The function may be called by the names: g01anc, nag_stat_quantiles_stream_fixed or nag_approx_quantiles_fixed.
A quantile is a value which divides a frequency distribution such that there is a given proportion of data values below the quantile. For example, the median of a dataset is the quantile because half the values are less than or equal to it.
g01anc uses a slightly modified version of an algorithm described in a paper by Zhang and Wang (2007) to determine -approximate quantiles of a data stream of real values, where is known. Given any quantile , an -approximate quantile is defined as an element in the data stream whose rank falls within . In case of more than one -approximate quantile being available, the one closest to is returned.
Zhang Q and Wang W (2007) A fast algorithm for approximate quantiles in high speed data streams Proceedings of the 19th International Conference on Scientific and Statistical Database Management IEEE Computer Society 29
1: – Integer *Input/Output
On entry: indicates the action required in the current call to g01anc.
Return the required length of rcomm and icomm in and respectively. n and eps must be set and licomm must be at least .
Initialise the communication arrays and process the first nb values from the data stream as supplied in rv.
Process the next block of nb values from the data stream. The calling program must update rv and (if required) nb, and re-enter g01anc with all other parameters unchanged.
Calculate the nq -approximate quantiles specified in q. The calling program must set q and nq and re-enter g01anc with all other parameters unchanged. This option can be chosen only when .
On exit: indicates output from a successful call.
Lengths of rcomm and icomm have been returned in and respectively.
g01anc has processed np data points and expects to be called again with additional data (i.e., ).
g01anc has returned the requested -approximate quantiles in qv. These quantiles are based on np data points.
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 entry, and .
Constraint: if then for all .
On entry, .
Number of data elements streamed, is not sufficient for a quantile query when .
Supply more data or reprocess the data with a higher eps value.
8Parallelism and Performance
g01anc is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.
The average time taken by g01anc is .
This example calculates -approximate quantile for , and for a data stream of values. The stream is read in four blocks of varying size.