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H_Rindler_calc.py
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H_Rindler_calc.py
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import pandas as pd
import itertools
from causalsetfunctions import find_entropy, linear
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
d_array = [2,3,4]
moleculetype = 'lambda'
for d in d_array:
if moleculetype == 'lambda':
df = pd.read_csv(f'H_Rindler{d}d_lambda.csv', names=['rho', 'H', 'b'], header=None)
df['rho'] = df['rho'].round(1)
elif moleculetype == 'v':
df = pd.read_csv(f'H_Rindler{d}d_v.csv', names=['rho', 'H', 'subgraphs', 'connected','b'], header=None)
df['rho'] = df['rho'].round(1)
#print(df)
rho_array = df['rho'].unique()
rho_array.sort()
y_entropyList = list()
x = list()
totalLinksList = list()
AoverlList = list()
totalLinksErrorList = list()
for rho in rho_array:
print('\n sprinkling density',rho, f'in {d} dimensions')
iterationsNo = df[df['rho'] == rho].shape[0]
print(f'number of iterations: {iterationsNo}')
if moleculetype == 'lambda':
totalHarray = [sum(x) for x in itertools.zip_longest(*[[int(x) if x != '' else 0 for x in a.replace('[', '').replace(']', '').split(', ')] for a in df[df['rho'] == rho]['H'].values], fillvalue=0)]
dataArray = np.array([x for x in itertools.zip_longest(*[[int(x) if x != '' else 0 for x in a.replace('[', '').replace(']', '').split(', ')] for a in df[df['rho'] == rho]['H'].values], fillvalue=0)])
elif moleculetype == 'v':
totalHarray = np.sum([df[df['rho'] == rho]['H'].values])
dataArray = [df[df['rho'] == rho]['H'].values]
print('total Harray \n', totalHarray)
print('p_i:', totalHarray/ np.sum(totalHarray))
if moleculetype == 'lambda':
totalLinks = 0
for i, value in enumerate(totalHarray):
totalLinks += (i+1)*value
print(f'Total Links: {totalLinks}')
elif moleculetype == 'v':
totalLinks = totalHarray
empiricalavalue = rho**((2-d)/d)*(totalLinks/iterationsNo)
totalLinksList.append(totalLinks/iterationsNo)
AoverlList.append((1/ rho**((2-d)/d)))
dataArrayLinks = dataArray
try:
for row in range(len(dataArray)):
dataArrayLinks[row,:] = dataArray[row,:]*(row+1)
except:
pass
LinksArray = np.sum(dataArrayLinks, axis = 0)
percaErr = np.std(LinksArray)/ (totalLinks/iterationsNo)
#due to flucutations in std<H1>
aerror = percaErr*empiricalavalue/ np.sqrt(iterationsNo)
print(f'Empirical a value {empiricalavalue} +- {aerror} ')
totalLinksErrorList.append(np.std(LinksArray)/(totalLinks/iterationsNo))
if moleculetype == 'lambda':
#theoryauncorrected
if d == 4:
theoryacorrected =0.173205
elif d== 3:
theoryacorrected = 0.2188
elif d== 2:
theoryacorrected = 1/3
print(f'theoretical a value for rho {d}d is {theoryacorrected} ')
if moleculetype == 'lambda':
#lambda molecules
#entropy = find_entropy(totalHarray, iterationsNo)
#links
entropy = totalLinks/iterationsNo
elif moleculetype == 'v':
entropy = totalHarray/ iterationsNo
#due to fluctiations in <N>, avr no. of molecules per realisation
MoleculeArray = np.sum(dataArray, axis = 0)
percEntropyError = np.std(MoleculeArray)/ ((np.sum(totalHarray)/ iterationsNo))
entropyerror = percEntropyError * entropy/ np.sqrt(iterationsNo)
print(f'Entropy: {entropy} +- {entropyerror}')
y_entropyList.append(entropy) #S_boltzmann agaisnt A/rho*
#y_entropyList.append(sum(totalHarray)/iterationsNo) #<N> against A/rho*
x.append(1/rho**((2-d)/d))
if moleculetype == 'lambda':
# Plots the link molecules of <H_links> against A/rho**(2-d/d)
plt.scatter(AoverlList, totalLinksList, label = 'Data')
plt.errorbar(AoverlList, totalLinksList, yerr = totalLinksErrorList, capsize = 4, linestyle = '')
popt, pcov = curve_fit(linear, AoverlList, totalLinksList)
xLinspace = np.linspace(min(AoverlList), max(AoverlList), 100)
plt.plot(xLinspace, linear(xLinspace, *popt), label = 'Linear Fit', color = 'red')
plt.xlabel(r'$A/{\l^{d-2}}$', fontsize = 25)
plt.ylabel(r'$\langle H_{links} \rangle$', fontsize = 25 )
print(f'\n \n \n a_Boltzmann value for {d}d is {popt[0]} +- {np.sqrt(pcov[0][0])}')
#plt.title(f'Link Counting for {d-1}+1 Rindler', fontsize = 25, pad = 20)
plt.xticks(fontsize = 20)
plt.yticks(fontsize = 20)
plt.legend(fontsize = 15)
plt.savefig(fr'C:\Users\leehi\OneDrive\Documents\Imperial_tings\Fourth_Year\MSci Project\Thesis\Plots\LinksEntropyRindler_{moleculetype}_{d}d.png', dpi = 300, bbox_inches='tight', transparent = True)
plt.show()
# Plots the lambda or v molecules
plt.rc('font', family='Arial')
#x = x[1:]
#y_entropyList = y_entropyList[1:]
plt.scatter(np.array(x), np.array(y_entropyList), label = 'Data')
plt.errorbar(np.array(x), np.array(y_entropyList), yerr = entropyerror, capsize = 4, linestyle = '')
plt.xlabel(r'$A/{\l^{d-2}}$', fontsize = 25)
if moleculetype == 'v':
plt.ylabel(r'$\langle H_V\rangle$', fontsize = 25 )
elif moleculetype == 'lambda':
plt.ylabel(r'$S_{Boltz}$', fontsize = 25 )
popt, pcov = curve_fit(linear, np.array(x), np.array(y_entropyList))
xLinspace = np.linspace(min(np.array(x)), max(np.array(x)), 100)
plt.plot(xLinspace, linear(xLinspace, *popt), label = 'Linear Fit', color = 'red')
#plt.title(f's_Boltzmann in Rindler in {d}d')
print(f'\n \n \n a_Boltzmann value for {d}d is {popt[0]} +- {np.sqrt(pcov[0][0])}')
#plt.title(f'Boltzmannian Entropy for {d-1}+1 Rindler', fontsize = 25, pad = 20)
plt.xticks(fontsize = 20)
plt.yticks(fontsize = 20)
plt.legend(fontsize = 15)
plt.savefig(fr'C:\Users\leehi\OneDrive\Documents\Imperial_tings\Fourth_Year\MSci Project\Thesis\Plots\BoltzEntropyRindler_{moleculetype}_{d}d.png', dpi = 300, bbox_inches='tight', transparent = True)
plt.show()
#%%
for d in d_array:
if moleculetype == 'lambda':
df = pd.read_csv(f'H_Rindler{d}d_lambda.csv', names=['rho', 'H', 'b'], header=None)
df['rho'] = df['rho'].round(1)
elif moleculetype == 'v':
df = pd.read_csv(f'H_Rindler{d}d_v.csv', names=['rho', 'H', 'subgraphs', 'connected','b'], header=None)
df['rho'] = df['rho'].round(1)
# Analyse b
dfb = df[df['b'] != 0] #dropped 0 (optional)
bList= list(dfb['b'].dropna()) #dropped Nans
colors = ['red', 'blue', 'green']
binsCount = [13,13, 7]
plt.hist(bList, bins = binsCount[int(d-2)], density = True, histtype = 'stepfilled', color = colors[int(d-2)], label = f'{d-1}+1 Data', alpha = 0.5)
plt.ylabel('Normalised Frequency')
plt.xlabel(r'$b_{max}$')
plt.legend()
plt.savefig(fr'C:\Users\leehi\OneDrive\Documents\Imperial_tings\Fourth_Year\MSci Project\Thesis\Plots\bepislonDistribution_Rindler_{moleculetype}.png', dpi = 300, bbox_inches='tight', transparent = True)
plt.show()