bhakti-thakur
44 lines
1.0 KiB
Markdown
44 lines
1.0 KiB
Markdown
```
|
|
import numpy as np
|
|
import matplotlib.pyplot as plt
|
|
|
|
|
|
def f(x):
|
|
return (x + 3)**2
|
|
|
|
def grad_f(x):
|
|
return 2 * (x + 3) # derivative of f(x)
|
|
|
|
|
|
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
|
|
|
|
|
|
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}")
|
|
|
|
|
|
print("Local minima at x =", x_current)
|
|
print("Function value at local minima y =", f(x_current))
|
|
|
|
|
|
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()
|
|
``` |