将以下代码转为python代码： # f(x, y) = x^2 + 10y^2; func = @(x)(x(1)^2 + 10 * x(2)^2); gfunc = @(x)([2*x(1); 20 * x(2)]); x0 = [10; 1]; alpha = 0.085; epsilon = 1e-5; [fmin, xmin, fk, xk] = gradient_descent_fix_stepsize(func, gfunc, x0, alpha, epsilon); x1 = -12:1e-2:12; x2 = -10:1e-2:10; [X1, X2] = meshgrid(x1, x2); F = X1.^2 + 10 * X2.^2; figure, contour(X1, X2, F, 50) hold on plot(xk(1,:), xk(2,:), 'LineWidth', 2) plot(xk(1,:), xk(2,:), 'o', 'LineWidth', 2) x0 = [-10; -1]; [fmin, xmin, fkBB, xkBB] = gradient_descent(func, gfunc, x0, epsilon); hold on plot(xkBB(1, :), xkBB(2, :), 'k', 'LineWidth', 2); plot(xkBB(1, :), xkBB(2, :), 'bo', 'LineWidth', 2);

以下是将该 MATLAB 代码转换为 Python 代码的结果：

import numpy as np
import matplotlib.pyplot as plt

def func(x):
    return x[0]**2 + 10 * x[1]**2

def gfunc(x):
    return np.array([2*x[0], 20*x[1]])

def gradient_descent_fix_stepsize(func, gfunc, x0, alpha, epsilon):
    xk = [x0]
    fk = [func(x0)]
    gk = [gfunc(x0)]
    while np.linalg.norm(gk[-1]) > epsilon:
        xk.append(xk[-1] - alpha * gk[-1])
        fk.append(func(xk[-1]))
        gk.append(gfunc(xk[-1]))
    return fk[-1], xk[-1], fk, np.array(xk).T

def gradient_descent(func, gfunc, x0, epsilon):
    xk = [x0]
    fk = [func(x0)]
    gk = [gfunc(x0)]
    while np.linalg.norm(gk[-1]) > epsilon:
        alpha = 0.001
        dk = -gk[-1]
        while func(xk[-1] + alpha * dk) > func(xk[-1]) + alpha * 0.1 * np.dot(gk[-1], dk):
            alpha = alpha * 0.5
        xk.append(xk[-1] + alpha * dk)
        fk.append(func(xk[-1]))
        gk.append(gfunc(xk[-1]))
    return fk[-1], xk[-1], fk, np.array(xk).T

x0 = np.array([10, 1])
alpha = 0.085
epsilon = 1e-5
fmin, xmin, fk, xk = gradient_descent_fix_stepsize(func, gfunc, x0, alpha, epsilon)

x1 = np.arange(-12, 12, 0.01)
x2 = np.arange(-10, 10, 0.01)
X1, X2 = np.meshgrid(x1, x2)
F = X1**2 + 10 * X2**2
plt.figure()
plt.contour(X1, X2, F, 50)
plt.plot(xk[0], xk[1], linewidth=2)
plt.plot(xk[0], xk[1], 'o', linewidth=2)

x0 = np.array([-10, -1])
fmin, xmin, fkBB, xkBB = gradient_descent(func, gfunc, x0, epsilon)
plt.plot(xkBB[0], xkBB[1], 'k', linewidth=2)
plt.plot(xkBB[0], xkBB[1], 'bo', linewidth=2)
plt.show()

需要注意的是，该代码中的 `gradient_descent_fix_stepsize` 和 `gradient_descent` 函数分别对应了原 MATLAB 代码中的 `gradient_descent_fix_stepsize` 和 `gradient_descent_BB` 函数，因为在原 MATLAB 代码中，`gradient_descent_BB` 函数实际上使用的是 Barzilai-Borwein 步长，而不是固定步长。