g01auf combines sets of summaries produced by
g01atf.
Assume a dataset containing
$n$ observations, denoted by
$x=\left\{{x}_{i}:i=1,2,\dots ,n\right\}$ and a set of weights,
$w=\left\{{w}_{i}:i=1,2,\dots ,n\right\}$, 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 (
$\overline{x}$), standard deviation (
${s}_{2}$), coefficients of skewness (
${s}_{3}$) and kurtosis (
${s}_{4}$), and the maximum and minimum values for the whole dataset.

1:
$\mathbf{b}$ – Integer
Input

On entry: $b$, the number of blocks the full dataset was split into.
Constraint:
${\mathbf{b}}\ge 1$.

2:
$\mathbf{mrcomm}\left(20,{\mathbf{b}}\right)$ – Real (Kind=nag_wp) array
Communication Array

On entry: the
$j$th column of
mrcomm must contain the information returned in
rcomm from one of the runs of
g01atf.

3:
$\mathbf{pn}$ – Integer
Output

On exit: the number of valid observations, that is the number of observations with
${w}_{i}>0$, for $\mathit{i}=1,2,\dots ,n$.

4:
$\mathbf{xmean}$ – Real (Kind=nag_wp)
Output

On exit: $\overline{x}$, the mean.

5:
$\mathbf{xsd}$ – Real (Kind=nag_wp)
Output

On exit: ${s}_{2}$, the standard deviation.

6:
$\mathbf{xskew}$ – Real (Kind=nag_wp)
Output

On exit: ${s}_{3}$, the coefficient of skewness.

7:
$\mathbf{xkurt}$ – Real (Kind=nag_wp)
Output

On exit: ${s}_{4}$, the coefficient of kurtosis.

8:
$\mathbf{xmin}$ – Real (Kind=nag_wp)
Output

On exit: the smallest value.

9:
$\mathbf{xmax}$ – Real (Kind=nag_wp)
Output

On exit: the largest value.

10:
$\mathbf{rcomm}\left(*\right)$ – Real (Kind=nag_wp) array
Communication 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:
$\mathbf{ifail}$ – Integer
Input/Output

On entry:
ifail must be set to
$0$,
$1\text{or}1$. If you are unfamiliar with this argument you should refer to
Section 4 in the Introduction to the NAG Library FL Interface for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value
$1\text{or}1$ 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 $\mathbf{1}\text{or}\mathbf{1}$ is used it is essential to test the value of ifail on exit.
On exit:
${\mathbf{ifail}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see
Section 6).
If on entry
${\mathbf{ifail}}=0$ or
$1$, explanatory error messages are output on the current error message unit (as defined by
x04aaf).
Not applicable.
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 floatingpoint 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.
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.