Newton's method

newtons-method.py

@@ -0,0 +1,26 @@
+#!/usr/bin/python
+from __future__ import division, print_function
+from math import pow
+import random
+
+epsilon = 1e-09
+
+def derive(function, x):
+    """Poor man's numerical derivation."""
+    return (function(x+epsilon)-function(x-epsilon))/(2*epsilon)
+
+def newton(function, x_0, max_i=50):
+    """Find a real root of a function using Newton's method."""
+    x = x_0
+    for i in range(max_i):
+        x = x - (function(x)/derive(function, x))
+        print('f({}) = {}'.format(x, function(x)))
+        if abs(function(x)) < epsilon:
+            return x
+            break
+    else:
+        return x
+
+
+print(newton(lambda x: x**4 + 3*x - 1, x_0=100*random.random()))
+#print(newton(lambda x: pow(x, 0.333), x_0=100*random.random()))