The routine may be called by the names g01auf or nagf_stat_summary_onevar_combine.
Assume a dataset containing observations, denoted by and a set of weights, , has been split into blocks, and each block summarised via a call to g01atf. Then g01auf takes the communication arrays returned by g01atf and returns the mean (), standard deviation (), coefficients of skewness () and kurtosis (), and the maximum and minimum values for the whole dataset.
West D H D (1979) Updating mean and variance estimates: An improved method Comm. ACM22 532–555
1: – IntegerInput
On entry: , the number of blocks the full dataset was split into.
2: – Real (Kind=nag_wp) arrayCommunication Array
On entry: the th column of mrcomm must contain the information returned in rcomm from one of the runs of g01atf.
3: – IntegerOutput
On exit: the number of valid observations, that is the number of observations with
, for .
4: – Real (Kind=nag_wp)Output
On exit: , the mean.
5: – Real (Kind=nag_wp)Output
On exit: , the standard deviation.
6: – Real (Kind=nag_wp)Output
On exit: , the coefficient of skewness.
7: – Real (Kind=nag_wp)Output
On exit: , the coefficient of kurtosis.
8: – Real (Kind=nag_wp)Output
On exit: the smallest value.
9: – Real (Kind=nag_wp)Output
On exit: the largest value.
10: – Real (Kind=nag_wp) arrayCommunication Array
Note: the dimension of the array rcomm
must be at least
On exit: an amalgamation of the information held in mrcomm. This is in the same format as rcomm from g01atf.
11: – IntegerInput/Output
On entry: ifail must be set to , or to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of means that an error message is printed while a value of means that it is not.
If halting is not appropriate, the value or is recommended. If message printing is undesirable, then the value is recommended. Otherwise, the value is recommended. When the value or is used it is essential to test the value of ifail on exit.
On exit: unless the routine detects an error or a warning has been flagged (see Section 6).
6Error Indicators and Warnings
If on entry or , explanatory error messages are output on the current error message unit (as defined by x04aaf).
On entry, the number of valid observations is zero.
On exit we were unable to calculate xskew or xkurt. A value of has been returned.
On exit we were unable to calculate xsd, xskew or xkurt. A value of has been returned.
An unexpected error has been triggered by this routine. Please
See Section 7 in the Introduction to the NAG Library FL 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 FL Interface for further information.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.
8Parallelism and Performance
g01auf is not threaded in any implementation.
The order that the 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.
This example summarises some simulated data. The data is supplied in three blocks, the first consisting of observations, the second observations and the last observations. Summaries are produced for each block of data separately and then an overall summary is produced.