| |
|
|
| import numpy as np |
| import pandas as pd |
| from scipy.optimize import linprog |
| from statsmodels.tsa.arima.model import ARIMA |
| import matplotlib.pyplot as plt |
|
|
| def run_math_analysis(topic: str): |
| if topic == "linear_algebra": |
| linear_algebra_demo() |
| elif topic == "probability": |
| probability_demo() |
| elif topic == "optimization": |
| optimization_demo() |
| elif topic == "game_theory": |
| game_theory_demo() |
| elif topic == "time_series": |
| time_series_demo() |
| elif topic == "markov": |
| markov_process_demo() |
| else: |
| print("❌ Unknown topic. Available: linear_algebra, probability, optimization, game_theory, time_series, markov") |
|
|
| def linear_algebra_demo(): |
| print("📐 Linear Algebra: Matrix-Vector Multiplication") |
| A = np.array([[1, 2], [3, 4]]) |
| B = np.array([[2], [1]]) |
| result = np.dot(A, B) |
| print("Matrix A:\n", A) |
| print("Vector B:\n", B) |
| print("A · B:\n", result) |
|
|
| def probability_demo(): |
| print("📊 Probability & Bayesian Inference Example") |
| prior = 0.3 |
| likelihood = 0.8 |
| evidence = 0.6 |
| posterior = (likelihood * prior) / evidence |
| print(f"Bayesian Posterior = P(H|E) = {posterior:.2f}") |
|
|
| def optimization_demo(): |
| print("🔧 Optimization: Linear Programming (Maximize 3x + 5y)") |
| c = [-3, -5] |
| A = [[1, 0], [0, 2], [3, 2]] |
| b = [4, 12, 18] |
| result = linprog(c, A_ub=A, b_ub=b) |
| if result.success: |
| print("Optimal values of x and y:", result.x) |
| print("Maximum value of objective function:", -result.fun) |
| else: |
| print("❌ Optimization failed:", result.message) |
|
|
| def game_theory_demo(): |
| print("🎲 Game Theory: Payoff Matrix") |
| matrix = np.array([[3, 0], [5, 1]]) |
| print("Player A vs Player B Payoff Matrix:") |
| print(matrix) |
| print("Interpret rows as Player A strategies and columns as Player B.") |
|
|
| def time_series_demo(): |
| print("📈 Time Series: ARIMA(1,1,1) Forecast") |
| np.random.seed(42) |
| series = pd.Series(np.random.randn(100).cumsum()) |
| model = ARIMA(series, order=(1, 1, 1)) |
| fit = model.fit() |
| forecast = fit.forecast(steps=10) |
| print("Forecasted next 10 values:") |
| print(forecast) |
|
|
| series.plot(label="Historical") |
| forecast.plot(label="Forecast", legend=True) |
| plt.title("Time Series Forecast (ARIMA)") |
| plt.xlabel("Time") |
| plt.ylabel("Value") |
| plt.grid(True) |
| plt.show() |
|
|
| def markov_process_demo(): |
| print("🔁 Markov Chain Simulation: Sunny vs Rainy") |
| transition_matrix = np.array([[0.9, 0.1], [0.5, 0.5]]) |
| state = np.array([1, 0]) |
| for day in range(5): |
| state = np.dot(state, transition_matrix) |
| print(f"Day {day + 1}: P(Sunny) = {state[0]:.2f}, P(Rainy) = {state[1]:.2f}") |
|
|
