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added metrics. @todo: implement n-dim

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Dennis Eichhorn 2019-09-04 20:39:11 +02:00
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261
Math/Topology/Metrics2D.php Normal file
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<?php
/**
* Orange Management
*
* PHP Version 7.4
*
* @package phpOMS\Math\Topology
* @copyright Dennis Eichhorn
* @license OMS License 1.0
* @version 1.0.0
* @link https://orange-management.org
*/
declare(strict_types=1);
namespace phpOMS\Math\Topology;
/**
* Metrics.
*
* @package phpOMS\Math\Topology
* @license OMS License 1.0
* @link https://orange-management.org
* @since 1.0.0
*/
final class Metrics2D
{
private function __construct()
{
}
/**
* Manhatten metric.
*
* @latex d(p, q) = \sum_{n=1}^N{|p_i - q_i|}
*
* @param array $a 2-D array with x and y coordinate
* @param array $b 2-D array with x and y coordinate
*
* @return float
*
* @since 1.0.0
*/
public static function manhattan(array $a, array $b) : float
{
return \abs($a['x'] - $b['x']) + \abs($a['y'] - $b['y']);
}
/**
* Euclidean metric.
*
* @latex d(p, q) = \sqrt{\sum_{n=1}^N{(p_i - q_i)^2}}
*
* @param array $a 2-D array with x and y coordinate
* @param array $b 2-D array with x and y coordinate
*
* @return float
*
* @since 1.0.0
*/
public static function euclidean(array $a, array $b) : float
{
$dx = \abs($a['x'] - $b['x']);
$dy = \abs($a['y'] - $b['y']);
return \sqrt($dx * $dx + $dy * $dy);
}
/**
* Euclidean metric.
*
* @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}
*
* @param array $a 2-D array with x and y coordinate
* @param array $b 2-D array with x and y coordinate
*
* @return float
*
* @since 1.0.0
*/
public static function octile(array $a, array $b) : float
{
$dx = \abs($a['x'] - $b['x']);
$dy = \abs($a['y'] - $b['y']);
return $dx < $dy ? (\sqrt(2) - 1) * $dx + $dy : (\sqrt(2) - 1) * $dy + $dx;
}
/**
* Chebyshev metric.
*
* @latex d(p, q) = \max_i{(|p_i - q_i|)}
*
* @param array $a 2-D array with x and y coordinate
* @param array $b 2-D array with x and y coordinate
*
* @return float
*
* @since 1.0.0
*/
public static function chebyshev(array $a, array $b) : float
{
return \max(
\abs($a['x'] - $b['x']),
\abs($a['y'] - $b['y'])
);
}
/**
* Minkowski metric.
*
* @latex d(p, q) = \sqrt[\lambda]{\sum_{n=1}^N{|p_i - q_i|^\lambda}}
*
* @param array $a 2-D array with x and y coordinate
* @param array $b 2-D array with x and y coordinate
* @param int $lambda
*
* @return float
*
* @since 1.0.0
*/
public static function minkowski(array $a, array $b, int $lambda) : float
{
return \pow(
\pow(\abs($a['x'] - $b['x']), $lambda)
+ \pow(\abs($a['y'] - $b['y']), $lambda),
1 / $lambda
);
}
/**
* Canberra metric.
*
* @latex d(p, q) = \sum_{n=1}^N{\frac{|p_i - q_i|}{|p_i| + |q_i|}
*
* @param array $a 2-D array with x and y coordinate
* @param array $b 2-D array with x and y coordinate
*
* @return float
*
* @since 1.0.0
*/
public static function canberra(array $a, array $b) : float
{
return \abs($a['x'] - $b['x']) / (\abs($a['x']) + \abs($b['x']))
+ \abs($a['y'] - $b['y']) / (\abs($a['y']) + \abs($b['y']));
}
/**
* Bray Curtis metric.
*
* @latex d(p, q) = \frac{\sum_{n=1}^N{|p_i - q_i|}}{\sum_{n=1}^N{(p_i + q_i)}}
*
* @param array $a 2-D array with x and y coordinate
* @param array $b 2-D array with x and y coordinate
*
* @return float
*
* @since 1.0.0
*/
public static function brayCurtis(array $a, array $b) : float
{
return \abs($a['x'] - $b['x']) / ($a['x'] + $b['x'])
+ \abs($a['y'] - $b['y']) / ($a['y'] + $b['y']);
}
/**
* Angular separation metric.
*
* @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}}
*
* @param array $a 2-D array with x and y coordinate
* @param array $b 2-D array with x and y coordinate
*
* @return float
*
* @since 1.0.0
*/
public static function angularSeparation(array $a, array $b) : float
{
return ($a['x'] * $b['x'] + $a['y'] * $b['y']) / (($a['x']**2 + $a['y']**2) * ($b['x'] ** 2 + $b['y'] ** 2));
}
/**
* Hamming metric.
*
* @latex d(p, q) = \sum_{n=1}^N{|p_i - q_i|}
*
* @param array $a 2-D array with x and y coordinate
* @param array $b 2-D array with x and y coordinate
*
* @return float
*
* @since 1.0.0
*/
public static function hamming(array $a, array $b) : float
{
return \abs($a['x'] - $b['x']) + \abs($a['y'] - $b['y']);
}
/**
* Ulams metric.
*
* Calculate the minimum amount of changes to make two arrays the same.
*
* In order to use this with objects the objects would have to implement some kind of value representation for comparison.
*
* @param array $a Array with elements
* @param array $b Array with same elements but different order
*
* @return int
*
* @since 1.0.0
*/
public static function ulam(array $a, array $b) : int
{
if (($size = \count($a)) !== \count($b)) {
throw new \Exception('Invalid dimensions');
}
$mp = [];
for ($i = 0; $i < $size; ++$i) {
$mp[$b[$i]] = $i;
}
for ($i = 0; $i < $size; ++$i) {
$b[$i] = $mp[$a[$i]];
}
$bPos = [];
for ($i = 0; $i < $size; ++$i) {
$bPos[$i] = [$b[$i], $i];
}
\usort($bPos, function ($e1, $e2) { return $e1[0] <=> $e2[0]; });
$vis = \array_fill(0, $size, false);
$ans = 0;
for ($i = 0; $i < $size; ++$i) {
if ($vis[$i] || $bPos[$i][1] === $i) {
continue;
}
$cycleSize = 0;
$j = $i;
while (!$vis[$j]) {
$vis[$j] = true;
$j = $bPos[$j][1];
++$cycleSize;
}
$ans += $cycleSize - 1;
}
return $ans;
}
}

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tests/Math/Topology/Metric2DTest.php Normal file
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<?php
/**
* Orange Management
*
* PHP Version 7.4
*
* @package tests
* @copyright Dennis Eichhorn
* @license OMS License 1.0
* @version 1.0.0
* @link https://orange-management.org
*/
declare(strict_types=1);
namespace phpOMS\tests\Math\Number;
use phpOMS\Math\Topology\Metric2D;
/**
* @internal
*/
class Metric2DTest extends \PHPUnit\Framework\TestCase
{
public function testManhattan() : void
{
self::assertEquals(
10.0,
Metric2D::manhattan(['x' => 0, 'y' => 3], ['x' => 7, 'y' => 6])
);
}
public function testEuclidean() : void
{
self::assertEqualsWithDelta(
7.615773,
Metric2D::euclidean(['x' => 0, 'y' => 3], ['x' => 7, 'y' => 6]),
0.1
);
}
public function testChebyshev() : void
{
self::assertEquals(
7.0,
Metric2D::chebyshev(['x' => 0, 'y' => 3], ['x' => 7, 'y' => 6])
);
}
public function testMinkowski() : void
{
self::assertEqualsWithDelta(
7.179,
Metric2D::minkowski(['x' => 0, 'y' => 3], ['x' => 7, 'y' => 6], 3),
0.1
);
}
public function testCanberra() : void
{
self::assertEqualsWithDelta(
1.333,
Metric2D::canberra(['x' => 0, 'y' => 3], ['x' => 7, 'y' => 6]),
0.1
);
}
public function testBrayCurtis() : void
{
self::assertEqualsWithDelta(
0.625,
Metric2D::brayCurtis(['x' => 0, 'y' => 3], ['x' => 7, 'y' => 6]),
0.1
);
}
public function testAngularSeparation() : void
{
self::assertEqualsWithDelta(
0.6508,
Metric2D::angularSeparation(['x' => 0, 'y' => 3], ['x' => 7, 'y' => 6]),
0.1
);
}
public function testHammingDistance() : void
{
self::assertEquals(
3.0,
Metric2D::hammingDistance([1, 1, 1, 1], [0, 1, 0, 0]),
);
}
public function testUlam(): void
{
self::assertEquals(
2,
Metric2D::hammingDistance([3, 6, 4, 8], [4, 6, 8, 3])
);
}
}