From 2de8ca64323af3577f10daee745ba763740e46d7 Mon Sep 17 00:00:00 2001
From: teridax <sven.vogel123@web.de>
Date: Tue, 25 Apr 2023 19:18:06 +0200
Subject: [PATCH] added zero point approximation

---
 main.py                              | 10 ++++++---
 newton_polynom/__init__.py           | 14 +++++++-----
 zero_point_approximation/__init__.py | 33 ++++++++++++++++++++++++++++
 3 files changed, 49 insertions(+), 8 deletions(-)
 create mode 100644 zero_point_approximation/__init__.py

diff --git a/main.py b/main.py
index fc9947e..e6d3e2a 100644
--- a/main.py
+++ b/main.py
@@ -17,7 +17,11 @@
 import fixpoint_approximation
 import linear_approximation
 import newton_polynom
+import zero_point_approximation
 
-# linear_approximation.test()
-# fixpoint_approximation.test()
-newton_polynom.test()
+
+if __name__ == '__main__':
+    linear_approximation.test()
+    fixpoint_approximation.test()
+    newton_polynom.test()
+    zero_point_approximation.test()
diff --git a/newton_polynom/__init__.py b/newton_polynom/__init__.py
index 6620b2b..936fc20 100644
--- a/newton_polynom/__init__.py
+++ b/newton_polynom/__init__.py
@@ -28,18 +28,22 @@ def combine_n(points):
 # returns a polynom that will intersect all supplied points as long as
 # the number of points is bigger than 1
 def newton_polynom(points):
+    polynom = ""
     for x in range(1, len(points)):
 
         if x == 1:
-            print(points[0][1], end=' + ')
+            polynom += '{r0:.2f} + '.format(r0=points[0][1])
         else:
-            print(end=' + ')
+            polynom += ' + '
 
-        print(combine_n(points[0:(x + 1)]), end='')
+        polynom += "{r:.2f}".format(r=combine_n(points[0:(x + 1)]))
 
         for y in range(x):
-            print(" * (x - {value:.2f})".format(value=points[y][0]), end='')
+            polynom += " * (x - {value:.2f})".format(value=points[y][0])
+
+    return polynom
 
 
 def test():
-    newton_polynom([[-1, 5], [2, -1], [3, -1], [4, 5], [8, 9]])
+    points = [[-1, 5], [2, -1], [3, -1], [4, 5], [8, 9]]
+    print("newton polynom: ", newton_polynom(points))
diff --git a/zero_point_approximation/__init__.py b/zero_point_approximation/__init__.py
new file mode 100644
index 0000000..308c996
--- /dev/null
+++ b/zero_point_approximation/__init__.py
@@ -0,0 +1,33 @@
+# Python module for approximating a zero point of any given function
+#                _ _   _               _
+# __      ___ __(_) |_| |_ ___ _ __   | |__  _   _
+# \ \ /\ / / '__| | __| __/ _ \ '_ \  | '_ \| | | |
+#  \ V  V /| |  | | |_| ||  __/ | | | | |_) | |_| |
+#   \_/\_/ |_|  |_|\__|\__\___|_| |_| |_.__/ \__, |
+#                                            |___/
+#  ____                  __     __               _
+# / ___|_   _____ _ __   \ \   / /__   __ _  ___| |
+# \___ \ \ / / _ \ '_ \   \ \ / / _ \ / _` |/ _ \ |
+#  ___) \ V /  __/ | | |   \ V / (_) | (_| |  __/ |
+# |____/ \_/ \___|_| |_|    \_/ \___/ \__, |\___|_|
+#                                     |___/
+# Licensed under the GPLv2 License, Version 2.0 (the "License");
+# Copyright (c) Sven Vogel
+
+def zero_point_approximation(interval, function, iterations):
+    for _ in range(iterations):
+        median = interval[1] - (interval[1] - interval[0]) / 2
+        if function(median) > 0:
+            interval[1] = median
+        else:
+            interval[0] = median
+
+    return interval
+
+
+def f(x):
+    return 4 * x * x * x - 7 * x * x + 5 * x - 12
+
+
+def test():
+    print("Zero-point approximation: ", zero_point_approximation(interval=[-9, 9], function=f, iterations=15))