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| 1 | <?php |
| 2 | /** |
| 3 | * Jingga |
| 4 | * |
| 5 | * PHP Version 8.1 |
| 6 | * |
| 7 | * @package phpOMS\Math\Solver\Root |
| 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\Solver\Root; |
| 16 | |
| 17 | /** |
| 18 | * Find the root of a function. |
| 19 | * |
| 20 | * @package phpOMS\Math\Solver\Root |
| 21 | * @license OMS License 2.0 |
| 22 | * @link https://jingga.app |
| 23 | * @since 1.0.0 |
| 24 | */ |
| 25 | final class Illinois |
| 26 | { |
| 27 | /** |
| 28 | * Epsilon for float comparison. |
| 29 | * |
| 30 | * @var float |
| 31 | * @since 1.0.0 |
| 32 | */ |
| 33 | public const EPSILON = 1e-6; |
| 34 | |
| 35 | /** |
| 36 | * Perform bisection to find the root of a function |
| 37 | * |
| 38 | * Iteratively searches for root between two points on the x-axis |
| 39 | * |
| 40 | * @param Callable $func Function defintion |
| 41 | * @param float $a Start value |
| 42 | * @param float $b End value |
| 43 | * @param int $maxIterations Maximum amount of iterations |
| 44 | * |
| 45 | * @throws \Exception |
| 46 | * |
| 47 | * @return float |
| 48 | * |
| 49 | * @since 1.0.0 |
| 50 | */ |
| 51 | public static function root(callable $func, float $a, float $b, int $maxIterations = 100) : float |
| 52 | { |
| 53 | if ($func($a) * $func($b) >= 0) { |
| 54 | throw new \Exception("Function values at endpoints must have opposite signs."); |
| 55 | } |
| 56 | |
| 57 | $c = $b; |
| 58 | $iteration = 0; |
| 59 | $sign = 1; |
| 60 | |
| 61 | while (($y = \abs($func($c))) > self::EPSILON && $iteration < $maxIterations) { |
| 62 | $fa = $func($a); |
| 63 | $fb = $func($b); |
| 64 | |
| 65 | if ($y === 0.0) { |
| 66 | return $c; |
| 67 | } |
| 68 | |
| 69 | // @todo: c might be wrong, could be that if and else must be switched |
| 70 | // @see https://en.wikipedia.org/wiki/Regula_falsi#The_Illinois_algorithm |
| 71 | if ($y * $fa < 0) { |
| 72 | $c = $sign === (int) ($y >= 0) |
| 73 | ? (0.5 * $a * $fb - $b * $fa) / (0.5 * $fb - $fa) |
| 74 | : ($a * $fb - $b * $fa) / ($fb - $fa); |
| 75 | |
| 76 | $b = $c; |
| 77 | } else { |
| 78 | $c = $sign === (int) ($y >= 0) |
| 79 | ? ($a * $fb - 0.5 * $b * $fa) / ($fb - 0.5 * $fa) |
| 80 | : ($a * $fb - $b * $fa) / ($fb - $fa); |
| 81 | |
| 82 | $a = $c; |
| 83 | } |
| 84 | |
| 85 | $sign = (int) ($y > 0); |
| 86 | |
| 87 | ++$iteration; |
| 88 | } |
| 89 | |
| 90 | return ($a + $b) / 2; |
| 91 | } |
| 92 | } |