Added 'Newton method' for interpolation

Author: cfgnunes

README.md

@@ -51,6 +51,7 @@ python3 main.py
 ### Interpolation
 
 - Lagrange method
+- Newton method
 - Neville method
 
 ### Algorithms for polynomials

interpolation.py

@@ -27,6 +27,33 @@ def lagrange(x, y, x_int):
     return [y_int]
 
 
+def newton(x, y, x_int):
+    """Interpolates a value using the 'Newton polynomial'.
+
+    Args:
+        x (numpy.ndarray): x values.
+        y (numpy.ndarray): y values.
+        x_int (float): value to interpolate.
+
+    Returns:
+        y_int (float): interpolated value.
+    """
+    m = x.size
+    del_y = y.copy()
+
+    # Calculate the divided differences
+    for k in range(1, m):
+        for i in range(m - 1, k - 1, -1):
+            del_y[i] = (del_y[i] - del_y[i - 1]) / (x[i] - x[i - k])
+
+    # Evaluate the Newton polynomial
+    y_int = del_y[-1]
+    for i in range(m - 2, -1, -1):
+        y_int = y_int * (x_int - x[i]) + del_y[i]
+
+    return [y_int]
+
+
 def neville(x, y, x_int):
     """Interpolates a value using the 'Neville polynomial'.
 

main.py

@@ -239,6 +239,24 @@ def run_example_lagrange():
     print(f"y_int = {y_int:.5f}")
 
 
+@print_docstring
+def run_interpolation_newton():
+    """Run an example 'Interpolation: Newton'."""
+    x = np.array([0.1, 0.3, 0.4, 0.6, 0.7])
+    y = np.array([0.3162, 0.5477, 0.6325, 0.7746, 0.8367])
+    x_int = 0.2
+
+    print("Inputs:")
+    print(f"x = {x}")
+    print(f"y = {y}")
+    print(f"x_int = {x_int}")
+
+    [y_int] = interpolation.newton(x, y, x_int)
+
+    print("Output:")
+    print(f"y_int = {y_int:.5f}")
+
+
 @print_docstring
 def run_example_neville():
     """Run an example 'Interpolation: Neville'."""
@@ -679,6 +697,7 @@ def main():
     run_example_muller()
     run_example_newton()
     run_example_lagrange()
+    run_interpolation_newton()
     run_example_neville()
     run_example_root_limits()
     run_example_briot_ruffini()