Updated code as per PR feedback 8

Author: prajwal-38

machine_learning/ridge_regression.py

@@ -1,13 +1,11 @@
+
 import numpy as np
 from matplotlib import pyplot as plt
 from sklearn import datasets
 
-
 # Ridge Regression function
 # reference : https://en.wikipedia.org/wiki/Ridge_regression
-def ridge_cost_function(
-    x: np.ndarray, y: np.ndarray, theta: np.ndarray, alpha: float
-) -> float:
+def ridge_cost_function(x: np.ndarray, y: np.ndarray, theta: np.ndarray, alpha: float) -> float:
     """
     Compute the Ridge regression cost function with L2 regularization.
 
@@ -29,21 +27,12 @@ def ridge_cost_function(
     """
     m = len(y)
     predictions = np.dot(x, theta)
-    cost = (1 / (2 * m)) * np.sum((predictions - y) ** 2) + (alpha / 2) * np.sum(
-        theta[1:] ** 2
-    )
+    cost = (1 / (2 * m)) * np.sum((predictions - y) ** 2) + \
+        (alpha / 2) * np.sum(theta[1:] ** 2)
 
     return cost
 
-
-def ridge_gradient_descent(
-    x: np.ndarray,
-    y: np.ndarray,
-    theta: np.ndarray,
-    alpha: float,
-    learning_rate: float,
-    max_iterations: int,
-) -> np.ndarray:
+def ridge_gradient_descent(x: np.ndarray, y: np.ndarray, theta: np.ndarray, alpha: float, learning_rate: float, max_iterations: int) -> np.ndarray:
     """
     Perform gradient descent to minimize the
     cost function and fit the Ridge regression model.
@@ -74,10 +63,8 @@ def ridge_gradient_descent(
 
     return theta
 
-
 if __name__ == "__main__":
     import doctest
-
     doctest.testmod()
 
     # Load California Housing dataset
@@ -97,9 +84,7 @@ def ridge_gradient_descent(
     learning_rate = 0.01
     max_iterations = 1000
 
-    optimized_theta = ridge_gradient_descent(
-        x, y, theta_initial, alpha, learning_rate, max_iterations
-    )
+    optimized_theta = ridge_gradient_descent(x, y, theta_initial, alpha, learning_rate, max_iterations)
     print(f"Optimized theta: {optimized_theta}")
 
     # Prediction
@@ -110,10 +95,11 @@ def predict(x, theta):
 
     # Plotting the results (here we visualize predicted vs actual values)
     plt.figure(figsize=(10, 6))
-    plt.scatter(y, y_pred, color="b", label="Predictions vs Actual")
-    plt.plot([min(y), max(y)], [min(y), max(y)], color="r", label="Perfect Fit")
+    plt.scatter(y, y_pred, color='b', label='Predictions vs Actual')
+    plt.plot([min(y), max(y)], [min(y), max(y)], color='r', label='Perfect Fit')
     plt.xlabel("Actual values")
     plt.ylabel("Predicted values")
     plt.title("Ridge Regression: Actual vs Predicted Values")
     plt.legend()
     plt.show()
+