---

import numpy as np
from scipy.optimize import minimize

def f(x):
    """Целевая функция из второго задания"""
    x1, x2 = x
    return 1.2 * (2 * x2 - x1**2)**2 + 10 * (1.1 - x1)**2

def nelder_mead(f, x0, eps=1e-6, alpha=1.0, beta=0.5, gamma=2.0, sigma=0.5):
    n = len(x0)
    simplex = np.zeros((n, n + 1))
    simplex[:, 0] = x0
    for i in range(1, n + 1):
        simplex[:, i] = x0.copy()
        simplex[i - 1, i] += 1.0

    f_vals = np.array([f(simplex[:, i]) for i in range(n + 1)])
    it = 0

    while np.std(f_vals) > eps and it < 1000:
        order = np.argsort(f_vals)
        simplex = simplex[:, order]
        f_vals = f_vals[order]

        xc = np.mean(simplex[:, :-1], axis=1)

        xr = xc + alpha * (xc - simplex[:, -1])
        fxr = f(xr)

        if f_vals[0] <= fxr < f_vals[-2]:
            simplex[:, -1] = xr
            f_vals[-1] = fxr
        elif fxr < f_vals[0]:
            xe = xc + gamma * (xr - xc)
            if f(xe) < fxr:
                simplex[:, -1] = xe
                f_vals[-1] = f(xe)
            else:
                simplex[:, -1] = xr
                f_vals[-1] = fxr
        else:
            xc_outer = xc + beta * (simplex[:, -1] - xc)
            if f(xc_outer) < f_vals[-1]:
                simplex[:, -1] = xc_outer
                f_vals[-1] = f(xc_outer)
            else:
                for i in range(1, n + 1):
                    simplex[:, i] = simplex[:, 0] + sigma * (simplex[:, i] - simplex[:, 0])
                f_vals = np.array([f(simplex[:, i]) for i in range(n + 1)])

        it += 1

    best_idx = np.argmin(f_vals)
    return simplex[:, best_idx], f_vals[best_idx], it

# Начальное приближение
x0 = np.array([2.0, 1.0])

# Собственная реализация
x_min, f_min, it = nelder_mead(f, x0)

print("Метод Нелдера-Мида (собственная реализация)")
print(f"Точка минимума: ({x_min[0]:.8f}, {x_min[1]:.8f})")
print(f"Значение функции: {f_min:.8f}")
print(f"Число итераций: {it}")

# Проверка через scipy
res = minimize(f, x0, method='Nelder-Mead')
print("\nПроверка (scipy.optimize.minimize):")
print(f"x = ({res.x[0]:.8f}, {res.x[1]:.8f})")
print(f"f = {res.fun:.8f}")