[{'role': 'system', 'content': "You are an expert in machine learning and your task is to classify the code snippets into categories from the provided list of categories. List of categories: ['helper_functions', 'load_data', 'data_exploration', 'data_preprocessing', 'evaluation', 'modelling', 'prediction', 'result_visualization', 'save_results', 'comment_only']"}, {'role': 'user', 'content': 'Identify to which category the provided code belongs and assign the code snippet to at least 1 but up to 5 categories based on the probabilities, ignore if the probability of the category is negligible. Strictly provide your response as a list. Avoid providing 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']"}]