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| 1 | <?php |
| 2 | /** |
| 3 | * Jingga |
| 4 | * |
| 5 | * PHP Version 8.1 |
| 6 | * |
| 7 | * @package phpOMS\Math\Topology |
| 8 | * @copyright Dennis Eichhorn |
| 9 | * @license OMS License 2.0 |
| 10 | * @version 1.0.0 |
| 11 | * @link https://jingga.app |
| 12 | */ |
| 13 | declare(strict_types=1); |
| 14 | |
| 15 | namespace phpOMS\Math\Topology; |
| 16 | |
| 17 | use phpOMS\Math\Matrix\Exception\InvalidDimensionException; |
| 18 | |
| 19 | /** |
| 20 | * Metrics. |
| 21 | * |
| 22 | * @package phpOMS\Math\Topology |
| 23 | * @license OMS License 2.0 |
| 24 | * @link https://jingga.app |
| 25 | * @since 1.0.0 |
| 26 | */ |
| 27 | final class MetricsND |
| 28 | { |
| 29 | /** |
| 30 | * Constructor |
| 31 | * |
| 32 | * @since 1.0.0 |
| 33 | * @codeCoverageIgnore |
| 34 | */ |
| 35 | private function __construct() |
| 36 | { |
| 37 | } |
| 38 | |
| 39 | /** |
| 40 | * Manhatten metric. |
| 41 | * |
| 42 | * @latex d(p, q) = \sum_{n=1}^N{|p_i - q_i|} |
| 43 | * |
| 44 | * @param array<int|string, int|float> $a n-D array |
| 45 | * @param array<int|string, int|float> $b n-D array |
| 46 | * |
| 47 | * @return float |
| 48 | * |
| 49 | * @throws InvalidDimensionException |
| 50 | * |
| 51 | * @since 1.0.0 |
| 52 | */ |
| 53 | public static function manhattan(array $a, array $b) : float |
| 54 | { |
| 55 | if (\count($a) !== \count($b)) { |
| 56 | throw new InvalidDimensionException(\count($a) . 'x' . \count($b)); |
| 57 | } |
| 58 | |
| 59 | $dist = 0.0; |
| 60 | foreach ($a as $key => $e) { |
| 61 | $dist += \abs($e - $b[$key]); |
| 62 | } |
| 63 | |
| 64 | return $dist; |
| 65 | } |
| 66 | |
| 67 | /** |
| 68 | * Euclidean metric. |
| 69 | * |
| 70 | * @latex d(p, q) = \sqrt{\sum_{n=1}^N{(p_i - q_i)^2}} |
| 71 | * |
| 72 | * @param array<int|string, int|float> $a n-D array |
| 73 | * @param array<int|string, int|float> $b n-D array |
| 74 | * |
| 75 | * @return float |
| 76 | * |
| 77 | * @throws InvalidDimensionException |
| 78 | * |
| 79 | * @since 1.0.0 |
| 80 | */ |
| 81 | public static function euclidean(array $a, array $b) : float |
| 82 | { |
| 83 | if (\count($a) !== \count($b)) { |
| 84 | throw new InvalidDimensionException(\count($a) . 'x' . \count($b)); |
| 85 | } |
| 86 | |
| 87 | $dist = 0.0; |
| 88 | foreach ($a as $key => $e) { |
| 89 | $dist += \abs($e - $b[$key]) ** 2; |
| 90 | } |
| 91 | |
| 92 | return \sqrt($dist); |
| 93 | } |
| 94 | |
| 95 | /** |
| 96 | * Cosine metric. |
| 97 | * |
| 98 | * @param array<int|string, int|float> $a n-D array |
| 99 | * @param array<int|string, int|float> $b n-D array |
| 100 | * |
| 101 | * @return float |
| 102 | * |
| 103 | * @throws InvalidDimensionException |
| 104 | * |
| 105 | * @since 1.0.0 |
| 106 | */ |
| 107 | public static function cosine(array $a, array $b) : float |
| 108 | { |
| 109 | if (($length = \count($a)) !== \count($b)) { |
| 110 | throw new InvalidDimensionException(\count($a) . 'x' . \count($b)); |
| 111 | } |
| 112 | |
| 113 | $dotProduct = 0; |
| 114 | for ($i = 0; $i < $length; ++$i) { |
| 115 | $dotProduct += $a[$i] * $b[$i]; |
| 116 | } |
| 117 | |
| 118 | $sumOfSquares = 0; |
| 119 | foreach ($a as $value) { |
| 120 | $sumOfSquares += $value * $value; |
| 121 | } |
| 122 | $magnitude1 = \sqrt($sumOfSquares); |
| 123 | |
| 124 | $sumOfSquares = 0; |
| 125 | foreach ($b as $value) { |
| 126 | $sumOfSquares += $value * $value; |
| 127 | } |
| 128 | $magnitude2 = \sqrt($sumOfSquares); |
| 129 | |
| 130 | if ($magnitude1 == 0 || $magnitude2 == 0) { |
| 131 | return \PHP_FLOAT_MAX; |
| 132 | } |
| 133 | |
| 134 | return $dotProduct / ($magnitude1 * $magnitude2); |
| 135 | } |
| 136 | |
| 137 | /** |
| 138 | * Chebyshev metric. |
| 139 | * |
| 140 | * @latex d(p, q) = \max_i{(|p_i - q_i|)} |
| 141 | * |
| 142 | * @param array<int|string, int|float> $a n-D array |
| 143 | * @param array<int|string, int|float> $b n-D array |
| 144 | * |
| 145 | * @return float |
| 146 | * |
| 147 | * @throws InvalidDimensionException |
| 148 | * |
| 149 | * @since 1.0.0 |
| 150 | */ |
| 151 | public static function chebyshev(array $a, array $b) : float |
| 152 | { |
| 153 | if (\count($a) !== \count($b)) { |
| 154 | throw new InvalidDimensionException(\count($a) . 'x' . \count($b)); |
| 155 | } |
| 156 | |
| 157 | $dist = []; |
| 158 | foreach ($a as $key => $e) { |
| 159 | $dist[] = \abs($e - $b[$key]); |
| 160 | } |
| 161 | |
| 162 | return (float) \max($dist); |
| 163 | } |
| 164 | |
| 165 | /** |
| 166 | * Minkowski metric. |
| 167 | * |
| 168 | * @latex d(p, q) = \sqrt[\lambda]{\sum_{n=1}^N{|p_i - q_i|^\lambda}} |
| 169 | * |
| 170 | * @param array<int|string, int|float> $a n-D array |
| 171 | * @param array<int|string, int|float> $b n-D array |
| 172 | * @param int $lambda Lambda |
| 173 | * |
| 174 | * @return float |
| 175 | * |
| 176 | * @throws InvalidDimensionException |
| 177 | * |
| 178 | * @since 1.0.0 |
| 179 | */ |
| 180 | public static function minkowski(array $a, array $b, int $lambda) : float |
| 181 | { |
| 182 | if (\count($a) !== \count($b)) { |
| 183 | throw new InvalidDimensionException(\count($a) . 'x' . \count($b)); |
| 184 | } |
| 185 | |
| 186 | $dist = 0.0; |
| 187 | foreach ($a as $key => $e) { |
| 188 | $dist += \pow(\abs($e - $b[$key]), $lambda); |
| 189 | } |
| 190 | |
| 191 | return \pow($dist, 1 / $lambda); |
| 192 | } |
| 193 | |
| 194 | /** |
| 195 | * Canberra metric. |
| 196 | * |
| 197 | * @latex d(p, q) = \sum_{n=1}^N{\frac{|p_i - q_i|}{|p_i| + |q_i|} |
| 198 | * |
| 199 | * @param array<int|string, int|float> $a n-D array |
| 200 | * @param array<int|string, int|float> $b n-D array |
| 201 | * |
| 202 | * @return float |
| 203 | * |
| 204 | * @throws InvalidDimensionException |
| 205 | * |
| 206 | * @since 1.0.0 |
| 207 | */ |
| 208 | public static function canberra(array $a, array $b) : float |
| 209 | { |
| 210 | if (\count($a) !== \count($b)) { |
| 211 | throw new InvalidDimensionException(\count($a) . 'x' . \count($b)); |
| 212 | } |
| 213 | |
| 214 | $dist = 0.0; |
| 215 | foreach ($a as $key => $e) { |
| 216 | $dist += \abs($e - $b[$key]) / (\abs($e) + \abs($b[$key])); |
| 217 | } |
| 218 | |
| 219 | return $dist; |
| 220 | } |
| 221 | |
| 222 | /** |
| 223 | * Bray Curtis metric. |
| 224 | * |
| 225 | * @latex d(p, q) = \frac{\sum_{n=1}^N{|p_i - q_i|}}{\sum_{n=1}^N{(p_i + q_i)}} |
| 226 | * |
| 227 | * @param array<int|string, int|float> $a n-D array |
| 228 | * @param array<int|string, int|float> $b n-D array |
| 229 | * |
| 230 | * @return float |
| 231 | * |
| 232 | * @throws InvalidDimensionException |
| 233 | * |
| 234 | * @since 1.0.0 |
| 235 | */ |
| 236 | public static function brayCurtis(array $a, array $b) : float |
| 237 | { |
| 238 | if (\count($a) !== \count($b)) { |
| 239 | throw new InvalidDimensionException(\count($a) . 'x' . \count($b)); |
| 240 | } |
| 241 | |
| 242 | $distTop = 0.0; |
| 243 | $distBottom = 0.0; |
| 244 | foreach ($a as $key => $e) { |
| 245 | $distTop += \abs($e - $b[$key]); |
| 246 | $distBottom += $e + $b[$key]; |
| 247 | } |
| 248 | |
| 249 | return $distTop / $distBottom; |
| 250 | } |
| 251 | |
| 252 | /** |
| 253 | * Angular separation metric. |
| 254 | * |
| 255 | * @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}} |
| 256 | * |
| 257 | * @param array<int|string, int|float> $a n-D array |
| 258 | * @param array<int|string, int|float> $b n-D array |
| 259 | * |
| 260 | * @return float |
| 261 | * |
| 262 | * @throws InvalidDimensionException |
| 263 | * |
| 264 | * @since 1.0.0 |
| 265 | */ |
| 266 | public static function angularSeparation(array $a, array $b) : float |
| 267 | { |
| 268 | if (\count($a) !== \count($b)) { |
| 269 | throw new InvalidDimensionException(\count($a) . 'x' . \count($b)); |
| 270 | } |
| 271 | |
| 272 | $distTop = 0.0; |
| 273 | $distBottomA = 0.0; |
| 274 | $distBottomB = 0.0; |
| 275 | foreach ($a as $key => $e) { |
| 276 | $distTop += $e * $b[$key]; |
| 277 | $distBottomA += $e ** 2; |
| 278 | $distBottomB += $b[$key] ** 2; |
| 279 | } |
| 280 | |
| 281 | return $distTop / \pow($distBottomA * $distBottomB, 1 / 2); |
| 282 | } |
| 283 | |
| 284 | /** |
| 285 | * Hamming metric. |
| 286 | * |
| 287 | * @latex d(p, q) = \sum_{n=1}^N{|p_i - q_i|} |
| 288 | * |
| 289 | * @param array<int|string, int|float> $a n-D array |
| 290 | * @param array<int|string, int|float> $b n-D array |
| 291 | * |
| 292 | * @return int |
| 293 | * |
| 294 | * @throws InvalidDimensionException |
| 295 | * |
| 296 | * @since 1.0.0 |
| 297 | */ |
| 298 | public static function hamming(array $a, array $b) : int |
| 299 | { |
| 300 | if (($size = \count($a)) !== \count($b)) { |
| 301 | throw new InvalidDimensionException(\count($a) . 'x' . \count($b)); |
| 302 | } |
| 303 | |
| 304 | $dist = 0; |
| 305 | for ($i = 0; $i < $size; ++$i) { |
| 306 | if ($a[$i] !== $b[$i]) { |
| 307 | ++$dist; |
| 308 | } |
| 309 | } |
| 310 | |
| 311 | return $dist; |
| 312 | } |
| 313 | } |