Project: s41467-024-45598-0 | Function: gen_topol_feats_temporal (python)

system: You are an expert Python programmer implementing algorithms from scientific papers.
Complete the masked function based on the algorithm description.
Follow Python best practices and maintain consistent code style.
Return **only** the complete Python function code.

user: Complete this Python function:

**DESCRIPTION:** Generates temporal topological features by averaging across multiple network layers and time points

**KEY TERMS:** {
  "A_orig": "original adjacency matrix",
  "A_tr": "list of training adjacency matrices at different time points",
  "edge_s": "sample edges",
  "df_feat": "concatenated features across time"
}

**CONTEXT CODE:**     edge_f_tr = np.loadtxt("./edge_tf_tr/edge_f.txt").astype('int')
    

    df_f_tr = gen_topol_feats(A_orig, A_tr, edge_f_tr)
    df_t_tr = gen_topol_feats(A_orig, A_tr, edge_t_tr)
    
    edge_t_ho = np.loadtxt("./edge_tf_ho/edge_t.txt").astype('int')
    edge_f_ho = np.loadtxt("./edge_tf_ho/edge_f.txt").astype('int')
    df_f_ho = gen_topol_feats(A_orig, A_ho, edge_f_ho)
    df_t_ho = gen_topol_feats(A_orig, A_ho, edge_t_ho)
    
    feat_path = "./ef_gen_tr/"
    if not os.path.isdir(feat_path):
        os.mkdir(feat_path)
    df_t_tr.to_pickle(feat_path + 'df_t')
    df_f_tr.to_pickle(feat_path + 'df_f')
    
    feat_path = "./ef_gen_ho/"
    if not os.path.isdir(feat_path):
        os.mkdir(feat_path)
    df_t_ho.to_pickle(feat_path + 'df_t')
    df_f_ho.to_pickle(feat_path + 'df_f')
    
    
    #### load dataframes for train and holdout sets ####
    df_tr = creat_full_set(df_t_tr,df_f_tr)
    df_ho = creat_full_set(df_t_ho,df_f_ho)
    
    #### creat and save feature matrices #### 
    dir_output = './feature_metrices'  # output path
    creat_numpy_files(dir_output, df_ho, df_tr)
    
    
    #### perform model selection #### 
    path_to_data = './feature_metrices' 
    path_to_results = './results'
    n_depths = [3, 6] # here is a sample search space
    n_ests = [25, 50, 100] # here is a sample search space
    n_depth, n_est = model_selection(path_to_data, path_to_results, n_depths, n_ests)
    
    
    #### perform model selection #### 
    auprc, auc , precision, recall = heldout_performance(path_to_data, path_to_results, n_depth, n_est)
    return auprc, auc, precision, recall

   



""
def gen_topol_feats_temporal(A_orig, A_tr, edge_s): 
    
    """ 
    This function generate topoligcal feature based on which layer it is
    It also averages out over the layers that has this edge
    and the layers that does not have this edge
    
    It also takes in a list of dictionary, and than it generate a df_feat 
    that is twice as long as the original ones. For example origianlly we have
    3 10000x45 dictionaries, now we just have one 20000 dictionary, but it correponds to 
    the 10000 sample edges that is generated.
    
    
    """
    # MASKED: Generates temporal topological features by averaging across multiple network layers and time points implementation
    raise NotImplementedError("This function is masked for testing purposes.")





def K_random_number_add_up_to_sum(k,summation):
    """
    The idea of this function is to generate 7 numbers that adds up to 10000
    so that we know how much we should sample from each of the layers randomly
    Check here for the details of the method of the algorithm:
    https://math.stackexchange.com/questions/1276206/method-of-generating-random-numbers-that-sum-to-100-is-this-truly-random
    """
    x = random.sample(range(summation),k-1)
    x.sort()
    output= []
    output.append(x[0]-1)
    for i in range(1,k-1):
        output.append(x[i]-x[i-1]-1)
   
    output.append(summation-x[-1])
    random.shuffle(output)
    return output

def creat_full_set_temporal(df_t,df_f,predict):
    
    """ 
    This reads dataframes created for positive and negative class, join them with their associated label.

    Input and Parameters:
    -------
    df_t: datafram of features for true edges
    df_f: datafram of features for true non-edges

    Returns
    -------
    df_all: a data frames with columns of features and ground truth 

    Examples:
    -------
    df_all = creat_full_set(df_t,df_f)
    """

    df_t = df_t.drop_duplicates(subset=['i','j'], keep="first")
    df_f = df_f.drop_duplicates(subset=['i','j'], keep="first")

    df_t.insert(2, "TP", 1, True)
    df_f.insert(2, "TP", 0, True)
    
    df_all = [df_t, df_f]
    df_all = pd.concat(df_all)
    
    df_all.loc[df_all['short_path'] == np.inf,'short_path'] = 1000*max(df_all.loc[~(df_all['short_path'] == np.inf),'short_path'],default=0)
    df_all.loc[df_all['diam_net'] == np.inf,'diam_net'] = 1e6
    
    # data cleaning
    for i in range(1,predict):
        df_all.loc[df_all['short_path_{}'.format(i)] == np.inf,'short_path_{}'.format(i)] = 1000*max(df_all.loc[~(df_all['short_path'] == np.inf),'short_path'],default=0)
        df_all.loc[df_all['diam_net_{}'.format(i)] == np.inf,'diam_net_{}'.format(i)] = 1e6
     
    return df_all


def creat_numpy_files_temporal(dir_results, df_ho, df_tr, predict):
    
    """ 
    This functiion multiplied the column number and attache verything that is important in the function
    """
    
    feature_set = ['com_ne', 'ave_deg_net', 'var_deg_net', 'ave_clust_net',
           'num_triangles_1', 'num_triangles_2', 
           'pag_rank1', 'pag_rank2', 'clust_coeff1', 'clust_coeff2',
           'ave_neigh_deg1', 'ave_neigh_deg2', 'eig_cent1', 'eig_cent2',
           'deg_cent1', 'deg_cent2', 'clos_cent1', 'clos_cent2', 'betw_cent1',
           'betw_cent2', 'load_cent1', 'load_cent2', 'ktz_cent1', 'ktz_cent2',
           'pref_attach', 'LHN', 'svd_edges', 'svd_edges_dot', 'svd_edges_mean',
           'svd_edges_approx', 'svd_edges_dot_approx', 'svd_edges_mean_approx',
           'short_path', 'deg_assort', 'transit_net', 'diam_net',
           'jacc_coeff', 'res_alloc_ind', 'adam_adar' , 'num_nodes','num_edges']  
    #'page_rank_pers_edges', removed
    
    
    full_feat_set = [None] * ((predict)*len(feature_set))
    len_of_feat = len(feature_set)
    


Complete the function implementation replacing "raise NotImplementedError".