def c1_test(self, plot=True):
"""
Plot the reconstructed Neumann data, as approximated by a Chebyshev
expansion. If the Chebyshev expansion shows "spikes" near the
interfaces of the segments, something is probably wrong.
"""
sample = self.get_boundary_sample()
do_exact = hasattr(self.problem, 'eval_d_u_outwards')
s_data = np.zeros(len(sample))
expansion_data = np.zeros(len(sample))
if do_exact:
exact_data = np.zeros(len(sample))
for l in range(len(sample)):
p = sample[l]
s_data[l] = p['s']
if do_exact:
exact_data[l] = self.problem.eval_d_u_outwards(p['arg'], p['sid']).real
r, th = domain_util.cart_to_polar(p['x'], p['y'])
sid = domain_util.get_sid(self.a, th)
if sid == 0:
arg = th
else:
arg = r
for JJ in range(len(self.B_desc)):
expansion_data[l] +=\
(self.c1[JJ] *
self.eval_dn_B_arg(0, JJ, arg, sid)).real
import matplotlib.pyplot as plt
if do_exact:
error = np.max(np.abs(exact_data - expansion_data))
print('c1 error: {}'.format(error))
plt.plot(s_data, exact_data, linewidth=5, color='#BBBBBB', label='Exact')
if not plot:
return
plt.plot(s_data, expansion_data, label='Expansion')
plt.legend(loc=2)
#plt.ylim(-1.5, 1.5)
plt.title('c1')
plt.xlabel('Arclength s')
plt.ylabel('Reconstructed Neumann data')
plt.show()
def c0_test(self, plot=True):
"""
Plot the Dirichlet data along with its Chebyshev expansion. If there
is more than a minor difference between the two, something is wrong.
"""
k = self.k
a = self.a
nu = self.nu
sample = self.get_boundary_sample()
s_data = np.zeros(len(sample))
exact_data = np.zeros(len(sample))
expansion_data = np.zeros(len(sample))
exact_data_outer = []
expansion_data_outer = []
for l in range(len(sample)):
p = sample[l]
s_data[l] = p['s']
r, th = domain_util.cart_to_polar(p['x'], p['y'])
sid = domain_util.get_sid(self.a, th)
exact_data[l] = self.problem.eval_bc(p['arg'], sid).real
if sid == 0:
arg = th
else:
arg = r
for JJ in range(len(self.B_desc)):
expansion_data[l] +=\
(self.c0[JJ] *
self.eval_dn_B_arg(0, JJ, arg, sid)).real
if sid == 0:
exact_data_outer.append(exact_data[l])
expansion_data_outer.append(expansion_data[l])
exact_data_outer = np.array(exact_data_outer)
expansion_data_outer = np.array(expansion_data_outer)
print('c0 error outer:', np.max(np.abs(exact_data_outer - expansion_data_outer)))
print('c0 error:', np.max(np.abs(exact_data - expansion_data)))
#for l in range(len(exact_data)):
# diff = abs(exact_data[l] - expansion_data[l])
# if diff > .06:
# print(sample[l], 'diff:', diff)
if not plot:
return
import matplotlib.pyplot as plt
plt.plot(s_data, exact_data, linewidth=5, color='#BBBBBB', label='Exact')
plt.plot(s_data, expansion_data, label='Expansion')
plt.legend(loc=0)
plt.title('c0')
plt.xlabel('Arclength s')
plt.ylabel('Dirichlet data')
plt.show()
