def plot_sample_and_theoretical_pdf_of_abs_fft_noise(
fft_well_log,
list_wave_number,
list_hurst_related_exponent,
list_characteristic_distance,
squared_energy_of_window,
variance_of_noise_in_time_domain,
output_directory,
output_file_base_name,
figure_output_settings,
):
figure = plt.figure()
# sample pdf (histogram)
for hurst_related_exponent_local, characteristic_dist_local in zip(
list_hurst_related_exponent, list_characteristic_distance
):
von_karman_energy_spectrum = calc_von_karman_energy_spectrum(
list_wave_number, hurst_related_exponent_local, characteristic_dist_local
)
rayleigh_rand_var_instance = calc_rayleigh_rand_var_instances_from_fft_well_log(
fft_well_log, von_karman_energy_spectrum
)
label_str = "(%.3f,%.3f)" % (hurst_related_exponent_local, characteristic_dist_local)
plt.hist(rayleigh_rand_var_instance, bins=100, normed=True, label=label_str, histtype="step")
plt.legend(loc="upper right")
# theoretical pdf
random_variable = make_rayleigh_rand_var_of_abs_fft_noise(
squared_energy_of_window, variance_of_noise_in_time_domain
)
support = np.linspace(0, max(np.abs(fft_well_log)))
plt.plot(support, random_variable.pdf(support))
output_file = output_directory + os.path.sep + output_file_base_name
ph.saveFigureToFile(figure, output_file, **figure_output_settings)
likelihood_by_hurst_characteristic = 1 / brute_opt_result[3]
# the third return argument of brute search is the search grid,
# so likelihood_by_hurst_characteristic should be the value *inside* those bounds.
# Therefore, remove the last value from likelihood_by_hurst_characteristic
likelihood_by_hurst_characteristic = likelihood_by_hurst_characteristic[:-1, :-1]
p = ax.pcolormesh(brute_opt_result[2][1],
brute_opt_result[2][0],
likelihood_by_hurst_characteristic)
figure.colorbar(p)
plt.xlabel('b (characteristic_distance)')
plt.xticks(rotation=90)
plt.ylabel('H (hurst_related_exponent)')
ax.set_title(exhaustive_search_result_str)
output_file_base_name = "true_v_opt_b_H"
output_file = output_directory + os.path.sep + output_file_base_name
plot_helper.saveFigureToFile(figure, output_file, **figure_output_settings)
# constrained optimization
do_box_constrained_optimization = 0
if do_box_constrained_optimization:
hurst_hurst_related_exponent_min = -0.49
hurst_hurst_related_exponent_max = 1.0
characteristic_dist_min = 1.0
characteristic_dist_max = 12.0
initial_guess = (0.5 * (hurst_hurst_related_exponent_min + hurst_hurst_related_exponent_max),
0.5 * (characteristic_dist_min + characteristic_dist_max))
minimize_result = optimize.minimize(likelihood_measure.calc_inverse_likelihood,
initial_guess,
args=params,
method="TNC",
