SciPy Tutorial (Enhanced)

# ===== 1. SciPy Installation =====
# pip install scipy
import numpy as np
from scipy import integrate, optimize, linalg, stats, signal

# ===== 2. Integration (Calculus) =====
print("===== Integration =====")

# f(x) = x^2 ကို 0 မှ 1 အထိ integrate
result, error = integrate.quad(lambda x: x**2, 0, 1)
print(f"∫ x² dx (0 to 1) = {result:.4f}")

# ===== 3. Optimization =====
print(f"\n===== Optimization =====")

# f(x) = x^2 + 2x + 1 ကို minimize
func = lambda x: x[0]**2 + 2*x[0] + 1
result = optimize.minimize(func, [0])
print(f"Minimum at x = {result.x[0]:.4f}")

# ===== 4. Linear Algebra =====
print(f"\n===== Linear Algebra =====")

A = np.array([[3, 2], [1, 4]])
b = np.array([7, 5])
x = linalg.solve(A, b)
print(f"Solution: {x}")

# ===== 5. Statistics =====
print(f"\n===== Statistics =====")

data = [2, 4, 4, 4, 5, 5, 7, 9]
print(f"Mean: {np.mean(data)}")
print(f"Median: {np.median(data)}")
mode_result = stats.mode(data, keepdims=True)
print(f"Mode: {mode_result.mode[0]}")
print(f"Std Dev: {np.std(data):.4f}")

# ===== 6. Signal Processing =====
print(f"\n===== Signal Processing =====")

t = np.linspace(0, 1, 500)
sig = np.sin(2 * np.pi * 10 * t)
freq, power = signal.periodogram(sig)
print(f"Frequencies (first 5): {freq[:5]}")

# ===== 7. Use Cases =====
print(f"\n===== Real-World Use Cases =====")
print("✅ Engineering → signal processing, control systems")
print("✅ Physics → calculus, integration, differential equations")
print("✅ Data science → statistics, probability distributions")
print("✅ Machine learning → optimization, linear algebra")