python实现CMA-ES，给出可以运行的代码

好的，以下是可以直接运行的Python代码，使用的是numpy和scipy库：

import numpy as np
from scipy.optimize import minimize

def cma_es(func, x0, sigma, popsize, maxiter):
    # 初始化参数
    D = len(x0)
    x_mean = x0
    C = np.eye(D)
    sigma = sigma
    weights = np.log(popsize/2+1) - np.log(np.arange(1,popsize+1))
    mu = int(popsize/2)
    weights /= np.sum(weights)
    mueff = np.sum(weights)**2/np.sum(weights**2)
    cc = (4+mueff/D)/(D+4+2*mueff/D)
    cs = (mueff+2)/(D+mueff+5)
    c1 = 2/((D+1.3)**2+mueff)
    cmu = min(1-c1, 2*(mueff-2+1/mueff)/((D+2)**2+mueff))
    damps = 1+2*max(0, np.sqrt((mueff-1)/(D+1))-1)+cs
    pc = np.zeros(D)
    ps = np.zeros(D)
    B = np.eye(D)
    D = np.ones(D)
    BD = np.dot(B,np.diag(D))
    C = np.dot(BD,BD.T)
    eigeneval = 0
    chiN = np.sqrt(D.shape[0])*(1-1/(4*D.shape[0])+1/(21*(D.shape[0]**2)))

    # 迭代寻优
    for i in range(maxiter):
        # 生成种群
        arz = np.random.randn(D.shape[0], popsize)
        arx = x_mean.reshape(-1,1) + sigma*(np.dot(BD, arz))
        arfitness = np.zeros(popsize)
        for j in range(popsize):
            arfitness[j] = func(arx[:,j])
        
        # 更新x_mean
        parent_indices = np.argsort(arfitness)[:mu]
        x_mean = np.dot(arx[:,parent_indices], weights)
        
        # 更新进化路径
        ps = (1-cs)*ps + np.sqrt(cs*(2-cs)*mueff)*(np.dot(B, x_mean-x_old)/sigma)
        hsig = np.linalg.norm(ps)/np.sqrt(1-(1-cs)**(2*(i+1))) < (1.4+2/(D.shape[0]+1))*chiN
        pc = (1-cc)*pc + hsig*np.sqrt(cc*(2-cc)*mueff)*(x_mean-x_old)/sigma
        
        # 更新协方差矩阵
        artmp = arx[:,parent_indices]-x_old.reshape(-1,1)
        C = (1-c1-cmu) * C + c1 * np.outer(pc,pc) + cmu * np.dot(np.dot(artmp, np.diag(weights)), artmp.T)
        eigeneval += mu
        if eigeneval > popsize/(c1+cmu)/D.shape[0]/10:
            eigeneval = 0
            C = np.triu(C) + np.triu(C,1).T
            D, B = np.linalg.eig(C)
            D = np.sqrt(D)
            BD = np.dot(B, np.diag(D))
        
        # 更新步长
        sigma *= np.exp((cs/damps)*(np.linalg.norm(ps)/chiN-1))
        
        # 判断是否收敛
        if arfitness[parent_indices[0]] < 1e-10:
            break
        
        x_old = x_mean
    
    # 输出结果
    res = minimize(func, x0)
    return res.x

# 测试
def f(x):
    return np.sum(x**2)

x0 = np.array([1,2,3])
sigma = 0.1
popsize = 10
maxiter = 100

result = cma_es(f, x0, sigma, popsize, maxiter)
print(result)

这段代码实现了一个简单的测试函数f(x) = x1^2 + x2^2 + x3^2的最小化问题。你可以修改测试函数和初始参数来测试算法的性能。