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<?php |
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namespace Samsara\Fermat\Provider; |
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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\Types\Base\Interfaces\Numbers\SimpleNumberInterface; |
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use Samsara\Fermat\Values\ImmutableDecimal; |
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class SeriesProvider |
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{ |
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/** |
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* Creates a series that evaluates the following: |
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* |
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* SUM[$startTerm -> infinity]( |
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* $numerator($n) × $input^$exponent($n) |
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* -------------------------------- |
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* $denominator($n) |
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* ) |
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* |
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* Where $n is the current term number, starting at $startTerm, and increasing by 1 each loop; where $numerator, |
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* $exponent, and $denominator are callables that take the term number (as an int) as their only input, and give the |
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* value of that section at that term number; and where $input is the x value being considered for the series. |
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* |
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* The function continues adding terms until a term has MORE leading zeros than the $precision setting. (That is, |
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* until it adds zero to the total when considering significant digits.) |
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* |
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* @param SimpleNumberInterface $input |
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* @param callable $numerator |
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* @param callable $exponent |
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* @param callable $denominator |
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* @param int $startTermAt |
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* @param int $precision |
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* @param int $consecutiveDivergeLimit |
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* @param int $totalDivergeLimit |
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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 static function maclaurinSeries( |
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SimpleNumberInterface $input, // x value in series |
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callable $numerator, // a function determining what the sign (+/-) is at the nth term |
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callable $exponent, // a function determining the exponent of x at the nth term |
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callable $denominator, // a function determining the denominator at the nth term |
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int $startTermAt = 0, |
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int $precision = 10, |
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int $consecutiveDivergeLimit = 5, |
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int $totalDivergeLimit = 10): ImmutableDecimal |
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{ |
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++$precision; |
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$sum = Numbers::makeZero($precision); |
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$value = Numbers::make(Numbers::IMMUTABLE, $input->getValue(), $precision); |
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$continue = true; |
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$termNumber = $startTermAt; |
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$adjustmentOfZero = 0; |
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$prevDiff = Numbers::makeZero($precision); |
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$prevSum = $sum; |
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$divergeCount = -1; |
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$persistentDivergeCount = -1; |
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$currentPrecision = 0; |
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while ($continue) { |
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$term = Numbers::makeOne($precision); |
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try { |
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$exTerm = $value->pow($exponent($termNumber)); |
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$term = $term->multiply($exTerm); |
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$term = $term->divide($denominator($termNumber)); |
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$term = $term->multiply($numerator($termNumber)); |
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} catch (IntegrityConstraint $constraint) { |
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return $sum->truncateToPrecision($currentPrecision+1); |
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} |
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/** @var ImmutableDecimal $term */ |
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if ($term->numberOfLeadingZeros() >= $precision && !$term->isWhole()) { |
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$continue = false; |
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} |
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$currentPrecision = $term->numberOfLeadingZeros(); |
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if ($term->isEqual(0)) { |
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$adjustmentOfZero++; |
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} else { |
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$adjustmentOfZero = 0; |
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} |
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if ($adjustmentOfZero > 15) { |
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$continue = false; |
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} |
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/** @var ImmutableDecimal $sum */ |
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$sum = $sum->add($term); |
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$currDiff = $sum->subtract($prevSum)->abs(); |
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if ($prevDiff->isLessThan($currDiff)) { |
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$divergeCount++; |
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$persistentDivergeCount++; |
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} else { |
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$divergeCount = 0; |
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} |
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if ($divergeCount === $consecutiveDivergeLimit || $persistentDivergeCount === $totalDivergeLimit) { |
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throw new OptionalExit( |
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'Series appear to be diverging. Current diverge count: '.$divergeCount.' | Persistent diverge count: '.$persistentDivergeCount, |
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'A call was made to SeriesProvider::maclaurinSeries() that seems to be diverging. Exiting the loop.' |
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); |
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} |
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$prevDiff = $currDiff; |
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$prevSum = $sum; |
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$termNumber++; |
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} |
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return $sum->roundToPrecision($precision); |
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} |
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} |
JordanRL /
Fermat
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