Initial commit

lab1/main.py

@@ -0,0 +1,141 @@
+import numpy as np
+
+
+def point_info(x, f):
+    return f'x = {x}, f(x) = {f(x)}'
+
+
+def hooke_jeeves(f, x0, delta0, epsilon, alpha):
+    x = np.array(x0)
+    delta = np.array(delta0)
+
+    iteration = 0
+
+    while np.linalg.norm(delta) > epsilon:
+        iteration += 1
+
+        print()
+        print('=' * 40)
+        print('Итерация', iteration)
+
+        print('Текущая базовая точка', point_info(x, f))
+
+        sample_x = exploratory_search(f, x, delta)
+
+        if f(sample_x) < f(x):
+            print('Исследующий поиск УДАЧНЫЙ')
+
+            x_p = sample_search(f, x, sample_x)
+
+            if f(x_p) < f(x):
+                print('Поиск по образцу УДАЧНЫЙ')
+                x = x_p
+            else:
+                print('Поиск по образцу ПРОВАЛЕН')
+                x = sample_x
+
+            print()
+            print('Новая базовая точка', point_info(x, f))
+
+        else:
+            print('Исследующий поиск ПРОВАЛЕН')
+
+            print('Уменьшаем шаг', delta, '->', delta / alpha)
+            delta = delta / alpha
+            print('ε =', np.linalg.norm(delta))
+
+    return x, f(x)
+
+
+def exploratory_search(f, x, delta):
+    print()
+    print('Выполняем исследующий поиск')
+
+    x_new = np.array(x)
+    f_x_new = f(x_new)
+
+    for i in range(len(x)):
+        x_up = x_new.copy()
+        x_down = x_new.copy()
+
+        x_up[i] += delta[i]
+        x_down[i] -= delta[i]
+
+        f_x_up = f(x_up)
+        f_x_down = f(x_down)
+
+        if (f_x_up < f_x_new and f_x_up < f_x_down):
+            x_new = x_up
+            f_x_new = f_x_up
+        elif (f_x_down < f_x_new):
+            x_new = x_down
+            f_x_new = f_x_down
+
+    if (any([x_new[i] != x[i] for i in range(len(x))])):
+        print('Найдена точка', x_new, f(x_new))
+    return x_new
+
+
+def sample_search(f, x1, x2):
+    print()
+    print('Выполняем поиск по образцу')
+    while f(x2) < f(x1):
+        x2, x1 = x2 + (x2 - x1), x2
+    print('Найдена точка', x2, f(x2))
+    return x2
+
+
+def f1():
+    x0 = [1, 0, 0]
+    delta0 = [1e+6, 1e+6, 1e+6]
+    alpha = 2
+    epsilon = 1e-4
+    def f(x): return x[0] ** 2 + 2 * x[1] ** 2 + 5 * \
+        x[2] ** 2 - 2 * x[0] * x[1] - 4 * x[0] * x[2] - 2 * x[2]
+
+
+def f2():
+    x0 = [1, 1]
+    delta0 = [1, 1]
+    alpha = 2
+    epsilon = 1e-6
+
+    def f(x): return x[0] ** 4 + x[1] ** 2 - 4 * x[0] * x[1]
+
+    x, val = hooke_jeeves(f, x0, delta0, epsilon, alpha)
+    return x, val
+
+
+def f3():
+    x0 = [1, 0]
+    delta0 = [1, 1]
+    alpha = 2
+    epsilon = 1e-5
+
+    def f(x): return x[0] * np.exp(x[0]) - (1 + np.exp(x[0])) * np.sin(x[1])
+
+    x, val = hooke_jeeves(f, x0, delta0, epsilon, alpha)
+    return x, val
+
+
+def example():
+    x0 = [-4, -4]
+    delta0 = [1, 1]
+    alpha = 2
+    epsilon = 1e-4
+
+    def f(x): return 8 * (x[0] ** 2) + 4 * x[0] * x[1] + 5 * (x[1] ** 2)
+
+    x, val = hooke_jeeves(f, x0, delta0, epsilon, alpha)
+    return x, val
+
+
+# x, val = f1()
+# x, val = f2()
+# x, val = f3()
+x, val = example()
+
+print()
+print('=' * 40)
+print("Точка экстремумв:", x)
+print("Минимальное значение функции:", val)