includes/libs/RunningStat.php

   1 <?php
   2 /**
   3  * Compute running mean, variance, and extrema of a stream of numbers.
   4  *
   5  * This program is free software; you can redistribute it and/or modify
   6  * it under the terms of the GNU General Public License as published by
   7  * the Free Software Foundation; either version 2 of the License, or
   8  * (at your option) any later version.
   9  *
  10  * This program is distributed in the hope that it will be useful,
  11  * but WITHOUT ANY WARRANTY; without even the implied warranty of
  12  * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
  13  * GNU General Public License for more details.
  14  *
  15  * You should have received a copy of the GNU General Public License along
  16  * with this program; if not, write to the Free Software Foundation, Inc.,
  17  * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
  18  * http://www.gnu.org/copyleft/gpl.html
  19  *
  20  * @file
  21  * @ingroup Profiler
  22  */
  23
  24 // Needed due to PHP non-bug <https://bugs.php.net/bug.php?id=49828>.
  25 define( 'NEGATIVE_INF', -INF );
  26
  27 /**
  28  * Represents a running summary of a stream of numbers.
  29  *
  30  * RunningStat instances are accumulator-like objects that provide a set of
  31  * continuously-updated summary statistics for a stream of numbers, without
  32  * requiring that each value be stored. The measures it provides are the
  33  * arithmetic mean, variance, standard deviation, and extrema (min and max);
  34  * together they describe the central tendency and statistical dispersion of a
  35  * set of values.
  36  *
  37  * One RunningStat instance can be merged into another; the resultant
  38  * RunningStat has the state it would have had if it had accumulated each
  39  * individual point. This allows data to be summarized in parallel and in
  40  * stages without loss of fidelity.
  41  *
  42  * Based on a C++ implementation by John D. Cook:
  43  *  <http://www.johndcook.com/standard_deviation.html>
  44  *  <http://www.johndcook.com/skewness_kurtosis.html>
  45  *
  46  * The in-line documentation for this class incorporates content from the
  47  * English Wikipedia articles "Variance", "Algorithms for calculating
  48  * variance", and "Standard deviation".
  49  *
  50  * @since 1.23
  51  */
  52 class RunningStat implements Countable {
  53
  54         /** @var int Number of samples. **/
  55         public $n = 0;
  56
  57         /** @var float The first moment (or mean, or expected value). **/
  58         public $m1 = 0.0;
  59
  60         /** @var float The second central moment (or variance). **/
  61         public $m2 = 0.0;
  62
  63         /** @var float The least value in the set. **/
  64         public $min = INF;
  65
  66         /** @var float The greatest value in the set. **/
  67         public $max = NEGATIVE_INF;
  68
  69         /**
  70          * Count the number of accumulated values.
  71          * @return int Number of values
  72          */
  73         public function count() {
  74                 return $this->n;
  75         }
  76
  77         /**
  78          * Add a number to the data set.
  79          * @param int|float $x Value to add
  80          */
  81         public function push( $x ) {
  82                 $x = (float) $x;
  83
  84                 $this->min = min( $this->min, $x );
  85                 $this->max = max( $this->max, $x );
  86
  87                 $n1 = $this->n;
  88                 $this->n += 1;
  89                 $delta = $x - $this->m1;
  90                 $delta_n = $delta / $this->n;
  91                 $this->m1 += $delta_n;
  92                 $this->m2 += $delta * $delta_n * $n1;
  93         }
  94
  95         /**
  96          * Get the mean, or expected value.
  97          *
  98          * The arithmetic mean is the sum of all measurements divided by the number
  99          * of observations in the data set.
 100          *
 101          * @return float Mean
 102          */
 103         public function getMean() {
 104                 return $this->m1;
 105         }
 106
 107         /**
 108          * Get the estimated variance.
 109          *
 110          * Variance measures how far a set of numbers is spread out. A small
 111          * variance indicates that the data points tend to be very close to the
 112          * mean (and hence to each other), while a high variance indicates that the
 113          * data points are very spread out from the mean and from each other.
 114          *
 115          * @return float Estimated variance
 116          */
 117         public function getVariance() {
 118                 if ( $this->n === 0 ) {
 119                         // The variance of the empty set is undefined.
 120                         return NAN;
 121                 } elseif ( $this->n === 1 ) {
 122                         return 0.0;
 123                 } else {
 124                         return $this->m2 / ( $this->n - 1.0 );
 125                 }
 126         }
 127
 128         /**
 129          * Get the estimated standard deviation.
 130          *
 131          * The standard deviation of a statistical population is the square root of
 132          * its variance. It shows how much variation from the mean exists. In
 133          * addition to expressing the variability of a population, the standard
 134          * deviation is commonly used to measure confidence in statistical conclusions.
 135          *
 136          * @return float Estimated standard deviation
 137          */
 138         public function getStdDev() {
 139                 return sqrt( $this->getVariance() );
 140         }
 141
 142         /**
 143          * Merge another RunningStat instance into this instance.
 144          *
 145          * This instance then has the state it would have had if all the data had
 146          * been accumulated by it alone.
 147          *
 148          * @param RunningStat RunningStat instance to merge into this one
 149          */
 150         public function merge( RunningStat $other ) {
 151                 // If the other RunningStat is empty, there's nothing to do.
 152                 if ( $other->n === 0 ) {
 153                         return;
 154                 }
 155
 156                 // If this RunningStat is empty, copy values from other RunningStat.
 157                 if ( $this->n === 0 ) {
 158                         $this->n = $other->n;
 159                         $this->m1 = $other->m1;
 160                         $this->m2 = $other->m2;
 161                         $this->min = $other->min;
 162                         $this->max = $other->max;
 163                         return;
 164                 }
 165
 166                 $n = $this->n + $other->n;
 167                 $delta = $other->m1 - $this->m1;
 168                 $delta2 = $delta * $delta;
 169
 170                 $this->m1 = ( ( $this->n * $this->m1 ) + ( $other->n * $other->m1 ) ) / $n;
 171                 $this->m2 = $this->m2 + $other->m2 + ( $delta2 * $this->n * $other->n / $n );
 172                 $this->min = min( $this->min, $other->min );
 173                 $this->max = max( $this->max, $other->max );
 174                 $this->n = $n;
 175         }
 176 }