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<?php
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namespace Samsara\Fermat\Provider\Distribution;
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use ReflectionException;
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use Samsara\Exceptions\UsageError\IntegrityConstraint;
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use Samsara\Exceptions\UsageError\OptionalExit;
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use Samsara\Fermat\Numbers;
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use Samsara\Fermat\Provider\Distribution\Base\Distribution;
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use Samsara\Fermat\Provider\PolyfillProvider;
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use Samsara\Fermat\Provider\SequenceProvider;
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use Samsara\Fermat\Provider\StatsProvider;
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use Samsara\Fermat\Types\Base\Interfaces\Numbers\DecimalInterface;
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use Samsara\Fermat\Types\Base\Interfaces\Evaluateables\FunctionInterface;
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use Samsara\Fermat\Types\Base\Interfaces\Numbers\NumberInterface;
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use Samsara\Fermat\Values\ImmutableDecimal;
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class Normal extends Distribution
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{
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/**
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* @var ImmutableDecimal
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*/
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private $mean;
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/**
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* @var ImmutableDecimal
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*/
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private $sd;
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/**
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* Normal constructor.
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*
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* @param int|float|DecimalInterface $mean
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* @param int|float|DecimalInterface $sd
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*
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* @throws IntegrityConstraint
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* @throws ReflectionException
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*/
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public function __construct($mean, $sd)
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{
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/** @var ImmutableDecimal $mean */
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$mean = Numbers::makeOrDont(Numbers::IMMUTABLE, $mean);
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/** @var ImmutableDecimal $sd */
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$sd = Numbers::makeOrDont(Numbers::IMMUTABLE, $sd);
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$this->mean = $mean;
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$this->sd = $sd;
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}
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/**
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* @return ImmutableDecimal
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*/
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public function getSD(): ImmutableDecimal
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{
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return $this->sd;
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}
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/**
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* @return ImmutableDecimal
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*/
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public function getMean(): ImmutableDecimal
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{
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return $this->mean;
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}
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/**
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* @param $x
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*
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* @return ImmutableDecimal
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* @throws IntegrityConstraint
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* @throws ReflectionException
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*/
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public function evaluateAt($x): ImmutableDecimal
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{
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$one = Numbers::makeOne();
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$twoPi = Numbers::make2Pi();
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$e = Numbers::makeE();
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$x = Numbers::makeOrDont(Numbers::IMMUTABLE, $x);
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$left = $one->divide($twoPi->multiply($this->getSD()->pow(2))->sqrt());
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$right = $e->pow($x->subtract($this->getMean())->pow(2)->divide($this->getSD()->pow(2)->multiply(2))->multiply(-1));
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/** @var ImmutableDecimal $value */
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$value = $left->multiply($right);
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return $value;
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}
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/**
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* @param int|float|DecimalInterface $p
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* @param int|float|DecimalInterface $x
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* @param int|float|DecimalInterface $mean
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*
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* @return Normal
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* @throws IntegrityConstraint
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* @throws OptionalExit
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* @throws ReflectionException
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*/
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public static function makeFromMean($p, $x, $mean): Normal
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{
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$one = Numbers::makeOne();
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$p = Numbers::makeOrDont(Numbers::IMMUTABLE, $p);
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$x = Numbers::makeOrDont(Numbers::IMMUTABLE, $x);
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$mean = Numbers::makeOrDont(Numbers::IMMUTABLE, $mean);
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$z = StatsProvider::inverseNormalCDF($one->subtract($p));
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$sd = $x->subtract($mean)->divide($z);
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return new Normal($mean, $sd);
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}
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/**
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* @param int|float|DecimalInterface $p
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* @param int|float|DecimalInterface $x
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* @param int|float|DecimalInterface $sd
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*
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* @return Normal
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* @throws IntegrityConstraint
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* @throws OptionalExit
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* @throws ReflectionException
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*/
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public static function makeFromSd($p, $x, $sd): Normal
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{
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$one = Numbers::makeOne();
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$p = Numbers::makeOrDont(Numbers::IMMUTABLE, $p);
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$x = Numbers::makeOrDont(Numbers::IMMUTABLE, $x);
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$sd = Numbers::makeOrDont(Numbers::IMMUTABLE, $sd);
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$z = StatsProvider::inverseNormalCDF($one->subtract($p));
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$mean = $x->subtract($z->multiply($sd));
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return new Normal($mean, $sd);
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}
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/**
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* @param int|float|DecimalInterface $x
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*
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* @return ImmutableDecimal
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* @throws IntegrityConstraint
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* @throws OptionalExit
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* @throws ReflectionException
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*/
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public function cdf($x): ImmutableDecimal
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{
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$x = Numbers::makeOrDont(Numbers::IMMUTABLE, $x);
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$oneHalf = Numbers::make(Numbers::IMMUTABLE, '0.5');
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$one = Numbers::makeOne();
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$sqrtTwo = Numbers::make(Numbers::IMMUTABLE, 2)->sqrt();
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/** @var ImmutableDecimal $cdf */
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$cdf = $oneHalf->multiply($one->add(StatsProvider::gaussErrorFunction(
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$x->subtract($this->mean)->divide($this->sd->multiply($sqrtTwo))
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)));
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return $cdf;
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}
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/**
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* @param int|float|DecimalInterface $x1
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* @param null|int|float|DecimalInterface $x2
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*
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* @return ImmutableDecimal
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* @throws IntegrityConstraint
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* @throws ReflectionException
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*/
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public function pdf($x1, $x2 = null): ImmutableDecimal
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{
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$x1 = Numbers::makeOrDont(Numbers::IMMUTABLE, $x1);
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if (is_null($x2)) {
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$separation = $x1->subtract($this->mean)->multiply(2)->abs();
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if ($this->mean->isLessThan($x1)) {
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$x2 = $x1->subtract($separation);
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} else {
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$x2 = $x1->add($separation);
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}
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}
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/** @var ImmutableDecimal $pdf */
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$pdf = $this->cdf($x1)->subtract($this->cdf($x2))->abs();
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return $pdf;
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}
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/**
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* @param FunctionInterface $function
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* @param $x
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* @return ImmutableDecimal
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* @throws IntegrityConstraint
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* @throws ReflectionException
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*/
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public function cdfProduct(FunctionInterface $function, $x): ImmutableDecimal
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{
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$loop = 0;
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$cdf = Numbers::makeZero();
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while (true) {
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if (count($function->describeShape()) === 0) {
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break;
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}
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$cdf = $cdf->add($function->evaluateAt($x)->multiply(SequenceProvider::nthPowerNegativeOne($loop)));
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$function = $function->derivativeExpression();
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}
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/** @var ImmutableDecimal $cdf */
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$cdf = $cdf->multiply($this->cdf($x));
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return $cdf;
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}
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/**
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* @param FunctionInterface $function
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* @param $x1
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* @param $x2
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*
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* @return ImmutableDecimal
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* @throws IntegrityConstraint
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* @throws ReflectionException
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*/
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public function pdfProduct(FunctionInterface $function, $x1, $x2): ImmutableDecimal
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{
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/** @var ImmutableDecimal $pdf */
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$pdf = $this->cdfProduct($function, $x2)->subtract($this->cdfProduct($function, $x1));
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return $pdf;
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}
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241
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/**
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* @param int|float|DecimalInterface $x
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243
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*
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* @return ImmutableDecimal
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* @throws IntegrityConstraint
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*/
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247
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public function percentBelowX($x): ImmutableDecimal
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{
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return $this->cdf($x);
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250
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}
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251
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252
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/**
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253
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* @param int|float|DecimalInterface $x
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254
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*
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255
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* @return ImmutableDecimal
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256
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* @throws IntegrityConstraint
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257
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* @throws ReflectionException
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258
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*/
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259
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public function percentAboveX($x): ImmutableDecimal
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{
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$one = Numbers::makeOne();
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262
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263
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/** @var ImmutableDecimal $perc */
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264
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$perc = $one->subtract($this->cdf($x));
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265
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266
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return $perc;
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267
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}
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268
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269
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/**
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270
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* @param int|float|DecimalInterface $x
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271
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*
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272
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* @return ImmutableDecimal
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273
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* @throws IntegrityConstraint
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274
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* @throws ReflectionException
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275
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*/
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276
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1 |
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public function zScoreOfX($x): ImmutableDecimal
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277
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{
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278
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/** @var ImmutableDecimal $x */
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279
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1 |
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$x = Numbers::makeOrDont(Numbers::IMMUTABLE, $x);
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280
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281
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/** @var ImmutableDecimal $z */
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282
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1 |
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$z = $x->subtract($this->mean)->divide($this->sd);
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283
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284
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1 |
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return $z;
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285
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}
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286
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287
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/**
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288
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* @param int|float|DecimalInterface $z
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289
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*
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290
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* @return ImmutableDecimal
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291
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* @throws IntegrityConstraint
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292
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* @throws ReflectionException
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293
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*/
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294
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1 |
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public function xFromZScore($z): ImmutableDecimal
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295
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{
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296
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1 |
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$z = Numbers::makeOrDont(Numbers::IMMUTABLE, $z);
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297
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298
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/** @var ImmutableDecimal $x */
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299
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1 |
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$x = $z->multiply($this->sd)->add($this->mean);
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300
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301
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1 |
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return $x;
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302
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}
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303
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304
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/**
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305
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* @return ImmutableDecimal
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306
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* @throws IntegrityConstraint
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307
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* @throws ReflectionException
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308
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*/
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309
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public function random(): ImmutableDecimal
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310
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{
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311
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$int1 = PolyfillProvider::randomInt(0, PHP_INT_MAX);
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312
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|
|
$int2 = PolyfillProvider::randomInt(0, PHP_INT_MAX);
|
|
313
|
|
|
|
|
314
|
|
|
$rand1 = Numbers::make(Numbers::IMMUTABLE, $int1, 20);
|
|
315
|
|
|
$rand1 = $rand1->divide(PHP_INT_MAX);
|
|
316
|
|
|
$rand2 = Numbers::make(Numbers::IMMUTABLE, $int2, 20);
|
|
317
|
|
|
$rand2 = $rand2->divide(PHP_INT_MAX);
|
|
318
|
|
|
|
|
319
|
|
|
$randomNumber = $rand1->ln()->multiply(-2)->sqrt()->multiply($rand2->multiply(Numbers::TAU)->cos(1, false));
|
|
|
|
|
|
|
320
|
|
|
/** @var ImmutableDecimal $randomNumber */
|
|
321
|
|
|
$randomNumber = $randomNumber->multiply($this->sd)->add($this->mean);
|
|
322
|
|
|
|
|
323
|
|
|
return $randomNumber;
|
|
324
|
|
|
}
|
|
325
|
|
|
|
|
326
|
|
|
/**
|
|
327
|
|
|
* @param int|float|NumberInterface $min
|
|
328
|
|
|
* @param int|float|NumberInterface $max
|
|
329
|
|
|
* @param int $maxIterations
|
|
330
|
|
|
*
|
|
331
|
|
|
* @return ImmutableDecimal
|
|
332
|
|
|
* @throws OptionalExit
|
|
333
|
|
|
* @throws IntegrityConstraint
|
|
334
|
|
|
* @throws ReflectionException
|
|
335
|
|
|
*/
|
|
336
|
|
|
public function rangeRandom($min = 0, $max = PHP_INT_MAX, int $maxIterations = 20): ImmutableDecimal
|
|
337
|
|
|
{
|
|
338
|
|
|
$i = 0;
|
|
339
|
|
|
|
|
340
|
|
|
do {
|
|
341
|
|
|
$randomNumber = $this->random();
|
|
342
|
|
|
$i++;
|
|
343
|
|
|
} while (($randomNumber->isGreaterThan($max) || $randomNumber->isLessThan($min)) && $i < $maxIterations);
|
|
344
|
|
|
|
|
345
|
|
|
if ($randomNumber->isGreaterThan($max) || $randomNumber->isLessThan($min)) {
|
|
346
|
|
|
throw new OptionalExit(
|
|
347
|
|
|
'All random numbers generated were outside of the requested range',
|
|
348
|
|
|
'A suitable random number, restricted by the $max ('.$max.') and $min ('.$min.'), could not be found within '.$maxIterations.' iterations'
|
|
|
|
|
|
|
349
|
|
|
);
|
|
350
|
|
|
}
|
|
351
|
|
|
|
|
352
|
|
|
return $randomNumber;
|
|
353
|
|
|
}
|
|
354
|
|
|
|
|
355
|
|
|
} |
JordanRL /
Fermat
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This check looks for calls to methods that do not seem to exist on a given type. It looks for the method on the type itself as well as in inherited classes or implemented interfaces.
This is most likely a typographical error or the method has been renamed.