integrators/idas.py

This example looks at the use of casadi::Integrator();

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See also
casadi::integrator();
casadi::integrator
CASADI_EXPORT Function integrator(const std::string &name, const std::string &solver, const SXDict &dae, const Dict &opts=Dict())
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31 from casadi import *
32 from numpy import *
33 from pylab import *
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43 L = SX.sym("L")
44 g = SX.sym("g")
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48 x=SX.sym("x")
49 y=SX.sym("y")
50 u=SX.sym("u")
51 v=SX.sym("v")
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55 lambd=SX.sym("lambda")
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59 x_all = vertcat(x,u,y,v)
60 z_all = lambd
61 p_all = vertcat(L,g)
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65 P_ = [5,10]
66 X_ = [3,-1.0/3,4,1.0/4]
67 XDOT_ = [-1.0/3,1147.0/240,1.0/4,-653.0/180]
68 Z_ = [1147.0/720]
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72 ode = vertcat(u,lambd*x,v,lambd*y+g)
73 alg = x**2+y**2-L**2
74 dae = {'x':x_all, 'z':z_all, 'p':p_all, 'ode':ode, 'alg':alg}
75 f = Function('f', [x_all, z_all, p_all], [ode, alg], ['x', 'z', 'p'], ['ode', 'alg'])
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79 res = f(p=P_, x=X_, z=Z_)
80 print(res['ode'])
81 print(res['alg'])
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86 j = jacobian(alg,lambd)
87 print(j)
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96 I = integrator('I', 'idas', dae, {'calc_ic':False, 'init_xdot':XDOT_})
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101 try:
102  I(p=P_, x0=X_, z0=Z_)
103 except Exception as e:
104  print(e)
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108 ode = vertcat(u,lambd*x)
109 alg = vertcat(x**2+y**2-L**2, u*x+v*y,u**2-g*y+v**2+L**2*lambd)
110 x_all = vertcat(x,u)
111 z_all = vertcat(y,v,lambd)
112 dae = {'x':x_all, 'z':z_all, 'p':p_all, 'ode':ode, 'alg':alg}
113 f = Function('f', [x_all, z_all, p_all], [ode, alg], ['x', 'z', 'p'], ['ode', 'alg'])
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117 P_ = [5,10]
118 X_ = [3,-1.0/3]
119 XDOT_ = [-1.0/3,1147.0/240]
120 Z_ = [4,1.0/4,1147.0/720]
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124 res = f(p=P_, x=X_, z=Z_)
125 print(res['ode'])
126 print(res['alg'])
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130 J = f.factory('J', f.name_in(), ['jac:alg:z'])
131 res = J(p=P_, x=X_, z=Z_)
132 print(array(res["jac_alg_z"]))
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138 I = integrator('I', 'idas', dae, {'t0':0, 'tf':1, 'init_xdot':XDOT_})
139 res = I(p=P_, x0=X_, z0=Z_)
140 print(res['xf'])
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147 P_ = [5,10]
148 X_ = [5,0]
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152 try:
153  I(p=P_, x0=X_, z0=Z_)
154 except Exception as e:
155  print(e)
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