def test_rkdae(s):
sys = GraphSystem(sq)
u0 = np.array([0.,0.,1.])
scheme = RKDAE(.1, tableau=RK.RadauIIA.tableaux[s])
sol = Solver(scheme, sys)
sol.initialize(u0=u0)
CompareExact('RadauIIA-{0}'.format(s)), sol, u0, 2
def setUp(self):
self.file = tempfile.NamedTemporaryFile()
self.path = self.file.name
self.family = os.path.basename(self.path)
self.prefix = os.path.dirname(self.path)
self.file.close()
from odelab.scheme.classic import ExplicitEuler
self.params = params = {
'family': self.family,
'system': System,
'system_params': {
'f': f
},
'solver': Solver,
'scheme': ExplicitEuler,
'scheme_params': {
'h': .1,
},
'initialize': {
'u0': np.array([1.]),
'time': 1.,
'name': self.name,
},
}
scheme = ExplicitEuler(**params['scheme_params'])
s = Solver(system=System(f), scheme=scheme, path=self.path)
s.catch_runtime = False
s.initialize(**params['initialize'])
s.run()
def test_orders(expected_orders, scheme, plot=False, tol=.2):
system = QuasiGraphSystem(fsin)
#system = GraphSystem(fsin)
u0 = np.array([0.,0.,1])
solver = Solver(scheme, system)
#compare_exact(sol, u0, 2)
sol = solver
errz = []
errl = []
ks = np.arange(1,5)
for k in ks:
scheme.h = pow(2,-k)
sol.initialize(u0=u0)
sol.run(1)
zexact = sol.system.exact(sol.final_time(),u0)[0]
lexact = sol.system.exact(sol.final_time(),u0)[2]
df = sol.final()[0] - zexact
logerrz = np.log2(np.abs(df))
logerrl = np.log2(np.abs(sol.final()[2] - lexact))
errz.append(logerrz)
errl.append(logerrl)
if plot:
plt.clf()
plt.subplot(1,2,1)
plt.title('z')
plt.plot(ks,errz,'o-')
plt.legend()
plt.subplot(1,2,2)
plt.title(u'λ')
plt.plot(ks,errl,'o-')
plt.legend()
regz = order.linear_regression(ks,errz,do_plot=False)
regl = order.linear_regression(ks,errl,do_plot=False)
oz = -regz[0]
ol = -regl[0]
assert ol > expected_orders[0] - tol
assert oz > expected_orders[1] - tol
return sol