feat: added newton's method

rf_methods.py

@@ -2,8 +2,8 @@ import numpy as np
 from typing import Callable
 
 
-def f(x: float) -> float:
-    return x ** 4 + x ** 3 + x ** 2 - 1
+# def f(x: float) -> float:
+#     return x ** 4 + x ** 3 + x ** 2 - 1
 
 
 def g(x: float) -> float:
@@ -91,7 +91,7 @@ def iter_bisection(init_start: float, init_stop: float, func:
 
     iter = 0
 
-    while np.abs(stop - start) > 1e-9:
+    while np.abs(stop - start) > 1e-8:
         if debug:
             print(f"Iter = {iter}\tx = {cN}\tf(x) = {func(cN)}")
 
@@ -107,12 +107,38 @@ def iter_bisection(init_start: float, init_stop: float, func:
     return cN
 
 
+def iter_newton_raphson(init_guess: float, f: Callable[[float], float],
+                        dfdx: Callable[[float], float], debug: bool) -> float:
+
+    prev = init_guess
+    curr = init_guess
+
+    iter = 0
+
+    while np.abs(f(curr)) > 1e-9:
+        if debug:
+            print(f"Iter = {iter}\tx = {curr}\tf(x) = {f(curr)}")
+        curr = prev - f(prev) / dfdx(prev)
+        prev = curr
+        iter += 1
+
+    return curr
+
+
 if __name__ == "__main__":
     # print(f"Bissection = {bissect_method(0.5, 2, g)}")
     # print(f"Regula falsi = {regula_falsi(-3, 7, h)}")
     # print(f"Bissection = {bissect_method(-3, 7, h)}")
     # print(f"Regula falsi = {rec_regula_falsi(0, 3, z)}")
-    print(f"Iter bisection= {iter_bisection(0.5, 2, g, False)}")
-    print(f"Rec bisection= {rec_bisection(0.5, 2, g, False)}")
-    print(f"Iter regula falsi= {iter_regula_falsi(0.5, 2, g, False)}")
-    print(f"Rec regula falsi = {rec_regula_falsi(0.5, 2, g, False)}")
+    # print(f"Iter bisection= {iter_bisection(0.5, 2, g, False)}")
+    # print(f"Rec bisection= {rec_bisection(0.5, 2, g, False)}")
+    # print(f"Iter regula falsi= {iter_regula_falsi(0.5, 2, g, False)}")
+    # print(f"Rec regula falsi = {rec_regula_falsi(0.5, 2, g, False)}")
+
+    def f(x):
+        return x ** 3 - 2 * x ** 2 + 1
+
+    def fprime(x):
+        return 3 * x ** 2 - 4 * x + 1
+
+    print(f"Newton = {iter_newton_raphson(0, f, fprime, True)}")