/// Factor representing a team difference that has not exceeded the draw margin. /// /// See the accompanying math paper for more details. class GaussianWithinFactor extends GaussianFactor { private $_epsilon; public function __construct($epsilon, Variable &$variable) { $this->_epsilon = $epsilon; $this->createVariableToMessageBinding($variable); } public function getLogNormalization() { $variables = $this->getVariables(); $marginal = $variables[0]->getValue(); $messages = $this->getMessages(); $message = $messages[0]->getValue(); $messageFromVariable = GaussianDistribution::divide($marginal, $message); $mean = $messageFromVariable->getMean(); $std = $messageFromVariable->getStandardDeviation(); $z = GaussianDistribution::cumulativeTo(($this->_epsilon - $mean)/$std) - GaussianDistribution::cumulativeTo((-$this->_epsilon - $mean)/$std); return -GaussianDistribution::logProductNormalization($messageFromVariable, $message) + log($z); } protected function updateMessage(Message &$message, Variable &$variable) { $oldMarginal = clone $variable->getValue(); $oldMessage = clone $message->getValue(); $messageFromVariable = GaussianDistribution::divide($oldMarginal, $oldMessage); $c = $messageFromVariable->getPrecision(); $d = $messageFromVariable->getPrecisionMean(); $sqrtC = sqrt($c); $dOnSqrtC = $d/$sqrtC; $epsilonTimesSqrtC = $this->_epsilon*$sqrtC; $d = $messageFromVariable->getPrecisionMean(); $denominator = 1.0 - TruncatedGaussianCorrectionFunctions::wWithinMargin($dOnSqrtC, $epsilonTimesSqrtC); $newPrecision = $c/$denominator; $newPrecisionMean = ($d + $sqrtC* TruncatedGaussianCorrectionFunctions::vWithinMargin($dOnSqrtC, $epsilonTimesSqrtC))/ $denominator; $newMarginal = GaussianDistribution::fromPrecisionMean($newPrecisionMean, $newPrecision); $newMessage = GaussianDistribution::divide( GaussianDistribution::multiply($oldMessage, $newMarginal), $oldMarginal); /// Update the message and marginal $message->setValue($newMessage); $variable->setValue($newMarginal); /// Return the difference in the new marginal return GaussianDistribution::subtract($newMarginal, $oldMarginal); } } ?>