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<?php
/**
* PSquare
*
* Represents a running, online estimate of a p-quantile for a series
* of observations using the P-squared algorithm, as documented in
* "The P-Square Algorithm for Dynamic Calculation of Percentiles and
* Histograms without Storing Observations," Communications of the ACM,
* October 1985 by R. Jain and I. Chlamtac.
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License along
* with this program; if not, write to the Free Software Foundation, Inc.,
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
* http://www.gnu.org/copyleft/gpl.html
*
* @file
* @author Ori Livneh <ori@wikimedia.org>
*/
namespace RunningStat;
/**
* Represents a running, online estimate of a p-quantile for a series
* of observations using the P-squared algorithm.
*/
class PSquare {
/** @var float Percentile to estimate. **/
private $p;
/** @var float[] Height of each marker. **/
private $heights = array();
/** @var int[] Position of each marker. **/
private $positions = array();
/** @var float[] Desired position of each marker. **/
private $desired = array();
/** @var int Number of observations. **/
private $numObservations = 0;
/**
* Constructor.
*
* @param float $p the percentile (defaults to 0.5, or median).
*/
public function __construct( $p = 0.5 ) {
$this->p = $p;
$this->positions = array( 0, 1, 2, 3, 4 );
$this->desired = array( 0, ( 2 * $p ), ( 4 * $p ), 2 + ( 2 * $p ), 4 );
$this->increments = array( 0, ( $p / 2 ), $p, ( ( 1 + $p ) / 2 ), 1 );
}
/**
* Get the total number of accumulated observations.
*
* @return int
*/
public function getCount() {
return $this->numObservations;
}
/**
* Add an observation.
*
* @param int|float $x Value to add
*/
public function addObservation( $x ) {
$this->numObservations++;
if ( $this->numObservations <= 5 ) {
$this->heights[] = $x;
if ( $this->numObservations === 5 ) {
sort( $this->heights );
}
return;
}
if ( $x < $this->heights[0] ) {
$this->heights[0] = $x;
$k = 0;
} elseif ( $x >= $this->heights[4] ) {
$this->heights[4] = $x;
$k = 3;
} else {
for ( $i = 1; $i < 5; $i++ ) {
if ( $x < $this->heights[$i] ) {
$k = $i - 1;
break;
}
}
}
for ( $i = $k + 1; $i < 5; $i++ ) {
$this->positions[$i]++;
}
for ( $i = 0; $i < 5; $i++ ) {
$this->desired[$i] += $this->increments[$i];
}
for ( $i = 1; $i < 4; $i++ ) {
$n = $this->positions[$i];
$nPrev = $this->positions[$i - 1];
$nNext = $this->positions[$i + 1];
$d = $this->desired[$i] - $n;
if ( ( $d >= 1 && $nNext - $n > 1 ) || ( $d <= -1 && $nPrev - $n < -1 ) ) {
$d = ( $d < 0 ) ? -1 : 1;
$q = $this->computeParabolic( $i, $d );
$qPrev = $this->heights[$i - 1];
$qNext = $this->heights[$i + 1];
if ( $qPrev < $q && $q < $qNext ) {
$this->heights[$i] = $q;
} else {
$this->heights[$i] = $this->computeLinear( $i, $d );
}
$this->positions[$i] += $d;
}
}
}
/**
* Use piecewise parabolic prediction to predict the ideal
* height of a marker.
*
* @param int $i index of marker to adjust
* @param int $d always -1 or 1
* @return float ideal height of marker
*/
private function computeParabolic( $i, $d ) {
$q = $this->heights[$i];
$qPrev = $this->heights[$i - 1];
$qNext = $this->heights[$i + 1];
$n = $this->positions[$i];
$nPrev = $this->positions[$i - 1];
$nNext = $this->positions[$i + 1];
return ( $q +
$d / ( $nNext - $nPrev ) *
(
( $n - $nPrev + $d ) * ( $qNext - $q ) / ( $nNext - $n ) +
( $nNext - $n - $d ) * ( $q - $qPrev ) / ( $n - $nPrev )
)
);
}
/**
* Linear formula to predict ideal position of a marker.
*
* @param int $i index of marker to adjust
* @param int $d always -1 or 1
* @return float ideal height of marker
*/
private function computeLinear( $i, $d ) {
$q = $this->heights[$i];
$n = $this->positions[$i];
return ( $q + $d *
( $this->heights[$i + $d] - $q ) /
( $this->positions[$i + $d] - $n )
);
}
/**
* Get the estimated p-quantile value.
*
* @return float
*/
public function getValue() {
// If we have five samples or fewer, fall back to a naive method.
if ( $this->getCount() <= 5 ) {
sort( $this->heights );
$i = $this->p * count( $this->heights );
if ( $i === floor( $i ) ) {
return ( $this->heights[$i - 1] + $this->heights[$i] ) / 2;
} else {
return $this->heights[floor( $i )];
}
return $result;
}
return $this->heights[2];
}
}
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