NAG CL Interface
g01auc (summary_​onevar_​combine)

1 Purpose

g01auc combines sets of summaries produced by g01atc.

2 Specification

#include <nag.h>
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 = xi : i=1,2,,n and a set of weights, w = wi : i=1,2,,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 (x¯), standard deviation (s2), coefficients of skewness (s3) and kurtosis (s4), and the maximum and minimum values for the whole dataset.
For a definition of x¯,s2,s3 and s4 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: b1.
2: mrcomm[20×b] const double Communication Array
Note: where MRCOMMi,j appears in this document, it refers to the array element mrcomm[j-1×20+i-1].
On entry: the jth 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 wi>0, for i=1,2,,n.
4: xmean double * Output
On exit: x¯, the mean.
5: xsd double * Output
On exit: s2, the standard deviation.
6: xskew double * Output
On exit: s3, the coefficient of skewness.
7: xkurt double * Output
On exit: s4, 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 rcommis notNULL.
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

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument value had an illegal value.
On exit we were unable to calculate xsd, xskew or xkurt. A value of 0 has been returned.
On entry, the number of valid observations is zero.
On entry, mrcomm is not in the expected format.
On entry, b=value.
Constraint: b1.
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.
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.
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.

10.1 Program Text

Program Text (g01auce.c)

10.2 Program Data

Program Data (g01auce.d)

10.3 Program Results

Program Results (g01auce.r)