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                #! /usr/bin/env python  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                #  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                # Copyright (C) 2016 Rich Lewis <[email protected]>  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                # License: 3-clause BSD  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                # skchem.features.descriptors.spectral  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                Spectral descriptors for scikit-chem.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                import numpy as np  | 
            
                            
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                from .decorators import (requires_h_depleted, requires_bo_amat,  | 
            
                            
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                                         requires_h_filled, requires_degrees)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                @requires_h_depleted  | 
            
            
                                                                        
                            
            
                                    
            
            
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                @requires_bo_amat  | 
            
            
                                                                        
                            
            
                                    
            
            
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                def original_burden_matrix(mol):  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    """ The original burden matrix.  | 
            
                            
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                    $$ [B]_{ii} = Z_i | 
            
            
                                                                        
                            
            
                                    
            
            
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                    [B]_{ij} = \frac{\pi^*}{10} $$ | 
            
            
                                                                        
                            
            
                                    
            
            
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                    Where $Z_i$ is the atomic number of the $i$th atom and $\pi^*_{ij}$ is the | 
            
            
                                                                        
                            
            
                                    
            
            
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                    conventional bond order between the $i$th and $j$th atoms.  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    Args:  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        mol (skchem.Mol):  | 
            
            
                                                                        
                            
            
                                    
            
            
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                            The molecule for which to calculate the modified burden matrix.  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    Returns:  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        np.ndarray  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    References:  | 
            
            
                                                                        
                            
            
                                    
            
            
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                        Molecular Descriptors for Cheminformatics p720  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    """  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    res = mol._bo_amat / 10  | 
            
                            
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                    res[np.diag_indices_from(res)] = mol.atoms.atomic_number  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    res[res == 0] = 0.001  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    return res  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                def burden(mol, n=1):  | 
            
                            
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                    """ Spectral descriptors using the original burden matrix. """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    eigs = np.linalg.eigvals(original_burden_matrix(mol))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    eigs.sort()  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    eigs = eigs[::-1]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    diff = n - len(eigs)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    print(diff, eigs)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    if diff > 0:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        res = np.pad(eigs, (diff, diff), 'edge')  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        return np.concatenate((res[diff:], res[:diff]))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    else:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        return np.array(eigs[:n] + eigs[-n:])  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                @requires_h_filled  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                @requires_bo_amat  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                def burden_matrix(mol, diag='electronegativity'):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    """ The Burden matrix, with variable diagonal elements.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    Args:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        mol (skchem.Mol):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                            The molecule for which to calculate the modified burden matrix.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    Returns:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        np.ndarray  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    References:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        Molecular Descriptors for Cheminformatics p720"""  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    diag = getattr(mol.atoms, diag)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    res = np.sqrt(mol._bo_amat)  | 
            
                            
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                    res[np.diag_indices_from(res)] = diag  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    return res  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                def bme(mol, L=15):  | 
            
                            
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                    """ The L highest Burden modified eigenvalues of the burden matrix.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    Args:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    res = np.zeros(L)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    eigs = np.linalg.eigvals(burden_matrix(mol))  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    res[:len(eigs)] = eigs  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    return np.sort(eigs)[:-L-1:-1]  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                @requires_h_depleted  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                @requires_bo_amat  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                @requires_degrees  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                def modified_burden_matrix(mol):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    """ The modified burden matrix, Q.  | 
            
                            
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                    $$ [Q]_{ii} = Z_i + 0.1 \cdot \delta_i + 0.01 \cdot n_i^{\pi} | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                     [Q]_{ij} = 0.4 / d_{ij}$$ | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    Where Z_i is the atomic number of $i$th atom, $\delta_i$ is the vertex  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    degree, $n_i^\pi$ is the number of $\pi$ electrons and d_{ij} is the | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    topological distance between $i$th and $j$th atoms  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    Args:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        mol (skchem.Mol):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                            The molecule for which to calculate the modified burden matrix.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    Returns:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        np.ndarray  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    References:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                        Molecular Descriptors for Cheminformatics p720  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    res = 0.4 / mol._bo_amat  | 
            
                            
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                    diag = mol.atoms.atomic_number + 0.1 * mol._degrees + \  | 
            
                            
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                           0.01 * mol.atoms.n_pi_electrons  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    res[np.diag_indices_from(res)] = diag  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    return res  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    129
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                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    130
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    131
                 | 
                                    
                                                     | 
                
                 | 
                def _bcutm(mol):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    132
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    133
                 | 
                                    
                                                     | 
                
                 | 
                    """ BCUT descriptors for atomic masses.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    134
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    135
                 | 
                                    
                                                     | 
                
                 | 
                    Args:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    136
                 | 
                                    
                                                     | 
                
                 | 
                        mol (skchem.Mol):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    137
                 | 
                                    
                                                     | 
                
                 | 
                            The molecule for which to calculate the modified burden matrix.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    138
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    139
                 | 
                                    
                                                     | 
                
                 | 
                    Returns:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    140
                 | 
                                    
                                                     | 
                
                 | 
                        np.ndarray  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    141
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    142
                 | 
                                    
                                                     | 
                
                 | 
                    Note:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    143
                 | 
                                    
                                                     | 
                
                 | 
                        These memoize.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    144
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    145
                 | 
                                    
                                                     | 
                
                 | 
                    References:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    146
                 | 
                                    
                                                     | 
                
                 | 
                        Molecular Descriptors for Cheminformatics p720  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    147
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    148
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    149
                 | 
                                    
                                                     | 
                
                 | 
                    mat = burden_matrix(mol, mol.atoms.atomic_mass)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    150
                 | 
                                    
                                                     | 
                
                 | 
                    mat._bcutm = np.linalg.eigvals(mat)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    151
                 | 
                                    
                                                     | 
                
                 | 
                    return mat  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    152
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    153
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    154
                 | 
                                    
                                                     | 
                
                 | 
                def _bcutp(mol, n=1):  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                                                                        
                        
                         
                                                                                        
                                                                                            
                                                                                     
                     | 
                
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    155
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    156
                 | 
                                    
                                                     | 
                
                 | 
                    """ BCUT descriptors using atomic polarizability.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    157
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    158
                 | 
                                    
                                                     | 
                
                 | 
                    Args:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    159
                 | 
                                    
                                                     | 
                
                 | 
                        mol (skchem.Mol):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    160
                 | 
                                    
                                                     | 
                
                 | 
                            The molecule for which to calculate the modified burden matrix.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    161
                 | 
                                    
                                                     | 
                
                 | 
                        n (skchem.Mol):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    162
                 | 
                                    
                                                     | 
                
                 | 
                            The number of highest and lowest eigenvalues to use.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    163
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    164
                 | 
                                    
                                                     | 
                
                 | 
                    Returns:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    165
                 | 
                                    
                                                     | 
                
                 | 
                        np.ndarray  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    166
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    167
                 | 
                                    
                                                     | 
                
                 | 
                    Note:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    168
                 | 
                                    
                                                     | 
                
                 | 
                        These memoize.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    169
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    170
                 | 
                                    
                                                     | 
                
                 | 
                    References:  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    171
                 | 
                                    
                                                     | 
                
                 | 
                        Molecular Descriptors for Cheminformatics p720  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    172
                 | 
                                    
                                                     | 
                
                 | 
                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    173
                 | 
                                    
                                                     | 
                
                 | 
                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    174
                 | 
                                    
                                                     | 
                
                 | 
                    mat = burden_matrix(mol, mol.atoms.atomic_mass)  | 
            
            
                                                                                                            
                                                                
            
                                    
            
            
                | 
                    175
                 | 
                                    
                                                     | 
                
                 | 
                    mat._bcutm = np.linalg.eigvals(mat)  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                                                        
            
                                    
            
            
                | 
                    176
                 | 
                                    
                                                     | 
                
                 | 
                    return mat  | 
            
                            
                    | 
                        
                     | 
                     | 
                     | 
                    
                                                                                                    
                        
                         
                                                                                        
                                                                                     
                     | 
                
            
                        
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