--- /dev/null
+<?php
+/**
+ * Compute running mean, variance, and extrema of a stream of numbers.
+ *
+ * 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
+ * @ingroup Profiler
+ */
+
+// Needed due to PHP non-bug <https://bugs.php.net/bug.php?id=49828>.
+define( 'NEGATIVE_INF', -INF );
+
+/**
+ * Represents a running summary of a stream of numbers.
+ *
+ * RunningStat instances are accumulator-like objects that provide a set of
+ * continuously-updated summary statistics for a stream of numbers, without
+ * requiring that each value be stored. The measures it provides are the
+ * arithmetic mean, variance, standard deviation, and extrema (min and max);
+ * together they describe the central tendency and statistical dispersion of a
+ * set of values.
+ *
+ * One RunningStat instance can be merged into another; the resultant
+ * RunningStat has the state it would have had if it had accumulated each
+ * individual point. This allows data to be summarized in parallel and in
+ * stages without loss of fidelity.
+ *
+ * Based on a C++ implementation by John D. Cook:
+ * <http://www.johndcook.com/standard_deviation.html>
+ * <http://www.johndcook.com/skewness_kurtosis.html>
+ *
+ * The in-line documentation for this class incorporates content from the
+ * English Wikipedia articles "Variance", "Algorithms for calculating
+ * variance", and "Standard deviation".
+ *
+ * @since 1.23
+ */
+class RunningStat implements Countable {
+
+ /** @var int Number of samples. **/
+ public $n = 0;
+
+ /** @var float The first moment (or mean, or expected value). **/
+ public $m1 = 0.0;
+
+ /** @var float The second central moment (or variance). **/
+ public $m2 = 0.0;
+
+ /** @var float The least value in the the set. **/
+ public $min = INF;
+
+ /** @var float The most value in the set. **/
+ public $max = NEGATIVE_INF;
+
+ /**
+ * Count the number of accumulated values.
+ * @return int Number of values
+ */
+ public function count() {
+ return $this->n;
+ }
+
+ /**
+ * Add a number to the data set.
+ * @param int|float $x Value to add
+ */
+ public function push( $x ) {
+ $x = (float) $x;
+
+ $this->min = min( $this->min, $x );
+ $this->max = max( $this->max, $x );
+
+ $n1 = $this->n;
+ $this->n += 1;
+ $delta = $x - $this->m1;
+ $delta_n = $delta / $this->n;
+ $this->m1 += $delta_n;
+ $this->m2 += $delta * $delta_n * $n1;
+ }
+
+ /**
+ * Get the mean, or expected value.
+ *
+ * The arithmetic mean is the sum of all measurements divided by the number
+ * of observations in the data set.
+ *
+ * @return float Mean
+ */
+ public function getMean() {
+ return $this->m1;
+ }
+
+ /**
+ * Get the estimated variance.
+ *
+ * Variance measures how far a set of numbers is spread out. A small
+ * variance indicates that the data points tend to be very close to the
+ * mean (and hence to each other), while a high variance indicates that the
+ * data points are very spread out from the mean and from each other.
+ *
+ * @return float Estimated variance
+ */
+ public function getVariance() {
+ if ( $this->n === 0 ) {
+ // The variance of the empty set is undefined.
+ return NAN;
+ } elseif ( $this->n === 1 ) {
+ return 0.0;
+ } else {
+ return $this->m2 / ( $this->n - 1.0 );
+ }
+ }
+
+ /**
+ * Get the estimated stanard deviation.
+ *
+ * The standard deviation of a statistical population is the square root of
+ * its variance. It shows shows how much variation from the mean exists. In
+ * addition to expressing the variability of a population, the standard
+ * deviation is commonly used to measure confidence in statistical conclusions.
+ *
+ * @return float Estimated standard deviation
+ */
+ public function getStdDev() {
+ return sqrt( $this->getVariance() );
+ }
+
+ /**
+ * Merge another RunningStat instance into this instance.
+ *
+ * This instance then has the state it would have had if all the data had
+ * been accumulated by it alone.
+ *
+ * @param RunningStat RunningStat instance to merge into this one
+ */
+ public function merge( RunningStat $other ) {
+ // If the other RunningStat is empty, there's nothing to do.
+ if ( $other->n === 0 ) {
+ return;
+ }
+
+ // If this RunningStat is empty, copy values from other RunningStat.
+ if ( $this->n === 0 ) {
+ $this->n = $other->n;
+ $this->m1 = $other->m1;
+ $this->m2 = $other->m2;
+ $this->min = $other->min;
+ $this->max = $other->max;
+ return;
+ }
+
+ $n = $this->n + $other->n;
+ $delta = $other->m1 - $this->m1;
+ $delta2 = $delta * $delta;
+
+ $this->m1 = ( ( $this->n * $this->m1 ) + ( $other->n * $other->m1 ) ) / $n;
+ $this->m2 = $this->m2 + $other->m2 + ( $delta2 * $this->n * $other->n / $n );
+ $this->min = min( $this->min, $other->min );
+ $this->max = max( $this->max, $other->max );
+ $this->n = $n;
+ }
+}
--- /dev/null
+<?php
+/**
+ * PHP Unit tests for RunningStat class.
+ * @covers RunningStat
+ */
+class RunningStatTest extends MediaWikiTestCase {
+
+ public $points = array(
+ 49.7168, 74.3804, 7.0115, 96.5769, 34.9458,
+ 36.9947, 33.8926, 89.0774, 23.7745, 73.5154,
+ 86.1322, 53.2124, 16.2046, 73.5130, 10.4209,
+ 42.7299, 49.3330, 47.0215, 34.9950, 18.2914,
+ );
+
+ /**
+ * Verify that the statistical moments and extrema computed by RunningStat
+ * match expected values.
+ * @covers RunningStat::push
+ * @covers RunningStat::count
+ * @covers RunningStat::getMean
+ * @covers RunningStat::getVariance
+ * @covers RunningStat::getStdDev
+ */
+ public function testRunningStatAccuracy() {
+ $rstat = new RunningStat();
+ foreach( $this->points as $point ) {
+ $rstat->push( $point );
+ }
+
+ $mean = array_sum( $this->points ) / count( $this->points );
+ $variance = array_sum( array_map( function ( $x ) use ( $mean ) {
+ return pow( $mean - $x, 2 );
+ }, $this->points ) ) / ( count( $rstat ) - 1 );
+ $stddev = sqrt( $variance );
+ $min = min( $this->points );
+ $max = max( $this->points );
+
+ $this->assertEquals( count( $rstat ), count( $this->points ) );
+ $this->assertEquals( $rstat->min, min( $this->points ) );
+ $this->assertEquals( $rstat->max, max( $this->points ) );
+ $this->assertEquals( $rstat->getMean(), $mean );
+ $this->assertEquals( $rstat->getVariance(), $variance );
+ $this->assertEquals( $rstat->getStdDev(), $stddev );
+ }
+
+ /**
+ * When one RunningStat instance is merged into another, the state of the
+ * target RunningInstance should have the state that it would have had if
+ * all the data had been accumulated by it alone.
+ * @covers RunningStat::merge
+ * @covers RunningStat::count
+ */
+ public function testRunningStatMerge() {
+ $expected = new RunningStat();
+
+ foreach( $this->points as $point ) {
+ $expected->push( $point );
+ }
+
+ // Split the data into two sets
+ $sets = array_chunk( $this->points, floor( count( $this->points ) / 2 ) );
+
+ // Accumulate the first half into one RunningStat object
+ $first = new RunningStat();
+ foreach( $sets[0] as $point ) {
+ $first->push( $point );
+ }
+
+ // Accumulate the second half into another RunningStat object
+ $second = new RunningStat();
+ foreach( $sets[1] as $point ) {
+ $second->push( $point );
+ }
+
+ // Merge the second RunningStat object into the first
+ $first->merge( $second );
+
+ $this->assertEquals( count( $first ), count( $this->points ) );
+ $this->assertEquals( $first, $expected );
+ }
+}
dépôts / lhc / web / wiklou.git / commitdiff