def convergence_test():
'''
Used to obtain plots of L1 norm versus parameters (Number of elements
or N_LGL).
'''
L1_norm_option_1 = np.zeros([15])
N_lgl = (np.arange(15) + 3).astype(float)
L1_norm_option_3 = np.zeros([15])
for i in range(0, 15):
test_waveEqn.change_parameters(i + 3, 15, i + 3)
u_diff = wave_equation.time_evolution()
L1_norm_option_1[i] = L1_norm(u_diff)
test_waveEqn.change_parameters(i + 3, 15, i + 4)
u_diff = wave_equation.time_evolution()
L1_norm_option_3[i] = L1_norm(u_diff)
print(L1_norm_option_1, L1_norm_option_3)
normalization = 0.00281 / (3 **(-3))
plt.loglog(N_lgl, L1_norm_option_1, marker='o', label='option 1')
plt.loglog(N_lgl, L1_norm_option_3, marker='o', label='option 3')
plt.xlabel('No. of LGL points')
plt.ylabel('L1 norm of error')
plt.title('L1 norm after 1 full advection')
plt.loglog(N_lgl, normalization * N_lgl **(-N_lgl), color='black',\
linestyle='--', label='$N_{LGL}^{-N_{LGL}}$')
plt.legend(loc='best')
plt.show()
return
#B_00 = 0.2
#B_01 = 0.5
#E_z_init = E_00 * af.sin(2 * np.pi * params.element_LGL) \
#+ E_01 * af.cos(2 * np.pi * params.element_LGL)
#B_y_init = B_00 * af.sin(2 * np.pi * params.element_LGL) \
#+ B_01 * af.cos(2 * np.pi * params.element_LGL)
## 2. Gaussian
#E_0 = 1.
#B_0 = 1.
#sigma = 0.1
#E_z_init = E_0 * np.e**(-(params.element_LGL)**2 / sigma**2)
#B_y_init = B_0 * np.e**(-(params.element_LGL)**2 / sigma**2)
###############################################################
####################### SET u_init ############################
###############################################################
#u_init = af.constant(0., d0 = params.N_LGL, d1 = params.N_Elements, d2 = 2)
#u_init[:, :, 0] = E_z_init
#u_init[:, :, 1] = B_y_init
u_init = params.u_init
u_diff = wave_equation.time_evolution(u_init)