alxarafe /
alixar
| Conditions | 71 |
| Paths | > 20000 |
| Total Lines | 377 |
| Code Lines | 272 |
| Lines | 0 |
| Ratio | 0 % |
| Changes | 0 | ||
Small methods make your code easier to understand, in particular if combined with a good name. Besides, if your method is small, finding a good name is usually much easier.
For example, if you find yourself adding comments to a method's body, this is usually a good sign to extract the commented part to a new method, and use the comment as a starting point when coming up with a good name for this new method.
Commonly applied refactorings include:
If many parameters/temporary variables are present:
| 1 | <?php |
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| 398 | private function hqr2() |
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| 399 | { |
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| 400 | // Initialize |
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| 401 | $nn = $this->n; |
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| 402 | $n = $nn - 1; |
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| 403 | $low = 0; |
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| 404 | $high = $nn - 1; |
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| 405 | $eps = pow(2.0, -52.0); |
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| 406 | $exshift = 0.0; |
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| 407 | $p = $q = $r = $s = $z = 0; |
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| 408 | // Store roots isolated by balanc and compute matrix norm |
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| 409 | $norm = 0.0; |
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| 410 | |||
| 411 | for ($i = 0; $i < $nn; ++$i) { |
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| 412 | if (($i < $low) or ($i > $high)) { |
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| 413 | $this->d[$i] = $this->H[$i][$i]; |
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| 414 | $this->e[$i] = 0.0; |
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| 415 | } |
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| 416 | for ($j = max($i - 1, 0); $j < $nn; ++$j) { |
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| 417 | $norm = $norm + abs($this->H[$i][$j]); |
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| 418 | } |
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| 419 | } |
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| 420 | |||
| 421 | // Outer loop over eigenvalue index |
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| 422 | $iter = 0; |
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| 423 | while ($n >= $low) { |
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| 424 | // Look for single small sub-diagonal element |
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| 425 | $l = $n; |
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| 426 | while ($l > $low) { |
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| 427 | $s = abs($this->H[$l - 1][$l - 1]) + abs($this->H[$l][$l]); |
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| 428 | if ($s == 0.0) { |
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| 429 | $s = $norm; |
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| 430 | } |
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| 431 | if (abs($this->H[$l][$l - 1]) < $eps * $s) { |
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| 432 | break; |
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| 433 | } |
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| 434 | --$l; |
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| 435 | } |
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| 436 | // Check for convergence |
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| 437 | // One root found |
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| 438 | if ($l == $n) { |
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| 439 | $this->H[$n][$n] = $this->H[$n][$n] + $exshift; |
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| 440 | $this->d[$n] = $this->H[$n][$n]; |
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| 441 | $this->e[$n] = 0.0; |
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| 442 | --$n; |
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| 443 | $iter = 0; |
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| 444 | // Two roots found |
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| 445 | } elseif ($l == $n - 1) { |
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| 446 | $w = $this->H[$n][$n - 1] * $this->H[$n - 1][$n]; |
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| 447 | $p = ($this->H[$n - 1][$n - 1] - $this->H[$n][$n]) / 2.0; |
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| 448 | $q = $p * $p + $w; |
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| 449 | $z = sqrt(abs($q)); |
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| 450 | $this->H[$n][$n] = $this->H[$n][$n] + $exshift; |
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| 451 | $this->H[$n - 1][$n - 1] = $this->H[$n - 1][$n - 1] + $exshift; |
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| 452 | $x = $this->H[$n][$n]; |
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| 453 | // Real pair |
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| 454 | if ($q >= 0) { |
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| 455 | if ($p >= 0) { |
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| 456 | $z = $p + $z; |
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| 457 | } else { |
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| 458 | $z = $p - $z; |
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| 459 | } |
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| 460 | $this->d[$n - 1] = $x + $z; |
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| 461 | $this->d[$n] = $this->d[$n - 1]; |
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| 462 | if ($z != 0.0) { |
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| 463 | $this->d[$n] = $x - $w / $z; |
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| 464 | } |
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| 465 | $this->e[$n - 1] = 0.0; |
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| 466 | $this->e[$n] = 0.0; |
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| 467 | $x = $this->H[$n][$n - 1]; |
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| 468 | $s = abs($x) + abs($z); |
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| 469 | $p = $x / $s; |
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| 470 | $q = $z / $s; |
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| 471 | $r = sqrt($p * $p + $q * $q); |
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| 472 | $p = $p / $r; |
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| 473 | $q = $q / $r; |
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| 474 | // Row modification |
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| 475 | for ($j = $n - 1; $j < $nn; ++$j) { |
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| 476 | $z = $this->H[$n - 1][$j]; |
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| 477 | $this->H[$n - 1][$j] = $q * $z + $p * $this->H[$n][$j]; |
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| 478 | $this->H[$n][$j] = $q * $this->H[$n][$j] - $p * $z; |
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| 479 | } |
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| 480 | // Column modification |
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| 481 | for ($i = 0; $i <= $n; ++$i) { |
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| 482 | $z = $this->H[$i][$n - 1]; |
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| 483 | $this->H[$i][$n - 1] = $q * $z + $p * $this->H[$i][$n]; |
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| 484 | $this->H[$i][$n] = $q * $this->H[$i][$n] - $p * $z; |
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| 485 | } |
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| 486 | // Accumulate transformations |
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| 487 | for ($i = $low; $i <= $high; ++$i) { |
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| 488 | $z = $this->V[$i][$n - 1]; |
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| 489 | $this->V[$i][$n - 1] = $q * $z + $p * $this->V[$i][$n]; |
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| 490 | $this->V[$i][$n] = $q * $this->V[$i][$n] - $p * $z; |
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| 491 | } |
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| 492 | // Complex pair |
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| 493 | } else { |
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| 494 | $this->d[$n - 1] = $x + $p; |
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| 495 | $this->d[$n] = $x + $p; |
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| 496 | $this->e[$n - 1] = $z; |
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| 497 | $this->e[$n] = -$z; |
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| 498 | } |
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| 499 | $n = $n - 2; |
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| 500 | $iter = 0; |
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| 501 | // No convergence yet |
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| 502 | } else { |
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| 503 | // Form shift |
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| 504 | $x = $this->H[$n][$n]; |
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| 505 | $y = 0.0; |
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| 506 | $w = 0.0; |
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| 507 | if ($l < $n) { |
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| 508 | $y = $this->H[$n - 1][$n - 1]; |
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| 509 | $w = $this->H[$n][$n - 1] * $this->H[$n - 1][$n]; |
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| 510 | } |
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| 511 | // Wilkinson's original ad hoc shift |
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| 512 | if ($iter == 10) { |
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| 513 | $exshift += $x; |
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| 514 | for ($i = $low; $i <= $n; ++$i) { |
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| 515 | $this->H[$i][$i] -= $x; |
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| 516 | } |
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| 517 | $s = abs($this->H[$n][$n - 1]) + abs($this->H[$n - 1][$n - 2]); |
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| 518 | $x = $y = 0.75 * $s; |
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| 519 | $w = -0.4375 * $s * $s; |
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| 520 | } |
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| 521 | // MATLAB's new ad hoc shift |
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| 522 | if ($iter == 30) { |
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| 523 | $s = ($y - $x) / 2.0; |
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| 524 | $s = $s * $s + $w; |
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| 525 | if ($s > 0) { |
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| 526 | $s = sqrt($s); |
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| 527 | if ($y < $x) { |
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| 528 | $s = -$s; |
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| 529 | } |
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| 530 | $s = $x - $w / (($y - $x) / 2.0 + $s); |
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| 531 | for ($i = $low; $i <= $n; ++$i) { |
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| 532 | $this->H[$i][$i] -= $s; |
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| 533 | } |
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| 534 | $exshift += $s; |
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| 535 | $x = $y = $w = 0.964; |
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| 536 | } |
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| 537 | } |
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| 538 | // Could check iteration count here. |
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| 539 | $iter = $iter + 1; |
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| 540 | // Look for two consecutive small sub-diagonal elements |
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| 541 | $m = $n - 2; |
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| 542 | while ($m >= $l) { |
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| 543 | $z = $this->H[$m][$m]; |
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| 544 | $r = $x - $z; |
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| 545 | $s = $y - $z; |
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| 546 | $p = ($r * $s - $w) / $this->H[$m + 1][$m] + $this->H[$m][$m + 1]; |
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| 547 | $q = $this->H[$m + 1][$m + 1] - $z - $r - $s; |
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| 548 | $r = $this->H[$m + 2][$m + 1]; |
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| 549 | $s = abs($p) + abs($q) + abs($r); |
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| 550 | $p = $p / $s; |
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| 551 | $q = $q / $s; |
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| 552 | $r = $r / $s; |
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| 553 | if ($m == $l) { |
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| 554 | break; |
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| 555 | } |
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| 556 | if ( |
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| 557 | abs($this->H[$m][$m - 1]) * (abs($q) + abs($r)) < |
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| 558 | $eps * (abs($p) * (abs($this->H[$m - 1][$m - 1]) + abs($z) + abs($this->H[$m + 1][$m + 1]))) |
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| 559 | ) { |
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| 560 | break; |
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| 561 | } |
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| 562 | --$m; |
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| 563 | } |
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| 564 | for ($i = $m + 2; $i <= $n; ++$i) { |
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| 565 | $this->H[$i][$i - 2] = 0.0; |
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| 566 | if ($i > $m + 2) { |
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| 567 | $this->H[$i][$i - 3] = 0.0; |
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| 568 | } |
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| 569 | } |
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| 570 | // Double QR step involving rows l:n and columns m:n |
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| 571 | for ($k = $m; $k <= $n - 1; ++$k) { |
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| 572 | $notlast = ($k != $n - 1); |
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| 573 | if ($k != $m) { |
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| 574 | $p = $this->H[$k][$k - 1]; |
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| 575 | $q = $this->H[$k + 1][$k - 1]; |
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| 576 | $r = ($notlast ? $this->H[$k + 2][$k - 1] : 0.0); |
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| 577 | $x = abs($p) + abs($q) + abs($r); |
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| 578 | if ($x != 0.0) { |
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| 579 | $p = $p / $x; |
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| 580 | $q = $q / $x; |
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| 581 | $r = $r / $x; |
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| 582 | } |
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| 583 | } |
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| 584 | if ($x == 0.0) { |
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| 585 | break; |
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| 586 | } |
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| 587 | $s = sqrt($p * $p + $q * $q + $r * $r); |
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| 588 | if ($p < 0) { |
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| 589 | $s = -$s; |
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| 590 | } |
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| 591 | if ($s != 0) { |
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| 592 | if ($k != $m) { |
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| 593 | $this->H[$k][$k - 1] = -$s * $x; |
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| 594 | } elseif ($l != $m) { |
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| 595 | $this->H[$k][$k - 1] = -$this->H[$k][$k - 1]; |
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| 596 | } |
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| 597 | $p = $p + $s; |
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| 598 | $x = $p / $s; |
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| 599 | $y = $q / $s; |
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| 600 | $z = $r / $s; |
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| 601 | $q = $q / $p; |
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| 602 | $r = $r / $p; |
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| 603 | // Row modification |
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| 604 | for ($j = $k; $j < $nn; ++$j) { |
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| 605 | $p = $this->H[$k][$j] + $q * $this->H[$k + 1][$j]; |
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| 606 | if ($notlast) { |
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| 607 | $p = $p + $r * $this->H[$k + 2][$j]; |
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| 608 | $this->H[$k + 2][$j] = $this->H[$k + 2][$j] - $p * $z; |
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| 609 | } |
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| 610 | $this->H[$k][$j] = $this->H[$k][$j] - $p * $x; |
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| 611 | $this->H[$k + 1][$j] = $this->H[$k + 1][$j] - $p * $y; |
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| 612 | } |
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| 613 | // Column modification |
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| 614 | $iMax = min($n, $k + 3); |
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| 615 | for ($i = 0; $i <= $iMax; ++$i) { |
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| 616 | $p = $x * $this->H[$i][$k] + $y * $this->H[$i][$k + 1]; |
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| 617 | if ($notlast) { |
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| 618 | $p = $p + $z * $this->H[$i][$k + 2]; |
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| 619 | $this->H[$i][$k + 2] = $this->H[$i][$k + 2] - $p * $r; |
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| 620 | } |
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| 621 | $this->H[$i][$k] = $this->H[$i][$k] - $p; |
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| 622 | $this->H[$i][$k + 1] = $this->H[$i][$k + 1] - $p * $q; |
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| 623 | } |
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| 624 | // Accumulate transformations |
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| 625 | for ($i = $low; $i <= $high; ++$i) { |
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| 626 | $p = $x * $this->V[$i][$k] + $y * $this->V[$i][$k + 1]; |
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| 627 | if ($notlast) { |
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| 628 | $p = $p + $z * $this->V[$i][$k + 2]; |
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| 629 | $this->V[$i][$k + 2] = $this->V[$i][$k + 2] - $p * $r; |
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| 630 | } |
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| 631 | $this->V[$i][$k] = $this->V[$i][$k] - $p; |
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| 632 | $this->V[$i][$k + 1] = $this->V[$i][$k + 1] - $p * $q; |
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| 633 | } |
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| 634 | } // ($s != 0) |
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| 635 | } // k loop |
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| 636 | } // check convergence |
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| 637 | } // while ($n >= $low) |
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| 638 | |||
| 639 | // Backsubstitute to find vectors of upper triangular form |
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| 640 | if ($norm == 0.0) { |
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| 641 | return; |
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| 642 | } |
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| 643 | |||
| 644 | for ($n = $nn - 1; $n >= 0; --$n) { |
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| 645 | $p = $this->d[$n]; |
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| 646 | $q = $this->e[$n]; |
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| 647 | // Real vector |
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| 648 | if ($q == 0) { |
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| 649 | $l = $n; |
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| 650 | $this->H[$n][$n] = 1.0; |
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| 651 | for ($i = $n - 1; $i >= 0; --$i) { |
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| 652 | $w = $this->H[$i][$i] - $p; |
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| 653 | $r = 0.0; |
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| 654 | for ($j = $l; $j <= $n; ++$j) { |
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| 655 | $r = $r + $this->H[$i][$j] * $this->H[$j][$n]; |
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| 656 | } |
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| 657 | if ($this->e[$i] < 0.0) { |
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| 658 | $z = $w; |
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| 659 | $s = $r; |
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| 660 | } else { |
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| 661 | $l = $i; |
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| 662 | if ($this->e[$i] == 0.0) { |
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| 663 | if ($w != 0.0) { |
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| 664 | $this->H[$i][$n] = -$r / $w; |
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| 665 | } else { |
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| 666 | $this->H[$i][$n] = -$r / ($eps * $norm); |
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| 667 | } |
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| 668 | // Solve real equations |
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| 669 | } else { |
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| 670 | $x = $this->H[$i][$i + 1]; |
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| 671 | $y = $this->H[$i + 1][$i]; |
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| 672 | $q = ($this->d[$i] - $p) * ($this->d[$i] - $p) + $this->e[$i] * $this->e[$i]; |
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| 673 | $t = ($x * $s - $z * $r) / $q; |
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| 674 | $this->H[$i][$n] = $t; |
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| 675 | if (abs($x) > abs($z)) { |
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| 676 | $this->H[$i + 1][$n] = (-$r - $w * $t) / $x; |
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| 677 | } else { |
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| 678 | $this->H[$i + 1][$n] = (-$s - $y * $t) / $z; |
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| 679 | } |
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| 680 | } |
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| 681 | // Overflow control |
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| 682 | $t = abs($this->H[$i][$n]); |
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| 683 | if (($eps * $t) * $t > 1) { |
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| 684 | for ($j = $i; $j <= $n; ++$j) { |
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| 685 | $this->H[$j][$n] = $this->H[$j][$n] / $t; |
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| 686 | } |
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| 687 | } |
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| 688 | } |
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| 689 | } |
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| 690 | // Complex vector |
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| 691 | } elseif ($q < 0) { |
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| 692 | $l = $n - 1; |
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| 693 | // Last vector component imaginary so matrix is triangular |
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| 694 | if (abs($this->H[$n][$n - 1]) > abs($this->H[$n - 1][$n])) { |
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| 695 | $this->H[$n - 1][$n - 1] = $q / $this->H[$n][$n - 1]; |
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| 696 | $this->H[$n - 1][$n] = -($this->H[$n][$n] - $p) / $this->H[$n][$n - 1]; |
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| 697 | } else { |
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| 698 | $this->cdiv(0.0, -$this->H[$n - 1][$n], $this->H[$n - 1][$n - 1] - $p, $q); |
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| 699 | $this->H[$n - 1][$n - 1] = $this->cdivr; |
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| 700 | $this->H[$n - 1][$n] = $this->cdivi; |
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| 701 | } |
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| 702 | $this->H[$n][$n - 1] = 0.0; |
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| 703 | $this->H[$n][$n] = 1.0; |
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| 704 | for ($i = $n - 2; $i >= 0; --$i) { |
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| 705 | // double ra,sa,vr,vi; |
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| 706 | $ra = 0.0; |
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| 707 | $sa = 0.0; |
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| 708 | for ($j = $l; $j <= $n; ++$j) { |
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| 709 | $ra = $ra + $this->H[$i][$j] * $this->H[$j][$n - 1]; |
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| 710 | $sa = $sa + $this->H[$i][$j] * $this->H[$j][$n]; |
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| 711 | } |
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| 712 | $w = $this->H[$i][$i] - $p; |
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| 713 | if ($this->e[$i] < 0.0) { |
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| 714 | $z = $w; |
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| 715 | $r = $ra; |
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| 716 | $s = $sa; |
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| 717 | } else { |
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| 718 | $l = $i; |
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| 719 | if ($this->e[$i] == 0) { |
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| 720 | $this->cdiv(-$ra, -$sa, $w, $q); |
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| 721 | $this->H[$i][$n - 1] = $this->cdivr; |
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| 722 | $this->H[$i][$n] = $this->cdivi; |
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| 723 | } else { |
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| 724 | // Solve complex equations |
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| 725 | $x = $this->H[$i][$i + 1]; |
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| 726 | $y = $this->H[$i + 1][$i]; |
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| 727 | $vr = ($this->d[$i] - $p) * ($this->d[$i] - $p) + $this->e[$i] * $this->e[$i] - $q * $q; |
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| 728 | $vi = ($this->d[$i] - $p) * 2.0 * $q; |
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| 729 | if ($vr == 0.0 & $vi == 0.0) { |
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| 730 | $vr = $eps * $norm * (abs($w) + abs($q) + abs($x) + abs($y) + abs($z)); |
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| 731 | } |
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| 732 | $this->cdiv($x * $r - $z * $ra + $q * $sa, $x * $s - $z * $sa - $q * $ra, $vr, $vi); |
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| 733 | $this->H[$i][$n - 1] = $this->cdivr; |
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| 734 | $this->H[$i][$n] = $this->cdivi; |
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| 735 | if (abs($x) > (abs($z) + abs($q))) { |
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| 736 | $this->H[$i + 1][$n - 1] = (-$ra - $w * $this->H[$i][$n - 1] + $q * $this->H[$i][$n]) / $x; |
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| 737 | $this->H[$i + 1][$n] = (-$sa - $w * $this->H[$i][$n] - $q * $this->H[$i][$n - 1]) / $x; |
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| 738 | } else { |
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| 739 | $this->cdiv(-$r - $y * $this->H[$i][$n - 1], -$s - $y * $this->H[$i][$n], $z, $q); |
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| 740 | $this->H[$i + 1][$n - 1] = $this->cdivr; |
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| 741 | $this->H[$i + 1][$n] = $this->cdivi; |
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| 742 | } |
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| 743 | } |
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| 744 | // Overflow control |
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| 745 | $t = max(abs($this->H[$i][$n - 1]), abs($this->H[$i][$n])); |
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| 746 | if (($eps * $t) * $t > 1) { |
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| 747 | for ($j = $i; $j <= $n; ++$j) { |
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| 748 | $this->H[$j][$n - 1] = $this->H[$j][$n - 1] / $t; |
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| 749 | $this->H[$j][$n] = $this->H[$j][$n] / $t; |
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| 750 | } |
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| 751 | } |
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| 752 | } // end else |
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| 753 | } // end for |
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| 754 | } // end else for complex case |
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| 755 | } // end for |
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| 756 | |||
| 757 | // Vectors of isolated roots |
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| 758 | for ($i = 0; $i < $nn; ++$i) { |
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| 759 | if ($i < $low | $i > $high) { |
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| 760 | for ($j = $i; $j < $nn; ++$j) { |
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| 761 | $this->V[$i][$j] = $this->H[$i][$j]; |
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| 762 | } |
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| 763 | } |
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| 764 | } |
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| 765 | |||
| 766 | // Back transformation to get eigenvectors of original matrix |
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| 767 | for ($j = $nn - 1; $j >= $low; --$j) { |
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| 768 | for ($i = $low; $i <= $high; ++$i) { |
||
| 769 | $z = 0.0; |
||
| 770 | $kMax = min($j, $high); |
||
| 771 | for ($k = $low; $k <= $kMax; ++$k) { |
||
| 772 | $z = $z + $this->V[$i][$k] * $this->H[$k][$j]; |
||
| 773 | } |
||
| 774 | $this->V[$i][$j] = $z; |
||
| 775 | } |
||
| 864 |
