From fde31c93a3f7fc16547c217ae5cfbacef503c46d Mon Sep 17 00:00:00 2001
From: billpaps <37051006+billpaps@users.noreply.github.com>
Date: Tue, 11 Feb 2020 10:20:24 +0200
Subject: [PATCH] Added Bisection algorithm (#1739)

* Create Bisection.py

Find root of

* Update Bisection.py

* Update Bisection.py

i changed the given function with one that i could make the doctests.

* Rename Bisection.py to bisection.py

* Update bisection.py

* Update bisection.py

* Update bisection.py

* Update bisection.py

* Update bisection.py

Made the changes that were requested

* Update bisection.py

* Update bisection.py

* Add wiki url

Co-authored-by: Christian Clauss <cclauss@me.com>
---
 maths/bisection.py | 61 ++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 61 insertions(+)
 create mode 100644 maths/bisection.py

diff --git a/maths/bisection.py b/maths/bisection.py
new file mode 100644
index 000000000..a9df15b77
--- /dev/null
+++ b/maths/bisection.py
@@ -0,0 +1,61 @@
+"""
+Given a function on floating number f(x) and two floating numbers ‘a’ and ‘b’ such that
+f(a) * f(b) < 0 and f(x) is continuous in [a, b].
+Here f(x) represents algebraic or transcendental equation.
+Find root of function in interval [a, b] (Or find a value of x such that f(x) is 0)
+
+https://en.wikipedia.org/wiki/Bisection_method
+"""
+def equation(x: float) -> float:
+    """
+    >>> equation(5)
+    -15
+    >>> equation(0)
+    10
+    >>> equation(-5)
+    -15
+    >>> equation(0.1)
+    9.99
+    >>> equation(-0.1)
+    9.99
+    """
+    return 10 - x * x
+
+
+def bisection(a: float, b: float) -> float:
+    """
+    >>> bisection(-2, 5)
+    3.1611328125
+    >>> bisection(0, 6)
+    3.158203125
+    >>> bisection(2, 3)
+    Traceback (most recent call last):
+    ...
+    ValueError: Wrong space!
+    """
+    # Bolzano theory in order to find if there is a root between a and b
+    if equation(a) * equation(b) >= 0:
+        raise ValueError("Wrong space!")
+
+    c = a
+    while (b - a) >= 0.01:
+        # Find middle point
+        c = (a + b) / 2
+        # Check if middle point is root
+        if equation(c) == 0.0:
+            break
+        # Decide the side to repeat the steps
+        if equation(c) * equation(a) < 0:
+            b = c
+        else:
+            a = c
+    return c
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+
+    print(bisection(-2, 5))
+    print(bisection(0, 6))