human
Give me a the Python code you requested given the following:
$f(x) = \sum_{k=0}^{M-1} \frac{1}{k+1} P_k(x)$
$M=70$
EZ provides perfect estimation when $N\geq M$, see the drop in the variance plot
assistant
#Here is the Python code you requested.
dim_max = 3
nb_repeats = 20

M = 70
N_min, N_max, N_step = 10, 100, 10

var_results = dict()

for d in range(1, dim_max+1):
    print('dimension =', d)
    
    jac_params = -0.5 + np.random.rand(d, 2)
    jac_params[0, :] = -0.5
    
    dpp_gp = MultivariateJacobiOPE(M, jac_params)
    coefs = 1.0 / np.arange(1, dpp_gp.N + 1)
    
    def f_gp(X):
        return np.sum(coefs*dpp_gp.eval_multiD_polynomials(X), axis=-1)

    var_results[(d, )] = jac_params
    
    for N in range(N_min, N_max+1, N_step):
        print('#points =', N)

        dpp = MultivariateJacobiOPE(N, jac_params)

        pool = mp.Pool(mp.cpu_count())

        results = pool.starmap(both_estimators, [(f_gp, dpp) for _ in range(nb_repeats)])
        results = np.array(results)
        var_results[(d, N)] = np.var(results, axis=0)

        pool.close()

j_par = {d: var_results.get((d, )) for d in range(1, dim_max + 1)}
var_N = {d: np.array([key[1] for key in var_results.keys() if len(key)==2 and key[0]==d])
            for d in range(1, dim_max + 1)}
var_res = {d: np.array([value for key, value in var_results.items() if len(key)==2 and key[0]==d]).T
            for d in range(1, dim_max + 1)}

CB_cols = ['#377eb8', '#ff7f00', '#4daf4a',
                  '#f781bf', '#a65628', '#984ea3',
                  '#999999', '#e41a1c', '#dede00']
markers = ['o', '^']
labels = ['BH', 'EZ']
for d in range(1, dim_max + 1):
    
    fig, ax = plt.subplots()
    plt.title(r'Dimension $d={}$, $M$ = {}'.format(d, M), fontsize=20)
    ax.set_xlabel(r'$N$', fontsize=22)
    ax.xaxis.set_label_coords(1.03, -0.0)
    ax.set_ylabel(r'$\mathrm{\mathbb{V}}$ar', fontsize=22, rotation='horizontal')
    ax.yaxis.set_label_coords(-0.06, 0.95)
    ax.tick_params(axis = 'both', which = 'major', labelsize = 17.5)
    ax.spines['top'].set_visible(False)
    ax.spines['right'].set_visible(False)

    for c, m, lab, var_estim in zip(CB_cols[:2], markers, labels, var_res[d]):

        ax.loglog(var_N[d], var_estim, m, c=c, markersize=8)

        x_plot =...