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<?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;
}
}
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