import pandas as pd
from sklearn.linear_model import LogisticRegression
from sklearn.metrics import roc_auc_score
from sklearn.cluster import KMeans

def variable_clustering_gini(data, default_flag, cluster_number="optimal"):
    """
    Perform variable clustering and calculate Gini values for a given dataset.

    This function clusters variables in the dataset based on the specified default flag and calculates Gini values
    for each variable using logistic regression. The number of clusters can be determined optimally using the elbow method
    or manually.

    Parameters:
    data (DataFrame): The dataset to be clustered and for which Gini values are calculated.
    default_flag (str): The name of the default flag variable in the dataset.
    cluster_number (int or str): The number of clusters to generate. If "optimal" is selected, the optimal number
                                  of clusters is determined using the elbow method (default is "optimal").

    Returns:
    DataFrame: A DataFrame containing the variables with their corresponding Gini values.

    Example:
    >>> import pandas as pd
    >>> # Assume data is defined
    >>> credit_data = pd.read_csv('credit_data.csv')  # Assuming 'credit_data.csv' contains the dataset
    >>> gini_values = variable_clustering_gini(credit_data, "default_flag", cluster_number="optimal")
    >>> print(gini_values)
    """

    def univariate_gini(data, default_flag):
        gini_values = {}
        for col in data.columns:
            if col != default_flag:
                X = data[col].values.reshape(-1, 1)
                y = data[default_flag]
                model = LogisticRegression()
                model.fit(X, y)
                y_pred = model.predict_proba(X)[:, 1]
                auc_score = roc_auc_score(y, y_pred)
                gini_values[col] = 2 * auc_score - 1
        return pd.DataFrame(list(gini_values.items()), columns=['Variable', 'Gini']).sort_values(by='Gini', ascending=False)

    def optimal_cluster(data):
        wcss = []
        for i in range(1, data.shape[1]):
            kmeans = KMeans(n_clusters=i, init='k-means++', max_iter=300, n_init=10, random_state=0)
            kmeans.fit(data.values.T)
            wcss.append(kmeans.inertia_)
        # Calculate the rate of decrease in WCSS
        rate_of_change = [(wcss[i] - wcss[i + 1]) / wcss[i] for i in range(len(wcss) - 1)]
        # Find the index of the maximum rate of change
        optimal_index = rate_of_change.index(max(rate_of_change))
        return optimal_index + 1  # Add 1 to get the optimal number of clusters

    def given_cluster(data, cluster_number):
        kmeans = KMeans(n_clusters=cluster_number, init='k-means++', max_iter=1000, n_init=1000)
        kmeans.fit(data.values.T)
        return kmeans.labels_

    # Calculate univariate Gini values
    gini_df = univariate_gini(data, default_flag)

    # Cluster variables
    if cluster_number == "optimal":
        cluster_number = optimal_cluster(data.drop(columns=[default_flag]))
    clusters = given_cluster(data.drop(columns=[default_flag]), cluster_number)
    variable_clusters = pd.DataFrame({'Group': clusters, 'Variable': data.drop(columns=[default_flag]).columns})

    # Merge variable clusters with Gini values
    merged_data = pd.merge(variable_clusters, gini_df, on='Variable')
    return merged_data
