g01au: FL CL CPP AD

NAG CL Interfaceg01auc (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

NAG CL Interface
g01auc (summary_onevar_combine)