Edit File by line

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} //end function solveIF

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/**

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* Solve factorial (!)

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* Will take any real positive number and solve for it's factorial. Eg.

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* `5!` will become `1*2*3*4*5` = `120` For integers

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* and

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* 5.2! will become gamma(6.2) for non-integers

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* DONE:

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* Solve for non-integer factorials 2015/07/02

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* @param Float $num Non-negative real number to get factorial of

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* @throws Exception if number is at or less than 0

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* @return Float Solved factorial

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protected function factorial($num) {

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if($num < 0) {

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throw new Exception("Factorial Error: Factorials don't exist for numbers < 0", NF_EOS_Parser::E_NAN);

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}

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//A non-integer! Gamma that sucker up!

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if(intval($num) != $num) {

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return $this->gamma($num + 1);

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}

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$tot = 1;

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for($i=1;$i<=$num;$i++) {

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$tot *= $i;

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}

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return $tot;

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} //end function factorial

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/**

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* Gamma Function

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* Because we can. This function exists as a catch-all for different

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* numerical approx. of gamma if I decide to add any past Lanczos'.

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* This method is public because a function doesn't currently exist

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* within this parser to use it. That will change in the future.

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* @param $z Number to compute gamma from

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* @return Float The gamma (hopefully, I'll test it after writing the code)

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public function gamma($z)

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{

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return $this->laGamma($z);

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}

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/**

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* Lanczos Approximation

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* The Lanczos Approximation method of finding gamma values

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* @link http://www.rskey.org/CMS/index.php/the-library/11

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* @link http://algolist.manual.ru/maths/count_fast/gamma_function.php

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* @link https://en.wikipedia.org/wiki/Lanczos_approximation

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* @param float $z Number to obtain the gamma of

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* @return float Gamma of inputted number

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* @throws Exception if Number is less than or equal to 0

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protected function laGamma($z)

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{

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//check validity of $z, throw error if not a valid number to be used with gamma

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if($z <= 0) {

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throw new Exception("Gamma cannot be calculated on numbers less than or equal to 0", NF_EOS_Parser::E_NAN);

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}

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// Set up coefficients

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$p = array(

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0 => 1.000000000190015,

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1 => 76.18009172947146,

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2 => -86.50532032941677,

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3 => 24.01409824083091,

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4 => -1.231739572450155,

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5 => 1.208650973866179E-3,

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6 => -5.395239384953E-6

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);

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//formula:

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// ((sqrt(2pi)/z)(p[0]+sum(p[n]/(z+n), 1, 6)))(z+5.5)^(z+0.5)*e^(-(z+5.5))

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// Break it down now...

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$g1 = sqrt(2*pi())/$z;

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//Next comes our summation

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$g2 =0;

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for($n=1;$n<=6;$n++) {

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$g2 += $p[$n]/($z+$n);

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}

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// Don't forget to add p[0] to it...

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$g2 += $p[0];

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$g3 = pow($z+5.5, $z + .5);

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$g4 = exp(-($z+5.5));

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//now just multiply them all together

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$gamma = $g1 * $g2 * $g3 * $g4;

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return $gamma;

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}

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} //end class 'Parser'

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