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added metrics. @todo: implement n-dim
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Math/Topology/Metrics2D.php
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261
Math/Topology/Metrics2D.php
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<?php
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/**
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* Orange Management
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*
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* PHP Version 7.4
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*
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* @package phpOMS\Math\Topology
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* @copyright Dennis Eichhorn
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* @license OMS License 1.0
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* @version 1.0.0
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* @link https://orange-management.org
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*/
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declare(strict_types=1);
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namespace phpOMS\Math\Topology;
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/**
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* Metrics.
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*
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* @package phpOMS\Math\Topology
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* @license OMS License 1.0
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* @link https://orange-management.org
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* @since 1.0.0
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*/
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final class Metrics2D
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{
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private function __construct()
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{
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}
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/**
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* Manhatten metric.
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*
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* @latex d(p, q) = \sum_{n=1}^N{|p_i - q_i|}
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*
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* @param array $a 2-D array with x and y coordinate
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* @param array $b 2-D array with x and y coordinate
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*
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* @return float
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*
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* @since 1.0.0
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*/
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public static function manhattan(array $a, array $b) : float
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{
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return \abs($a['x'] - $b['x']) + \abs($a['y'] - $b['y']);
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}
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/**
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* Euclidean metric.
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*
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* @latex d(p, q) = \sqrt{\sum_{n=1}^N{(p_i - q_i)^2}}
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*
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* @param array $a 2-D array with x and y coordinate
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* @param array $b 2-D array with x and y coordinate
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*
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* @return float
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*
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* @since 1.0.0
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*/
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public static function euclidean(array $a, array $b) : float
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{
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$dx = \abs($a['x'] - $b['x']);
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$dy = \abs($a['y'] - $b['y']);
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return \sqrt($dx * $dx + $dy * $dy);
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}
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/**
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* Euclidean metric.
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*
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* @latex d(p, q) = \begin{cases}(\sqrt{2} - 1) \times |p_i - q_i| + |p_{i+1} - q_{i+1}|,& \text{if } |p_i - q_i| < |p_{i+1} - q_{i+1}|\\(\sqrt{2} - 1) \times |p_{i+1} - q_{i+1}| + |p_i - q_i|,&\text{if } |p_i - q_i| \geq |p_{i+1} - q_{i+1}|\end{cases}
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*
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* @param array $a 2-D array with x and y coordinate
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* @param array $b 2-D array with x and y coordinate
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*
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* @return float
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*
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* @since 1.0.0
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*/
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public static function octile(array $a, array $b) : float
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{
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$dx = \abs($a['x'] - $b['x']);
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$dy = \abs($a['y'] - $b['y']);
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return $dx < $dy ? (\sqrt(2) - 1) * $dx + $dy : (\sqrt(2) - 1) * $dy + $dx;
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}
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/**
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* Chebyshev metric.
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*
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* @latex d(p, q) = \max_i{(|p_i - q_i|)}
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*
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* @param array $a 2-D array with x and y coordinate
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* @param array $b 2-D array with x and y coordinate
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*
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* @return float
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*
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* @since 1.0.0
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*/
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public static function chebyshev(array $a, array $b) : float
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{
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return \max(
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\abs($a['x'] - $b['x']),
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\abs($a['y'] - $b['y'])
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);
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}
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/**
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* Minkowski metric.
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*
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* @latex d(p, q) = \sqrt[\lambda]{\sum_{n=1}^N{|p_i - q_i|^\lambda}}
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*
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* @param array $a 2-D array with x and y coordinate
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* @param array $b 2-D array with x and y coordinate
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* @param int $lambda
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*
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* @return float
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*
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* @since 1.0.0
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*/
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public static function minkowski(array $a, array $b, int $lambda) : float
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{
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return \pow(
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\pow(\abs($a['x'] - $b['x']), $lambda)
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+ \pow(\abs($a['y'] - $b['y']), $lambda),
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1 / $lambda
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);
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}
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/**
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* Canberra metric.
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*
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* @latex d(p, q) = \sum_{n=1}^N{\frac{|p_i - q_i|}{|p_i| + |q_i|}
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*
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* @param array $a 2-D array with x and y coordinate
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* @param array $b 2-D array with x and y coordinate
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*
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* @return float
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*
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* @since 1.0.0
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*/
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public static function canberra(array $a, array $b) : float
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{
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return \abs($a['x'] - $b['x']) / (\abs($a['x']) + \abs($b['x']))
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+ \abs($a['y'] - $b['y']) / (\abs($a['y']) + \abs($b['y']));
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}
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/**
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* Bray Curtis metric.
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*
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* @latex d(p, q) = \frac{\sum_{n=1}^N{|p_i - q_i|}}{\sum_{n=1}^N{(p_i + q_i)}}
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*
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* @param array $a 2-D array with x and y coordinate
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* @param array $b 2-D array with x and y coordinate
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*
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* @return float
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*
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* @since 1.0.0
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*/
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public static function brayCurtis(array $a, array $b) : float
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{
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return \abs($a['x'] - $b['x']) / ($a['x'] + $b['x'])
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+ \abs($a['y'] - $b['y']) / ($a['y'] + $b['y']);
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}
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/**
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* Angular separation metric.
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*
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* @latex d(p, q) = \frac{\sum_{n=1}^N{p_i * q_i}}{\left(\sum_{n=1}^N{p_i^2} * \sum_{n=1}^N{q_i^2}\right)^\frac{1}{2}}
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*
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* @param array $a 2-D array with x and y coordinate
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* @param array $b 2-D array with x and y coordinate
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*
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* @return float
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*
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* @since 1.0.0
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*/
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public static function angularSeparation(array $a, array $b) : float
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{
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return ($a['x'] * $b['x'] + $a['y'] * $b['y']) / (($a['x']**2 + $a['y']**2) * ($b['x'] ** 2 + $b['y'] ** 2));
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}
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/**
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* Hamming metric.
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*
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* @latex d(p, q) = \sum_{n=1}^N{|p_i - q_i|}
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*
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* @param array $a 2-D array with x and y coordinate
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* @param array $b 2-D array with x and y coordinate
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*
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* @return float
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*
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* @since 1.0.0
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*/
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public static function hamming(array $a, array $b) : float
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{
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return \abs($a['x'] - $b['x']) + \abs($a['y'] - $b['y']);
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}
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/**
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* Ulams metric.
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*
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* Calculate the minimum amount of changes to make two arrays the same.
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*
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* In order to use this with objects the objects would have to implement some kind of value representation for comparison.
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*
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* @param array $a Array with elements
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* @param array $b Array with same elements but different order
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*
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* @return int
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*
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* @since 1.0.0
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*/
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public static function ulam(array $a, array $b) : int
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{
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if (($size = \count($a)) !== \count($b)) {
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throw new \Exception('Invalid dimensions');
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}
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$mp = [];
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for ($i = 0; $i < $size; ++$i) {
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$mp[$b[$i]] = $i;
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}
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for ($i = 0; $i < $size; ++$i) {
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$b[$i] = $mp[$a[$i]];
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}
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$bPos = [];
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for ($i = 0; $i < $size; ++$i) {
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$bPos[$i] = [$b[$i], $i];
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}
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\usort($bPos, function ($e1, $e2) { return $e1[0] <=> $e2[0]; });
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$vis = \array_fill(0, $size, false);
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$ans = 0;
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for ($i = 0; $i < $size; ++$i) {
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if ($vis[$i] || $bPos[$i][1] === $i) {
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continue;
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}
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$cycleSize = 0;
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$j = $i;
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while (!$vis[$j]) {
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$vis[$j] = true;
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$j = $bPos[$j][1];
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++$cycleSize;
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}
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$ans += $cycleSize - 1;
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}
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return $ans;
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}
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}
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100
tests/Math/Topology/Metric2DTest.php
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100
tests/Math/Topology/Metric2DTest.php
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@ -0,0 +1,100 @@
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<?php
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/**
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* Orange Management
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*
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* PHP Version 7.4
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*
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* @package tests
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* @copyright Dennis Eichhorn
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* @license OMS License 1.0
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* @version 1.0.0
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* @link https://orange-management.org
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*/
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declare(strict_types=1);
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namespace phpOMS\tests\Math\Number;
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use phpOMS\Math\Topology\Metric2D;
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/**
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* @internal
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*/
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class Metric2DTest extends \PHPUnit\Framework\TestCase
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{
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public function testManhattan() : void
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{
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self::assertEquals(
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10.0,
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Metric2D::manhattan(['x' => 0, 'y' => 3], ['x' => 7, 'y' => 6])
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);
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}
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public function testEuclidean() : void
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{
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self::assertEqualsWithDelta(
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7.615773,
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Metric2D::euclidean(['x' => 0, 'y' => 3], ['x' => 7, 'y' => 6]),
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0.1
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);
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}
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public function testChebyshev() : void
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{
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self::assertEquals(
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7.0,
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Metric2D::chebyshev(['x' => 0, 'y' => 3], ['x' => 7, 'y' => 6])
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);
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}
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public function testMinkowski() : void
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{
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self::assertEqualsWithDelta(
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7.179,
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Metric2D::minkowski(['x' => 0, 'y' => 3], ['x' => 7, 'y' => 6], 3),
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0.1
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);
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}
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public function testCanberra() : void
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{
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self::assertEqualsWithDelta(
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1.333,
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Metric2D::canberra(['x' => 0, 'y' => 3], ['x' => 7, 'y' => 6]),
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0.1
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);
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}
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public function testBrayCurtis() : void
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{
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self::assertEqualsWithDelta(
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0.625,
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Metric2D::brayCurtis(['x' => 0, 'y' => 3], ['x' => 7, 'y' => 6]),
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0.1
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);
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}
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public function testAngularSeparation() : void
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{
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self::assertEqualsWithDelta(
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0.6508,
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Metric2D::angularSeparation(['x' => 0, 'y' => 3], ['x' => 7, 'y' => 6]),
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0.1
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);
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}
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public function testHammingDistance() : void
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{
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self::assertEquals(
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3.0,
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Metric2D::hammingDistance([1, 1, 1, 1], [0, 1, 0, 0]),
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);
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}
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public function testUlam(): void
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{
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self::assertEquals(
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2,
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Metric2D::hammingDistance([3, 6, 4, 8], [4, 6, 8, 3])
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);
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}
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}
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