Normalized Discounted Cumulative Gain

def dcg(relevances, rank=10):
    """Discounted cumulative gain at rank (DCG)"""
    relevances = np.asarray(relevances)[:rank]
    n_relevances = len(relevances)
    if n_relevances == 0:
        return 0.

    discounts = np.log2(np.arange(n_relevances) + 2)
    return np.sum(relevances / discounts)
 
 
def ndcg(relevances, rank=10):
    """Normalized discounted cumulative gain (NDGC)"""
    best_dcg = dcg(sorted(relevances, reverse=True), rank)
    if best_dcg == 0:
        return 0.

    return dcg(relevances, rank) / best_dcg