From a0d06838c2e304a96fadfd068f363cf19085f85c Mon Sep 17 00:00:00 2001
From: Kshitij <notkshitij@git.kska.io>
Date: Sun, 2 Nov 2025 23:34:41 +0530
Subject: [PATCH] Added code for practical A4 in markdown format.

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+# Practical-A3 (Gradient Descent Algorithm)
+
+Problem Statement: Implement Gradient Descent Algorithm to find the local minima of a function. For example, find the local minima of the function y=(x+3)² starting from the point x=2.
+
+---
+ 
+## Steps
+
+1. Define the function and its derivative
+2. Initialize parameters for Gradient Descent
+3. Gradient Descent Loop
+4. Print the result
+5. Plotting
+
+---
+
+## Code
+
+0. Import libraries:
+
+```python3
+import numpy as np
+import matplotlib.pyplot as plt
+```
+
+1. Define the function and its derivative:
+
+```python3
+def f(x):
+    return (x + 3)**2
+
+def grad_f(x):
+    return 2 * (x + 3)  # derivative of f(x)
+```
+
+2. Initialize parameters for Gradient Descent:
+
+```python3
+x_current = 2          # starting point
+learning_rate = 0.1    # step size
+tolerance = 1e-6       # convergence tolerance
+max_iterations = 25    # maximum iterations
+history = [x_current]  # sotring history
+```
+
+3. Gradient Descent Loop:
+
+```python3
+for i in range(max_iterations):
+    gradient = grad_f(x_current)
+    x_next = x_current - learning_rate * gradient  # update step
+    
+    # Check convergence
+    if abs(x_next - x_current) < tolerance:
+        print(f"Converged after {i+1} iterations.")
+        break
+    
+    x_current = x_next
+    history.append(x_current)
+    print(f"Iteration {i+1}: x = {x_current:.4f}, f(x) = {f(x_current):.4f}")
+```
+
+4. Print the result:
+
+```python3
+print("Local minima at x =", x_current)
+print("Function value at local minima y =", f(x_current))
+```
+
+5. Plotting:
+
+```python3
+plt.plot(history, [f(val) for val in history], marker='o')
+plt.xlabel("x values")
+plt.ylabel("f(x)")
+plt.title("Gradient Descent Convergence")
+plt.grid()
+plt.show()
+```
+
+---
+