/**
* Guassian distribution density
*
* @param int $x
* @return float
*/
protected function gaussianDensity($x)
{
$y = -(1 / 2) * pow($x / $this->deviation, 2);
$y = exp($y);
$y = 1 / sqrt(2 * pi()) * $y;
return $y;
}
public function inverse($p)
{
$Y = $p->x - $this->x0;
$X = $p->y - $this->y0;
$rotI = $Y / $this->R;
$rotB = 2 * (atan(exp(X / $this->R)) - Sourcemap_Proj::PI / 4.0);
$b = asin(cos($this->b0) * sin($rotB) + sin($this->b0) * cos($rotB) * cos($rotI));
$I = atan(sin($rotI) / (cos($this->b0) * cos($rotI) - sin($this->b0) * tan($rotB)));
$lambda = $this->lambda0 + $I / $this->alpha;
$S = 0.0;
$phy = $b;
$prevPhy = -1000.0;
$iteration = 0;
while (abs($phy - $prevPhy) > 1.0E-7) {
if (++$iteration > 20) {
throw new Exception("Infinity...");
}
//S = log(tan(Sourcemap_Proj::PI / 4.0 + $phy / 2.0));
$S = 1.0 / $this->alpha * (log(tan(Sourcemap_Proj::PI / 4.0 + $b / 2.0)) - $this->K) + $this->e * log(tan(Sourcemap_Proj::PI / 4.0 + asin($this->e * sin($phy)) / 2.0));
$prevPhy = $phy;
$phy = 2.0 * atan(exp($S)) - Sourcemap_Proj::PI / 2.0;
}
$p->x = $lambda;
$p->y = $phy;
return $p;
}
/**
* Computes the humidex index.
*
* @param integer $t Temperature in celcius.
* @param integer $dew Dew point temperature in celcius.
* @return float The computed humidex.
*
* @since 2.0.0
*/
private function get_humidex($t, $dew)
{
$dew = $dew + 273.15;
$e = 6.11 * exp(5417.753 * (1 / 273.16 - 1 / $dew));
$result = $t + 0.5555 * ($e - 10);
return round($result);
}
function sa($members)
{
$T = 100.0;
$now_temp = 10000;
$n = count($members);
$status = 0;
$best = 1000000000;
while ($T > 0) {
do {
$t1 = rand(0, $n - 1);
$t2 = rand(0, $n - 1);
} while ($t1 == $t2);
$now = sqr(abs($members[$t1]['chosen1'] - $t1)) + sqr(abs($members[$t2]['chosen1'] - $t2));
$new = sqr(abs($members[$t1]['chosen1'] - $t2)) + sqr(abs($members[$t2]['chosen1'] - $t1));
if ($new < $now || lcg_value() <= exp(($now - $new) / $T)) {
$temp = $members[$t1];
$members[$t1] = $members[$t2];
$members[$t2] = $temp;
$status += $new - $now;
if ($status < $best) {
$res = $members;
}
}
$T -= 0.02;
}
return $res;
}
/**
* @param float $a
* @param float $b
*
* @return float
*/
public function compute($a, $b)
{
$score = 2 * Product::scalar($a, $b);
$squares = Product::scalar($a, $a) + Product::scalar($b, $b);
$result = exp(-$this->gamma * ($squares - $score));
return $result;
}
public function MetersToLatLon($mx, $my)
{
$lon = $mx / $this->originShift * 180.0;
$lat = $my / $this->originShift * 180.0;
$lat = 180 / pi() * (2 * atan(exp($lat * pi() / 180.0)) - pi() / 2.0);
return array($lat, $lon);
}
/**
* Poisson distribution - probability mass function
* A discrete probability distribution that expresses the probability of a given number of events
* occurring in a fixed interval of time and/or space if these events occur with a known average
* rate and independently of the time since the last event.
* https://en.wikipedia.org/wiki/Poisson_distribution
*
* λᵏℯ^⁻λ
* P(k events in an interval) = ------
* k!
*
* @param int $k events in the interval
* @param float $λ average number of successful events per interval
*
* @return float The Poisson probability of observing k successful events in an interval
*/
public static function PMF(int $k, float $λ) : float
{
Support::checkLimits(self::LIMITS, ['k' => $k, 'λ' => $λ]);
$λᵏℯ＾−λ = pow($λ, $k) * exp(-$λ);
$k！ = Combinatorics::factorial($k);
return $λᵏℯ＾−λ / $k！;
}
public function getIntersect($dp = 0)
{
if ($dp != 0) {
return round(exp($this->_intersect), $dp);
}
return exp($this->_intersect);
}
/**
* @throws RegressionException
*/
public function calculate()
{
if ($this->sourceSequence === null) {
throw new RegressionException('The input sequence is not set');
}
if (count($this->sourceSequence) < $this->dimension) {
throw new RegressionException(sprintf('The dimension of the sequence of at least %s', $this->dimension));
}
foreach ($this->sourceSequence as $k => $v) {
if ($v[1] !== null) {
$this->sumIndex[0] += $v[0];
$this->sumIndex[1] += $v[1];
$this->sumIndex[2] += $v[0] * $v[0] * $v[1];
$this->sumIndex[3] += $v[1] * log($v[1]);
$this->sumIndex[4] += $v[0] * $v[1] * log($v[1]);
$this->sumIndex[5] += $v[0] * $v[1];
}
}
$denominator = $this->sumIndex[1] * $this->sumIndex[2] - $this->sumIndex[5] * $this->sumIndex[5];
$A = exp(($this->sumIndex[2] * $this->sumIndex[3] - $this->sumIndex[5] * $this->sumIndex[4]) / $denominator);
$B = ($this->sumIndex[1] * $this->sumIndex[4] - $this->sumIndex[5] * $this->sumIndex[3]) / $denominator;
foreach ($this->sourceSequence as $i => $val) {
$coordinate = [$val[0], $A * exp($B * $val[0])];
$this->resultSequence[] = $coordinate;
}
$this->equation = sprintf('y = %s+ e^(%sx)', round($A, 2), round($B, 2));
$this->push();
}
function relh($tmpc, $dwpc)
{
$e = 6.112 * exp(17.67 * (double) $dwpc / ((double) $dwpc + 243.5));
$es = 6.112 * exp(17.67 * (double) $tmpc / ((double) $tmpc + 243.5));
$relh = $e / $es * 100.0;
return round($relh, 0);
}
static function metersToLatLon($mx, $my)
{
$lng = $mx / self::originShift() * 180.0;
$lat = $my / self::originShift() * 180.0;
$lat = 180 / pi() * (2 * atan(exp($lat * pi() / 180.0)) - pi() / 2.0);
return new GoogleMapPoint($lat, $lng);
}
public function classify($string)
{
if ($this->total_samples === 0) {
return array();
}
$tokens = $this->tokenizer->tokenize($string);
$total_score = 0;
$scores = array();
foreach ($this->subjects as $subject => $subject_data) {
$subject_data['prior_value'] = log($subject_data['count_samples'] / $this->total_samples);
$this->subjects[$subject] = $subject_data;
$scores[$subject] = 0;
foreach ($tokens as $token) {
$count = isset($this->tokens[$token][$subject]) ? $this->tokens[$token][$subject] : 0;
$scores[$subject] += log(($count + 1) / ($subject_data['count_tokens'] + $this->total_tokens));
}
$scores[$subject] = $subject_data['prior_value'] + $scores[$subject];
$total_score += $scores[$subject];
}
$min = min($scores);
$sum = 0;
foreach ($scores as $subject => $score) {
$scores[$subject] = exp($score - $min);
$sum += $scores[$subject];
}
$total = 1 / $sum;
foreach ($scores as $subject => $score) {
$scores[$subject] = $score * $total;
}
arsort($scores);
$max = max($scores);
$maxs = array_search(max($scores), $scores);
return $maxs;
}
public function evaluate()
{
if (is_array($result = parent::evaluate())) {
throw new ParsingException('exp accept only one argument');
}
return (double) exp($result);
}
/**
* @throws RegressionException
*/
public function calculate()
{
if ($this->sourceSequence === null) {
throw new RegressionException('The input sequence is not set');
}
if (count($this->sourceSequence) < $this->dimension) {
throw new RegressionException(sprintf('The dimension of the sequence of at least %s', $this->dimension));
}
$k = 0;
foreach ($this->sourceSequence as $k => $v) {
if ($v[1] !== null) {
$this->sumIndex[0] += log($v[0]);
$this->sumIndex[1] += log($v[0]) * log($v[1]);
$this->sumIndex[2] += log($v[1]);
$this->sumIndex[3] += pow(log($v[0]), 2);
}
}
$k += 1;
$B = ($k * $this->sumIndex[1] - $this->sumIndex[2] * $this->sumIndex[0]) / ($k * $this->sumIndex[3] - $this->sumIndex[0] * $this->sumIndex[0]);
$A = exp(($this->sumIndex[2] - $B * $this->sumIndex[0]) / $k);
foreach ($this->sourceSequence as $i => $val) {
$coordinate = [$val[0], $A * pow($val[0], $B)];
$this->resultSequence[] = $coordinate;
}
$this->equation = sprintf('y = %s + x^%s', round($A, 2), round($B, 2));
$this->push();
}
/**
* @param array $data
*
* @return int|void
*/
public function pValue(array $data)
{
$n = count($data);
if ($n < 5) {
throw new TooLessDataException();
}
$data = $this->normalize($data);
sort($data, SORT_NUMERIC);
$nd = new NormalDistribution();
$s = 0.0;
foreach ($data as $i => $v) {
$cdf = $nd->normalCdf($v);
$i++;
$s += (2.0 * $i - 1.0) * log($cdf) + (2 * ($n - $i) + 1) * log(1 - $cdf);
}
$a2 = -$n - 1 / $n * $s;
$a2 = $a2 * (1 + 0.75 / $n + 2.25 / pow($n, 2));
if ($a2 >= 0.6) {
return exp(1.2937 - 5.709 * $a2 + 0.0186 * pow($a2, 2));
}
if (0.34 < $a2 and $a2 < 0.6) {
return exp(0.9177 - 4.279 * $a2 - 1.38 * pow($a2, 2));
}
if (0.2 < $a2 and $a2 < 0.34) {
return 1 - exp(-8.318 + 42.796 * $a2 - 59.938 * pow($a2, 2));
}
if ($a2 <= 0.2) {
return 1 - exp(-13.436 + 101.14 * $a2 - 223.73 * pow($a2, 2));
}
}
function expm1($x) {
if (abs($x) < 1e-5) {
return $x + 0.5*$x*$x;
} else {
return exp($x) - 1.0;
}
}
/**
* Compute the denominators which is the predicted expectation of
* each feature given a set of weights L and a set of features for
* each document for each class.
*
* @param $feature_array All the data known about the training set
* @param $l The current set of weights to be initialized
* @return void
*/
protected function prepareFprime(array &$feature_array, array &$l)
{
$this->denominators = array();
foreach ($feature_array as $offset => $doc) {
$numerator = array_fill_keys(array_keys($doc), 0.0);
$denominator = 0.0;
foreach ($doc as $cl => $f) {
if (!is_array($f)) {
continue;
}
$tmp = 0.0;
foreach ($f as $i) {
$tmp += $l[$i];
}
$tmp = exp($tmp);
$numerator[$cl] += $tmp;
$denominator += $tmp;
}
foreach ($doc as $class => $features) {
if (!is_array($features)) {
continue;
}
foreach ($features as $fi) {
if (!isset($this->denominators[$fi])) {
$this->denominators[$fi] = 0;
}
$this->denominators[$fi] += $numerator[$class] / $denominator;
}
}
}
}
public function __construct($ltDays = 42, $stDays = 7)
{
$this->ltDays = $ltDays;
$this->stDays = $stDays;
$this->ltExp = exp(-1 / $this->ltDays);
$this->stExp = exp(-1 / $this->stDays);
}
public function key($key)
{
if ($this->numeric($key)) {
$this->pushValue(floatval($key));
} else {
if ($key == "+") {
$this->pushValue($this->pop() + $this->pop());
} else {
if ($key == "-") {
$t = $this->pop();
$this->push($this->pop() - $t);
} else {
if ($key == "*") {
$this->pushValue($this->pop() * $this->pop());
} else {
if ($key == "enter") {
$this->push();
} else {
if ($key == "clx") {
$this->r[0] = 0;
} else {
if ($key == "/") {
$t = $this->pop();
if ($t != 0) {
$this->pushValue($this->pop() / $t);
}
} else {
if ($key == "x^y") {
$this->pushValue(exp(log($this->pop()) * $this->pop()));
} else {
if ($key == "clr") {
$this->r[0] = 0;
$this->r[1] = 0;
$this->r[2] = 0;
$this->r[3] = 0;
} else {
if ($key == "chs") {
$this->r[0] = -$this->r[0];
} else {
if ($key == "sin") {
$this->pushValue(sin(deg2rad($this->pop())));
} else {
if ($key == "chs") {
$this->r[0] = -$this->r[0];
} else {
throw new Exception("can't do key: " . $key);
}
}
}
}
}
}
}
}
}
}
}
}
}
function cmpByRatingLeech(&$a, &$b)
{
$aPeer = max($a["totalLeech"] + $a["totalSeed"], $a['sum_peers']);
$bPeer = max($b["totalLeech"] + $b["totalSeed"], $b['sum_peers']);
$a['sortVal'] = exp(-$aPeer / 5000.0) * exp($a['kinopoiskRating']);
$b['sortVal'] = exp(-$bPeer / 5000.0) * exp($b['kinopoiskRating']);
return $a["sortVal"] < $b["sortVal"];
}
public function fromPointToLatLon(Coord2D $point)
{
$origin = $this->_pixelOrigin;
$lng = ($point->x - $origin->x) / $this->_pixelsPerLonDegree;
$latRadians = ($point->y - $origin->y) / -$this->_pixelsPerLonRadian;
$lat = $this->radiansToDegrees(2 * atan(exp($latRadians)) - pi() / 2);
return new GeoPoint($lat, $lng);
}
/**
* Gets the probaibiliy using the pmf function of a certain outcome
* @param float $x Outcome
* @return float
* @throws UnexpectedValueException if x is not an int
*/
public function get_probability($x)
{
if (is_int($x)) {
return gmp_fact($this->n) / (gmp_fact($x) * gmp_fact($this->n - $x)) * exp($this->p, $x) * exp(1 - $this->p, $this->n - $x);
} else {
throw new UnexpectedValueException('UnexpectedValueException occured because BionomailDistribution is not continous so x cannot be a non-integer');
}
}
public function get_probability($x)
{
if (is_numeric($x)) {
return exp($this->lambda, $x) * exp(M_E, $this->lambda * -1) / gmp_fact($x);
} else {
throw new UnexpectedValueException();
}
}
function fromPixelToLL($x, $y, $zoom)
{
$e = $this->zc[$zoom];
$f = ($x - $e) / $this->Bc[$zoom];
$g = ($y - $e) / -$this->Cc[$zoom];
$h = 180.0 / M_PI * (2 * atan(exp($g)) - 0.5 * M_PI);
return array($f, $h);
}
/**
* Cumulative distribution function
*
* f(x;λ) = 1 − ℯ^⁻λx x ≥ 0
* = 0 x < 0
*
* @param float $λ often called the rate parameter
* @param float $x the random variable
*
* @return float
*/
public static function CDF(float $x, float $λ) : float
{
if ($x < 0) {
return 0;
}
Support::checkLimits(self::LIMITS, ['x' => $x, 'λ' => $λ]);
return 1 - exp(-$λ * $x);
}
function createResultArray($ro, $steps)
{
$resultArray = array();
for ($k = 0; $k < $steps; $k++) {
$resultArray[] = pow($ro, $k) * exp(-$ro) / factorial($k);
}
return $resultArray;
}
private function computeBrevityPenalty($referenceLength, $translationLength)
{
if ($translationLength <= $referenceLength) {
return exp(1 - $referenceLength / $translationLength);
} else {
return 1;
}
}
/**
* <table border="1">
<tr><td><strong>Humidex Range</strong></td><td><strong>Degree of Comfort</strong></td></tr>
<tr><td>20-29</td><td style="color: #4CD900;">Comfortable</td></tr>
<tr><td>30-39</td><td style="color: #FFD800;">Some Discomfort</td></tr>
<tr><td>40-45</td><td style="color: #FF6A00;">Great Discomfort</td></tr>
<tr><td>>45</td><td style="color: #FF0000;">Dangerous</td></tr>
</table>
*
* @return float
*/
public function calc() : float
{
$dewpointK = $this->getDewPoint() + 273.15;
$e = 6.11 * exp(5417.753 * (1 / 273.16 - 1 / $dewpointK));
$h = 0.5555 * ($e - 10.0);
$humidex = $this->getTemp() + $h;
return $humidex;
}
/**
* Laplace distribution - cumulative distribution function
* From -∞ to x (lower CDF)
* https://en.wikipedia.org/wiki/Laplace_distribution
*
* 1 / x - μ \
* F(x) = - exp| ------ | if x < μ
* 2 \ b /
*
* 1 / x - μ \
* F(x) = 1 - - exp| - ------ | if x ≥ μ
* 2 \ b /
*
* @param number $x
* @param number $μ location parameter
* @param number $b scale parameter (diversity) b > 0
*
* @return float
*/
public static function CDF($x, $μ, $b) : float
{
Support::checkLimits(self::LIMITS, ['x' => $x, 'μ' => $μ, 'b' => $b]);
if ($x < $μ) {
return 1 / 2 * exp(($x - $μ) / $b);
}
return 1 - 1 / 2 * exp(-($x - $μ) / $b);
}
function neyron(array $w, array $x)
{
$result = 0;
foreach ($w as $key => $value) {
$result += $w[$key] * $x[$key];
}
return 1 / (1 + exp(-$result));
}