142 lines
3.2 KiB
Python
142 lines
3.2 KiB
Python
import numpy as np
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def point_info(x, f):
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return f'x = {x}, f(x) = {f(x)}'
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def hooke_jeeves(f, x0, delta0, epsilon, alpha):
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x = np.array(x0)
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delta = np.array(delta0)
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iteration = 0
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while np.linalg.norm(delta) > epsilon:
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iteration += 1
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print()
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print('=' * 40)
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print('Итерация', iteration)
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print('Текущая базовая точка', point_info(x, f))
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sample_x = exploratory_search(f, x, delta)
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if f(sample_x) < f(x):
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print('Исследующий поиск УДАЧНЫЙ')
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x_p = sample_search(f, x, sample_x)
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if f(x_p) < f(x):
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print('Поиск по образцу УДАЧНЫЙ')
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x = x_p
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else:
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print('Поиск по образцу ПРОВАЛЕН')
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x = sample_x
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print()
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print('Новая базовая точка', point_info(x, f))
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else:
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print('Исследующий поиск ПРОВАЛЕН')
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print('Уменьшаем шаг', delta, '->', delta / alpha)
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delta = delta / alpha
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print('ε =', np.linalg.norm(delta))
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return x, f(x)
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def exploratory_search(f, x, delta):
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print()
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print('Выполняем исследующий поиск')
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x_new = np.array(x)
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f_x_new = f(x_new)
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for i in range(len(x)):
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x_up = x_new.copy()
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x_down = x_new.copy()
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x_up[i] += delta[i]
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x_down[i] -= delta[i]
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f_x_up = f(x_up)
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f_x_down = f(x_down)
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if (f_x_up < f_x_new and f_x_up < f_x_down):
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x_new = x_up
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f_x_new = f_x_up
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elif (f_x_down < f_x_new):
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x_new = x_down
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f_x_new = f_x_down
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if (any([x_new[i] != x[i] for i in range(len(x))])):
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print('Найдена точка', x_new, f(x_new))
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return x_new
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def sample_search(f, x1, x2):
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print()
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print('Выполняем поиск по образцу')
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while f(x2) < f(x1):
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x2, x1 = x2 + (x2 - x1), x2
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print('Найдена точка', x2, f(x2))
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return x2
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def f1():
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x0 = [1, 0, 0]
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delta0 = [1e+6, 1e+6, 1e+6]
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alpha = 2
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epsilon = 1e-4
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def f(x): return x[0] ** 2 + 2 * x[1] ** 2 + 5 * \
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x[2] ** 2 - 2 * x[0] * x[1] - 4 * x[0] * x[2] - 2 * x[2]
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def f2():
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x0 = [1, 1]
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delta0 = [1, 1]
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alpha = 2
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epsilon = 1e-6
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def f(x): return x[0] ** 4 + x[1] ** 2 - 4 * x[0] * x[1]
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x, val = hooke_jeeves(f, x0, delta0, epsilon, alpha)
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return x, val
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def f3():
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x0 = [1, 0]
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delta0 = [1, 1]
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alpha = 2
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epsilon = 1e-5
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def f(x): return x[0] * np.exp(x[0]) - (1 + np.exp(x[0])) * np.sin(x[1])
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x, val = hooke_jeeves(f, x0, delta0, epsilon, alpha)
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return x, val
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def example():
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x0 = [-4, -4]
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delta0 = [1, 1]
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alpha = 2
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epsilon = 1e-4
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def f(x): return 8 * (x[0] ** 2) + 4 * x[0] * x[1] + 5 * (x[1] ** 2)
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x, val = hooke_jeeves(f, x0, delta0, epsilon, alpha)
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return x, val
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# x, val = f1()
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# x, val = f2()
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# x, val = f3()
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x, val = example()
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print()
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print('=' * 40)
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print("Точка экстремумв:", x)
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print("Минимальное значение функции:", val)
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