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| 1 | <?php |
| 2 | /** |
| 3 | * Jingga |
| 4 | * |
| 5 | * PHP Version 8.1 |
| 6 | * |
| 7 | * @package phpOMS\Math\Statistic |
| 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\Statistic; |
| 16 | |
| 17 | use phpOMS\Math\Exception\ZeroDivisionException; |
| 18 | use phpOMS\Math\Matrix\Exception\InvalidDimensionException; |
| 19 | |
| 20 | /** |
| 21 | * Average class. |
| 22 | * |
| 23 | * @package phpOMS\Math\Statistic |
| 24 | * @license OMS License 2.0 |
| 25 | * @link https://jingga.app |
| 26 | * @since 1.0.0 |
| 27 | */ |
| 28 | final class Average |
| 29 | { |
| 30 | public const MA3 = [1 / 3, 1 / 3]; |
| 31 | |
| 32 | public const MA5 = [0.2, 0.2, 0.2]; |
| 33 | |
| 34 | public const MA2X12 = [5 / 6, 5 / 6, 5 / 6, 5 / 6, 5 / 6, 5 / 6, 0.42]; |
| 35 | |
| 36 | public const MA3X3 = [1 / 3, 2 / 9, 1 / 9]; |
| 37 | |
| 38 | public const MA3X5 = [0.2, 0.2, 2 / 15, 4 / 6]; |
| 39 | |
| 40 | public const MAS15 = [0.231, 0.209, 0.144, 2 / 3, 0.009, -0.016, -0.019, -0.009]; |
| 41 | |
| 42 | public const MAS21 = [0.171, 0.163, 0.134, 0.37, 0.51, 0.017, -0.006, -0.014, -0.014, -0.009, -0.003]; |
| 43 | |
| 44 | public const MAH5 = [0.558, 0.294, -0.73]; |
| 45 | |
| 46 | public const MAH9 = [0.330, 0.267, 0.119, -0.010, -0.041]; |
| 47 | |
| 48 | public const MAH13 = [0.240, 0.214, 0.147, 0.66, 0, -0.028, -0.019]; |
| 49 | |
| 50 | public const MAH23 = [0.148, 0.138, 0.122, 0.097, 0.068, 0.039, 0.013, -0.005, -0.015, -0.016, -0.011, -0.004]; |
| 51 | |
| 52 | /** |
| 53 | * Constructor. |
| 54 | * |
| 55 | * @since 1.0.0 |
| 56 | * @codeCoverageIgnore |
| 57 | */ |
| 58 | private function __construct() |
| 59 | { |
| 60 | } |
| 61 | |
| 62 | /** |
| 63 | * Average change. |
| 64 | * |
| 65 | * @param array<int, int|float> $x Dataset |
| 66 | * @param int $h Future steps |
| 67 | * |
| 68 | * @return float |
| 69 | * |
| 70 | * @since 1.0.0 |
| 71 | */ |
| 72 | public static function averageDatasetChange(array $x, int $h = 1) : float |
| 73 | { |
| 74 | $count = \count($x); |
| 75 | |
| 76 | return $h * ($x[$count - 1] - $x[0]) / ($count - 1); |
| 77 | } |
| 78 | |
| 79 | /** |
| 80 | * Moving average of dataset (SMA) |
| 81 | * |
| 82 | * @param array<int, int|float> $x Dataset |
| 83 | * @param int $order Periods to use for average |
| 84 | * @param array<int, int|float> $weight Weight for moving average |
| 85 | * @param bool $symmetric Cyclic moving average |
| 86 | * |
| 87 | * @return float[] Moving average of data |
| 88 | * |
| 89 | * @throws \Exception |
| 90 | * |
| 91 | * @since 1.0.0 |
| 92 | */ |
| 93 | public static function totalMovingAverage(array $x, int $order, array $weight = null, bool $symmetric = false) : array |
| 94 | { |
| 95 | $periods = (int) ($order / ($symmetric ? 2 : 1)); |
| 96 | $count = \count($x) - ($symmetric ? $periods : 0); |
| 97 | $avg = []; |
| 98 | |
| 99 | for ($i = $periods - 1; $i < $count; ++$i) { |
| 100 | $avg[] = self::movingAverage($x, $i, $order, $weight, $symmetric); |
| 101 | } |
| 102 | |
| 103 | return $avg; |
| 104 | } |
| 105 | |
| 106 | /** |
| 107 | * Moving average of element in dataset (SMA) |
| 108 | * |
| 109 | * @param array<int, int|float> $x Dataset |
| 110 | * @param int $t Current period |
| 111 | * @param int $order Periods to use for average |
| 112 | * @param array<int, int|float> $weight Weight for moving average |
| 113 | * @param bool $symmetric Cyclic moving average |
| 114 | * |
| 115 | * @return float Moving average |
| 116 | * |
| 117 | * @throws \Exception |
| 118 | * |
| 119 | * @since 1.0.0 |
| 120 | */ |
| 121 | public static function movingAverage(array $x, int $t, int $order, array $weight = null, bool $symmetric = false) : float |
| 122 | { |
| 123 | $periods = (int) ($order / ($symmetric ? 2 : 1)); |
| 124 | $count = \count($x); |
| 125 | |
| 126 | if ($count < $t || $count < $periods || ($symmetric && $t + $periods >= $count)) { |
| 127 | throw new \Exception('Periods'); |
| 128 | } |
| 129 | |
| 130 | $t += 2; |
| 131 | $end = $symmetric ? $t + $periods - 1 : $t - 1; |
| 132 | $start = $t - 1 - $periods; |
| 133 | |
| 134 | if (!empty($weight)) { |
| 135 | return self::weightedAverage(\array_slice($x, $start, $end - $start), \array_slice($weight, $start, $end - $start)); |
| 136 | } else { |
| 137 | return self::arithmeticMean(\array_slice($x, $start, $end - $start)); |
| 138 | } |
| 139 | } |
| 140 | |
| 141 | /** |
| 142 | * Calculate weighted average. |
| 143 | * |
| 144 | * Example: ([1, 2, 3, 4], [0.25, 0.5, 0.125, 0.125]) |
| 145 | * |
| 146 | * @param array<int, int|float> $values Values |
| 147 | * @param array<int, int|float> $weight Weight for values |
| 148 | * |
| 149 | * @return float |
| 150 | * |
| 151 | * @throws InvalidDimensionException This exception is thrown in case both parameters have different array length |
| 152 | * |
| 153 | * @since 1.0.0 |
| 154 | */ |
| 155 | public static function weightedAverage(array $values, array $weight) : float |
| 156 | { |
| 157 | if (($count = \count($values)) !== \count($weight)) { |
| 158 | throw new InvalidDimensionException(\count($values) . 'x' . \count($weight)); |
| 159 | } |
| 160 | |
| 161 | $avg = 0.0; |
| 162 | |
| 163 | for ($i = 0; $i < $count; ++$i) { |
| 164 | $avg += $values[$i] * $weight[$i]; |
| 165 | } |
| 166 | |
| 167 | return $avg; |
| 168 | } |
| 169 | |
| 170 | /** |
| 171 | * Calculate the arithmetic mean. |
| 172 | * |
| 173 | * Example: ([1, 2, 2, 3, 4, 4, 2]) |
| 174 | * |
| 175 | * @latex \mu = mean = \frac{1}{n}\sum_{i=1}^{n}a_i |
| 176 | * |
| 177 | * @param array<int, int|float> $values Values |
| 178 | * @param int $offset Offset for outlier |
| 179 | * |
| 180 | * @return float |
| 181 | * |
| 182 | * @throws ZeroDivisionException This exception is thrown if the values array is empty |
| 183 | * |
| 184 | * @since 1.0.0 |
| 185 | */ |
| 186 | public static function arithmeticMean(array $values, int $offset = 0) : float |
| 187 | { |
| 188 | $count = \count($values); |
| 189 | if ($count <= $offset * 2) { |
| 190 | throw new ZeroDivisionException(); |
| 191 | } |
| 192 | |
| 193 | if ($offset > 0) { |
| 194 | \sort($values); |
| 195 | $values = \array_slice($values, $offset, -$offset); |
| 196 | $count -= $offset * 2; |
| 197 | } |
| 198 | |
| 199 | return \array_sum($values) / $count; |
| 200 | } |
| 201 | |
| 202 | /** |
| 203 | * Calculate the mode. |
| 204 | * |
| 205 | * Example: ([1, 2, 2, 3, 4, 4, 2]) |
| 206 | * |
| 207 | * @param array<int, int|float> $values Values |
| 208 | * @param int $offset Offset for outlier |
| 209 | * |
| 210 | * @return float |
| 211 | * |
| 212 | * @since 1.0.0 |
| 213 | */ |
| 214 | public static function mode(array $values, int $offset = 0) : float |
| 215 | { |
| 216 | if ($offset > 0) { |
| 217 | \sort($values); |
| 218 | $values = \array_slice($values, $offset, -$offset); |
| 219 | } |
| 220 | |
| 221 | $count = \array_count_values($values); |
| 222 | $best = \max($count); |
| 223 | |
| 224 | return (float) (\array_keys($count, $best)[0] ?? 0.0); |
| 225 | } |
| 226 | |
| 227 | /** |
| 228 | * Calculate the median. |
| 229 | * |
| 230 | * Example: ([1, 2, 2, 3, 4, 4, 2]) |
| 231 | * |
| 232 | * @param array<int, int|float> $values Values |
| 233 | * @param int $offset Offset for outlier |
| 234 | * |
| 235 | * @return float |
| 236 | * |
| 237 | * @since 1.0.0 |
| 238 | */ |
| 239 | public static function median(array $values, int $offset = 0) : float |
| 240 | { |
| 241 | \sort($values); |
| 242 | |
| 243 | if ($offset > 0) { |
| 244 | $values = \array_slice($values, $offset, -$offset); |
| 245 | } |
| 246 | |
| 247 | $count = \count($values); |
| 248 | $middleval = (int) \floor(($count - 1) / 2); |
| 249 | |
| 250 | if ($count % 2 !== 0) { |
| 251 | $median = $values[$middleval]; |
| 252 | } else { |
| 253 | $low = $values[$middleval]; |
| 254 | $high = $values[$middleval + 1]; |
| 255 | $median = ($low + $high) / 2; |
| 256 | } |
| 257 | |
| 258 | return $median; |
| 259 | } |
| 260 | |
| 261 | /** |
| 262 | * Calculate the geometric mean. |
| 263 | * |
| 264 | * Example: ([1, 2, 2, 3, 4, 4, 2]) |
| 265 | * |
| 266 | * @param array<int, int|float> $values Values |
| 267 | * @param int $offset Offset for outlier |
| 268 | * |
| 269 | * @return float |
| 270 | * |
| 271 | * @throws ZeroDivisionException This exception is thrown if the values array is empty |
| 272 | * |
| 273 | * @since 1.0.0 |
| 274 | */ |
| 275 | public static function geometricMean(array $values, int $offset = 0) : float |
| 276 | { |
| 277 | $count = \count($values); |
| 278 | if ($count <= $offset * 2) { |
| 279 | throw new ZeroDivisionException(); |
| 280 | } |
| 281 | |
| 282 | if ($offset > 0) { |
| 283 | \sort($values); |
| 284 | $values = \array_slice($values, $offset, -$offset); |
| 285 | $count -= $offset * 2; |
| 286 | } |
| 287 | |
| 288 | return \pow(\array_product($values), 1 / $count); |
| 289 | } |
| 290 | |
| 291 | /** |
| 292 | * Calculate the harmonic mean. |
| 293 | * |
| 294 | * Example: ([1, 2, 2, 3, 4, 4, 2]) |
| 295 | * |
| 296 | * @param array<int, int|float> $values Values |
| 297 | * @param int $offset Offset for outlier |
| 298 | * |
| 299 | * @return float |
| 300 | * |
| 301 | * @throws ZeroDivisionException This exception is thrown if a value in the values array is 0 or if the values array is empty |
| 302 | * |
| 303 | * @since 1.0.0 |
| 304 | */ |
| 305 | public static function harmonicMean(array $values, int $offset = 0) : float |
| 306 | { |
| 307 | $count = \count($values); |
| 308 | if ($count <= $offset * 2) { |
| 309 | throw new ZeroDivisionException(); |
| 310 | } |
| 311 | |
| 312 | if ($offset > 0) { |
| 313 | \sort($values); |
| 314 | $values = \array_slice($values, $offset, -$offset); |
| 315 | $count -= $offset * 2; |
| 316 | } |
| 317 | |
| 318 | $sum = 0.0; |
| 319 | foreach ($values as $value) { |
| 320 | if ($value === 0) { |
| 321 | throw new ZeroDivisionException(); |
| 322 | } |
| 323 | |
| 324 | $sum += 1 / $value; |
| 325 | } |
| 326 | |
| 327 | return 1 / ($sum / $count); |
| 328 | } |
| 329 | |
| 330 | /** |
| 331 | * Calculate the angle mean. |
| 332 | * |
| 333 | * Example: ([1, 2, 2, 3, 4, 4, 2]) |
| 334 | * |
| 335 | * @param array<int, int|float> $angles Angles |
| 336 | * @param int $offset Offset for outlier |
| 337 | * |
| 338 | * @return float |
| 339 | * |
| 340 | * @throws ZeroDivisionException |
| 341 | * |
| 342 | * @since 1.0.0 |
| 343 | */ |
| 344 | public static function angleMean(array $angles, int $offset = 0) : float |
| 345 | { |
| 346 | $count = \count($angles); |
| 347 | if ($count <= $offset * 2) { |
| 348 | throw new ZeroDivisionException(); |
| 349 | } |
| 350 | |
| 351 | if ($offset > 0) { |
| 352 | \sort($angles); |
| 353 | $angles = \array_slice($angles, $offset, -$offset); |
| 354 | $count -= $offset * 2; |
| 355 | } |
| 356 | |
| 357 | $y = 0; |
| 358 | $x = 0; |
| 359 | |
| 360 | for ($i = 0; $i < $count; ++$i) { |
| 361 | $x += \cos(\deg2rad($angles[$i])); |
| 362 | $y += \sin(\deg2rad($angles[$i])); |
| 363 | } |
| 364 | |
| 365 | $x /= $count; |
| 366 | $y /= $count; |
| 367 | |
| 368 | return \rad2deg(\atan2($y, $x)); |
| 369 | } |
| 370 | |
| 371 | /** |
| 372 | * Calculate the angle mean. |
| 373 | * |
| 374 | * Example: ([1, 2, 2, 3, 4, 4, 2]) |
| 375 | * |
| 376 | * @param array<int, int|float> $angles Angles |
| 377 | * @param int $offset Offset for outlier |
| 378 | * |
| 379 | * @return float |
| 380 | * |
| 381 | * @throws ZeroDivisionException |
| 382 | * |
| 383 | * @since 1.0.0 |
| 384 | */ |
| 385 | public static function angleMean2(array $angles, int $offset = 0) : float |
| 386 | { |
| 387 | $count = \count($angles); |
| 388 | if ($count <= $offset * 2) { |
| 389 | throw new ZeroDivisionException(); |
| 390 | } |
| 391 | |
| 392 | if ($offset > 0) { |
| 393 | \sort($angles); |
| 394 | $angles = \array_slice($angles, $offset, -$offset); |
| 395 | $count -= $offset * 2; |
| 396 | } |
| 397 | |
| 398 | $sins = 0.0; |
| 399 | $coss = 0.0; |
| 400 | |
| 401 | foreach ($angles as $a) { |
| 402 | $sins += \sin(\deg2rad($a)); |
| 403 | $coss += \cos(\deg2rad($a)); |
| 404 | } |
| 405 | |
| 406 | $avgsin = $sins / (0.0 + $count); |
| 407 | $avgcos = $coss / (0.0 + $count); |
| 408 | $avgang = \rad2deg(\atan2($avgsin, $avgcos)); |
| 409 | |
| 410 | while ($avgang < 0.0) { |
| 411 | $avgang += 360.0; |
| 412 | } |
| 413 | |
| 414 | return $avgang; |
| 415 | } |
| 416 | } |