#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ Created on Thu Mar 7 19:29:46 2024 @author: silviamassaro """ import numpy as np import random import matplotlib.pyplot as plt import math from scipy import integrate # ========================== Definiton of (d0, d1) in km ====================== d0_km= 10 d1_km= 288 # ========================== Definiton of (T0, T1) in cm ====================== T= [100,10] # =========================Beta distributions for eccentricity ================ # Beta parameters to calculate (and sample) the equatorial eccentricity: # alpha_equatorial= 2.3911 # beta_equatorial = 1.0184 # beta_params = { # "equatorial": (alpha_equatorial, beta_equatorial), # } # Beta parameters to calculate (and sample) the mid-latitude eccentricity: alpha_midlatitude = 4.3004 beta_midlatitude = 1.0285 beta_params = { "midlatitude": (alpha_midlatitude, beta_midlatitude), } #Dictionary to memorize the sampled values of eccentricity based on equatorial #and mid-latitude volcanic belts: eps = {} num_samples = 1000 for choice in beta_params.keys(): alpha, beta = beta_params[choice] sampled_values = [random.betavariate(alpha, beta) for _ in range(num_samples)] eps[choice] = sampled_values print(f"Sampled eccentricity values {choice}: {eps[choice]}") #%%CALCULATIONS: #Define the range of sqrt(A)=x (for x0 and x1) r = math.sqrt(3.14) total_uniform=np.zeros(3000) # DEFINE THE FUNCTION TO CREATE UNIFORM DISTRIBUTION: def uniform_probability_function(x, mag_left, mag_right): if x >= mag_left and x <= mag_right: return 1 / (mag_right - mag_left) else: return 0 def calculate_percentile(min_value, max_value, percentile): if 0 <= percentile <= 1: return min_value + percentile * (max_value - min_value) else: raise ValueError("Il percentile deve essere compreso tra 0 e 1") # DEFINE LISTS USEFUL FOR HISTOGRAMS GRAPHS: #In these lists you can find the final results of Magnitude (min and max) that #will be shown in the histogram: dati_simu = [] mag_values = set() dati_mag_left=[] dati_mag_right=[] mag_medi=[] dati_vol_left=[] dati_vol_right=[] dati_mass_left=[] dati_mass_right=[] min_x = float('inf') max_x = float('-inf') #LOOP TO CHECK THE NECESSARY CONDITION TO CARRY ON THE CALCULATION: count=0 # Calculation of k and y: for eps_value in eps.values(): for val in eps_value: valore_float = float(val) eps2 = valore_float ** 2 k = 1 - eps2 y = pow(k, 0.25) ##WARNING: war = d0_km * 2 / k if d1_km > war: left0 = 0.5 * r * d0_km * y right0 = d0_km * r * y / k left1 = 0.5 * r * d1_km * y right1 = r * d1_km * y / k #print('***** Calculations for x0, x1 *****') #print(left0, ' < x0 < ', right0) #print(left1, ' < x1 < ', right1) count=count+1 #STEPS TO OBTAIN THE MAGNITUDE: #Calculate Lamba_thick range (in km) #Definition of the parameters used for l_left (minimum value): a1= (pow(d1_km,2)/4) a0 = (pow(d0_km,2)/pow(k,2)) a = a1-a0 b = math.log(T[0]/T[1]) arg1=a/b #Definition of the parameters used for l_right (maximum value): c1 = pow(d1_km,2)/pow(k,2) c0 = pow(d0_km,2)/4 c= c1-c0 arg2=c/b #lambda_left < lambda < lambda_right l_left_I= r*y*np.sqrt(arg1) l_right_I= r*y*np.sqrt(arg2) #print (l_left_I, ' < lambda < ', l_right_I) #Calculate Volume (in m^3) #volume_min(left) < volume < volume_max(right) vol_left= (3*1e06)*pow(l_left_I,1.53) vol_right= (3*1e06)*pow(l_right_I,1.53) dati_vol_left.append(vol_left) dati_vol_right.append(vol_right) print ('***** Calculations for Volumes *****') print (vol_left/1e9, ' < Volume (km^3) < ', vol_right/1e9) #Calculate Mass (in kg) rho= 1000 #bulk density of the deposit in (kg/m^3) mass_left = rho*vol_left mass_right = rho*vol_right dati_mass_left.append(mass_left) dati_mass_right.append(mass_right) #print (mass_left, ' < Mass (kg) < ', mass_right) #Calculation of the Magnitude (from Mason et al., 2004): #Magnitude_min(left) < Magnitude < Magnitude(right): mag_left= math.log10(mass_left)-7.0 mag_right= math.log10(mass_right)-7.0 dati_mag_left.append(mag_left) dati_mag_right.append(mag_right) print ('***** Calculations for Magnitude *****') print ('mag_min:', mag_left, 'mag_max:', mag_right) min_x = min(min_x, mag_left) max_x = max(max_x, mag_right) #For each sampled eccentricity, a mixing data function is created for each (mag_left, mag_right) data: integral_result, _ = integrate.quad(uniform_probability_function, mag_left, mag_right, args=(mag_left, mag_right)) #print("Area under the curve:", integral_result) # Creation of x values: x_values = np.linspace(min_x,max_x, 3000) #For each x, the probability values are calculated: probability_values = [uniform_probability_function(x, mag_left, mag_right) for x in x_values] total_uniform+=probability_values # ============================================================================= #******************************* PLOTS *************************************** # ============================================================================= #NORMALIZED UNIFORM DISTRIBUTION considering the normalized probability for #each couple of data (mag_min, mag_max): plt.plot(x_values, probability_values) plt.fill_between(x_values, probability_values, alpha=0.5) # ONLY FOR THE HISTOGRAM: Put Magnitude_min and Magnitude_max in different lists # so as to create histograms: dati_mag_medi=(mag_left+mag_right)/2 mag_medi.append(dati_mag_medi) dati_mag_left.append(mag_left) mag_values.add(mag_left) dati_mag_right.append(mag_right) mag_values.add(mag_right) plt.ylabel('Density of Probability') plt.title('Mixing distribution') plt.grid(True) plt.savefig('mixing.png', dpi=300, bbox_inches='tight') plt.show() print('Number of iterations:',count) # GRAPH OF THE NORMALIZED UNIFORM DISTRIBUTION (SUM): somma_area_finale=np.trapz(total_uniform) total_uniform_norm=total_uniform/somma_area_finale area_total_uniform_norm=np.trapz(total_uniform_norm) #print("Total area under the normalized curve:", area_total_uniform_norm) # CALCULATION OF THE CUMULATIVE PROBABILITY: cumulative_prob = np.cumsum(total_uniform_norm) # DRAW THE PERCENTILES ON THE GRAPH: (i.e., 1sigma, 2sigma) percentiles = [5, 16, 50, 84, 95] # Puoi aggiungere altri valori desiderati percentile_values = [np.interp(p / 100, cumulative_prob, x_values) for p in percentiles] plt.plot(x_values, total_uniform_norm) plt.fill_between(x_values, total_uniform_norm, alpha=0.5) # VERTICAL LINES FOR PERCENTILES: for percentile_value, color, percentile in zip(percentile_values, ['purple', 'green', 'red','orange', 'blue'], percentiles): plt.axvline(x=percentile_value, color=color, linestyle='--', label=f'Percentile {percentile}°') for p, value in zip(percentiles, percentile_values): print(f"Percentile {p}°: {value}") #LEGEND: min_x = np.min(x_values) max_x = np.max(x_values) min_y = np.min(total_uniform_norm) max_y = np.max(total_uniform_norm) plt.text(max_x - (max_x - min_x) * 1, max_y - (max_y - min_y) * 0.9, f'count: {count}', fontsize=12, ha='left', va='bottom', color='black') plt.ylabel('Normalized Probability') plt.xlabel('Magnitudo') plt.title('Normalized Uniform Distribution - FL, Etna') plt.legend(loc='best') plt.grid(False) plt.savefig('Test_FL_uniform.png', dpi=300) plt.show() # HISTOGRAMI: counts_right, bins_right = np.histogram(dati_mag_right, bins=8, range=(3, 7)) total_data_right = len(dati_mag_right) normalized_frequency_right = counts_right / total_data_right counts_left, bins_left = np.histogram(dati_mag_left, bins=8, range=(3, 7)) total_data_left = len(dati_mag_left) normalized_frequency_left = counts_left / total_data_left #CREATION OF THE HISTOGRAM OF THE SIMULATED DATA HAVING THE NORMALIZED FREQUENCY: fig, ax = plt.subplots() right_bars = ax.bar(bins_right[:-1], normalized_frequency_right, width=(bins_right[1]-bins_right[0]), color='orange', alpha=0.5, edgecolor='black', label='Modeled mag_right') left_bars = ax.bar(bins_left[:-1], normalized_frequency_left, width=(bins_left[1]-bins_left[0]), color='blue', alpha=0.5, edgecolor='black', label='Modeled mag_left') # AXES: ax.set_ylim(0, 1.1) # x-ticks: ax.set_xticks(np.concatenate([bins_right, bins_left])) xtick_labels = np.concatenate([bins_right, bins_left]) ax.set_xticklabels(xtick_labels, rotation=45) # WIDTH OF x-ticks: for bar in right_bars: bar.set_x(bar.get_x() - (bins_right[1] - bins_right[0]) / 2) for bar in left_bars: bar.set_x(bar.get_x() - (bins_left[1] - bins_left[0]) / 2) ax.set_xlabel('Magnitude') ax.set_ylabel('Normalized Frequency') ax.set_title('Test case: FL, Etna') ax.legend() # LEGEND: legend = ax.legend(fontsize='small') plt.savefig('Test_FL_histo.png', dpi=300, bbox_inches='tight') plt.show()