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