From 040aebd836e0ef162e5e7e8b7b4d5e79a3b9f227 Mon Sep 17 00:00:00 2001
From: Dennis Eichhorn <spl1nes.com@googlemail.com>
Date: Fri, 25 Dec 2015 18:41:48 +0100
Subject: [PATCH] Preparing for differentiation and integration

---
 Math/Differential/FiniteDifference.php | 31 ++++++++++++++++++++++++++
 Math/Integral/Gauss.php                |  0
 Math/Parser/Evaluator.php              |  0
 3 files changed, 31 insertions(+)
 create mode 100644 Math/Differential/FiniteDifference.php
 create mode 100644 Math/Integral/Gauss.php
 create mode 100644 Math/Parser/Evaluator.php

diff --git a/Math/Differential/FiniteDifference.php b/Math/Differential/FiniteDifference.php
new file mode 100644
index 000000000..75ec8090a
--- /dev/null
+++ b/Math/Differential/FiniteDifference.php
@@ -0,0 +1,31 @@
+<?php
+
+class FiniteDifference
+{
+    const EPSILON = 0.00001;
+
+    public static function getNewtonDifferenceQuotient(\string $formula, array $variables, \int $derivative = 1) : \float
+    {
+        return (Evaluator::evaluate($formula, ['x' => $variables['x'] + self::EPSILON]) - Evaluator::evaluate($formula, ['x' => $variables['x']])) / self::EPSILON;
+    }
+
+    public static function getSymmetricDifferenceQuotient(\string $formula, array $variables, \int $derivative = 1) : \float
+    {
+        return (Evaluator::evaluate($formula, ['x' => $variables['x'] + self::EPSILON]) - Evaluator::evaluate($formula, ['x' => $variables['x'] - self::EPSILON])) / (2 * self::EPSILON);
+    }
+
+    public static function getFivePointStencil(\string $formula, array $variables, \int $derivative = 1) : \float
+    {
+        if ($derivative === 1) {
+            return (-Evaluator::evaluate($formula, ['x' => $variables['x'] + 2 * self::EPSILON]) + 8 * Evaluator::evaluate($formula, ['x' => $variables['x'] + self::EPSILON]) - 8 * Evaluator::evaluate($formula, ['x' => $variables['x'] - self::EPSILON]) + Evaluator::evaluate($formula, ['x' => $variables['x'] - 2 * self::EPSILON])) / (12 * self::EPSILON);
+        } elseif ($derivative === 2) {
+            return (-Evaluator::evaluate($formula, ['x' => $variables['x'] + 2 * self::EPSILON]) + 16 * Evaluator::evaluate($formula, ['x' => $variables['x'] + self::EPSILON]) - 30 * Evaluator::evaluate($formula, ['x' => $variables['x']]) + 16 * Evaluator::evaluate($formula, ['x' => $variables['x'] - self::EPSILON]) - Evaluator::evaluate($formula, ['x' => $variables['x'] - 2 * self::EPSILON])) / (12 * self::EPSILON ** 2);
+        } elseif ($derivative === 3) {
+            return (Evaluator::evaluate($formula, ['x' => $variables['x'] + 2 * self::EPSILON]) - 2 * Evaluator::evaluate($formula, ['x' => $variables['x'] + self::EPSILON]) + 2 * Evaluator::evaluate($formula, ['x' => $variables['x'] - self::EPSILON]) - Evaluator::evaluate($formula, ['x' => $variables['x'] - 2 * self::EPSILON])) / (2 * self::EPSILON ** 3);
+        } elseif ($derivative === 4) {
+            return (Evaluator::evaluate($formula, ['x' => $variables['x'] + 2 * self::EPSILON]) - 4 * Evaluator::evaluate($formula, ['x' => $variables['x'] + self::EPSILON]) + 6 * Evaluator::evaluate($formula, ['x' => $variables['x']]) - 4 * Evaluator::evaluate($formula, ['x' => $variables['x'] - self::EPSILON]) + Evaluator::evaluate($formula, ['x' => $variables['x'] - 2 * self::EPSILON])) / (self::EPSILON ** 4);
+        }
+
+        throw new \Exception('Derivative too high');
+    }
+}
diff --git a/Math/Integral/Gauss.php b/Math/Integral/Gauss.php
new file mode 100644
index 000000000..e69de29bb
diff --git a/Math/Parser/Evaluator.php b/Math/Parser/Evaluator.php
new file mode 100644
index 000000000..e69de29bb