def show_timeorder_info(Dt, mesh_sizes, errors):
'''Performs consistency check for the given problem/method combination and
show some information about it. Useful for debugging.
'''
# Compute the numerical order of convergence.
orders = {}
for key in errors:
orders[key] = _compute_numerical_order_of_convergence(Dt, errors[key])
# Print the data to the screen
for i, mesh_size in enumerate(mesh_sizes):
print
print('Mesh size %d:' % mesh_size)
print('dt = %e' % Dt[0]),
for label, e in errors.items():
print(' err_%s = %e' % (label, e[i][0])),
print
for j in range(len(Dt) - 1):
print(' '),
for label, o in orders.items():
print(' ord_%s = %e' % (label, o[i][j])),
print
print('dt = %e' % Dt[j+1]),
for label, e in errors.items():
print(' err_%s = %e' % (label, e[i][j+1])),
print
# Create a figure
for label, err in errors.items():
pp.figure()
ax = pp.axes()
# Plot the actual data.
for i, mesh_size in enumerate(mesh_sizes):
pp.loglog(Dt, err[i], '-o', label=mesh_size)
# Compare with order curves.
pp.autoscale(False)
e0 = err[-1][0]
for o in range(7):
pp.loglog([Dt[0], Dt[-1]],
[e0, e0 * (Dt[-1] / Dt[0]) ** o],
color='0.7')
pp.xlabel('dt')
pp.ylabel('||%s-%s_h||' % (label, label))
# pp.title('Method: %s' % method['name'])
ppl.legend(ax, loc=4)
pp.show()
return
# Extract parameters and errors
Sbar = L.params["Sest"].value
r = np.exp([L.params["r" + str(i)].value for i in range(periodicity)])
alphaSbar = L.params["alpha"].value
errup = np.exp(
np.log(r) +
[2 * L.params["r" + str(i)].stderr for i in range(periodicity)])
errdn = np.exp(
np.log(r) -
[2 * L.params["r" + str(i)].stderr for i in range(periodicity)])
# Plot
subplot(121)
plt.axvline(x=Sbar, color=colours[1], linewidth=3)
plt.axvline(x=1 / zeta, color=colours[2], linewidth=3)
plt.loglog(Svals, l, linewidth=3)
title("Goodness of Fit")
xlabel(r"$\bar{S}$")
ylabel(r"$\chi^2$")
legend([
r"Profile Likelihood $\bar{S}$ = " + str(int(Sbar)),
r"Taylor Expansion $\bar{S}$ = " + str(int(1 / zeta))
])
subplot(122)
#plt.plot(rstar, linewidth=2)
plt.plot(r, linewidth=3)
plt.fill_between(range(periodicity), errup, errdn, color=colours[0], alpha=0.3)
plt.plot(rstar * zeta, linewidth=3)
xlim([0, periodicity])
title("Periodicity")
r = np.exp([L.params["r" + str(i)].value for i in range(periodicity)])
alphaSbar = L.params["alpha"].value
errup = np.exp(np.log(r) + [2*L.params["r" + str(i)].stderr for i in range(periodicity)])
errdn = np.exp(np.log(r) - [2*L.params["r" + str(i)].stderr for i in range(periodicity)])
# Plot
subplot(121)
plt.axvline(x=Sbar, color=colours[1], linewidth=3)
plt.axvline(x=1/zeta, color=colours[2], linewidth=3)
plt.loglog(Svals, l, linewidth=3)
title("Goodness of Fit")
xlabel(r"$\bar{S}$")
ylabel(r"$\chi^2$")
legend([r"Profile Likelihood $\bar{S}$ = " + str(int(Sbar)), r"Taylor Expansion $\bar{S}$ = " + str(int(1/zeta))])
subplot(122)
#plt.plot(rstar, linewidth=2)
plt.plot(r, linewidth=3)
plt.fill_between(range(periodicity), errup, errdn, color=colours[0], alpha=0.3)
plt.plot(rstar * zeta, linewidth=3)
xlim([0, periodicity])
title("Periodicity")
xlabel("Period")
legend(["Using Full Equation", "Using Taylor Expansion"])
