<s> from __future__ import print_function , division <EOL> __all__ = [ '<STR_LIT>' ] <EOL> from sympy import diff , zeros , Matrix , eye , sympify <EOL> from sympy . physics . vector import dynamicsymbols , ReferenceFrame <EOL> from sympy . physics . mechanics . functions import ( find_dynamicsymbols , msubs , <EOL> _f_list_parser ) <EOL> from sympy . physics . mechanics . linearize import Linearizer <EOL> from sympy . utilities import default_sort_key <EOL> from sympy . utilities . exceptions import SymPyDeprecationWarning <EOL> from sympy . utilities . iterables import iterable <EOL> class LagrangesMethod ( object ) : <EOL> """<STR_LIT>""" <EOL> def __init__ ( self , Lagrangian , qs , coneqs = None , forcelist = None , <EOL> frame = None , hol_coneqs = None , nonhol_coneqs = None ) : <EOL> """<STR_LIT>""" <EOL> self . _L = Matrix ( [ sympify ( Lagrangian ) ] ) <EOL> self . eom = None <EOL> self . _m_cd = Matrix ( ) <EOL> self . _m_d = Matrix ( ) <EOL> self . _f_cd = Matrix ( ) <EOL> self . _f_d = Matrix ( ) <EOL> self . lam_coeffs = Matrix ( ) <EOL> forcelist = forcelist if forcelist else [ ] <EOL> if not iterable ( forcelist ) : <EOL> raise TypeError ( '<STR_LIT>' ) <EOL> self . _forcelist = forcelist <EOL> if frame and not isinstance ( frame , ReferenceFrame ) : <EOL> raise TypeError ( '<STR_LIT>' ) <EOL> self . inertial = frame <EOL> self . lam_vec = Matrix ( ) <EOL> self . _term1 = Matrix ( ) <EOL> self . _term2 = Matrix ( ) <EOL> self . _term3 = Matrix ( ) <EOL> self . _term4 = Matrix ( ) <EOL> if not iterable ( qs ) : <EOL> raise TypeError ( '<STR_LIT>' ) <EOL> self . _q = Matrix ( qs ) <EOL> self . _qdots = self . q . diff ( dynamicsymbols . _t ) <EOL> self . _qdoubledots = self . _qdots . diff ( dynamicsymbols . _t ) <EOL> if coneqs : <EOL> SymPyDeprecationWarning ( "<STR_LIT>" <EOL> "<STR_LIT>" <EOL> "<STR_LIT>" ) . warn ( ) <EOL> self . coneqs = coneqs <EOL> else : <EOL> mat_build = lambda x : Matrix ( x ) if x else Matrix ( ) <EOL> hol_coneqs = mat_build ( hol_coneqs ) <EOL> nonhol_coneqs = mat_build ( nonhol_coneqs ) <EOL> self . coneqs = Matrix ( [ hol_coneqs . diff ( dynamicsymbols . _t ) , <EOL> nonhol_coneqs ] ) <EOL> self . _hol_coneqs = hol_coneqs <EOL> def form_lagranges_equations ( self ) : <EOL> """<STR_LIT>""" <EOL> qds = self . _qdots <EOL> qdd_zero = dict ( ( i , <NUM_LIT:0> ) for i in self . _qdoubledots ) <EOL> n = len ( self . q ) <EOL> self . _term1 = self . _L . jacobian ( qds ) <EOL> self . _term1 = self . _term1 . diff ( dynamicsymbols . _t ) . T <EOL> self . _term2 = self . _L . jacobian ( self . q ) . T <EOL> if self . coneqs : <EOL> coneqs = self . coneqs <EOL> m = len ( coneqs ) <EOL> self . lam_vec = Matrix ( dynamicsymbols ( '<STR_LIT>' + str ( m + <NUM_LIT:1> ) ) ) <EOL> self . lam_coeffs = - coneqs . jacobian ( qds ) <EOL> self . _term3 = self . lam_coeffs . T * self . lam_vec <EOL> diffconeqs = coneqs . diff ( dynamicsymbols . _t ) <EOL> self . _m_cd = diffconeqs . jacobian ( self . _qdoubledots ) <EOL> self . _f_cd = - diffconeqs . subs ( qdd_zero ) <EOL> else : <EOL> self . _term3 = zeros ( n , <NUM_LIT:1> ) <EOL> if self . forcelist : <EOL> N = self . inertial <EOL> self . _term4 = zeros ( n , <NUM_LIT:1> ) <EOL> for i , qd in enumerate ( qds ) : <EOL> flist = zip ( * _f_list_parser ( self . forcelist , N ) ) <EOL> self . _term4 [ i ] = sum ( v . diff ( qd , N ) & f for ( v , f ) in flist ) <EOL> else : <EOL> self . _term4 = zeros ( n , <NUM_LIT:1> ) <EOL> without_lam = self . _term1 - self . _term2 - self . _term4 <EOL> self . _m_d = without_lam . jacobian ( self . _qdoubledots ) <EOL> self . _f_d = - without_lam . subs ( qdd_zero ) <EOL> self . eom = without_lam - self . _term3 <EOL> return self . eom <EOL> @ property <EOL> def mass_matrix ( self ) : <EOL> """<STR_LIT>""" <EOL> if self . eom is None : <EOL> raise ValueError ( '<STR_LIT>' ) <EOL> if self . coneqs : <EOL> return ( self . _m_d ) . row_join ( self . lam_coeffs . T ) <EOL> else : <EOL> return self . _m_d <EOL> @ property <EOL> def mass_matrix_full ( self ) : <EOL> """<STR_LIT>""" <EOL> if self . eom is None : <EOL> raise ValueError ( '<STR_LIT>' ) <EOL> n = len ( self . q ) <EOL> m = len ( self . coneqs ) <EOL> row1 = eye ( n ) . row_join ( zeros ( n , n + m ) ) <EOL> row2 = zeros ( n , n ) . row_join ( self . mass_matrix ) <EOL> if self . coneqs : <EOL> row3 = zeros ( m , n ) . row_join ( self . _m_cd ) . row_join ( zeros ( m , m ) ) <EOL> return row1 . col_join ( row2 ) . col_join ( row3 ) <EOL> else : <EOL> return row1 . col_join ( row2 ) <EOL> @ property <EOL> def forcing ( self ) : <EOL> """<STR_LIT>""" <EOL> if self . eom is None : <EOL> raise ValueError ( '<STR_LIT>' ) <EOL> return self . _f_d <EOL> @ property <EOL> def forcing_full ( self ) : <EOL> """<STR_LIT>""" <EOL> if self . eom is None : <EOL> raise ValueError ( '<STR_LIT>' ) <EOL> if self . coneqs : <EOL> return self . _qdots . col_join ( self . forcing ) . col_join ( self . _f_cd ) <EOL> else : <EOL> return self . _qdots . col_join ( self . forcing ) <EOL> def to_linearizer ( self , q_ind = None , qd_ind = None , q_dep = None , qd_dep = None ) : <EOL> """<STR_LIT>""" <EOL> t = dynamicsymbols . _t <EOL> q = self . q <EOL> u = self . _qdots <EOL> ud = u . diff ( t ) <EOL> lams = self . lam_vec <EOL> mat_build = lambda x : Matrix ( x ) if x else Matrix ( ) <EOL> q_i = mat_build ( q_ind ) <EOL> q_d = mat_build ( q_dep ) <EOL> u_i = mat_build ( qd_ind ) <EOL> u_d = mat_build ( qd_dep ) <EOL> f_c = self . _hol_coneqs <EOL> f_v = self . coneqs <EOL> f_a = f_v . diff ( t ) <EOL> f_0 = u <EOL> f_1 = - u <EOL> f_2 = self . _term1 <EOL> f_3 = - ( self . _term2 + self . _term4 ) <EOL> f_4 = - self . _term3 <EOL> if len ( q_d ) != len ( f_c ) or len ( u_d ) != len ( f_v ) : <EOL> raise ValueError ( ( "<STR_LIT>" + <EOL> "<STR_LIT>" ) . format ( len ( f_c ) , len ( f_v ) ) ) <EOL> if set ( Matrix ( [ q_i , q_d ] ) ) != set ( q ) : <EOL> raise ValueError ( "<STR_LIT>" + <EOL> "<STR_LIT>" ) <EOL> if set ( Matrix ( [ u_i , u_d ] ) ) != set ( u ) : <EOL> raise ValueError ( "<STR_LIT>" + <EOL> "<STR_LIT>" ) <EOL> insyms = set ( Matrix ( [ q , u , ud , lams ] ) ) <EOL> r = list ( find_dynamicsymbols ( f_3 , insyms ) ) <EOL> r . sort ( key = default_sort_key ) <EOL> for i in r : <EOL> if diff ( i , dynamicsymbols . _t ) in r : <EOL> raise ValueError ( '<STR_LIT>' ) <EOL> return Linearizer ( f_0 , f_1 , f_2 , f_3 , f_4 , f_c , f_v , f_a , q , u , q_i , <EOL> q_d , u_i , u_d , r , lams ) <EOL> def linearize ( self , q_ind = None , qd_ind = None , q_dep = None , qd_dep = None , <EOL> ** kwargs ) : <EOL> """<STR_LIT>""" <EOL> linearizer = self . to_linearizer ( q_ind , qd_ind , q_dep , qd_dep ) <EOL> result = linearizer . linearize ( ** kwargs ) <EOL> return result + ( linearizer . r , ) <EOL> def solve_multipliers ( self , op_point = None , sol_type = '<STR_LIT>' ) : <EOL> """<STR_LIT>""" <EOL> k = len ( self . lam_vec ) <EOL> if k == <NUM_LIT:0> : <EOL> raise ValueError ( "<STR_LIT>" ) <EOL> if isinstance ( op_point , dict ) : <EOL> op_point_dict = op_point <EOL> elif iterable ( op_point ) : <EOL> op_point_dict = { } <EOL> for op in op_point : <EOL> op_point_dict . update ( op ) <EOL> elif op_point is None : <EOL> op_point_dict = { } <EOL> else : <EOL> raise TypeError ( "<STR_LIT>" <EOL> "<STR_LIT>" ) <EOL> mass_matrix = self . mass_matrix . col_join ( ( - self . lam_coeffs . row_join ( <EOL> zeros ( k , k ) ) ) ) <EOL> force_matrix = self . forcing . col_join ( self . _f_cd ) <EOL> mass_matrix = msubs ( mass_matrix , op_point_dict ) <EOL> force_matrix = msubs ( force_matrix , op_point_dict ) <EOL> sol_list = mass_matrix . LUsolve ( - force_matrix ) [ - k : ] <EOL> if sol_type == '<STR_LIT>' : <EOL> return dict ( zip ( self . lam_vec , sol_list ) ) <EOL> elif sol_type == '<STR_LIT>' : <EOL> return Matrix ( sol_list ) <EOL> else : <EOL> raise ValueError ( "<STR_LIT>" . format ( sol_type ) ) <EOL> def rhs ( self , inv_method = None , ** kwargs ) : <EOL> """<STR_LIT>""" <EOL> if '<STR_LIT>' in kwargs : <EOL> SymPyDeprecationWarning ( feature = "<STR_LIT>" , <EOL> useinstead = "<STR_LIT>" , <EOL> deprecated_since_version = "<STR_LIT>" ) . warn ( ) <EOL> inv_method = kwargs [ '<STR_LIT>' ] <EOL> if inv_method is None : <EOL> self . _rhs = self . mass_matrix_full . LUsolve ( self . forcing_full ) <EOL> else : <EOL> self . _rhs = ( self . mass_matrix_full . inv ( inv_method , <EOL> try_block_diag = True ) * self . forcing_full ) <EOL> return self . _rhs <EOL> @ property <EOL> def q ( self ) : <EOL> return self . _q <EOL> @ property <EOL> def u ( self ) : <EOL> return self . _qdots <EOL> @ property <EOL> def forcelist ( self ) : <EOL> return self . _forcelist </s>
