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