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| 1 | <?php |
| 2 | /** |
| 3 | * Jingga |
| 4 | * |
| 5 | * PHP Version 8.1 |
| 6 | * |
| 7 | * @package phpOMS\Math\Functions |
| 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\Functions; |
| 16 | |
| 17 | /** |
| 18 | * Well known functions and helpers class. |
| 19 | * |
| 20 | * @package phpOMS\Math\Functions |
| 21 | * @license OMS License 2.0 |
| 22 | * @link https://jingga.app |
| 23 | * @since 1.0.0 |
| 24 | */ |
| 25 | final class Functions |
| 26 | { |
| 27 | /** |
| 28 | * Epsilon for float comparison. |
| 29 | * |
| 30 | * @var float |
| 31 | * @since 1.0.0 |
| 32 | */ |
| 33 | public const EPSILON = 4.88e-04; |
| 34 | |
| 35 | /** |
| 36 | * Constructor. |
| 37 | * |
| 38 | * @since 1.0.0 |
| 39 | * @codeCoverageIgnore |
| 40 | */ |
| 41 | private function __construct() |
| 42 | { |
| 43 | } |
| 44 | |
| 45 | /** |
| 46 | * Calculate gammar function value. |
| 47 | * |
| 48 | * Example: (7, 2) |
| 49 | * |
| 50 | * @param int $n Factorial upper bound |
| 51 | * @param int $start Factorial starting value |
| 52 | * |
| 53 | * @return int |
| 54 | * |
| 55 | * @since 1.0.0 |
| 56 | */ |
| 57 | public static function fact(int $n, int $start = 1) : int |
| 58 | { |
| 59 | $fact = 1; |
| 60 | |
| 61 | for ($i = $start; $i < $n + 1; ++$i) { |
| 62 | $fact *= $i; |
| 63 | } |
| 64 | |
| 65 | return $fact; |
| 66 | } |
| 67 | |
| 68 | /** |
| 69 | * Calculate binomial coefficient |
| 70 | * |
| 71 | * Algorithm optimized for large factorials without the use of big int or string manipulation. |
| 72 | * |
| 73 | * Example: (7, 2) |
| 74 | * |
| 75 | * @param int $n n |
| 76 | * @param int $k k |
| 77 | * |
| 78 | * @return int |
| 79 | * |
| 80 | * @since 1.0.0 |
| 81 | */ |
| 82 | public static function binomialCoefficient(int $n, int $k) : int |
| 83 | { |
| 84 | $max = \max([$k, $n - $k]); |
| 85 | $min = \min([$k, $n - $k]); |
| 86 | |
| 87 | $fact = 1; |
| 88 | $range = \array_reverse(\range(1, $min)); |
| 89 | |
| 90 | for ($i = $max + 1; $i < $n + 1; ++$i) { |
| 91 | $div = 1; |
| 92 | foreach ($range as $key => $d) { |
| 93 | if ($i % $d === 0) { |
| 94 | $div = $d; |
| 95 | |
| 96 | unset($range[$key]); |
| 97 | break; |
| 98 | } |
| 99 | } |
| 100 | |
| 101 | $fact *= $i / $div; |
| 102 | } |
| 103 | |
| 104 | $fact2 = 1; |
| 105 | |
| 106 | foreach ($range as $d) { |
| 107 | $fact2 *= $d; |
| 108 | } |
| 109 | |
| 110 | return (int) ($fact / $fact2); |
| 111 | } |
| 112 | |
| 113 | /** |
| 114 | * Calculate ackermann function. |
| 115 | * |
| 116 | * @param int $m m |
| 117 | * @param int $n n |
| 118 | * |
| 119 | * @return int |
| 120 | * |
| 121 | * @since 1.0.0 |
| 122 | */ |
| 123 | public static function ackermann(int $m, int $n) : int |
| 124 | { |
| 125 | if ($m === 0) { |
| 126 | return $n + 1; |
| 127 | } elseif ($n === 0) { |
| 128 | return self::ackermann($m - 1, 1); |
| 129 | } |
| 130 | |
| 131 | return self::ackermann($m - 1, self::ackermann($m, $n - 1)); |
| 132 | } |
| 133 | |
| 134 | /** |
| 135 | * Calculate inverse modular. |
| 136 | * |
| 137 | * @param int $a a |
| 138 | * @param int $n Modulo |
| 139 | * |
| 140 | * @return int |
| 141 | * |
| 142 | * @since 1.0.0 |
| 143 | */ |
| 144 | public static function invMod(int $a, int $n) : int |
| 145 | { |
| 146 | if ($n < 0) { |
| 147 | $n = -$n; |
| 148 | } |
| 149 | |
| 150 | if ($a < 0) { |
| 151 | $a = $n - (-$a % $n); |
| 152 | } |
| 153 | |
| 154 | $t = 0; |
| 155 | $nt = 1; |
| 156 | $r = $n; |
| 157 | $nr = $a % $n; |
| 158 | |
| 159 | while ($nr != 0) { |
| 160 | $quot = (int) ($r / $nr); |
| 161 | $tmp = $nt; |
| 162 | $nt = $t - $quot * $nt; |
| 163 | $t = $tmp; |
| 164 | $tmp = $nr; |
| 165 | $nr = $r - $quot * $nr; |
| 166 | $r = $tmp; |
| 167 | } |
| 168 | |
| 169 | if ($r > 1) { |
| 170 | return -1; |
| 171 | } |
| 172 | |
| 173 | if ($t < 0) { |
| 174 | $t += $n; |
| 175 | } |
| 176 | |
| 177 | return $t; |
| 178 | } |
| 179 | |
| 180 | /** |
| 181 | * Modular implementation for negative values. |
| 182 | * |
| 183 | * @param int $a a |
| 184 | * @param int $b b |
| 185 | * |
| 186 | * @return int |
| 187 | * |
| 188 | * @since 1.0.0 |
| 189 | */ |
| 190 | public static function mod(int $a, int $b) : int |
| 191 | { |
| 192 | if ($a < 0) { |
| 193 | return ($a + $b) % $b; |
| 194 | } |
| 195 | |
| 196 | return $a % $b; |
| 197 | } |
| 198 | |
| 199 | /** |
| 200 | * Check if value is odd. |
| 201 | * |
| 202 | * @param int $a Value to test |
| 203 | * |
| 204 | * @return bool |
| 205 | * |
| 206 | * @since 1.0.0 |
| 207 | */ |
| 208 | public static function isOdd(int $a) : bool |
| 209 | { |
| 210 | return (bool) ($a & 1); |
| 211 | } |
| 212 | |
| 213 | /** |
| 214 | * Check if value is even. |
| 215 | * |
| 216 | * @param int $a Value to test |
| 217 | * |
| 218 | * @return bool |
| 219 | * |
| 220 | * @since 1.0.0 |
| 221 | */ |
| 222 | public static function isEven(int $a) : bool |
| 223 | { |
| 224 | return !((bool) ($a & 1)); |
| 225 | } |
| 226 | |
| 227 | /** |
| 228 | * Gets the relative position on a circular construct. |
| 229 | * |
| 230 | * @example The relative fiscal month (August) in a company where the fiscal year starts in July. |
| 231 | * @example 2 = getRelativeDegree(8, 12, 7); |
| 232 | * |
| 233 | * @param int $value Value to get degree |
| 234 | * @param int $length Circle size |
| 235 | * @param int $start Start value |
| 236 | * |
| 237 | * @return int Lowest value is 0 and highest value is length - 1 |
| 238 | * |
| 239 | * @since 1.0.0 |
| 240 | */ |
| 241 | public static function getRelativeDegree(int $value, int $length, int $start = 0) : int |
| 242 | { |
| 243 | return \abs(self::mod($value - $start, $length)); |
| 244 | } |
| 245 | |
| 246 | /** |
| 247 | * Error function coefficients for approximation |
| 248 | * |
| 249 | * @var float[] |
| 250 | * @since 1.0.0 |
| 251 | */ |
| 252 | private const ERF_COF = [ |
| 253 | -1.3026537197817094, 6.4196979235649026e-1, |
| 254 | 1.9476473204185836e-2,-9.561514786808631e-3,-9.46595344482036e-4, |
| 255 | 3.66839497852761e-4,4.2523324806907e-5,-2.0278578112534e-5, |
| 256 | -1.624290004647e-6,1.303655835580e-6,1.5626441722e-8,-8.5238095915e-8, |
| 257 | 6.529054439e-9,5.059343495e-9,-9.91364156e-10,-2.27365122e-10, |
| 258 | 9.6467911e-11, 2.394038e-12,-6.886027e-12,8.94487e-13, 3.13092e-13, |
| 259 | -1.12708e-13,3.81e-16,7.106e-15,-1.523e-15,-9.4e-17,1.21e-16,-2.8e-17, |
| 260 | ]; |
| 261 | |
| 262 | /** |
| 263 | * Error function |
| 264 | * |
| 265 | * @param float $x X-Value |
| 266 | * |
| 267 | * @return float |
| 268 | * |
| 269 | * @since 1.0.0 |
| 270 | */ |
| 271 | public static function getErf(float $x) : float |
| 272 | { |
| 273 | return $x > 0.0 |
| 274 | ? 1.0 - self::erfccheb($x) |
| 275 | : self::erfccheb(-$x) - 1.0; |
| 276 | } |
| 277 | |
| 278 | /** |
| 279 | * Complementary error function |
| 280 | * |
| 281 | * @param float $x X-Value |
| 282 | * |
| 283 | * @return float |
| 284 | * |
| 285 | * @since 1.0.0 |
| 286 | */ |
| 287 | public static function getErfc(float $x) : float |
| 288 | { |
| 289 | return $x > 0.0 |
| 290 | ? self::erfccheb($x) |
| 291 | : 2.0 - self::erfccheb(-$x); |
| 292 | } |
| 293 | |
| 294 | /** |
| 295 | * Error function helper function |
| 296 | * |
| 297 | * @param float $z Z-Value |
| 298 | * |
| 299 | * @return float |
| 300 | * |
| 301 | * @throws \InvalidArgumentException |
| 302 | * |
| 303 | * @since 1.0.0 |
| 304 | */ |
| 305 | private static function erfccheb(float $z) : float |
| 306 | { |
| 307 | $d = 0.; |
| 308 | $dd = 0.; |
| 309 | |
| 310 | $ncof = \count(self::ERF_COF); |
| 311 | |
| 312 | if ($z < 0.) { |
| 313 | throw new \InvalidArgumentException("erfccheb requires nonnegative argument"); |
| 314 | } |
| 315 | |
| 316 | $t = 2. / (2. + $z); |
| 317 | $ty = 4. * $t - 2.; |
| 318 | |
| 319 | for ($j = $ncof - 1; $j > 0; --$j) { |
| 320 | $tmp = $d; |
| 321 | $d = $ty * $d - $dd + self::ERF_COF[$j]; |
| 322 | $dd = $tmp; |
| 323 | } |
| 324 | |
| 325 | return $t * \exp(-$z * $z + 0.5 * (self::ERF_COF[0] + $ty * $d) - $dd); |
| 326 | } |
| 327 | |
| 328 | /** |
| 329 | * Inverse complementary error function |
| 330 | * |
| 331 | * @param float $p P-Value |
| 332 | * |
| 333 | * @return float |
| 334 | * |
| 335 | * @since 1.0.0 |
| 336 | */ |
| 337 | public static function getInvErfc(float $p) : float |
| 338 | { |
| 339 | if ($p >= 2.0) { |
| 340 | return -100.; |
| 341 | } elseif ($p <= 0.0) { |
| 342 | return 100.; |
| 343 | } |
| 344 | |
| 345 | $pp = ($p < 1.0) ? $p : 2. - $p; |
| 346 | $t = \sqrt(-2. * \log($pp / 2.)); |
| 347 | $x = -0.70711 * ((2.30753 + $t * 0.27061) / (1. + $t * (0.99229 + $t * 0.04481)) - $t); |
| 348 | |
| 349 | for ($j = 0; $j < 2; ++$j) { |
| 350 | $err = self::getErfc($x) - $pp; |
| 351 | $x += $err / (1.12837916709551257 * \exp(-($x * $x)) - $x * $err); |
| 352 | } |
| 353 | |
| 354 | return ($p < 1.0? $x : -$x); |
| 355 | } |
| 356 | |
| 357 | /** |
| 358 | * Generalized hypergeometric function. |
| 359 | * |
| 360 | * pFq(a1, ..., ap; b1, ..., bq; z) |
| 361 | * |
| 362 | * @param array<int, float|int> $a Array of values |
| 363 | * @param array<int, float|int> $b Array of values |
| 364 | * @param float $z Z |
| 365 | * |
| 366 | * @return float |
| 367 | * |
| 368 | * @since 1.0.0 |
| 369 | */ |
| 370 | public static function generalizedHypergeometricFunction(array $a, array $b, float $z) : float |
| 371 | { |
| 372 | $sum = 0.0; |
| 373 | $aProd = \array_fill(0, 20, []); |
| 374 | $bProd = \array_fill(0, 20, []); |
| 375 | |
| 376 | for ($n = 0; $n < 20; ++$n) { |
| 377 | foreach ($a as $key => $value) { |
| 378 | $aProd[$n][$key] = $n === 0 ? 1 : $aProd[$n - 1][$key] * ($value + $n - 1); |
| 379 | } |
| 380 | |
| 381 | foreach ($b as $key => $value) { |
| 382 | $bProd[$n][$key] = $n === 0 ? 1 : $bProd[$n - 1][$key] * ($value + $n - 1); |
| 383 | } |
| 384 | |
| 385 | $temp = \array_product($aProd[$n]) / \array_product($bProd[$n]); |
| 386 | $sum += $temp * $z ** $n / self::fact($n); |
| 387 | } |
| 388 | |
| 389 | return $sum; |
| 390 | } |
| 391 | } |