[Summary view]

Differences Between: [Versions 400 and 401] [Versions 401 and 402] [Versions 401 and 403]

   1  <?php
   2  
   3  namespace PhpOffice\PhpSpreadsheet\Calculation\Statistical\Distributions;
   4  
   5  use PhpOffice\PhpSpreadsheet\Calculation\ArrayEnabled;
   6  use PhpOffice\PhpSpreadsheet\Calculation\Exception;
   7  use PhpOffice\PhpSpreadsheet\Calculation\Functions;
   8  use PhpOffice\PhpSpreadsheet\Calculation\Information\ExcelError;
   9  
  10  class Beta
  11  {
  12      use ArrayEnabled;
  13  
  14      private const MAX_ITERATIONS = 256;
  15  
  16      private const LOG_GAMMA_X_MAX_VALUE = 2.55e305;
  17  
  18      private const XMININ = 2.23e-308;
  19  
  20      /**
  21       * BETADIST.
  22       *
  23       * Returns the beta distribution.
  24       *
  25       * @param mixed $value Float value at which you want to evaluate the distribution
  26       *                      Or can be an array of values
  27       * @param mixed $alpha Parameter to the distribution as a float
  28       *                      Or can be an array of values
  29       * @param mixed $beta Parameter to the distribution as a float
  30       *                      Or can be an array of values
  31       * @param mixed $rMin as an float
  32       *                      Or can be an array of values
  33       * @param mixed $rMax as an float
  34       *                      Or can be an array of values
  35       *
  36       * @return array|float|string
  37       *         If an array of numbers is passed as an argument, then the returned result will also be an array
  38       *            with the same dimensions
  39       */
  40      public static function distribution($value, $alpha, $beta, $rMin = 0.0, $rMax = 1.0)
  41      {
  42          if (is_array($value) || is_array($alpha) || is_array($beta) || is_array($rMin) || is_array($rMax)) {
  43              return self::evaluateArrayArguments([self::class, __FUNCTION__], $value, $alpha, $beta, $rMin, $rMax);
  44          }
  45  
  46          $rMin = $rMin ?? 0.0;
  47          $rMax = $rMax ?? 1.0;
  48  
  49          try {
  50              $value = DistributionValidations::validateFloat($value);
  51              $alpha = DistributionValidations::validateFloat($alpha);
  52              $beta = DistributionValidations::validateFloat($beta);
  53              $rMax = DistributionValidations::validateFloat($rMax);
  54              $rMin = DistributionValidations::validateFloat($rMin);
  55          } catch (Exception $e) {
  56              return $e->getMessage();
  57          }
  58  
  59          if ($rMin > $rMax) {
  60              $tmp = $rMin;
  61              $rMin = $rMax;
  62              $rMax = $tmp;
  63          }
  64          if (($value < $rMin) || ($value > $rMax) || ($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax)) {
  65              return ExcelError::NAN();
  66          }
  67  
  68          $value -= $rMin;
  69          $value /= ($rMax - $rMin);
  70  
  71          return self::incompleteBeta($value, $alpha, $beta);
  72      }
  73  
  74      /**
  75       * BETAINV.
  76       *
  77       * Returns the inverse of the Beta distribution.
  78       *
  79       * @param mixed $probability Float probability at which you want to evaluate the distribution
  80       *                      Or can be an array of values
  81       * @param mixed $alpha Parameter to the distribution as a float
  82       *                      Or can be an array of values
  83       * @param mixed $beta Parameter to the distribution as a float
  84       *                      Or can be an array of values
  85       * @param mixed $rMin Minimum value as a float
  86       *                      Or can be an array of values
  87       * @param mixed $rMax Maximum value as a float
  88       *                      Or can be an array of values
  89       *
  90       * @return array|float|string
  91       *         If an array of numbers is passed as an argument, then the returned result will also be an array
  92       *            with the same dimensions
  93       */
  94      public static function inverse($probability, $alpha, $beta, $rMin = 0.0, $rMax = 1.0)
  95      {
  96          if (is_array($probability) || is_array($alpha) || is_array($beta) || is_array($rMin) || is_array($rMax)) {
  97              return self::evaluateArrayArguments([self::class, __FUNCTION__], $probability, $alpha, $beta, $rMin, $rMax);
  98          }
  99  
 100          $rMin = $rMin ?? 0.0;
 101          $rMax = $rMax ?? 1.0;
 102  
 103          try {
 104              $probability = DistributionValidations::validateProbability($probability);
 105              $alpha = DistributionValidations::validateFloat($alpha);
 106              $beta = DistributionValidations::validateFloat($beta);
 107              $rMax = DistributionValidations::validateFloat($rMax);
 108              $rMin = DistributionValidations::validateFloat($rMin);
 109          } catch (Exception $e) {
 110              return $e->getMessage();
 111          }
 112  
 113          if ($rMin > $rMax) {
 114              $tmp = $rMin;
 115              $rMin = $rMax;
 116              $rMax = $tmp;
 117          }
 118          if (($alpha <= 0) || ($beta <= 0) || ($rMin == $rMax) || ($probability <= 0.0)) {
 119              return ExcelError::NAN();
 120          }
 121  
 122          return self::calculateInverse($probability, $alpha, $beta, $rMin, $rMax);
 123      }
 124  
 125      /**
 126       * @return float|string
 127       */
 128      private static function calculateInverse(float $probability, float $alpha, float $beta, float $rMin, float $rMax)
 129      {
 130          $a = 0;
 131          $b = 2;
 132  
 133          $i = 0;
 134          while ((($b - $a) > Functions::PRECISION) && (++$i <= self::MAX_ITERATIONS)) {
 135              $guess = ($a + $b) / 2;
 136              $result = self::distribution($guess, $alpha, $beta);
 137              if (($result === $probability) || ($result === 0.0)) {
 138                  $b = $a;
 139              } elseif ($result > $probability) {
 140                  $b = $guess;
 141              } else {
 142                  $a = $guess;
 143              }
 144          }
 145  
 146          if ($i === self::MAX_ITERATIONS) {
 147              return ExcelError::NA();
 148          }
 149  
 150          return round($rMin + $guess * ($rMax - $rMin), 12);
 151      }
 152  
 153      /**
 154       * Incomplete beta function.
 155       *
 156       * @author Jaco van Kooten
 157       * @author Paul Meagher
 158       *
 159       * The computation is based on formulas from Numerical Recipes, Chapter 6.4 (W.H. Press et al, 1992).
 160       *
 161       * @param float $x require 0<=x<=1
 162       * @param float $p require p>0
 163       * @param float $q require q>0
 164       *
 165       * @return float 0 if x<0, p<=0, q<=0 or p+q>2.55E305 and 1 if x>1 to avoid errors and over/underflow
 166       */
 167      public static function incompleteBeta(float $x, float $p, float $q): float
 168      {
 169          if ($x <= 0.0) {
 170              return 0.0;
 171          } elseif ($x >= 1.0) {
 172              return 1.0;
 173          } elseif (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > self::LOG_GAMMA_X_MAX_VALUE)) {
 174              return 0.0;
 175          }
 176  
 177          $beta_gam = exp((0 - self::logBeta($p, $q)) + $p * log($x) + $q * log(1.0 - $x));
 178          if ($x < ($p + 1.0) / ($p + $q + 2.0)) {
 179              return $beta_gam * self::betaFraction($x, $p, $q) / $p;
 180          }
 181  
 182          return 1.0 - ($beta_gam * self::betaFraction(1 - $x, $q, $p) / $q);
 183      }
 184  
 185      // Function cache for logBeta function
 186      private static $logBetaCacheP = 0.0;
 187  
 188      private static $logBetaCacheQ = 0.0;
 189  
 190      private static $logBetaCacheResult = 0.0;
 191  
 192      /**
 193       * The natural logarithm of the beta function.
 194       *
 195       * @param float $p require p>0
 196       * @param float $q require q>0
 197       *
 198       * @return float 0 if p<=0, q<=0 or p+q>2.55E305 to avoid errors and over/underflow
 199       *
 200       * @author Jaco van Kooten
 201       */
 202      private static function logBeta(float $p, float $q): float
 203      {
 204          if ($p != self::$logBetaCacheP || $q != self::$logBetaCacheQ) {
 205              self::$logBetaCacheP = $p;
 206              self::$logBetaCacheQ = $q;
 207              if (($p <= 0.0) || ($q <= 0.0) || (($p + $q) > self::LOG_GAMMA_X_MAX_VALUE)) {
 208                  self::$logBetaCacheResult = 0.0;
 209              } else {
 210                  self::$logBetaCacheResult = Gamma::logGamma($p) + Gamma::logGamma($q) - Gamma::logGamma($p + $q);
 211              }
 212          }
 213  
 214          return self::$logBetaCacheResult;
 215      }
 216  
 217      /**
 218       * Evaluates of continued fraction part of incomplete beta function.
 219       * Based on an idea from Numerical Recipes (W.H. Press et al, 1992).
 220       *
 221       * @author Jaco van Kooten
 222       */
 223      private static function betaFraction(float $x, float $p, float $q): float
 224      {
 225          $c = 1.0;
 226          $sum_pq = $p + $q;
 227          $p_plus = $p + 1.0;
 228          $p_minus = $p - 1.0;
 229          $h = 1.0 - $sum_pq * $x / $p_plus;
 230          if (abs($h) < self::XMININ) {
 231              $h = self::XMININ;
 232          }
 233          $h = 1.0 / $h;
 234          $frac = $h;
 235          $m = 1;
 236          $delta = 0.0;
 237          while ($m <= self::MAX_ITERATIONS && abs($delta - 1.0) > Functions::PRECISION) {
 238              $m2 = 2 * $m;
 239              // even index for d
 240              $d = $m * ($q - $m) * $x / (($p_minus + $m2) * ($p + $m2));
 241              $h = 1.0 + $d * $h;
 242              if (abs($h) < self::XMININ) {
 243                  $h = self::XMININ;
 244              }
 245              $h = 1.0 / $h;
 246              $c = 1.0 + $d / $c;
 247              if (abs($c) < self::XMININ) {
 248                  $c = self::XMININ;
 249              }
 250              $frac *= $h * $c;
 251              // odd index for d
 252              $d = -($p + $m) * ($sum_pq + $m) * $x / (($p + $m2) * ($p_plus + $m2));
 253              $h = 1.0 + $d * $h;
 254              if (abs($h) < self::XMININ) {
 255                  $h = self::XMININ;
 256              }
 257              $h = 1.0 / $h;
 258              $c = 1.0 + $d / $c;
 259              if (abs($c) < self::XMININ) {
 260                  $c = self::XMININ;
 261              }
 262              $delta = $h * $c;
 263              $frac *= $delta;
 264              ++$m;
 265          }
 266  
 267          return $frac;
 268      }
 269  
 270      private static function betaValue(float $a, float $b): float
 271      {
 272          return (Gamma::gammaValue($a) * Gamma::gammaValue($b)) /
 273              Gamma::gammaValue($a + $b);
 274      }
 275  
 276      private static function regularizedIncompleteBeta(float $value, float $a, float $b): float
 277      {
 278          return self::incompleteBeta($value, $a, $b) / self::betaValue($a, $b);
 279      }
 280  }