From 7310527c78c9b8b12cde9316fa70bf7e1da10792 Mon Sep 17 00:00:00 2001
From: teridax <sven.vogel123@web.de>
Date: Tue, 25 Apr 2023 15:37:03 +0200
Subject: [PATCH] added several modules

---
 fixpoint_approximation/__init__.py | 34 +++++++++++++++++++++++++
 linear_approximation/__init__.py   | 28 +++++++++++++++++++++
 main.py                            | 23 +++++++++++++++++
 newton_polynom/__init__.py         | 40 ++++++++++++++++++++++++++++++
 4 files changed, 125 insertions(+)
 create mode 100644 fixpoint_approximation/__init__.py
 create mode 100644 linear_approximation/__init__.py
 create mode 100644 main.py
 create mode 100644 newton_polynom/__init__.py

diff --git a/fixpoint_approximation/__init__.py b/fixpoint_approximation/__init__.py
new file mode 100644
index 0000000..a316fd2
--- /dev/null
+++ b/fixpoint_approximation/__init__.py
@@ -0,0 +1,34 @@
+# Python module for approximating the fixpoint of special linear functions
+#                _ _   _               _
+# __      ___ __(_) |_| |_ ___ _ __   | |__  _   _
+# \ \ /\ / / '__| | __| __/ _ \ '_ \  | '_ \| | | |
+#  \ V  V /| |  | | |_| ||  __/ | | | | |_) | |_| |
+#   \_/\_/ |_|  |_|\__|\__\___|_| |_| |_.__/ \__, |
+#                                            |___/
+#  ____                  __     __               _
+# / ___|_   _____ _ __   \ \   / /__   __ _  ___| |
+# \___ \ \ / / _ \ '_ \   \ \ / / _ \ / _` |/ _ \ |
+#  ___) \ V /  __/ | | |   \ V / (_) | (_| |  __/ |
+# |____/ \_/ \___|_| |_|    \_/ \___/ \__, |\___|_|
+#                                     |___/
+# Licensed under the GPLv2 License, Version 2.0 (the "License");
+# Copyright (c) Sven Vogel
+
+
+# iteratively approximate the fixpoint of specific linear functions
+def fixpoint_approximation(start, function, iterations):
+    x = start
+    for _ in range(iterations):
+        x = function(x)
+
+    return x
+
+
+# in order to work the linear function has to be in the form:
+# ]-1.0, 1.0[ * x + k
+def linear_function(x):
+    return 0.25 * x - 3
+
+
+def test():
+    print("fixpoint approximation: ", fixpoint_approximation(start=1.0, function=linear_function, iterations=400))
diff --git a/linear_approximation/__init__.py b/linear_approximation/__init__.py
new file mode 100644
index 0000000..4137a44
--- /dev/null
+++ b/linear_approximation/__init__.py
@@ -0,0 +1,28 @@
+# Python module for linearly approximating the derivative of any function
+#                _ _   _               _
+# __      ___ __(_) |_| |_ ___ _ __   | |__  _   _
+# \ \ /\ / / '__| | __| __/ _ \ '_ \  | '_ \| | | |
+#  \ V  V /| |  | | |_| ||  __/ | | | | |_) | |_| |
+#   \_/\_/ |_|  |_|\__|\__\___|_| |_| |_.__/ \__, |
+#                                            |___/
+#  ____                  __     __               _
+# / ___|_   _____ _ __   \ \   / /__   __ _  ___| |
+# \___ \ \ / / _ \ '_ \   \ \ / / _ \ / _` |/ _ \ |
+#  ___) \ V /  __/ | | |   \ V / (_) | (_| |  __/ |
+# |____/ \_/ \___|_| |_|    \_/ \___/ \__, |\___|_|
+#                                     |___/
+# Licensed under the GPLv2 License, Version 2.0 (the "License");
+# Copyright (c) Sven Vogel
+
+# linearly approximate a functions derivative in an interval
+def linear_approximate(interval, function):
+    return (function(interval[1]) - function(interval[0])) / (interval[1] - interval[0])
+
+
+# function to linearly approximate
+def f(x):
+    return 3 + x * x - 5 * x
+
+
+def test():
+    print("linear approximation: ", linear_approximate([2.0, 3.0], f))
diff --git a/main.py b/main.py
new file mode 100644
index 0000000..fc9947e
--- /dev/null
+++ b/main.py
@@ -0,0 +1,23 @@
+# Python file for testing various approximation algorithms
+#                _ _   _               _
+# __      ___ __(_) |_| |_ ___ _ __   | |__  _   _
+# \ \ /\ / / '__| | __| __/ _ \ '_ \  | '_ \| | | |
+#  \ V  V /| |  | | |_| ||  __/ | | | | |_) | |_| |
+#   \_/\_/ |_|  |_|\__|\__\___|_| |_| |_.__/ \__, |
+#                                            |___/
+#  ____                  __     __               _
+# / ___|_   _____ _ __   \ \   / /__   __ _  ___| |
+# \___ \ \ / / _ \ '_ \   \ \ / / _ \ / _` |/ _ \ |
+#  ___) \ V /  __/ | | |   \ V / (_) | (_| |  __/ |
+# |____/ \_/ \___|_| |_|    \_/ \___/ \__, |\___|_|
+#                                     |___/
+# Licensed under the GPLv2 License, Version 2.0 (the "License");
+# Copyright (c) Sven Vogel
+
+import fixpoint_approximation
+import linear_approximation
+import newton_polynom
+
+# linear_approximation.test()
+# fixpoint_approximation.test()
+newton_polynom.test()
diff --git a/newton_polynom/__init__.py b/newton_polynom/__init__.py
new file mode 100644
index 0000000..f71e814
--- /dev/null
+++ b/newton_polynom/__init__.py
@@ -0,0 +1,40 @@
+# Python module for calculating the newton polynom from given points
+#                _ _   _               _
+# __      ___ __(_) |_| |_ ___ _ __   | |__  _   _
+# \ \ /\ / / '__| | __| __/ _ \ '_ \  | '_ \| | | |
+#  \ V  V /| |  | | |_| ||  __/ | | | | |_) | |_| |
+#   \_/\_/ |_|  |_|\__|\__\___|_| |_| |_.__/ \__, |
+#                                            |___/
+#  ____                  __     __               _
+# / ___|_   _____ _ __   \ \   / /__   __ _  ___| |
+# \___ \ \ / / _ \ '_ \   \ \ / / _ \ / _` |/ _ \ |
+#  ___) \ V /  __/ | | |   \ V / (_) | (_| |  __/ |
+# |____/ \_/ \___|_| |_|    \_/ \___/ \__, |\___|_|
+#                                     |___/
+# Licensed under the GPLv2 License, Version 2.0 (the "License");
+# Copyright (c) Sven Vogel
+
+def combine(p0, p1):
+    return (p1[1] - p1[0]) / (p0[1] - p0[0])
+
+
+def combine_n(*points):
+    k = len(points) - 1
+
+    if k == 1:
+        return combine(points[0], points[1])
+    else:
+        return (combine_n(points[1:k]) - combine_n(points[0:(k - 1)])) / (points[k][0] - points[0][0])
+
+
+def newton_polynom(*points):
+    for x in range(len(points)):
+
+        print(combine_n(points[0:x]))
+
+        for y in range(x):
+            print(format(" * (x - %s)", points[y][0]))
+
+
+def test():
+    newton_polynom([1, 2], [3, 4], [9, -5])