| 
                    1
                 | 
                                    
                                                     | 
                
                 | 
                #! /usr/bin/env python  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    2
                 | 
                                    
                                                     | 
                
                 | 
                #  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    3
                 | 
                                    
                                                     | 
                
                 | 
                # Copyright (C) 2016 Rich Lewis <[email protected]>  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    4
                 | 
                                    
                                                     | 
                
                 | 
                # License: 3-clause BSD  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    5
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    6
                 | 
                                    
                                                     | 
                
                 | 
                """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    7
                 | 
                                    
                                                     | 
                
                 | 
                # skchem.features.descriptors.information  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    8
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    9
                 | 
                                    
                                                     | 
                
                 | 
                Information content indices.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    10
                 | 
                                    
                                                     | 
                
                 | 
                """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    11
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    12
                 | 
                                    
                                                     | 
                
                 | 
                from functools import partial  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    13
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    14
                 | 
                                    
                                                     | 
                
                 | 
                import pandas as pd  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    15
                 | 
                                    
                                                     | 
                
                 | 
                import numpy as np  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    16
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    17
                 | 
                                    
                                                     | 
                
                 | 
                from .decorators import requires_dmat, requires_h_filled  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    18
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    19
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    20
                 | 
                                    
                                                     | 
                
                 | 
                def entropy(l):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    21
                 | 
                                    
                                                     | 
                
                 | 
                    """ Entropy for a list.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    22
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    23
                 | 
                                    
                                                     | 
                
                 | 
                    Examples:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    24
                 | 
                                    
                                                     | 
                
                 | 
                        >>> entropy([1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3])  # doctest: +ELLIPSIS  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    25
                 | 
                                    
                                                     | 
                
                 | 
                        1.505...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    26
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    27
                 | 
                                    
                                                     | 
                
                 | 
                        >>> entropy([1, 1, 1, 1, 2, 3, 4, 5, 5, 6, 7, 7, 8, 8, 8, 8])   # doctest: +ELLIPSIS  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    28
                 | 
                                    
                                                     | 
                
                 | 
                        2.75...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    29
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    30
                 | 
                                    
                                                     | 
                
                 | 
                    n_envs = pd.value_counts(l).values  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    31
                 | 
                                    
                                                     | 
                
                 | 
                    l = n_envs / len(l)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    32
                 | 
                                    
                                                     | 
                
                 | 
                    return sum(- l * np.log2(l))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    33
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    34
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    35
                 | 
                                    
                                                     | 
                
                 | 
                @requires_h_filled  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    36
                 | 
                                    
                                                     | 
                
                 | 
                @requires_dmat  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    37
                 | 
                                    
                                                     | 
                
                 | 
                def _ic(mol, m):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    38
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    39
                 | 
                                    
                                                     | 
                
                 | 
                    """ neighbourhood information content of orders 0 to n """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    40
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    41
                 | 
                                    
                                                     | 
                
                 | 
                    res = np.zeros((m + 1,))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    42
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    43
                 | 
                                    
                                                     | 
                
                 | 
                    if len(mol.atoms) == 0:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    44
                 | 
                                    
                                                     | 
                
                 | 
                        return res  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    45
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    46
                 | 
                                    
                                                     | 
                
                 | 
                    n_atoms = len(mol.atoms)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    47
                 | 
                                    
                                                     | 
                
                 | 
                    atomic = mol.atoms.atomic_number  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    48
                 | 
                                    
                                                     | 
                
                 | 
                    env = atomic.copy()  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    49
                 | 
                                    
                                                     | 
                
                 | 
                    d_mat = mol._dMat  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    50
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    51
                 | 
                                    
                                                     | 
                
                 | 
                    for i in range(m + 1):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    52
                 | 
                                    
                                                     | 
                
                 | 
                        shell_mat = d_mat == i  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    53
                 | 
                                    
                                                     | 
                
                 | 
                        arr = np.zeros((n_atoms, n_atoms))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    54
                 | 
                                    
                                                     | 
                
                 | 
                        np.fill_diagonal(arr, env)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    55
                 | 
                                    
                                                     | 
                
                 | 
                        arr[shell_mat] = np.tile(atomic, n_atoms)[shell_mat.flatten()]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    56
                 | 
                                    
                                                     | 
                
                 | 
                        # hash the envs - string fastest immutable  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    57
                 | 
                                    
                                                     | 
                
                 | 
                        env = np.array([hash(np.sort(x).tostring()) for x in arr])  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    58
                 | 
                                    
                                                     | 
                
                 | 
                        res[i] = entropy(env)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    59
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    60
                 | 
                                    
                                                     | 
                
                 | 
                    return np.array(res)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    61
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    62
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    63
                 | 
                                    
                                                     | 
                
                 | 
                def ic(mol, m):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                        
                        
                         
                                                                                        
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    64
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    65
                 | 
                                    
                                                     | 
                
                 | 
                    """ Neighborhood Information Content of order m.  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                                                                            
                        
                         
                                                                                        
                                                                                            
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    66
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    67
                 | 
                                    
                                                     | 
                
                 | 
                    The $m$th order neighbourhood Information Content $IC_m$ is calculated as  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    68
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    69
                 | 
                                    
                                                     | 
                
                 | 
                    $$ IC_m = - \sum{g=1}{G}{\log_2{\frac{A_g}{A}}} = - \sum{g=1}{G}{p_g \cdot \log_2{p_g} $$ | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    70
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    71
                 | 
                                    
                                                     | 
                
                 | 
                    where $G$ is the number of equivalence classes and $A_g$ is the cardinality  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    72
                 | 
                                    
                                                     | 
                
                 | 
                    of the $g$th equivalence class, and $p_g$ is the probability of randomly  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    73
                 | 
                                    
                                                     | 
                
                 | 
                    selecting a vertex of the $g$th class.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    74
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    75
                 | 
                                    
                                                     | 
                
                 | 
                    Args:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    76
                 | 
                                    
                                                     | 
                
                 | 
                        mol (skchem.Mol):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    77
                 | 
                                    
                                                     | 
                
                 | 
                            The molecule for which to calculate the descriptor.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    78
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    79
                 | 
                                    
                                                     | 
                
                 | 
                        m (int):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    80
                 | 
                                    
                                                     | 
                
                 | 
                            The order of the environments to use.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    81
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    82
                 | 
                                    
                                                     | 
                
                 | 
                    Returns:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    83
                 | 
                                    
                                                     | 
                
                 | 
                        float  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    84
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    85
                 | 
                                    
                                                     | 
                
                 | 
                    Note:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    86
                 | 
                                    
                                                     | 
                
                 | 
                        The function memoizes orders below 7.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    87
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    88
                 | 
                                    
                                                     | 
                
                 | 
                    Examples:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    89
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    90
                 | 
                                    
                                                     | 
                
                 | 
                        From MDC:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    91
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    92
                 | 
                                    
                                                     | 
                
                 | 
                        >>> import skchem  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    93
                 | 
                                    
                                                     | 
                
                 | 
                        >>> mol = skchem.Mol.from_smiles('CC(C)=CC') | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    94
                 | 
                                    
                                                     | 
                
                 | 
                        >>> ic(mol, 0)  # doctest: +ELLIPSIS  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    95
                 | 
                                    
                                                     | 
                
                 | 
                        0.918...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    96
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    97
                 | 
                                    
                                                     | 
                
                 | 
                        >>> ic(mol, 1)  # doctest: +ELLIPSIS  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    98
                 | 
                                    
                                                     | 
                
                 | 
                        1.375...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    99
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    100
                 | 
                                    
                                                     | 
                
                 | 
                        >>> ic(mol, 2)  # doctest: +ELLIPSIS  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    101
                 | 
                                    
                                                     | 
                
                 | 
                        1.871...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    102
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    103
                 | 
                                    
                                                     | 
                
                 | 
                        >>> ic(mol, 3)  # doctest: +ELLIPSIS  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    104
                 | 
                                    
                                                     | 
                
                 | 
                        2.422...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    105
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    106
                 | 
                                    
                                                     | 
                
                 | 
                    References:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    107
                 | 
                                    
                                                     | 
                
                 | 
                        Molecular Descriptors for Chemoinformatics, pp 408-411  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    108
                 | 
                                    
                                                     | 
                
                 | 
                        doi:10.1002/9783527628766  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    109
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    110
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    111
                 | 
                                    
                                                     | 
                
                 | 
                    if m > 6:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    112
                 | 
                                    
                                                     | 
                
                 | 
                        return _ic(mol, m)[m]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    113
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    114
                 | 
                                    
                                                     | 
                
                 | 
                    if not hasattr(mol, '_ic'):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    115
                 | 
                                    
                                                     | 
                
                 | 
                        mol._ic = _ic(mol, 6)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    116
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    117
                 | 
                                    
                                                     | 
                
                 | 
                    return mol._ic[m]  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    118
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                                                                
            
                                    
            
            
                | 
                    119
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    120
                 | 
                                    
                                                     | 
                
                 | 
                @requires_h_filled  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    121
                 | 
                                    
                                                     | 
                
                 | 
                def tic(mol, m):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                        
                            
            
                                    
            
            
                | 
                    122
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    123
                 | 
                                    
                                                     | 
                
                 | 
                    """ Neighborhood Total Information Content of order m.  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                        
                            
            
                                    
            
            
                | 
                    124
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    125
                 | 
                                    
                                                     | 
                
                 | 
                    The $m$th order total neighbourhood Information Content $TIC_m$  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    126
                 | 
                                    
                                                     | 
                
                 | 
                    is defined as:  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    127
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    128
                 | 
                                    
                                                     | 
                
                 | 
                    $$ IC_m = A \cdot IC_m $$  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    129
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    130
                 | 
                                    
                                                     | 
                
                 | 
                    where $A$ is the number of graph vertices.  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    131
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    132
                 | 
                                    
                                                     | 
                
                 | 
                    Args:  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    133
                 | 
                                    
                                                     | 
                
                 | 
                        mol (skchem.Mol):  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    134
                 | 
                                    
                                                     | 
                
                 | 
                            The molecule for which to calculate the descriptor.  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    135
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    136
                 | 
                                    
                                                     | 
                
                 | 
                        m (int):  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    137
                 | 
                                    
                                                     | 
                
                 | 
                            The order of the environments to use.  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    138
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    139
                 | 
                                    
                                                     | 
                
                 | 
                    Returns:  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    140
                 | 
                                    
                                                     | 
                
                 | 
                        float  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    141
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    142
                 | 
                                    
                                                     | 
                
                 | 
                    Examples:  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    143
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    144
                 | 
                                    
                                                     | 
                
                 | 
                        From MDC:  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    145
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    146
                 | 
                                    
                                                     | 
                
                 | 
                        >>> import skchem  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    147
                 | 
                                    
                                                     | 
                
                 | 
                        >>> mol = skchem.Mol.from_smiles('CC(C)=CC') | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    148
                 | 
                                    
                                                     | 
                
                 | 
                        >>> tic(mol, 0)  # doctest: +ELLIPSIS  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    149
                 | 
                                    
                                                     | 
                
                 | 
                        13.774...  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    150
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    151
                 | 
                                    
                                                     | 
                
                 | 
                        >>> tic(mol, 1)  # doctest: +ELLIPSIS  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    152
                 | 
                                    
                                                     | 
                
                 | 
                        20.629...  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    153
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    154
                 | 
                                    
                                                     | 
                
                 | 
                        >>> tic(mol, 2)  # doctest: +ELLIPSIS  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    155
                 | 
                                    
                                                     | 
                
                 | 
                        28.074...  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    156
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    157
                 | 
                                    
                                                     | 
                
                 | 
                        >>> tic(mol, 3)  # doctest: +ELLIPSIS  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    158
                 | 
                                    
                                                     | 
                
                 | 
                        36.338...  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    159
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    160
                 | 
                                    
                                                     | 
                
                 | 
                    References:  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    161
                 | 
                                    
                                                     | 
                
                 | 
                        Molecular Descriptors for Chemoinformatics, pp 408-411  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    162
                 | 
                                    
                                                     | 
                
                 | 
                        doi:10.1002/9783527628766  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    163
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    164
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                        
                            
            
                                    
            
            
                | 
                    165
                 | 
                                    
                                                     | 
                
                 | 
                    return len(mol.atoms) * ic(mol, m)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    166
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    167
                 | 
                                    
                                                     | 
                
                 | 
                @requires_h_filled  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    168
                 | 
                                    
                                                     | 
                
                 | 
                def sic(mol, m):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    169
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    170
                 | 
                                    
                                                     | 
                
                 | 
                    """ Structural Information Content of order *m*.  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    171
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    172
                 | 
                                    
                                                     | 
                
                 | 
                    The m'th order SIC_m is defined in a normalized form of the information  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    173
                 | 
                                    
                                                     | 
                
                 | 
                    content to delete the influence of graph size.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    174
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    175
                 | 
                                    
                                                     | 
                
                 | 
                    $$ SIC_m = \frac{IC_m}{\log_2{A}} $$ | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    176
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    177
                 | 
                                    
                                                     | 
                
                 | 
                    Args:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    178
                 | 
                                    
                                                     | 
                
                 | 
                        mol (skchem.Mol):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    179
                 | 
                                    
                                                     | 
                
                 | 
                            The molecule for which to calculate the descriptor.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    180
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    181
                 | 
                                    
                                                     | 
                
                 | 
                        m (int):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    182
                 | 
                                    
                                                     | 
                
                 | 
                            The order of sugraphs to use.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    183
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    184
                 | 
                                    
                                                     | 
                
                 | 
                    Returns:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    185
                 | 
                                    
                                                     | 
                
                 | 
                        float  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    186
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    187
                 | 
                                    
                                                     | 
                
                 | 
                    Examples:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    188
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    189
                 | 
                                    
                                                     | 
                
                 | 
                        From MDC:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    190
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    191
                 | 
                                    
                                                     | 
                
                 | 
                        >>> import skchem  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    192
                 | 
                                    
                                                     | 
                
                 | 
                        >>> mol = skchem.Mol.from_smiles('CC(C)=CC') | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    193
                 | 
                                    
                                                     | 
                
                 | 
                        >>> sic(mol, 0)  # doctest: +ELLIPSIS  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    194
                 | 
                                    
                                                     | 
                
                 | 
                        0.235...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    195
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    196
                 | 
                                    
                                                     | 
                
                 | 
                        >>> sic(mol, 1)  # doctest: +ELLIPSIS  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    197
                 | 
                                    
                                                     | 
                
                 | 
                        0.352...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    198
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    199
                 | 
                                    
                                                     | 
                
                 | 
                        >>> sic(mol, 2)  # doctest: +ELLIPSIS  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    200
                 | 
                                    
                                                     | 
                
                 | 
                        0.479...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    201
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    202
                 | 
                                    
                                                     | 
                
                 | 
                        >>> sic(mol, 3)  # doctest: +ELLIPSIS  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    203
                 | 
                                    
                                                     | 
                
                 | 
                        0.620...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    204
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    205
                 | 
                                    
                                                     | 
                
                 | 
                    References:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    206
                 | 
                                    
                                                     | 
                
                 | 
                        Molecular Descriptors for Chemoinformatics, pp 408-411  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    207
                 | 
                                    
                                                     | 
                
                 | 
                        doi:10.1002/9783527628766  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    208
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    209
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    210
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    211
                 | 
                                    
                                                     | 
                
                 | 
                    n_atoms = len(mol.atoms)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    212
                 | 
                                    
                                                     | 
                
                 | 
                    if n_atoms <= 1:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    213
                 | 
                                    
                                                     | 
                
                 | 
                        return 0.0  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    214
                 | 
                                    
                                                     | 
                
                 | 
                    return ic(mol, m) / np.log2(n_atoms)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    215
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    216
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    217
                 | 
                                    
                                                     | 
                
                 | 
                @requires_h_filled  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    218
                 | 
                                    
                                                     | 
                
                 | 
                def bic(mol, m):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    219
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    220
                 | 
                                    
                                                     | 
                
                 | 
                    """ Bonding Information Content of order $m$.  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                                                                            
                        
                         
                                                                                        
                                                                                            
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    221
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    222
                 | 
                                    
                                                     | 
                
                 | 
                    The $m$th order $BIC_m$ is defined in a normalized form as the $SIC_m$, but  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    223
                 | 
                                    
                                                     | 
                
                 | 
                    taking into account the number of edges and their multiplicity,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    224
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    225
                 | 
                                    
                                                     | 
                
                 | 
                    $$ BIC_m = \frac{IC_m}{\log{2}{(\sum{b=1}{B} \pi_b^{*})}} $$ | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    226
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    227
                 | 
                                    
                                                     | 
                
                 | 
                    where B is the number of edges and $\pi_b^{*} is the conventional bond | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    228
                 | 
                                    
                                                     | 
                
                 | 
                    order of the edge $b$. In the original definition, the denominator was  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    229
                 | 
                                    
                                                     | 
                
                 | 
                    simply considered to be the edge number $B$.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    230
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    231
                 | 
                                    
                                                     | 
                
                 | 
                    Args:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    232
                 | 
                                    
                                                     | 
                
                 | 
                        mol (skchem.Mol):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    233
                 | 
                                    
                                                     | 
                
                 | 
                            The molecule for which to calculate the descriptor.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    234
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    235
                 | 
                                    
                                                     | 
                
                 | 
                        m (int):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    236
                 | 
                                    
                                                     | 
                
                 | 
                            The order of the sugraphs to use.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    237
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    238
                 | 
                                    
                                                     | 
                
                 | 
                    Returns:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    239
                 | 
                                    
                                                     | 
                
                 | 
                        float  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    240
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    241
                 | 
                                    
                                                     | 
                
                 | 
                    Examples:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    242
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    243
                 | 
                                    
                                                     | 
                
                 | 
                        From MDC:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    244
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    245
                 | 
                                    
                                                     | 
                
                 | 
                        >>> import skchem  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    246
                 | 
                                    
                                                     | 
                
                 | 
                        >>> mol = skchem.Mol.from_smiles('CC(C)=CC') | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    247
                 | 
                                    
                                                     | 
                
                 | 
                        >>> bic(mol, 0)  # doctest: +ELLIPSIS  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    248
                 | 
                                    
                                                     | 
                
                 | 
                        0.235...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    249
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    250
                 | 
                                    
                                                     | 
                
                 | 
                        >>> bic(mol, 1)  # doctest: +ELLIPSIS  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    251
                 | 
                                    
                                                     | 
                
                 | 
                        0.352...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    252
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    253
                 | 
                                    
                                                     | 
                
                 | 
                        >>> bic(mol, 2)  # doctest: +ELLIPSIS  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    254
                 | 
                                    
                                                     | 
                
                 | 
                        0.479...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    255
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    256
                 | 
                                    
                                                     | 
                
                 | 
                        >>> bic(mol, 3)  # doctest: +ELLIPSIS  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    257
                 | 
                                    
                                                     | 
                
                 | 
                        0.620...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    258
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    259
                 | 
                                    
                                                     | 
                
                 | 
                    References:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    260
                 | 
                                    
                                                     | 
                
                 | 
                        Molecular Descriptors for Chemoinformatics, pp 408-411  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    261
                 | 
                                    
                                                     | 
                
                 | 
                        doi:10.1002/9783527628766  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    262
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    263
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    264
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    265
                 | 
                                    
                                                     | 
                
                 | 
                    return ic(mol, m) / np.log2(sum(mol.bonds.order))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    266
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    267
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    268
                 | 
                                    
                                                     | 
                
                 | 
                @requires_h_filled  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    269
                 | 
                                    
                                                     | 
                
                 | 
                def cic(mol, m):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    270
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    271
                 | 
                                    
                                                     | 
                
                 | 
                    """ Complementary Information Content of order $m$.  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    272
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    273
                 | 
                                    
                                                     | 
                
                 | 
                    The $m$th order $CIC_m$ measures the deviation of $IC_m$ from its maximum  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    274
                 | 
                                    
                                                     | 
                
                 | 
                    value, that corresponds to the vertex partition into equivalence classes  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    275
                 | 
                                    
                                                     | 
                
                 | 
                    containing one element each:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    276
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    277
                 | 
                                    
                                                     | 
                
                 | 
                    $$ CIC_m = \log{2}{A} - IC_m $$ | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    278
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    279
                 | 
                                    
                                                     | 
                
                 | 
                    where $A$ is the number of graph vertices.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    280
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    281
                 | 
                                    
                                                     | 
                
                 | 
                    Args:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    282
                 | 
                                    
                                                     | 
                
                 | 
                        mol (skchem.Mol):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    283
                 | 
                                    
                                                     | 
                
                 | 
                            The molecule for which to calculate the descriptor.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    284
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    285
                 | 
                                    
                                                     | 
                
                 | 
                        m (int):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    286
                 | 
                                    
                                                     | 
                
                 | 
                            The order of sugraphs to use.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    287
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    288
                 | 
                                    
                                                     | 
                
                 | 
                    Returns:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    289
                 | 
                                    
                                                     | 
                
                 | 
                        float  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    290
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    291
                 | 
                                    
                                                     | 
                
                 | 
                    Examples:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    292
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    293
                 | 
                                    
                                                     | 
                
                 | 
                        From MDC:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    294
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    295
                 | 
                                    
                                                     | 
                
                 | 
                        >>> import skchem  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    296
                 | 
                                    
                                                     | 
                
                 | 
                        >>> mol = skchem.Mol.from_smiles('CC(C)=CC') | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    297
                 | 
                                    
                                                     | 
                
                 | 
                        >>> cic(mol, 0)  # doctest: +ELLIPSIS  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    298
                 | 
                                    
                                                     | 
                
                 | 
                        2.988...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    299
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    300
                 | 
                                    
                                                     | 
                
                 | 
                        >>> cic(mol, 1)  # doctest: +ELLIPSIS  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    301
                 | 
                                    
                                                     | 
                
                 | 
                        2.531...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    302
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    303
                 | 
                                    
                                                     | 
                
                 | 
                        >>> cic(mol, 2)  # doctest: +ELLIPSIS  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    304
                 | 
                                    
                                                     | 
                
                 | 
                        2.035...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    305
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    306
                 | 
                                    
                                                     | 
                
                 | 
                        >>> cic(mol, 3)  # doctest: +ELLIPSIS  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    307
                 | 
                                    
                                                     | 
                
                 | 
                        1.484...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    308
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    309
                 | 
                                    
                                                     | 
                
                 | 
                    References:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    310
                 | 
                                    
                                                     | 
                
                 | 
                        Molecular Descriptors for Chemoinformatics, pp 408-411  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    311
                 | 
                                    
                                                     | 
                
                 | 
                        doi:10.1002/9783527628766  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    312
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    313
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    314
                 | 
                                    
                                                     | 
                
                 | 
                    n_atoms = len(mol.atoms)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    315
                 | 
                                    
                                                     | 
                
                 | 
                    if n_atoms <= 1:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    316
                 | 
                                    
                                                     | 
                
                 | 
                        return 0.0  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    317
                 | 
                                    
                                                     | 
                
                 | 
                    return np.log2(n_atoms) - ic(mol, m)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    318
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    319
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    320
                 | 
                                    
                                                     | 
                
                 | 
                def ric(mol, m):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    321
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    322
                 | 
                                    
                                                     | 
                
                 | 
                    """ The redundant information content.  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    323
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    324
                 | 
                                    
                                                     | 
                
                 | 
                    A measure of relative redundancy of a graph obtained by normalizing the  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    325
                 | 
                                    
                                                     | 
                
                 | 
                    complementary information content, defined as:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    326
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    327
                 | 
                                    
                                                     | 
                
                 | 
                    $$ R_m = \frac{CIC_m}{\log{2}{A}} = 1 - SIC_m $$ | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    328
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    329
                 | 
                                    
                                                     | 
                
                 | 
                    Args:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    330
                 | 
                                    
                                                     | 
                
                 | 
                        mol (skchem.Mol):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    331
                 | 
                                    
                                                     | 
                
                 | 
                            The molecule for which to calculate the descriptor.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    332
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    333
                 | 
                                    
                                                     | 
                
                 | 
                        m (int):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    334
                 | 
                                    
                                                     | 
                
                 | 
                            The order of sugraphs to use.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    335
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    336
                 | 
                                    
                                                     | 
                
                 | 
                    Returns:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    337
                 | 
                                    
                                                     | 
                
                 | 
                        float  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    338
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    339
                 | 
                                    
                                                     | 
                
                 | 
                    Examples:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    340
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    341
                 | 
                                    
                                                     | 
                
                 | 
                        Extrapolated from MDC:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    342
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    343
                 | 
                                    
                                                     | 
                
                 | 
                        >>> import skchem  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    344
                 | 
                                    
                                                     | 
                
                 | 
                        >>> mol = skchem.Mol.from_smiles('CC(C)=CC') | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    345
                 | 
                                    
                                                     | 
                
                 | 
                        >>> ric(mol, 0)  # doctest: +ELLIPSIS  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    346
                 | 
                                    
                                                     | 
                
                 | 
                        -1.988...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    347
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    348
                 | 
                                    
                                                     | 
                
                 | 
                        >>> ric(mol, 1)  # doctest: +ELLIPSIS  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    349
                 | 
                                    
                                                     | 
                
                 | 
                        -1.531...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    350
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    351
                 | 
                                    
                                                     | 
                
                 | 
                        >>> ric(mol, 2)  # doctest: +ELLIPSIS  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    352
                 | 
                                    
                                                     | 
                
                 | 
                        -1.035...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    353
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    354
                 | 
                                    
                                                     | 
                
                 | 
                        >>> ric(mol, 3)  # doctest: +ELLIPSIS  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    355
                 | 
                                    
                                                     | 
                
                 | 
                        -0.484...  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    356
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    357
                 | 
                                    
                                                     | 
                
                 | 
                    References:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    358
                 | 
                                    
                                                     | 
                
                 | 
                        Molecular Descriptors for Chemoinformatics, pp 408-411  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    359
                 | 
                                    
                                                     | 
                
                 | 
                        doi:10.1002/9783527628766  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    360
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    361
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    362
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    363
                 | 
                                    
                                                     | 
                
                 | 
                    return 1 - cic(mol, m)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    364
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    365
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    366
                 | 
                                    
                                                     | 
                
                 | 
                def ord_neigh(mol):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    367
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    368
                 | 
                                    
                                                     | 
                
                 | 
                    """ The order of neighbourhood.  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                                                                                                                                
                        
                         
                                                                                        
                                                                                            
                                                                                            
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    369
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    370
                 | 
                                    
                                                     | 
                
                 | 
                    The order of neighbourhood is defined as the order $m$ of the $IC_m$ index  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    371
                 | 
                                    
                                                     | 
                
                 | 
                    when it reaches the maximum value:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    372
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    373
                 | 
                                    
                                                     | 
                
                 | 
                    \DeclareMathOperator*{\argmax}{arg\,max} | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    374
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    375
                 | 
                                    
                                                     | 
                
                 | 
                    $$ O = \min \Big( \argmax_m IC_m \Big) $$  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    376
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    377
                 | 
                                    
                                                     | 
                
                 | 
                    Args:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    378
                 | 
                                    
                                                     | 
                
                 | 
                        mol (skchem.Mol):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    379
                 | 
                                    
                                                     | 
                
                 | 
                            The molecule for which to calculate the descriptor.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    380
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    381
                 | 
                                    
                                                     | 
                
                 | 
                    Returns:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    382
                 | 
                                    
                                                     | 
                
                 | 
                        int  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    383
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    384
                 | 
                                    
                                                     | 
                
                 | 
                    Examples:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    385
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    386
                 | 
                                    
                                                     | 
                
                 | 
                        From MDC:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    387
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    388
                 | 
                                    
                                                     | 
                
                 | 
                        >>> import skchem  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    389
                 | 
                                    
                                                     | 
                
                 | 
                        >>> mol = skchem.Mol.from_smiles('CC(C)=CC') | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    390
                 | 
                                    
                                                     | 
                
                 | 
                        >>> ord_neigh(mol)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    391
                 | 
                                    
                                                     | 
                
                 | 
                        3  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    392
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    393
                 | 
                                    
                                                     | 
                
                 | 
                    References:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    394
                 | 
                                    
                                                     | 
                
                 | 
                        Molecular Descriptors for Chemoinformatics, pp 408-411  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    395
                 | 
                                    
                                                     | 
                
                 | 
                        doi:10.1002/9783527628766  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    396
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    397
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    398
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    399
                 | 
                                    
                                                     | 
                
                 | 
                    if not hasattr(mol, '_ic'):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    400
                 | 
                                    
                                                     | 
                
                 | 
                        mol._ic = _ic(mol, 6)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    401
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    402
                 | 
                                    
                                                     | 
                
                 | 
                    res = np.argmax(mol._ic)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    403
                 | 
                                    
                                                     | 
                
                 | 
                    if res == 6:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    404
                 | 
                                    
                                                     | 
                
                 | 
                        return np.argmax(_ic(mol, 20))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    405
                 | 
                                    
                                                     | 
                
                 | 
                    else:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    406
                 | 
                                    
                                                     | 
                
                 | 
                        return res  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    407
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    408
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    409
                 | 
                                    
                                                     | 
                
                 | 
                DESCRIPTORS = {'ic_{}'.format(i): partial(ic, m=i) for i in range(7)} | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    410
                 | 
                                    
                                                     | 
                
                 | 
                DESCRIPTORS.update({'tic_{}'.format(i): partial(ic, m=i) for i in range(7)}) | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    411
                 | 
                                    
                                                     | 
                
                 | 
                DESCRIPTORS.update({'sic_{}'.format(i): partial(sic, m=i) for i in range(7)}) | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    412
                 | 
                                    
                                                     | 
                
                 | 
                DESCRIPTORS.update({'cic_{}'.format(i): partial(cic, m=i) for i in range(7)}) | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    413
                 | 
                                    
                                                     | 
                
                 | 
                DESCRIPTORS.update({'bic_{}'.format(i): partial(bic, m=i) for i in range(7)}) | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    414
                 | 
                                    
                                                     | 
                
                 | 
                DESCRIPTORS.update({'ric_{}'.format(i): partial(ric, m=i) for i in range(7)}) | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    415
                 | 
                                    
                                                     | 
                
                 | 
                DESCRIPTORS['ord_neigh'] = ord_neigh  | 
            
            
                                                                                                            
                                                                
            
                                    
            
            
                | 
                    416
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                        
            
                                    
            
            
                | 
                    417
                 | 
                                    
                                                     | 
                
                 | 
                __all__ = ['ic', 'tic','sic', 'cic', 'bic', 'ric', 'ord_neigh', 'DESCRIPTORS']  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                        
                        
                         
                                                                                        
                                                                                            
                                                                                     
                     | 
                
            
                        
This can be caused by one of the following:
1. Missing Dependencies
This error could indicate a configuration issue of Pylint. Make sure that your libraries are available by adding the necessary commands.
2. Missing __init__.py files
This error could also result from missing
__init__.pyfiles in your module folders. Make sure that you place one file in each sub-folder.