Equation solvers

Math/Solver/Root/Bisection.php

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+<?php
+/**
+ * Jingga
+ *
+ * PHP Version 8.1
+ *
+ * @package   phpOMS\Math\Solver\Root
+ * @copyright Dennis Eichhorn
+ * @license   OMS License 2.0
+ * @version   1.0.0
+ * @link      https://jingga.app
+ */
+declare(strict_types=1);
+
+namespace phpOMS\Math\Solver\Root;
+
+/**
+ * Basic math function evaluation.
+ *
+ * @package phpOMS\Math\Solver\Root
+ * @license OMS License 2.0
+ * @link    https://jingga.app
+ * @since   1.0.0
+ *
+ * @todo: implement
+ */
+final class Bisection
+{
+    public const EPSILON = 1e-6;
+
+    public static function bisection(Callable $func, float $a, float $b, $maxIterations = 100) {
+        if ($func($a) * $func($b) >= 0) {
+            throw new \Exception("Function values at endpoints must have opposite signs.");
+        }
+
+        $iteration = 0;
+        while (($b - $a) / 2 > self::EPSILON && $iteration < $maxIterations) {
+            $c = ($a + $b) / 2;
+
+            $y = $func($c);
+
+            if ($y === 0.0) {
+                return $c;
+            }
+
+            if ($y * $func($a) < 0) {
+                $b = $c;
+            } else {
+                $a = $c;
+            }
+
+            ++$iteration;
+        }
+
+        return ($a + $b) / 2;
+    }
+}

Math/Solver/Root/Illinois.php

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+<?php
+/**
+ * Jingga
+ *
+ * PHP Version 8.1
+ *
+ * @package   phpOMS\Math\Solver\Root
+ * @copyright Dennis Eichhorn
+ * @license   OMS License 2.0
+ * @version   1.0.0
+ * @link      https://jingga.app
+ */
+declare(strict_types=1);
+
+namespace phpOMS\Math\Solver\Root;
+
+/**
+ * Basic math function evaluation.
+ *
+ * @package phpOMS\Math\Solver\Root
+ * @license OMS License 2.0
+ * @link    https://jingga.app
+ * @since   1.0.0
+ *
+ * @todo: implement
+ */
+final class Illinois
+{
+    public const EPSILON = 1e-6;
+
+    public static function bisection(Callable $func, float $a, float $b, $maxIterations = 100) {
+        if ($func($a) * $func($b) >= 0) {
+            throw new \Exception("Function values at endpoints must have opposite signs.");
+        }
+
+        $c = $b;
+        $iteration = 0;
+        $sign = 1;
+
+        while (($y = \abs($func($c))) > self::EPSILON && $iteration < $maxIterations) {
+            $fa = $func($a);
+            $fb = $func($b);
+
+            if ($y === 0.0) {
+                return $c;
+            }
+
+            // @todo: c might be wrong, could be that if and else must be switched
+            // @see https://en.wikipedia.org/wiki/Regula_falsi#The_Illinois_algorithm
+            if ($y * $fa < 0) {
+                $c = $sign === (int) ($y >= 0)
+                    ? (0.5 * $a * $fb - $b * $fa) / (0.5 * $fb - $fa)
+                    : ($a * $fb - $b * $fa) / ($fb - $fa);
+
+                $b = $c;
+            } else {
+                $c = $sign === (int) ($y >= 0)
+                    ? ($a * $fb - 0.5 * $b * $fa) / ($fb - 0.5 * $fa)
+                    : ($a * $fb - $b * $fa) / ($fb - $fa);
+
+                $a = $c;
+            }
+
+            $sign = (int) ($y > 0);
+
+            ++$iteration;
+        }
+
+        return ($a + $b) / 2;
+    }
+}

Math/Solver/Root/RegulaFalsi.php

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+<?php
+/**
+ * Jingga
+ *
+ * PHP Version 8.1
+ *
+ * @package   phpOMS\Math\Solver\Root
+ * @copyright Dennis Eichhorn
+ * @license   OMS License 2.0
+ * @version   1.0.0
+ * @link      https://jingga.app
+ */
+declare(strict_types=1);
+
+namespace phpOMS\Math\Solver\Root;
+
+/**
+ * Basic math function evaluation.
+ *
+ * @package phpOMS\Math\Solver\Root
+ * @license OMS License 2.0
+ * @link    https://jingga.app
+ * @since   1.0.0
+ *
+ * @todo: implement
+ */
+final class RegulaFalsi
+{
+    public const EPSILON = 1e-6;
+
+    public static function bisection(Callable $func, float $a, float $b, $maxIterations = 100) {
+        if ($func($a) * $func($b) >= 0) {
+            throw new \Exception("Function values at endpoints must have opposite signs.");
+        }
+
+        $c = $b;
+        $iteration = 0;
+
+        while (($y = \abs($func($c))) > self::EPSILON && $iteration < $maxIterations) {
+            $fa = $func($a);
+            $fb = $func($b);
+
+            $c = ($a * $fb - $b * $fa) / ($fb - $fa);
+
+            if ($y === 0.0) {
+                return $c;
+            }
+
+            if ($y * $fa < 0) {
+                $b = $c;
+            } else {
+                $a = $c;
+            }
+
+            ++$iteration;
+        }
+
+        return ($a + $b) / 2;
+    }
+}