def test_quasigraph(self, plot=False):
sol = self.solver
errz = []
errl = []
ks = np.arange(1, 5)
for k in ks:
self.scheme.h = pow(2, -k)
sol.initialize(u0=self.u0,
time=1,
name='{0}_{1}'.format(type(self).__name__, k))
sol.run()
zexact = sol.system.exact(sol.final_time(), self.u0)[0]
lexact = sol.system.exact(sol.final_time(), self.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)
pl.clf()
pl.subplot(1, 2, 1)
pl.title('z')
regz = order.linear_regression(ks, errz, do_plot=True)
pl.plot(ks, errz, 'o-')
pl.legend()
pl.subplot(1, 2, 2)
pl.title(u'λ')
regl = order.linear_regression(ks, errl, do_plot=True)
pl.plot(ks, errl, 'o-')
pl.legend()
oz = -regz[0]
ol = -regl[0]
nt.assert_greater(ol, self.expected_orders[0] - self.tol)
nt.assert_greater(oz, self.expected_orders[1] - self.tol)
return sol
def test_quasigraph(self, plot=False):
sol = self.solver
errz = []
errl = []
ks = np.arange(1,5)
for k in ks:
self.scheme.h = pow(2,-k)
sol.initialize(u0=self.u0,time=1, name='{0}_{1}'.format(type(self).__name__, k))
sol.run()
zexact = sol.system.exact(sol.final_time(),self.u0)[0]
lexact = sol.system.exact(sol.final_time(),self.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)
plt.clf()
plt.subplot(1,2,1)
plt.title('z')
regz = order.linear_regression(ks,errz,do_plot=True)
plt.plot(ks,errz,'o-')
plt.legend()
plt.subplot(1,2,2)
plt.title(u'λ')
regl = order.linear_regression(ks,errl,do_plot=True)
plt.plot(ks,errl,'o-')
plt.legend()
oz = -regz[0]
ol = -regl[0]
nt.assert_greater(ol, self.expected_orders[0] - self.tol)
nt.assert_greater(oz, self.expected_orders[1] - self.tol)
return sol
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
