[{'role': 'system', 'content': "You are an expert in machine learning and your task is to classify code snippets into one of the following categories: ['helper_functions', 'load_data', 'data_exploration', 'data_preprocessing', 'evaluation', 'modelling', 'prediction', 'result_visualization', 'save_results', 'comment_only']."}, {'role': 'user', 'content': 'Identify the single most appropriate category to which the provided code belongs. Provide your response as a single category label without any additional information, commentary, or personal opinions.\\nPython Code:from scipy.optimize.minpack import curve_fit\nfrom sklearn.metrics import r2_score\nfrom scipy.special import expit\n\ndef Gompertz(a, c, t, t0):    \n    Q = a * np.exp(-np.exp(-c*(t-t0)))\n    return Q\ndef Boltzman(a, c, t, t0):\n    Q = a / (1 + np.exp(-c*(t-t0)))\n    return Q\nemerging_countries = [\'Albania\', \'Andorra\', \'Argentina\', \'Armenia\', \'Azerbaijan\', \'Bahrain\', \n                      \'Barbados\', \'Bhtan\', \'Bulgaria\', \'Burkina Faso\', \'Cambodia\', \'Chile\', \n                      \'Colombia\', \'Congo (Kinshasa)\', \'Costa Rica\', \'Cote dIvoire\', \'Croatia\', \n                      \'Cuba\', \'Cyprus\', \'Czechia\', \'Dominican Republic\', \'Egypt\', \'Estonia\', \n                      \'Georgia\', \'Greece\', \'Honduras\', \'Iceland\', \'Iraq\', \'Israel\', \'Jamaica\', \n                      \'Japan\', \'Jordan\', \'Kuwait\', \'Latvia\', \'Lebanon\', \'Lithuania\', \n                      \'Luxembourg\', \'Malaysia\', \'Maldives\', \'Malta\', \'Mauritania\', \'Mauritius\', \'Monaco\',\n                      \'Mongolia\', \'Montenegro\', \'Morocco\', \'Namibia\', \'Nigeria\', \'North Macedonia\', \n                      \'Norway\', \'Oman\', \'Panama\',\'Paraguay\', \'Rawanda\', \'Saint Lucia\', \'San Marino\', \n                      \'Senegal\', \'Seychelles\', \'Singapore\',\'Slovakia\', \'Slovenia\', \'Sri Lanka\', \'Thailand\', \n                      \'Tunisia\', \'Uganda\', \'Uruguay\', \'Venezuela\']\ndef get_bounds_fatal (country, isState, y_train):\n    x = \'\'\n    for c in emerging_countries:\n        if country == c: \n            x = c; break\n    maximum = max(y_train)\n    if maximum == 0.0: maximum = 1.0         \n    if country == \'China\':\n        lower = [0, 0.02, 0]\n        upper = [2.0*maximum,0.16, 40]\n    elif country == \'Iran\':\n        lower = [0, 0.00, 0]\n        upper = [3.0*maximum,0.11, 68]\n    elif country == \'Italy\':\n        lower = [0, 0.00, 0]\n        upper = [3.0*maximum,0.13, 72]       \n    elif country == \'US\':\n        lower = [0, 0.02, 0]\n        if maximum <=10:upper = [4.0*maximum, 0.30, 85] \n        else:           upper = [3.5*maximum, 0.20, 90] \n    elif country == \'France\':\n        lower = [0, 0.02, 0]\n        if maximum <=10:upper = [4.0*maximum,0.18, 80]\n        else:           upper = [4.0*maximum,0.15, 90] \n    elif country == \'Spain\':\n        lower = [0, 0.02, 0]\n        upper = [3.0*maximum,0.15, 78]\n    elif country == \'Germany\':\n        lower = [0.0, 0.02, 0]\n        upper = [3.0*maximum,0.20, 85] \n    elif country == \'Belgium\':\n        lower = [0.0, 0.02, 0]\n        upper = [3.0*maximum,0.25, 88] \n    elif country == \'Turkey\':\n        lower = [0.0, 0.02, 0]\n        upper = [3.5*maximum,0.22, 90]\n    elif country == \'Netherlands\':\n        lower = [0.0, 0.02, 0]\n        upper = [4.0*maximum,0.14, 88] \n    elif country == \'Switzerland\':\n        lower = [0.0, 0.02, 0]\n        upper = [4.0*maximum,0.12, 90] \n    elif country == \'United Kingdom\':\n        lower = [0.0, 0.02, 0]\n        upper = [4.5*maximum,0.16, 95]\n    elif country == \'Portugal\':\n        lower = [100, 0.02, 0]\n        upper = [4.5*maximum,0.12, 95]  \n    elif country == \'Sweden\':\n        lower = [100, 0.02, 0]\n        upper = [4.0*maximum,0.18, 90] \n    elif country == \'Brazil\':\n        lower = [100, 0.02, 0]\n        upper = [3.5*maximum,0.20, 90] \n    elif country == \'Indonesia\':\n        lower = [100, 0.02, 0]\n        upper = [4.5*maximum,0.10, 95]  \n    elif country == \'Austria\':\n        lower = [0, 0.02, 0]\n        upper = [4.5*maximum,0.10, 95]  \n    elif country == \'Ireland\':\n        lower = [0, 0.02, 0]\n        upper = [4.5*maximum,0.15, 95]          \n    elif country == \'Canada\':\n        lower = [0, 0.02, 0]\n        if maximum <=10: upper = [2.0*maximum, 0.20, 65] \n        else:            upper = [4.5*maximum, 0.16, 95]     \n    elif country == \'India\':\n        lower = [0, 0.02, 0]\n        upper = [4.5*maximum,0.20, 95]  \n    elif country == \'Ecuador\':\n        lower = [0, 0.02, 0]\n        upper = [4.5*maximum,0.16, 96]  \n    elif country == \'Romania\':\n        lower = [0, 0.02, 0]\n        upper = [4.5*maximum,0.15, 95]  \n    elif country == \'Philippines\':\n        lower = [0, 0.02, 0]\n        upper = [4.5*maximum,0.12, 95]    \n    elif country == \'Algeria\':\n        lower = [0, 0.02, 0]\n        upper = [4.5*maximum,0.12, 95]     \n    elif country == \'Mexico\':\n        lower = [0, 0.02, 0]\n        upper = [4.5*maximum,0.20, 95]       \n    elif country == \'Denmark\':\n        lower = [0, 0.02, 0]\n        if maximum <=10:upper = [4.0*maximum, 0.30, 80] \n        else:           upper = [4.5*maximum,0.12, 94]      \n    elif country == \'Poland\':\n        lower = [0, 0.02, 0]\n        upper = [4.0*maximum,0.20, 94]  \n    elif country == \'Korea, South\':\n        lower = [0, 0.02, 0]\n        upper = [2.5*maximum,0.10, 52] \n    elif country == \'Peru\':\n        lower = [0.0, 0.02, 0]\n        upper = [4.5*maximum,0.18, 95] \n    elif country == \'Australia\':\n        lower = [0, 0.02, 0]\n        if maximum <=10: upper = [2.0*maximum, 0.20, 45] \n        else:            upper = [2.5*maximum,0.20, 70]\n    elif country == \'Pakistan\':\n        lower = [0.0, 0.02, 0] \n        upper = [4.5*maximum,0.12,95]\n    elif country == \'Saudi Arabia\':\n        lower = [0.0, 0.02, 0] \n        upper = [4.5*maximum,0.15,95]     \n    elif country == \'Afghanistan\':\n        lower = [0.0, 0.02, 0] \n        upper = [4.5*maximum,0.12,95]\n    elif country == \'Diamond Princess\':\n        lower = [0.0, 0.02, 0] \n        upper = [1.0*maximum,0.50,2] \n    elif country == \'Hungary\':\n        lower = [0.0, 0.02, 0] \n        upper = [4.5*maximum,0.14,94]\n    elif country == \'New Zealand\':\n        lower = [0.0, 0.02, 0] \n        upper = [4.0*maximum,0.14,90]\n    elif country == \'Somalia\':\n        lower = [0.0, 0.02, 0] \n        upper = [4.5*maximum,0.10,94] \n    elif country == x:\n        lower = [0.0, 0.02, 0] \n        upper = [3.5*maximum,0.15,85]  \n    else:\n        lower = [0.0, 0.02, 0] \n        if isState:\n            if maximum <=10:upper = [4.0*maximum,0.30,80] \n            else:           upper = [4.5*maximum,0.15,80]\n        else: \n            if maximum <=10:upper = [4.0*maximum,0.60,85] \n            else:           upper = [4.5*maximum,0.18,95]  \n                \n    return lower, upper\n\ndef get_bounds_confirm (country, isState, y_train):\n    x = \'\'\n    for c in emerging_countries:\n        if country == c: \n            x = c; break\n    maximum = max(y_train)\n    if maximum == 0.0: maximum = 1.0        \n    if country == \'China\':\n        lower = [0, 0.02, 0]\n        upper = [2.0*maximum,0.20,30]\n    elif country == \'Iran\':\n        lower = [0, 0.00, 0]\n        upper = [3.0*maximum,0.12,70]\n    elif country == \'Italy\':\n        lower = [0, 0.00, 0]\n        upper = [3.0*maximum,0.12, 70]\n    elif country == \'US\':\n        lower = [0, 0.02, 0]\n        if maximum <=10:upper = [4.0*maximum, 0.30, 80] \n        else:           upper = [3.0*maximum, 0.18, 85]     \n    elif country == \'France\':\n        lower = [0, 0.02, 0]\n        if maximum <=10:upper = [4.0*maximum, 0.15, 80] \n        else:           upper = [4.5*maximum, 0.10, 90]             \n    elif country == \'Spain\':\n        lower = [0, 0.02, 0]\n        upper = [3.0*maximum,0.13, 75] \n    elif country == \'Germany\':\n        lower = [0, 0.02, 0]\n        upper = [3.0*maximum,0.13, 75] \n    elif country == \'Belgium\':\n        lower = [0, 0.02, 0]\n        upper = [3.0*maximum,0.15, 78]\n    elif country == \'Turkey\':\n        lower = [0, 0.02, 0]\n        upper = [3.5*maximum,0.20, 90] \n    elif country == \'Netherlands\':\n        lower = [0, 0.02, 0]\n        upper = [4.0*maximum,0.10, 88] \n    elif country == \'Switzerland\':\n        lower = [0, 0.02, 0]\n        upper = [3.5*maximum,0.10, 75]  \n    elif country == \'United Kingdom\':\n        lower = [0, 0.02, 0]\n        upper = [4.5*maximum,0.12, 95] \n    elif country == \'Portugal\':\n        lower = [0, 0.02, 0]\n        upper = [4.0*maximum,0.11, 88]   \n    elif country == \'Sweden\':\n        lower = [0, 0.02, 0]\n        upper = [4.0*maximum,0.10, 88]    \n    elif country == \'Brazil\':\n        lower = [0, 0.02, 0]\n        upper = [3.5*maximum,0.18, 88]  \n    elif country == \'Indonesia\':\n        lower = [0, 0.02, 0]\n        upper = [5.5*maximum,0.09, 100] \n    elif country == \'Austria\':\n        lower = [0, 0.02, 0]\n        upper = [3.5*maximum,0.12, 75] \n    elif country == \'Ireland\':\n        lower = [0, 0.02, 0]\n        upper = [4.5*maximum,0.12, 95]          \n    elif country == \'Canada\':\n        lower = [0, 0.02, 0]\n        if maximum <=10: upper = [3.0*maximum, 0.28, 75] \n        else:            upper = [4.5*maximum, 0.12, 93]            \n    elif country == \'India\':\n        lower = [0, 0.02, 0]\n        upper = [4.5*maximum,0.16, 96] \n    elif country == \'Ecuador\':\n        lower = [0, 0.02, 0]\n        upper = [4.5*maximum,0.20, 95] \n    elif country == \'Romania\':\n        lower = [0, 0.02, 0]\n        upper = [4.5*maximum,0.11, 93]  \n    elif country == \'Philippines\':\n        lower = [0, 0.02, 0]\n        upper = [5.5*maximum,0.12, 95]  \n    elif country == \'Algeria\':\n        lower = [0, 0.02, 0]\n        upper = [5.5*maximum,0.10, 98] \n    elif country == \'Mexico\':\n        lower = [100, 0.02, 0]\n        upper = [4.5*maximum,0.15, 95]        \n    elif country == \'Denmark\':\n        lower = [0, 0.02, 0]\n        if isState:\n            if maximum <= 10: upper = [2.0*maximum,0.20,80] \n            else:             upper = [2.5*maximum,0.25, 55]    \n        else:\n            if maximum <=10: upper = [2.0*maximum,0.30, 40] \n            else:            upper = [5.5*maximum,0.06, 100]       \n    elif country == \'Poland\':\n        lower = [0, 0.02, 0]\n        upper = [4.5*maximum,0.11, 94]\n    elif country == \'Korea, South\':\n        lower = [0, 0.02, 0]\n        upper = [2.0*maximum,0.25, 18] \n    elif country == \'Peru\':\n        lower = [0, 0.02, 0]\n        upper = [4.5*maximum,0.20, 96] \n    elif country == \'Australia\':\n        lower = [0, 0.02, 0]\n        if maximum <=10: upper = [2.0*maximum, 0.25, 45] \n        else:            upper = [2.5*maximum,0.18, 65] \n    elif country == \'Pakistan\':\n        lower = [0.0, 0.02, 0] \n        upper = [4.5*maximum,0.10,94]\n    elif country == \'Saudi Arabia\':\n        lower = [0.0, 0.02, 0] \n        upper = [4.5*maximum,0.10,94]    \n    elif country == \'Afghanistan\':\n        lower = [0.0, 0.02, 0] \n        upper = [4.5*maximum,0.12,94]\n    elif country == \'Diamond Princess\':\n        lower = [0.0, 0.02, 0] \n        upper = [1.0*maximum,1.0,1.0]\n    elif country == \'Hungary\':\n        lower = [0.0, 0.02, 0] \n        upper = [4.5*maximum,0.10,94]  \n    elif country == \'New Zealand\':\n        lower = [0.0, 0.02, 0] \n        upper = [4.5*maximum,0.15,85] \n    elif country == \'Somalia\':\n        lower = [0.0, 0.02, 0] \n        upper = [1.0*maximum,0.08,50] \n    elif country == x:\n        lower = [0.0, 0.02, 0] \n        upper = [3.5*maximum,0.10,80]  \n    else:\n        lower = [0.0, 0.02, 0] \n        if isState:\n            if maximum <= 200: upper = [2.0*maximum,0.20,80] \n            else:              upper = [4.5*maximum,0.20,80]\n        else:  \n            if maximum <= 200: upper = [3.0*maximum,0.20,85]  \n            else:              upper = [4.5*maximum,0.20,96]    \n                \n    return lower, upper \n\nplt.rcParams.update({\'font.size\': 12})\nfig,(ax0,ax1) = plt.subplots(1,2,figsize=(20, 8))\nfig,(ax2,ax3) = plt.subplots(1,2,figsize=(20, 8))\n\nrainbow_col= plt.cm.jet(np.linspace(0,1,len(countries)))\n\nfor country, c in tqdm(zip(countries,rainbow_col)): \n    #print(\'\\\n\\\n\\\n\\\n country ==>\', country)\n    df_country_train = df_max_fatality_country[df_max_fatality_country[\'Country_Region\']==country] \n    df_country_test = test_data[test_data[\'Country_Region\']==country]  \n    if country != \'China\':\n        df_country_train = df_country_train.reset_index().loc[df_country_train.reset_index().Date>\'2020-02-22\'] #17\n        n_days_sans_China =train_data.Date.nunique() - df_country_train.Date.nunique()        \n    else:\n        df_country_train = df_country_train.reset_index()\n        n_days_sans_China = 0\n        \n    n_train_days =df_country_train.Date.nunique()    \n    x_train = range(n_train_days)\n    x_test  = range(n_train_days+n_test_days-overlap_days)#n_test_days+overlap_days)\n    y_train_f = df_country_train[\'Fatalities\']\n    y_train_c = df_country_train[\'ConfirmedCases\'] \n    y_train_cn = (df_country_train[\'ConfirmedCases\'] - df_country_train[\'ConfirmedCases\'].shift(1)).fillna(0.0).replace([-np.inf, np.inf],  0.0)\n    y_train_fn = (df_country_train[\'Fatalities\'] - df_country_train[\'Fatalities\'].shift(1)).fillna(0.0).replace([-np.inf, np.inf],  0.0)\n    \n    ###### Fatalities:   \n    lower, upper = get_bounds_fatal (country, 0, y_train_f)\n    popt_f, pcov_f = curve_fit(Gompertz, x_train, y_train_f, method=\'trf\', bounds=(lower,upper))\n    a_max, estimated_c, estimated_t0 = popt_f\n    y_predict_f = Gompertz(a_max, estimated_c, x_test, estimated_t0)\n    y_predict_f_at_t0 =  Gompertz(a_max, estimated_c, estimated_t0, estimated_t0)\n    #print(\'\\\nfatalities ==>, max: \',a_max, \', slope: %.2f\'% estimated_c, \', inflection point: \', \n    #      estimated_t0, \', r2 score: %.2f\'% r2_score(y_train_f[:], y_predict_f[0:n_train_days]))\n    y_fn = np.array([])\n    fn = [y_predict_f[i]-y_predict_f[i-1] if i!=0 else y_predict_f[i] for i in range(len(y_predict_f))]    \n    y_predict_fn = np.append(y_fn, fn)\n   \n    ###### Confirmed cases:    \n    lower_c,upper_c = get_bounds_confirm (country, 0, y_train_c)\n    popt_c, pcov_c = curve_fit(Gompertz, x_train, y_train_c, method=\'trf\', bounds=(lower_c,upper_c))\n    a_max_c, estimated_c_c, estimated_t0_c = popt_c\n    y_predict_c = Gompertz(a_max_c, estimated_c_c, x_test, estimated_t0_c)\n    y_predict_c_at_t0 =  Gompertz(a_max_c, estimated_c_c, estimated_t0_c, estimated_t0_c)\n    #print(\'confirmed ==> max: \',a_max_c, \', slope: %.2f\'% estimated_c_c, \', inflection point: \', \n    #      estimated_t0_c, \', r2 score: %.2f\'% r2_score(y_train_c[:], y_predict_c[0:n_train_days]))\n    y_cn = np.array([])\n    cn = [y_predict_c[i]-y_predict_c[i-1] if i!=0 else y_predict_c[i] for i in range(len(y_predict_c))]    \n    y_predict_cn = np.append(y_cn, cn)\n       \n    ## ===== Move the x-axis of trained and test datasets to allign with dates in China ======\n    extend_days_test = [i+len(x_test) for i in range(n_days_sans_China)]\n    x_test       = np.append(x_test, extend_days_test) \n    y_predict_c  = np.pad(y_predict_c, (n_days_sans_China, 0), \'constant\')\n    y_predict_cn = np.pad(y_predict_cn,(n_days_sans_China, 0), \'constant\')\n    y_predict_f  = np.pad(y_predict_f, (n_days_sans_China, 0), \'constant\')\n    y_predict_fn = np.pad(y_predict_fn, (n_days_sans_China, 0), \'constant\')\n    inflection_c = estimated_t0_c+n_days_sans_China\n\n    extend_days_train = [i+len(x_train) for i in range(n_days_sans_China)]\n    x_train      = np.append(x_train, extend_days_train)\n    y_train_c    = np.pad(y_train_c, (n_days_sans_China, 0), \'constant\')\n    y_train_cn   = np.pad(y_train_cn, (n_days_sans_China, 0), \'constant\')\n    y_train_f    = np.pad(y_train_f, (n_days_sans_China, 0), \'constant\')\n    y_train_fn  = np.pad(y_train_fn, (n_days_sans_China, 0), \'constant\')\n    inflection_f = estimated_t0+n_days_sans_China\n    \n    ## ===== Plot =======\n    ax0.plot(x_test, y_predict_c, linewidth=2, label=country, color=c) \n    ax0.plot(inflection_c, y_predict_c_at_t0, marker=\'o\', markersize=6, color=\'green\')#, label=\'inflection\')\n    ax0.plot(x_train, y_train_c, linewidth=2, color=c,linestyle=\'dotted\')#, label=\'train_\'+country)   \n    ax0.set_title("Total Confirmed Cases")\n    ax0.set_xlabel("Number of days")\n    ax0.set_ylabel("Confirmed Cases")\n    ax0.legend()#loc=\'center left\',bbox_to_anchor=(1.0, 0.5))\n    \n    ax1.plot(x_test, y_predict_f, linewidth=2, label=country,color=c) \n    ax1.plot(inflection_f, y_predict_f_at_t0, marker=\'o\', markersize=6, color=\'green\')\n    ax1.plot(x_train, y_train_f, linewidth=2,color=c, linestyle=\'dotted\')#, label=\'train_\'+country)    \n    ax1.set_title("Total Fatalities")\n    ax1.set_xlabel("Number of days")\n    ax1.set_ylabel("Fatalities")\n    ax1.legend()#loc=\'center left\',bbox_to_anchor=(1.0, 0.5))\n    \n    ax2.plot(x_test, y_predict_cn, linewidth=2, label=country, color=c) \n    ax2.scatter(x_train, y_train_cn, linewidth=2, color=c, linestyle=\'dotted\')#, label=\'train_\'+country)   \n    ax2.set_title("New Confirmed Cases")\n    ax2.set_xlabel("Number of days")\n    ax2.set_ylabel("New Confirmed Cases")\n    ax2.legend()#loc=\'center left\',bbox_to_anchor=(1.0, 0.5))\n    \n    ax3.plot(x_test, y_predict_fn, linewidth=2, label=country, color=c) \n    ax3.scatter(x_train, y_train_fn, linewidth=2, color=c, linestyle=\'dotted\')#, label=\'train_\'+country)   \n    ax3.set_title("New Fatalities")\n    ax3.set_xlabel("Number of days")\n    ax3.set_ylabel("New Fatalities")\n    ax3.legend()#loc=\'center left\',bbox_to_anchor=(1.0, 0.5))\''}, {'role': 'assistant', 'content': 'result_visualization'}]