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<?php /** * 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 Wikimedia; use Serializable; /** * Represents a running, online estimate of a p-quantile for a series * of observations using the P-squared algorithm. * * The algorithm is from "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. */ class PSquare implements Serializable { /** * Percentile to estimate. * @var float $p */ private $p; /** * Position of each marker. * @var int[] $positions */ private $positions; /** * Desired position of each marker. * @var float[] $desired */ private $desired; /** @var float[] $increments */ private $increments; /** * Number of observations. * @var int $numObservations */ private $numObservations = 0; /** * Height of each marker. * @var float[] $heights */ private $heights = []; /** * @param float $p the percentile (defaults to 0.5, or median). */ public function __construct( $p = 0.5 ) { $this->p = $p; $this->positions = [ 0, 1, 2, 3, 4 ]; $this->desired = [ 0, ( 2 * $p ), ( 4 * $p ), 2 + ( 2 * $p ), 4 ]; $this->increments = [ 0, ( $p / 2 ), $p, ( ( 1 + $p ) / 2 ), 1 ]; } /** * Export state, e.g. for serializing and caching. * * @return array */ public function __serialize(): array { return [ 'percentile' => $this->p, 'positions' => $this->positions, 'desired' => $this->desired, 'increments' => $this->increments, 'numObservations' => $this->numObservations, 'heights' => $this->heights, ]; } /** * @param array $data */ public function __unserialize( array $data ): void { $this->p = $data['percentile']; $this->positions = $data['positions']; $this->desired = $data['desired']; $this->increments = $data['increments']; $this->numObservations = $data['numObservations']; $this->heights = $data['heights']; } public function serialize() { // TODO: Remove once PHP 7.4+ is required return serialize( $this->__serialize() ); } /** * @param string $serialized */ public function unserialize( $serialized ): void { // TODO: Remove once PHP 7.4+ is required $this->__unserialize( unserialize( $serialized ) ); } /** * 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; } } } // @phan-suppress-next-line PhanPossiblyUndeclaredVariable 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 $this->heights[2]; } }
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