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                    1
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                """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    2
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                Classes for representing boundary value problems.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    3
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                    4
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                @author : David R. Pugh  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    5
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                    6
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                """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    7
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                    8
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                    9
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                class TwoPointBVPLike(object):  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    10
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                    11
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                    @property  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    12
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                    def bcs_lower(self):  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    13
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                        """  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    14
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                        Function that calculates the difference between the lower boundary  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    15
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                        conditions and the current values of the model dependent variables.  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    16
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                    17
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                        :getter: Return the current boundary condition.  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    18
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                        :type: function  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    19
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                    20
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                        """  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    21
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                        return self._bcs_lower  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    22
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                    23
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                    @property  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    24
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                    def bcs_upper(self):  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    25
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                        """  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    26
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                        Function that calculates the difference between the upper boundary  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    27
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                        conditions and the current values of the model dependent variables.  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    28
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                    29
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                        :getter: Return the current boundary condition.  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    30
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                        :type: function  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    31
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                    32
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                        """  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    33
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                        return self._bcs_upper  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    34
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                    35
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                    @property  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    36
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                    def number_bcs_lower(self):  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    37
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                        """  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    38
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                        The number of lower boundary conditions (BCS).  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    39
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                    40
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                        :getter: Return the number of lower BCS.  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    41
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                        :type: int  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    42
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                    43
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                        """  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    44
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                        return self._number_bcs_lower  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    45
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                    46
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                    @property  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    47
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                    def number_odes(self):  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    48
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                        """  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    49
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                        The number of Ordinary Differential Equations (ODEs) in the system.  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    50
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                    51
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                        :getter: Return the number of ODEs.  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    52
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                        :type: int  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    53
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                    54
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                        """  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    55
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                        return self._number_odes  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    56
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                    57
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                    @property  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    58
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                    def params(self):  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    59
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                        """  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    60
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                        A dictionary of parameters.  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    61
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                    62
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                        :getter: Return the current parameters.  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    63
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                        :type: function  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    64
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                    65
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                        """  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    66
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                        return self._params  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    67
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                    68
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                    @property  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    69
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                    def rhs(self):  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    70
                 | 
                                    
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                        """  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    71
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                        Function which calculates the value of the right-hand side of a  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    72
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                        system of Ordinary Differential Equations (ODEs).  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    73
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                    74
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                        :getter: Return the current rhs.  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    75
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                        :type: function  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    76
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                    77
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                        """  | 
            
            
                                                                        
                            
            
                                    
            
            
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                    78
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                        return self._rhs  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    79
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                    80
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                    81
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                class TwoPointBVP(TwoPointBVPLike):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    82
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                    r"""  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    83
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                    Class for representing Two-Point Boundary Value Problems (BVP).  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    84
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                    85
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                    Attributes  | 
            
            
                                                                                                            
                            
            
                                    
            
            
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                    86
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                    ----------  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    87
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                    bcs_lower : function  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    88
                 | 
                                    
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                 | 
                        Function that calculates the difference between the lower boundary  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    89
                 | 
                                    
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                        conditions and the current values of the model dependent variables.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    90
                 | 
                                    
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                    bcs_upper : function  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    91
                 | 
                                    
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                 | 
                        Function that calculates the difference between the upper boundary  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    92
                 | 
                                    
                                                     | 
                
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                        conditions and the current values of the model dependent variables.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    93
                 | 
                                    
                                                     | 
                
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                    number_bcs_lower : int  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    94
                 | 
                                    
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                        The number of lower boundary conditions (BCS).  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    95
                 | 
                                    
                                                     | 
                
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                    number_odes : int  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    96
                 | 
                                    
                                                     | 
                
                 | 
                        The number of Ordinary Differential Equations (ODEs) in the system.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    97
                 | 
                                    
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                    params : dict(str: float)  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    98
                 | 
                                    
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                        A dictionary of parameters.  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    99
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                    rhs : function  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    100
                 | 
                                    
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                        Function which calculates the value of the right-hand side of a  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    101
                 | 
                                    
                                                     | 
                
                 | 
                        system of Ordinary Differential Equations (ODEs).  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    102
                 | 
                                    
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                 | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    103
                 | 
                                    
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                    """  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    104
                 | 
                                    
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                | 
                    105
                 | 
                                    
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                 | 
                    def __init__(self, bcs_lower, bcs_upper, number_bcs_lower, number_odes,  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    106
                 | 
                                    
                                                     | 
                
                 | 
                                 params, rhs):  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    107
                 | 
                                    
                                                     | 
                
                 | 
                        self._bcs_lower = bcs_lower  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    108
                 | 
                                    
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                        self._bcs_upper = bcs_upper  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    109
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                        self._number_bcs_lower = number_bcs_lower  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    110
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                        self._number_odes = number_odes  | 
            
            
                                                                                                            
                            
            
                                    
            
            
                | 
                    111
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                        self._params = dict(params)  # shallow copy!  | 
            
            
                                                                                                            
                                                                
            
                                    
            
            
                | 
                    112
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                 | 
                        self._rhs = rhs  | 
            
            
                                                        
            
                                    
            
            
                | 
                    113
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                 |