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| 1 | <?php |
| 2 | /** |
| 3 | * Jingga |
| 4 | * |
| 5 | * PHP Version 8.1 |
| 6 | * |
| 7 | * @package phpOMS\Math\Matrix |
| 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\Matrix; |
| 16 | |
| 17 | use phpOMS\Math\Matrix\Exception\InvalidDimensionException; |
| 18 | |
| 19 | /** |
| 20 | * Matrix class |
| 21 | * |
| 22 | * @package phpOMS\Math\Matrix |
| 23 | * @license OMS License 2.0 |
| 24 | * @link https://jingga.app |
| 25 | * @since 1.0.0 |
| 26 | * |
| 27 | * @phpstan-implements \ArrayAccess<string, mixed> |
| 28 | * @phpstan-implements \Iterator<string, mixed> |
| 29 | */ |
| 30 | class Matrix implements \ArrayAccess, \Iterator |
| 31 | { |
| 32 | /** |
| 33 | * Epsilon for float comparison. |
| 34 | * |
| 35 | * @var float |
| 36 | * @since 1.0.0 |
| 37 | */ |
| 38 | public const EPSILON = 4.88e-04; |
| 39 | |
| 40 | /** |
| 41 | * Matrix. |
| 42 | * |
| 43 | * @var array<int, array<int, int|float>> |
| 44 | * @since 1.0.0 |
| 45 | */ |
| 46 | public array $matrix = []; |
| 47 | |
| 48 | /** |
| 49 | * Columns. |
| 50 | * |
| 51 | * @var int<0, max> |
| 52 | * @since 1.0.0 |
| 53 | */ |
| 54 | protected int $n = 0; |
| 55 | |
| 56 | /** |
| 57 | * Rows. |
| 58 | * |
| 59 | * @var int<0, max> |
| 60 | * @since 1.0.0 |
| 61 | */ |
| 62 | protected int $m = 0; |
| 63 | |
| 64 | /** |
| 65 | * Iterator position. |
| 66 | * |
| 67 | * @var int |
| 68 | * @since 1.0.0 |
| 69 | */ |
| 70 | protected int $position = 0; |
| 71 | |
| 72 | /** |
| 73 | * Constructor. |
| 74 | * |
| 75 | * @param int<0, max> $m Rows |
| 76 | * @param int<0, max> $n Columns |
| 77 | * |
| 78 | * @since 1.0.0 |
| 79 | */ |
| 80 | public function __construct(int $m = 1, int $n = 1) |
| 81 | { |
| 82 | $this->n = $n; |
| 83 | $this->m = $m; |
| 84 | |
| 85 | for ($i = 0; $i < $m; ++$i) { |
| 86 | $this->matrix[$i] = \array_fill(0, $n, 0); |
| 87 | } |
| 88 | } |
| 89 | |
| 90 | /** |
| 91 | * Create matrix from array |
| 92 | * |
| 93 | * @param array $matrix Matrix array |
| 94 | * |
| 95 | * @return self |
| 96 | * |
| 97 | * @since 1.0.0 |
| 98 | */ |
| 99 | public static function fromArray(array $matrix) : self |
| 100 | { |
| 101 | $m = new self(); |
| 102 | $m->setMatrix($matrix); |
| 103 | |
| 104 | return $m; |
| 105 | } |
| 106 | |
| 107 | /** |
| 108 | * Set value. |
| 109 | * |
| 110 | * @param int $m Row |
| 111 | * @param int $n Column |
| 112 | * @param int|float $value Value |
| 113 | * |
| 114 | * @return void |
| 115 | * |
| 116 | * @throws InvalidDimensionException |
| 117 | * |
| 118 | * @since 1.0.0 |
| 119 | */ |
| 120 | public function set(int $m, int $n, int | float $value) : void |
| 121 | { |
| 122 | if (!isset($this->matrix[$m], $this->matrix[$m][$n])) { |
| 123 | throw new InvalidDimensionException($m . 'x' . $n); |
| 124 | } |
| 125 | |
| 126 | $this->matrix[$m][$n] = $value; |
| 127 | } |
| 128 | |
| 129 | /** |
| 130 | * Get value. |
| 131 | * |
| 132 | * @param int $m Row |
| 133 | * @param int $n Column |
| 134 | * |
| 135 | * @return int|float |
| 136 | * |
| 137 | * @throws InvalidDimensionException |
| 138 | * |
| 139 | * @since 1.0.0 |
| 140 | */ |
| 141 | public function get(int $m, int $n = 0) : int | float |
| 142 | { |
| 143 | if (!isset($this->matrix[$m], $this->matrix[$m][$n])) { |
| 144 | throw new InvalidDimensionException($m . 'x' . $n); |
| 145 | } |
| 146 | |
| 147 | return $this->matrix[$m][$n]; |
| 148 | } |
| 149 | |
| 150 | /** |
| 151 | * Transpose matrix. |
| 152 | * |
| 153 | * @return Matrix |
| 154 | * |
| 155 | * @since 1.0.0 |
| 156 | */ |
| 157 | public function transpose() : self |
| 158 | { |
| 159 | $matrix = new self($this->n, $this->m); |
| 160 | $matrix->setMatrix(\array_map(null, ...$this->matrix)); |
| 161 | |
| 162 | return $matrix; |
| 163 | } |
| 164 | |
| 165 | /** |
| 166 | * Get matrix array. |
| 167 | * |
| 168 | * @return array<int, array<int, mixed>> |
| 169 | * |
| 170 | * @since 1.0.0 |
| 171 | */ |
| 172 | public function getMatrix() : array |
| 173 | { |
| 174 | return $this->matrix; |
| 175 | } |
| 176 | |
| 177 | /** |
| 178 | * Get sub matrix array. |
| 179 | * |
| 180 | * @param int $iRow Start row |
| 181 | * @param int $lRow End row |
| 182 | * @param int $iCol Start col |
| 183 | * @param int $lCol End col |
| 184 | * |
| 185 | * @return Matrix |
| 186 | * |
| 187 | * @since 1.0.0 |
| 188 | */ |
| 189 | public function getSubMatrix(int $iRow, int $lRow, int $iCol, int $lCol) : self |
| 190 | { |
| 191 | $X = [[]]; |
| 192 | for ($i = $iRow; $i <= $lRow; ++$i) { |
| 193 | for ($j = $iCol; $j <= $lCol; ++$j) { |
| 194 | $X[$i - $iRow][$j - $iCol] = $this->matrix[$i][$j]; |
| 195 | } |
| 196 | } |
| 197 | |
| 198 | $matrix = new self(); |
| 199 | $matrix->setMatrix($X); |
| 200 | |
| 201 | return $matrix; |
| 202 | } |
| 203 | |
| 204 | /** |
| 205 | * Get sub matrix array. |
| 206 | * |
| 207 | * @param int[] $rows Row indices |
| 208 | * @param int[] $cols Row indices |
| 209 | * |
| 210 | * @return Matrix |
| 211 | * |
| 212 | * @since 1.0.0 |
| 213 | */ |
| 214 | public function getSubMatrixByColumnsRows(array $rows, array $cols) : self |
| 215 | { |
| 216 | $X = [[]]; |
| 217 | $rlength = \count($rows); |
| 218 | $clength = \count($cols); |
| 219 | |
| 220 | for ($i = 0; $i < $rlength; ++$i) { |
| 221 | for ($j = 0; $j < $clength; ++$j) { |
| 222 | $X[$i][$j] = $this->matrix[$rows[$i]][$cols[$j]]; |
| 223 | } |
| 224 | } |
| 225 | |
| 226 | $matrix = new self(); |
| 227 | $matrix->setMatrix($X); |
| 228 | |
| 229 | return $matrix; |
| 230 | } |
| 231 | |
| 232 | /** |
| 233 | * Get sub matrix array. |
| 234 | * |
| 235 | * @param int $iRow Start row |
| 236 | * @param int $lRow End row |
| 237 | * @param int[] $cols Row indices |
| 238 | * |
| 239 | * @return Matrix |
| 240 | * |
| 241 | * @since 1.0.0 |
| 242 | */ |
| 243 | public function getSubMatrixByColumns(int $iRow, int $lRow, array $cols) : self |
| 244 | { |
| 245 | $X = [[]]; |
| 246 | $length = \count($cols); |
| 247 | |
| 248 | for ($i = $iRow; $i <= $lRow; ++$i) { |
| 249 | for ($j = 0; $j < $length; ++$j) { |
| 250 | $X[$i - $iRow][$j] = $this->matrix[$i][$cols[$j]]; |
| 251 | } |
| 252 | } |
| 253 | |
| 254 | $matrix = new self(); |
| 255 | $matrix->setMatrix($X); |
| 256 | |
| 257 | return $matrix; |
| 258 | } |
| 259 | |
| 260 | /** |
| 261 | * Get sub matrix array. |
| 262 | * |
| 263 | * @param int[] $rows Row indices |
| 264 | * @param int $iCol Start col |
| 265 | * @param int $lCol End col |
| 266 | * |
| 267 | * @return Matrix |
| 268 | * |
| 269 | * @since 1.0.0 |
| 270 | */ |
| 271 | public function getSubMatrixByRows(array $rows, int $iCol, int $lCol) : self |
| 272 | { |
| 273 | $X = [[]]; |
| 274 | $length = \count($rows); |
| 275 | |
| 276 | for ($i = 0; $i < $length; ++$i) { |
| 277 | for ($j = $iCol; $j <= $lCol; ++$j) { |
| 278 | $X[$i][$j - $iCol] = $this->matrix[$rows[$i]][$j]; |
| 279 | } |
| 280 | } |
| 281 | |
| 282 | $matrix = new self(); |
| 283 | $matrix->setMatrix($X); |
| 284 | |
| 285 | return $matrix; |
| 286 | } |
| 287 | |
| 288 | /** |
| 289 | * Get matrix array. |
| 290 | * |
| 291 | * @return array<int, array<int, int|float>> |
| 292 | * |
| 293 | * @since 1.0.0 |
| 294 | */ |
| 295 | public function toArray() : array |
| 296 | { |
| 297 | return $this->matrix; |
| 298 | } |
| 299 | |
| 300 | /** |
| 301 | * Is symmetric. |
| 302 | * |
| 303 | * @return bool |
| 304 | * |
| 305 | * @since 1.0.0 |
| 306 | */ |
| 307 | public function isSymmetric() : bool |
| 308 | { |
| 309 | $isSymmetric = true; |
| 310 | for ($j = 0; ($j < $this->m) & $isSymmetric; ++$j) { |
| 311 | for ($i = 0; ($i < $this->n) & $isSymmetric; ++$i) { |
| 312 | $isSymmetric = ($this->matrix[$i][$j] === $this->matrix[$j][$i]); |
| 313 | } |
| 314 | } |
| 315 | |
| 316 | return $isSymmetric; |
| 317 | } |
| 318 | |
| 319 | /** |
| 320 | * Get matrix rank. |
| 321 | * |
| 322 | * @return int |
| 323 | * |
| 324 | * @since 1.0.0 |
| 325 | */ |
| 326 | public function rank() : int |
| 327 | { |
| 328 | $matrix = $this->matrix; |
| 329 | $mDim = $this->m; |
| 330 | $nDim = $this->n; |
| 331 | |
| 332 | $rank = 0; |
| 333 | $selected = \array_fill(0, $mDim, false); |
| 334 | |
| 335 | for ($i = 0; $i < $nDim; ++$i) { |
| 336 | for ($j = 0; $j < $mDim; ++$j) { |
| 337 | if (!$selected[$j] && \abs($matrix[$j][$i]) > self::EPSILON) { |
| 338 | break; |
| 339 | } |
| 340 | } |
| 341 | |
| 342 | if ($j === $mDim) { |
| 343 | continue; |
| 344 | } |
| 345 | |
| 346 | ++$rank; |
| 347 | $selected[$j] = true; |
| 348 | for ($p = $i + 1; $p < $nDim; ++$p) { |
| 349 | $matrix[$j][$p] /= $matrix[$j][$i]; |
| 350 | } |
| 351 | |
| 352 | for ($k = 0; $k < $mDim; ++$k) { |
| 353 | if ($k !== $j && \abs($matrix[$k][$i]) > self::EPSILON) { |
| 354 | for ($p = $i + 1; $p < $nDim; ++$p) { |
| 355 | $matrix[$k][$p] -= $matrix[$j][$p] * $matrix[$k][$i]; |
| 356 | } |
| 357 | } |
| 358 | } |
| 359 | } |
| 360 | |
| 361 | return $rank; |
| 362 | } |
| 363 | |
| 364 | /** |
| 365 | * Set matrix array. |
| 366 | * |
| 367 | * @param array<int, array<int|float>> $matrix Matrix |
| 368 | * |
| 369 | * @return Matrix |
| 370 | * |
| 371 | * @since 1.0.0 |
| 372 | */ |
| 373 | public function setMatrix(array $matrix) : self |
| 374 | { |
| 375 | $this->m = \count($matrix); |
| 376 | $this->n = \is_array($matrix[0] ?? 1) ? \count($matrix[0]) : 1; |
| 377 | $this->matrix = $matrix; |
| 378 | |
| 379 | return $this; |
| 380 | } |
| 381 | |
| 382 | /** |
| 383 | * Subtract right. |
| 384 | * |
| 385 | * @param int|float|self $value Value |
| 386 | * |
| 387 | * @return Matrix |
| 388 | * |
| 389 | * @since 1.0.0 |
| 390 | */ |
| 391 | public function sub(int | float | self $value) : self |
| 392 | { |
| 393 | if (\is_numeric($value)) { |
| 394 | return $this->addScalar(-$value); |
| 395 | } |
| 396 | |
| 397 | return $this->add($value->mult(-1)); |
| 398 | } |
| 399 | |
| 400 | /** |
| 401 | * Add right. |
| 402 | * |
| 403 | * @param int|float|self $value Value |
| 404 | * |
| 405 | * @return Matrix |
| 406 | * |
| 407 | * @since 1.0.0 |
| 408 | */ |
| 409 | public function add(int | float | self $value) : self |
| 410 | { |
| 411 | if (\is_numeric($value)) { |
| 412 | return $this->addScalar($value); |
| 413 | } |
| 414 | |
| 415 | return $this->addMatrix($value); |
| 416 | } |
| 417 | |
| 418 | /** |
| 419 | * Add matrix. |
| 420 | * |
| 421 | * @param Matrix $matrix Matrix to add |
| 422 | * |
| 423 | * @return Matrix |
| 424 | * |
| 425 | * @throws InvalidDimensionException |
| 426 | * |
| 427 | * @since 1.0.0 |
| 428 | */ |
| 429 | private function addMatrix(self $matrix) : self |
| 430 | { |
| 431 | if ($this->m !== $matrix->getM() || $this->n !== $matrix->getN()) { |
| 432 | throw new InvalidDimensionException($matrix->getM() . 'x' . $matrix->getN()); |
| 433 | } |
| 434 | |
| 435 | $matrixArr = $matrix->getMatrix(); |
| 436 | $newMatrixArr = $this->matrix; |
| 437 | |
| 438 | foreach ($newMatrixArr as $i => $vector) { |
| 439 | foreach ($vector as $j => $_) { |
| 440 | $newMatrixArr[$i][$j] += $matrixArr[$i][$j]; |
| 441 | } |
| 442 | } |
| 443 | |
| 444 | $newMatrix = new self($this->m, $this->n); |
| 445 | $newMatrix->setMatrix($newMatrixArr); |
| 446 | |
| 447 | return $newMatrix; |
| 448 | } |
| 449 | |
| 450 | /** |
| 451 | * Get matrix rows. |
| 452 | * |
| 453 | * @return int<0, max> |
| 454 | * |
| 455 | * @since 1.0.0 |
| 456 | */ |
| 457 | public function getM() : int |
| 458 | { |
| 459 | return $this->m; |
| 460 | } |
| 461 | |
| 462 | /** |
| 463 | * Get matrix columns. |
| 464 | * |
| 465 | * @return int<0, max> |
| 466 | * |
| 467 | * @since 1.0.0 |
| 468 | */ |
| 469 | public function getN() : int |
| 470 | { |
| 471 | return $this->n; |
| 472 | } |
| 473 | |
| 474 | /** |
| 475 | * Add scalar. |
| 476 | * |
| 477 | * @param int|float $scalar Scalar |
| 478 | * |
| 479 | * @return Matrix |
| 480 | * |
| 481 | * @since 1.0.0 |
| 482 | */ |
| 483 | private function addScalar(int | float $scalar) : self |
| 484 | { |
| 485 | $newMatrixArr = $this->matrix; |
| 486 | |
| 487 | foreach ($newMatrixArr as $i => $vector) { |
| 488 | foreach ($vector as $j => $value) { |
| 489 | $newMatrixArr[$i][$j] += $scalar; |
| 490 | } |
| 491 | } |
| 492 | |
| 493 | $newMatrix = new self($this->m, $this->n); |
| 494 | $newMatrix->setMatrix($newMatrixArr); |
| 495 | |
| 496 | return $newMatrix; |
| 497 | } |
| 498 | |
| 499 | /** |
| 500 | * Multiply right. |
| 501 | * |
| 502 | * @param int|float|self $value Factor |
| 503 | * |
| 504 | * @return Matrix |
| 505 | * |
| 506 | * @since 1.0.0 |
| 507 | */ |
| 508 | public function mult(int | float | self $value) : self |
| 509 | { |
| 510 | if (\is_numeric($value)) { |
| 511 | return $this->multScalar($value); |
| 512 | } |
| 513 | |
| 514 | return $this->multMatrix($value); |
| 515 | } |
| 516 | |
| 517 | /** |
| 518 | * Multiply matrix. |
| 519 | * |
| 520 | * @param Matrix $matrix Matrix to multiply with |
| 521 | * |
| 522 | * @return Matrix |
| 523 | * |
| 524 | * @throws InvalidDimensionException |
| 525 | * |
| 526 | * @since 1.0.0 |
| 527 | */ |
| 528 | private function multMatrix(self $matrix) : self |
| 529 | { |
| 530 | $nDim = $matrix->getN(); |
| 531 | $mDim = $matrix->getM(); |
| 532 | |
| 533 | if ($mDim !== $this->n) { |
| 534 | throw new InvalidDimensionException($mDim . 'x' . $nDim); |
| 535 | } |
| 536 | |
| 537 | $matrixArr = $matrix->getMatrix(); |
| 538 | $newMatrix = new self($this->m, $nDim); |
| 539 | $newMatrixArr = $newMatrix->getMatrix(); |
| 540 | |
| 541 | for ($i = 0; $i < $this->m; ++$i) { // Row of $this |
| 542 | for ($c = 0; $c < $nDim; ++$c) { // Column of $matrix |
| 543 | $temp = 0; |
| 544 | |
| 545 | for ($j = 0; $j < $mDim; ++$j) { // Row of $matrix |
| 546 | $temp += ($this->matrix[$i][$j] ?? 0) * ($matrixArr[$j][$c] ?? 0); |
| 547 | } |
| 548 | |
| 549 | $newMatrixArr[$i][$c] = $temp; |
| 550 | } |
| 551 | } |
| 552 | |
| 553 | $newMatrix->setMatrix($newMatrixArr); /* @phpstan-ignore-line */ |
| 554 | |
| 555 | return $newMatrix; |
| 556 | } |
| 557 | |
| 558 | /** |
| 559 | * Multiply matrix. |
| 560 | * |
| 561 | * @param int|float $scalar Scalar value |
| 562 | * |
| 563 | * @return Matrix |
| 564 | * |
| 565 | * @since 1.0.0 |
| 566 | */ |
| 567 | private function multScalar(int | float $scalar) : self |
| 568 | { |
| 569 | $newMatrixArr = $this->matrix; |
| 570 | |
| 571 | foreach ($newMatrixArr as $i => $vector) { |
| 572 | foreach ($vector as $j => $value) { |
| 573 | $newMatrixArr[$i][$j] *= $scalar; |
| 574 | } |
| 575 | } |
| 576 | |
| 577 | $newMatrix = new self($this->m, $this->n); |
| 578 | $newMatrix->setMatrix($newMatrixArr); |
| 579 | |
| 580 | return $newMatrix; |
| 581 | } |
| 582 | |
| 583 | /** |
| 584 | * Upper triangulize matrix. |
| 585 | * |
| 586 | * @return Matrix |
| 587 | * |
| 588 | * @since 1.0.0 |
| 589 | */ |
| 590 | public function upperTriangular() : self |
| 591 | { |
| 592 | $matrix = new self($this->n, $this->n); |
| 593 | |
| 594 | $matrixArr = $this->matrix; |
| 595 | $this->upperTrianglize($matrixArr); |
| 596 | $matrix->setMatrix($matrixArr); |
| 597 | |
| 598 | return $matrix; |
| 599 | } |
| 600 | |
| 601 | /** |
| 602 | * Trianglize matrix. |
| 603 | * |
| 604 | * @param array<int, array<int|float>> $arr Matrix to trianglize |
| 605 | * |
| 606 | * @return int Det sign |
| 607 | * |
| 608 | * @since 1.0.0 |
| 609 | */ |
| 610 | private function upperTrianglize(array &$arr) : int |
| 611 | { |
| 612 | $n = $this->n; |
| 613 | $sign = 1; |
| 614 | |
| 615 | for ($i = 0; $i < $n; ++$i) { |
| 616 | $max = 0; |
| 617 | |
| 618 | for ($j = $i; $j < $n; ++$j) { |
| 619 | if (\abs($arr[$j][$i]) > \abs($arr[$max][$i])) { |
| 620 | $max = $j; |
| 621 | } |
| 622 | } |
| 623 | |
| 624 | if ($max !== 0) { |
| 625 | $sign = -$sign; |
| 626 | $temp = $arr[$i]; |
| 627 | $arr[$i] = $arr[$max]; |
| 628 | $arr[$max] = $temp; |
| 629 | } |
| 630 | |
| 631 | if (!$arr[$i][$i]) { |
| 632 | return 0; |
| 633 | } |
| 634 | |
| 635 | for ($j = $i + 1; $j < $n; ++$j) { |
| 636 | $r = $arr[$j][$i] / $arr[$i][$i]; |
| 637 | |
| 638 | if (!$r) { |
| 639 | continue; |
| 640 | } |
| 641 | |
| 642 | for ($c = $i; $c < $n; ++$c) { |
| 643 | $arr[$j][$c] -= $arr[$i][$c] * $r; |
| 644 | } |
| 645 | } |
| 646 | } |
| 647 | |
| 648 | return $sign; |
| 649 | } |
| 650 | |
| 651 | /** |
| 652 | * Inverse matrix. |
| 653 | * |
| 654 | * @return Matrix |
| 655 | * |
| 656 | * @throws InvalidDimensionException |
| 657 | * |
| 658 | * @since 1.0.0 |
| 659 | */ |
| 660 | public function inverse() : self |
| 661 | { |
| 662 | return $this->solve(new IdentityMatrix($this->m)); |
| 663 | } |
| 664 | |
| 665 | /** |
| 666 | * Solve matrix |
| 667 | * |
| 668 | * @param Matrix $B Matrix/Vector b |
| 669 | * |
| 670 | * @return Matrix|Vector |
| 671 | * |
| 672 | * @since 1.0.0 |
| 673 | */ |
| 674 | public function solve(self $B) : self |
| 675 | { |
| 676 | $M = $this->m === $this->n ? new LUDecomposition($this) : new QRDecomposition($this); |
| 677 | |
| 678 | return $M->solve($B); |
| 679 | } |
| 680 | |
| 681 | /** |
| 682 | * Calculate det. |
| 683 | * |
| 684 | * @return float |
| 685 | * |
| 686 | * @since 1.0.0 |
| 687 | */ |
| 688 | public function det() : float |
| 689 | { |
| 690 | $L = new LUDecomposition($this); |
| 691 | |
| 692 | return $L->det(); |
| 693 | } |
| 694 | |
| 695 | /** |
| 696 | * Dot product |
| 697 | * |
| 698 | * @param self $B Matrix |
| 699 | * |
| 700 | * @return self |
| 701 | * |
| 702 | * @since 1.0.0 |
| 703 | */ |
| 704 | public function dot(self $B) : self |
| 705 | { |
| 706 | $value1 = $this->matrix; |
| 707 | $value2 = $B->getMatrix(); |
| 708 | |
| 709 | $m1 = \count($value1); |
| 710 | $n1 = ($isMatrix1 = \is_array($value1[0])) ? \count($value1[0]) : 1; |
| 711 | |
| 712 | $m2 = \count($value2); |
| 713 | $n2 = ($isMatrix2 = \is_array($value2[0])) ? \count($value2[0]) : 1; |
| 714 | |
| 715 | $result = null; |
| 716 | |
| 717 | if ($isMatrix1 && $isMatrix2) { |
| 718 | if ($m2 !== $n1) { |
| 719 | throw new InvalidDimensionException($m2 . 'x' . $n2 . ' not compatible with ' . $m1 . 'x' . $n1); |
| 720 | } |
| 721 | |
| 722 | $result = [[]]; |
| 723 | for ($i = 0; $i < $m1; ++$i) { // Row of 1 |
| 724 | for ($c = 0; $c < $n2; ++$c) { // Column of 2 |
| 725 | $temp = 0; |
| 726 | |
| 727 | for ($j = 0; $j < $m2; ++$j) { // Row of 2 |
| 728 | $temp += $value1[$i][$j] * $value2[$j][$c]; |
| 729 | } |
| 730 | |
| 731 | $result[$i][$c] = $temp; |
| 732 | } |
| 733 | } |
| 734 | |
| 735 | return self::fromArray($result); |
| 736 | } elseif (!$isMatrix1 && !$isMatrix2) { |
| 737 | if ($m1 !== $m2) { |
| 738 | throw new InvalidDimensionException($m1 . 'x' . $m2); |
| 739 | } |
| 740 | |
| 741 | $result = 0; |
| 742 | for ($i = 0; $i < $m1; ++$i) { |
| 743 | /** @var array $value1 */ |
| 744 | /** @var array $value2 */ |
| 745 | $result += $value1[$i] * $value2[$i]; |
| 746 | } |
| 747 | |
| 748 | return self::fromArray([[$result]]); |
| 749 | } elseif ($isMatrix1 && !$isMatrix2) { |
| 750 | $result = []; |
| 751 | for ($i = 0; $i < $m1; ++$i) { // Row of 1 |
| 752 | $temp = 0; |
| 753 | |
| 754 | for ($c = 0; $c < $m2; ++$c) { // Row of 2 |
| 755 | /** @var array $value2 */ |
| 756 | $temp += $value1[$i][$c] * $value2[$c]; |
| 757 | } |
| 758 | |
| 759 | $result[$i] = $temp; |
| 760 | } |
| 761 | |
| 762 | return self::fromArray($result); |
| 763 | } |
| 764 | |
| 765 | throw new \InvalidArgumentException(); |
| 766 | } |
| 767 | |
| 768 | /** |
| 769 | * Sum the elements in the matrix |
| 770 | * |
| 771 | * @param int $axis Axis (-1 -> all dimensions, 0 -> columns, 1 -> rows) |
| 772 | * |
| 773 | * @return int|float|self Returns int or float for axis -1 |
| 774 | * |
| 775 | * @since 1.0.0 |
| 776 | */ |
| 777 | public function sum(int $axis = -1) : int|float|self |
| 778 | { |
| 779 | if ($axis === -1) { |
| 780 | $sum = 0; |
| 781 | |
| 782 | foreach ($this->matrix as $row) { |
| 783 | $sum += \array_sum($row); |
| 784 | } |
| 785 | |
| 786 | return $sum; |
| 787 | } elseif ($axis === 0) { |
| 788 | $sum = []; |
| 789 | foreach ($this->matrix as $row) { |
| 790 | foreach ($row as $idx2 => $value) { |
| 791 | if (!isset($sum[$idx2])) { |
| 792 | $sum[$idx2] = 0; |
| 793 | } |
| 794 | |
| 795 | $sum[$idx2] += $value; |
| 796 | } |
| 797 | } |
| 798 | |
| 799 | return self::fromArray($sum); |
| 800 | } elseif ($axis === 1) { |
| 801 | $sum = []; |
| 802 | foreach ($this->matrix as $idx => $row) { |
| 803 | $sum[$idx] = \array_sum($row); |
| 804 | } |
| 805 | |
| 806 | return self::fromArray($sum); |
| 807 | } |
| 808 | |
| 809 | return new self(); |
| 810 | } |
| 811 | |
| 812 | /** |
| 813 | * Is matrix a diagonal matrix |
| 814 | * |
| 815 | * @return bool |
| 816 | * |
| 817 | * @since 1.0.0 |
| 818 | */ |
| 819 | public function isDiagonal() : bool |
| 820 | { |
| 821 | if ($this->m !== $this->n) { |
| 822 | return false; |
| 823 | } |
| 824 | |
| 825 | for ($i = 0; $i < $this->m; ++$i) { |
| 826 | for ($j = 0; $j < $this->n; ++$j) { |
| 827 | if ($i !== $j && \abs($this->matrix[$i][$j]) > self::EPSILON) { |
| 828 | return false; |
| 829 | } |
| 830 | } |
| 831 | } |
| 832 | |
| 833 | return true; |
| 834 | } |
| 835 | |
| 836 | /** |
| 837 | * Calculate the power of a matrix |
| 838 | * |
| 839 | * @param int|float $exponent Exponent |
| 840 | * |
| 841 | * @return self |
| 842 | * |
| 843 | * @throws InvalidDimensionException |
| 844 | * |
| 845 | * @since 1.0.0 |
| 846 | */ |
| 847 | public function pow(int | float $exponent) : self |
| 848 | { |
| 849 | if ($this->isDiagonal()) { |
| 850 | $matrix = []; |
| 851 | |
| 852 | for ($i = 0; $i < $this->m; ++$i) { |
| 853 | $row = []; |
| 854 | for ($j = 0; $j < $this->m; ++$j) { |
| 855 | $row[] = $i === $j ? \pow($this->matrix[$i][$j], $exponent) : 0; |
| 856 | } |
| 857 | |
| 858 | $matrix[] = $row; |
| 859 | } |
| 860 | |
| 861 | return self::fromArray($matrix); |
| 862 | } elseif (\is_int($exponent)) { |
| 863 | if ($this->m !== $this->n) { |
| 864 | throw new InvalidDimensionException($this->m . 'x' . $this->n); |
| 865 | } |
| 866 | |
| 867 | $matrix = new IdentityMatrix($this->m); |
| 868 | for ($i = 0; $i < $exponent; ++$i) { |
| 869 | $matrix = $matrix->mult($this); |
| 870 | } |
| 871 | |
| 872 | return $matrix; |
| 873 | } else { |
| 874 | // @todo: implement |
| 875 | throw new \Exception('Not yet implemented'); |
| 876 | } |
| 877 | } |
| 878 | |
| 879 | /** |
| 880 | * Calculate e^M |
| 881 | * |
| 882 | * @param int $iterations Iterations for approximation |
| 883 | * |
| 884 | * @return self |
| 885 | * |
| 886 | * @since 1.0.0 |
| 887 | */ |
| 888 | public function exp(int $iterations = 10) : self |
| 889 | { |
| 890 | if ($this->m !== $this->n) { |
| 891 | throw new InvalidDimensionException($this->m . 'x' . $this->n); |
| 892 | } |
| 893 | |
| 894 | $identity = new IdentityMatrix($this->m); |
| 895 | $matrix = $identity; |
| 896 | |
| 897 | $factorial = 1; |
| 898 | $pow = $matrix; |
| 899 | |
| 900 | for ($i = 1; $i <= $iterations; ++$i) { |
| 901 | $factorial *= $i; |
| 902 | $coeff = 1 / $factorial; |
| 903 | |
| 904 | $term = $pow->mult($coeff); |
| 905 | $matrix = $matrix->add($term); |
| 906 | $pow = $pow->mult($matrix); // @todo: maybe wrong order? |
| 907 | } |
| 908 | |
| 909 | return $matrix; |
| 910 | } |
| 911 | |
| 912 | /** |
| 913 | * {@inheritdoc} |
| 914 | */ |
| 915 | public function current() : int |
| 916 | { |
| 917 | $row = (int) ($this->position / $this->m); |
| 918 | |
| 919 | return $this->matrix[$row][$this->position - $row * $this->n]; |
| 920 | } |
| 921 | |
| 922 | /** |
| 923 | * {@inheritdoc} |
| 924 | */ |
| 925 | public function offsetGet(mixed $offset) : mixed |
| 926 | { |
| 927 | if (!\is_int($offset)) { |
| 928 | return 0; |
| 929 | } |
| 930 | |
| 931 | $offset = (int) $offset; |
| 932 | $row = (int) ($offset / $this->m); |
| 933 | |
| 934 | return $this->matrix[$row][$offset - $row * $this->n]; |
| 935 | } |
| 936 | |
| 937 | /** |
| 938 | * {@inheritdoc} |
| 939 | */ |
| 940 | public function next() : void |
| 941 | { |
| 942 | ++$this->position; |
| 943 | } |
| 944 | |
| 945 | /** |
| 946 | * {@inheritdoc} |
| 947 | */ |
| 948 | public function key() : mixed |
| 949 | { |
| 950 | return $this->position; |
| 951 | } |
| 952 | |
| 953 | /** |
| 954 | * {@inheritdoc} |
| 955 | */ |
| 956 | public function valid() : bool |
| 957 | { |
| 958 | return $this->offsetExists($this->position); |
| 959 | } |
| 960 | |
| 961 | /** |
| 962 | * {@inheritdoc} |
| 963 | */ |
| 964 | public function offsetExists(mixed $offset) : bool |
| 965 | { |
| 966 | if (!\is_int($offset)) { |
| 967 | return false; |
| 968 | } |
| 969 | |
| 970 | $offset = (int) $offset; |
| 971 | $row = (int) ($offset / $this->m); |
| 972 | |
| 973 | return isset($this->matrix[$row][$offset - $row * $this->n]); |
| 974 | } |
| 975 | |
| 976 | /** |
| 977 | * {@inheritdoc} |
| 978 | */ |
| 979 | public function rewind() : void |
| 980 | { |
| 981 | $this->position = 0; |
| 982 | } |
| 983 | |
| 984 | /** |
| 985 | * {@inheritdoc} |
| 986 | */ |
| 987 | public function offsetSet(mixed $offset, mixed $value) : void |
| 988 | { |
| 989 | if (!\is_int($offset) || !\is_numeric($value)) { |
| 990 | return; |
| 991 | } |
| 992 | |
| 993 | $offset = (int) $offset; |
| 994 | $row = (int) ($offset / $this->m); |
| 995 | $this->matrix[$row][$offset - $row * $this->n] = $value; /* @phpstan-ignore-line */ |
| 996 | } |
| 997 | |
| 998 | /** |
| 999 | * {@inheritdoc} |
| 1000 | */ |
| 1001 | public function offsetUnset(mixed $offset) : void |
| 1002 | { |
| 1003 | if (!\is_int($offset)) { |
| 1004 | return; |
| 1005 | } |
| 1006 | |
| 1007 | $offset = (int) $offset; |
| 1008 | $row = (int) ($offset / $this->m); |
| 1009 | unset($this->matrix[$row][$offset - $row * $this->n]); |
| 1010 | } |
| 1011 | } |