naginterfaces.library.stat.quantiles_stream_arbitrary¶

naginterfaces.library.stat.quantiles_stream_arbitrary(ind, rv, nb, eps, q, nq, rcomm, icomm)[source]¶

quantiles_stream_arbitrary finds approximate quantiles from a large arbitrary-sized data stream using an out-of-core algorithm.

For full information please refer to the NAG Library document for g01ap

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/g01/g01apf.html

Parameters

indint

On initial entry: must be set to $0$ .Indicates the action required in the current call to quantiles_stream_arbitrary.

$i n d = 0$

Initialize the communication arrays and attempt to process the first $n b$ values from the data stream. $e p s$ , $r v$ and $n b$ must be set and $licomm$ must be at least $10$ .

$i n d = 1$

Attempt to process the next block of $n b$ values from the data stream. The calling program must update $r v$ and (if required) $n b$ , and re-enter quantiles_stream_arbitrary with all other parameters unchanged.

$i n d = 2$

Continue calculation following the reallocation of either or both of the communication arrays $r c o m m$ and $i c o m m$ .

$i n d = 3$

Calculate the $n q$ $ϵ$ -approximate quantiles specified in $q$ . The calling program must set $q$ and $n q$ and re-enter quantiles_stream_arbitrary with all other parameters unchanged. This option can be chosen only when $n p \geq ⌈ e x p (1.0) / e p s ⌉$ .

rvfloat, array-like, shape $(:)$

Note: the required length for this argument is determined as follows: if $i n d in (0, 1, 2)$ : $n b$ ; otherwise: $0$ .

If $i n d = 0$ , $1$ or $2$ , the vector containing the current block of data, otherwise $r v$ is not referenced.

nbint

If $i n d = 0$ , $1$ or $2$ , the size of the current block of data. The size of blocks of data in array $r v$ can vary;, therefore, $n b$ can change between calls to quantiles_stream_arbitrary.

epsfloat

Approximation factor $ϵ$ .

qfloat, array-like, shape $(:)$

Note: the required length for this argument is determined as follows: if $i n d = 3$ : $n q$ ; otherwise: $0$ .

If $i n d = 3$ , the quantiles to be calculated, otherwise $q$ is not referenced. Note that $q [i] = 0.0$ , corresponds to the minimum value and $q [i] = 1.0$ to the maximum value.

nqint

If $i n d = 3$ , the number of quantiles requested, otherwise $n q$ is not referenced.

rcommfloat, ndarray, shape $(lrcomm)$ , modified in place

On entry: if $i n d = 1$ or $2$ then the first $l$ elements of $r c o m m$ as supplied to quantiles_stream_arbitrary must be identical to the first $l$ elements of $r c o m m$ returned from the last call to quantiles_stream_arbitrary, where $l$ is the value of $lrcomm$ used in the last call. In other words, the contents of $r c o m m$ must not be altered between calls to this function. If $r c o m m$ needs to be reallocated then its contents must be preserved. If $i n d = 0$ then $r c o m m$ need not be set.

On exit: $r c o m m$ holds information required by subsequent calls to quantiles_stream_arbitrary.

icommint, ndarray, shape $(licomm)$ , modified in place

On entry: if $i n d = 1$ or $2$ then the first $l$ elements of $i c o m m$ as supplied to quantiles_stream_arbitrary must be identical to the first $l$ elements of $i c o m m$ returned from the last call to quantiles_stream_arbitrary, where $l$ is the value of $licomm$ used in the last call. In other words, the contents of $i c o m m$ must not be altered between calls to this function. If $i c o m m$ needs to be reallocated then its contents must be preserved. If $i n d = 0$ then $i c o m m$ need not be set.

On exit: $i c o m m [0]$ holds the minimum required length for $r c o m m$ and $i c o m m [1]$ holds the minimum required length for $i c o m m$ . The remaining elements of $i c o m m$ are used for communication between subsequent calls to quantiles_stream_arbitrary.

Returns

indint

Indicates output from the call.

$i n d = 1$

quantiles_stream_arbitrary has processed $n p$ data points and expects to be called again with additional data.

$i n d = 2$

Either one or more of the communication arrays $r c o m m$ and $i c o m m$ is too small. The new minimum lengths of $r c o m m$ and $i c o m m$ have been returned in $i c o m m [0]$ and $i c o m m [1]$ respectively. If the new minimum length is greater than the current length then the corresponding communication array needs to be reallocated, its contents preserved and quantiles_stream_arbitrary called again with all other parameters unchanged.

If there is more data to be processed, it is recommended that $lrcomm$ and $licomm$ are made significantly bigger than the minimum to limit the number of reallocations.

$i n d = 3$

quantiles_stream_arbitrary has returned the requested $ϵ$ -approximate quantiles in $q v$ . These quantiles are based on $n p$ data points.

npint

$m$ , the number of elements processed so far.

qvfloat, ndarray, shape $(:)$

If $i n d = 3$ , $q v [i]$ contains the $ϵ$ -approximate quantiles specified by the value provided in $q [i]$ .

Raises

NagValueError

(errno $1$ )

On entry, $i n d = ⟨ v a l u e ⟩$ .

Constraint: $i n d = 0$ , $1$ , $2$ or $3$ .

(errno $2$ )

On entry, $e p s = ⟨ v a l u e ⟩$ .

Constraint: $0.0 < e p s \leq 1.0$ .

(errno $3$ )

On entry, $i n d = 0$ , $1$ or $2$ and $n b = ⟨ v a l u e ⟩$ .

Constraint: if $i n d = 0$ , $1$ or $2$ then $n b > 0$ .

(errno $6$ )

The contents of $i c o m m$ have been altered between calls to this function.

(errno $7$ )

The contents of $r c o m m$ have been altered between calls to this function.

(errno $8$ )

Number of data elements streamed, $⟨ v a l u e ⟩$ is not sufficient for a quantile query when $e p s = ⟨ v a l u e ⟩$ .

Supply more data or reprocess the data with a higher $e p s$ value.

(errno $9$ )

On entry, $i n d = 3$ and $n q = ⟨ v a l u e ⟩$ .

Constraint: if $i n d = 3$ then $n q > 0$ .

(errno $10$ )

On entry, $i n d = 3$ and $q [⟨ v a l u e ⟩] = ⟨ v a l u e ⟩$ .

Constraint: if $i n d = 3$ then $0.0 \leq q [i] \leq 1.0$ for all $i$ .

Notes

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 $0.5$ quantile because half the values are less than or equal to it.

quantiles_stream_arbitrary uses a slightly modified version of an algorithm described in a paper by Zhang and Wang (2007) to determine $ϵ$ -approximate quantiles of a large arbitrary-sized data stream of real values, where $ϵ$ is a user-defined approximation factor. Let $m$ denote the number of data elements processed so far then, given any quantile $q \in [0.0, 1.0]$ , an $ϵ$ -approximate quantile is defined as an element in the data stream whose rank falls within $[(q - ϵ) m, (q + ϵ) m]$ . In case of more than one $ϵ$ -approximate quantile being available, the one closest to $q m$ is used.

References: 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

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naginterfaces.library.stat.quantiles_stream_arbitrary¶

naginterfaces.library.stat.quantiles_​stream_​arbitrary¶

naginterfaces.library.stat.quantiles_stream_arbitrary¶