some work

lab2/HookJeeves.py

@@ -0,0 +1,159 @@
+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, r=lambda x: True):
+    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, r=r)
+
+        if f(sample_x) < f(x):
+            print("Исследующий поиск УДАЧНЫЙ")
+
+            x_p = sample_search(f, x, sample_x, r=r)
+
+            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, r=lambda x: True):
+    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, r=lambda x: True):
+    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 = [0, 0]
+    delta0 = [1e6, 1e6, 1e6]
+    alpha = 2
+    epsilon = 1e-4
+
+    c = [[1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 1]]
+
+    r = [[-1000, 1000], [-100, 100]]
+
+    def f(x):
+        return sum(
+            [
+                sum([c[i][j] * x[i] ** j for j in range(len(c[i]))])
+                for i in range(len(c))
+            ]
+        )
+
+    x, val = hooke_jeeves(f, x0, delta0, epsilon, alpha, r=r)
+    return x, val
+
+
+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
+
+
+if __name__ == "__main__":
+
+    x, val = f1()
+    # x, val = f2()
+    # x, val = f3()
+    # x, val = example()
+
+    print()
+    print("=" * 40)
+    print("Точка экстремумв:", x)
+    print("Минимальное значение функции:", val)