77 lines
2.5 KiB
Python
77 lines
2.5 KiB
Python
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import numpy as np
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import matplotlib.pyplot as plt
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import csv
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data = csv.reader(open("fires_thefts.csv"), delimiter=',')
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x = list()
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y = list()
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for xi, yi in data:
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x.append(float(xi))
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y.append(float(yi))
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def h(theta, x):
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return theta[0] + theta[1] * x
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def J(h, theta, x, y):
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"""Funkcja kosztu"""
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m = len(y)
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return 1.0 / (2 * m) * sum((h(theta, x[i]) - y[i]) ** 2 for i in range(m))
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def gradient_descent(h, cost_fun, theta, x, y, alpha, eps):
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current_cost = cost_fun(h, theta, x, y)
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history = [
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[current_cost, theta]
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] # zapiszmy wartości kosztu i parametrów, by potem zrobić wykres
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m = len(y)
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while True:
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new_theta = [
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theta[0] - alpha / float(m) * sum(h(theta, x[i]) - y[i] for i in range(m)),
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theta[1]
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- alpha / float(m) * sum((h(theta, x[i]) - y[i]) * x[i] for i in range(m)),
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]
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theta = new_theta # jednoczesna aktualizacja - używamy zmiennej tymczasowej
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try:
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prev_cost = current_cost
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current_cost = cost_fun(h, theta, x, y)
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except OverflowError:
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break
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if abs(prev_cost - current_cost) <= eps:
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break
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history.append([current_cost, theta])
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return theta, history
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alfa = 0.001
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eps = 0.00001
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best_theta, history = gradient_descent(h, J, [0.0, 0.0], x, y, alfa, eps)
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print("Wynik = ", np.matrix(best_theta), ", J(θ) = %.4f" % history[-1][0], "po %d iteracjach" % len(history))
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print("Wynik dla eps = ", float(eps), ", α = ", alfa)
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print("Predykcja dla 50 pożarów: ", h(best_theta, 50))
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print("Predykcja dla 100 pożarów: ", h(best_theta, 100))
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print("Predykcja dla 200 pożarów: ", h(best_theta, 200))
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best_theta, history_1 = gradient_descent(h, J, [0.0, 0.0], x, y, 0.01, eps)
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best_theta, history_01 = gradient_descent(h, J, [0.0, 0.0], x, y, 0.025, eps)
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best_theta, history_0076 = gradient_descent(h, J, [0.0, 0.0], x, y, 0.0076, eps)
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fig = plt.figure(figsize=(10, 8))
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ax = fig.add_subplot(1, 1, 1)
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ax.set_ylabel('Warto funkcji kosztu J(θ)')
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ax.set_xlabel('Ilość iteracji')
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ax.set_title("Wykres zależności między kosztem a różnymi wartościami α")
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x_axis = np.arange(0, 201, 1)
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y_01 = [history_1[i][0] for i in x_axis]
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y_025 = [history_01[i][0] for i in x_axis]
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y_0076 = [history_0076[i][0] for i in x_axis]
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ax.plot(x_axis, y_01, color='brown', marker="x", label='0.01')
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ax.plot(x_axis, y_025, color='purple', marker="o", label='0.025')
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ax.plot(x_axis, y_0076, color='orange', marker="^", label='0.0076')
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ax.legend()
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plt.axis([0, 180, 0, 10**10])
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plt.show()
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