def test_exact(self, scheme): self.sys = VerticalRollingDisk() self.scheme = scheme ohm_phi = 2. ohm_theta = 1. phi_0 = 0 self.u0 = self.sys.initial(np.array([0,0,phi_0,0.,0,0,ohm_phi,ohm_theta,0,0])) R = self.sys.radius m = self.sys.mass # consistent initial velocities vx = self.u0[4] = R*ohm_theta*np.cos(phi_0) vy = self.u0[5] = R*ohm_theta*np.sin(phi_0) # lagrange multipliers: used only used as a guess in RK methods self.u0[8], self.u0[9] = -m*ohm_phi*R*ohm_theta*np.sin(phi_0), m*ohm_phi*R*ohm_theta*np.cos(phi_0) self.scheme.h = self.h self.s = Solver(self.scheme, self.sys) self.s.initialize(self.u0,) self.s.run(1.) ## self.s.plot(components=[6,7]) self.check_solution()
from odelab import Solver from odelab.scheme.classic import RungeKutta4 from odelab.system.classic import VanderPol s = Solver(scheme=RungeKutta4(.1), system=VanderPol()) s.initialize([2.7,0], name='2.7') s.run(10.) s.plot2D() s.initialize([1.3,0], name='1.3') s.run(10.) s.plot2D()
from odelab import Solver from odelab.scheme.classic import RungeKutta4 from odelab.system.classic import VanderPol s = Solver(scheme=RungeKutta4(.1), system=VanderPol()) s.initialize([2.7, 0], name='2.7') s.run(10.) s.plot2D() s.initialize([1.3, 0], name='1.3') s.run(10.) s.plot2D()
class TestVerticalRollingDisk:
h = .1
def test_exact(self, scheme):
self.sys = VerticalRollingDisk()
self.scheme = scheme
ohm_phi = 2.
ohm_theta = 1.
phi_0 = 0
self.u0 = self.sys.initial(np.array([0,0,phi_0,0.,0,0,ohm_phi,ohm_theta,0,0]))
R = self.sys.radius
m = self.sys.mass
# consistent initial velocities
vx = self.u0[4] = R*ohm_theta*np.cos(phi_0)
vy = self.u0[5] = R*ohm_theta*np.sin(phi_0)
# lagrange multipliers: used only used as a guess in RK methods
self.u0[8], self.u0[9] = -m*ohm_phi*R*ohm_theta*np.sin(phi_0), m*ohm_phi*R*ohm_theta*np.cos(phi_0)
self.scheme.h = self.h
self.s = Solver(self.scheme, self.sys)
self.s.initialize(self.u0,)
self.s.run(1.)
## self.s.plot(components=[6,7])
self.check_solution()
def check_solution(self, decimal=1):
npt.assert_array_almost_equal(self.s.final()[:8], self.sys.exact(np.array([self.s.final_time()]),u0=self.u0)[:8,0], decimal=decimal)
def check_energy(self, decimal):
energy = self.sys.energy
npt.assert_almost_equal(energy(self.s.final()), energy(self.s.initial()), decimal=decimal)
experiences = {'50': (.01,50), '1000': (.1,1000.)}
def run_experience(self, exp_name):
h,time = self.experiences[exp_name]
self.s.initialize(h=h,time=time)
self.s.run()
from odelab import Solver, System
from odelab.scheme.classic import ExplicitEuler
def f(t, u):
return -u
s = Solver(scheme=ExplicitEuler(0.1), system=System(f))
s.initialize(u0=1.0)
s.run(1.0)
s.plot()
from odelab import Solver, System from odelab.scheme.classic import ExplicitEuler def f(t,u): return -u s = Solver(scheme=ExplicitEuler(.1), system=System(f)) s.initialize(u0=1.) s.run(1.) s.plot()