def samples_logs():
x = np.array([100., 100.])
mu = np.zeros(2)
sigma = np.array([[12., 10.], [10., 16.]])
samples, logs = metropolis.metropolis(x, mu, sigma, n_samples=2500)
plt.plot(samples[:,0], samples[:,1], '.')
plt.savefig('samples.pdf')
plt.clf()
plt.plot(logs)
plt.savefig('logprobs.pdf')
def test_metropolis( self ):
"""
Testing metropolis algorithm using KS test.
"""
metropolisGen = metropolis.metropolis( self.desiredDistribution.pdf, 0, self.computableGen, self.skipSteps )
#sample from generator
x = []
for i in xrange( self.n ):
x.append( metropolisGen.next()[0] )
#check using KS test, that produxed sample is from given distribution
KSPValue = scipy.stats.kstest( x, self.desiredDistribution.cdf )[ 0 ]
#if p value is greater than 0.05, we should accept hypotisys, that sample from given distribution
self.assertGreater( KSPValue, 0.05 )
def test():
num_chars = 1
key = gen_key()
print('[INF] Permutation: ', key)
plain_text = read_text(PLAIN_TEXT_FILENAME)
train_text = read_text(TRAIN_TEXT_FILENAME)
cipher_text = encrypt(plain_text, key)
print('[INF] Texts are read and encrypted.')
stat = get_statistics(train_text, num_chars)
sampler = metropolis.metropolis(
desiredPDF=ft.partial(get_pdf, text=cipher_text, stat=stat, num_chars=num_chars),
initValue=rm.uniform(26),
computableRVS=lambda t: rm.applyedTranspostions(t),
skipIterations=2)
print('[INF] Initialization')
samples = [sampler.next()[0]]
print('[INF] Sampling...')
samples += [sampler.next() for i in xrange(1000)]
for sample in samples:
print(sample)
# exemplo, a distribuição de proposta foi
# um passeio aleatório simétrico.
import numpy as np
from passeio_aleatorio import PasseioAleatorio
from metropolis import metropolis
# Definir Parâmetros do Problema
problema_2 = PasseioAleatorio()
# Definir Parâmetros do Método
estado_inicial_2 = 2
num_iteracoes_2 = 1000000
# Executar Algoritmo de Metropolis-Hastings
cadeia_2 = metropolis(problema_2, estado_inicial_2, num_iteracoes_2)
# Calcular Frequências de Estados na Cadeia Resultante
estados, contagem = np.unique(cadeia_2, return_counts=True)
frequencia = contagem / len(cadeia_2)
# Somar incidência de estados acima de 9
soma_acima_9 = np.sum(frequencia[8:])
freq_finais = np.append(frequencia[:8], soma_acima_9)
# Exibir Resultados
print("\n----------------- Exemplo 2 -----------------\n")
print("Frequências da Cadeia Obtida:")
for i in range(0, 8):
print("{} : {}".format(i + 1, freq_finais[i]))
init = 0.2
epsilon = 1.1
L = 10
chain_L = 350
hmc = hmc_sampler(post1, prior1, epsilon, L, numpy.array([init]))
#output = hmc.sample()
#print(output)
#exit()
store_array = numpy.zeros(shape=(chain_L, 2))
for i in range(0, chain_L):
jitt = numpy.random.normal(size=1) * 0.01
hmc = hmc_sampler(post1, prior1, epsilon + jitt, L, numpy.array([init]))
output = hmc.sample()
init = output[1]
#print(init)
store_array[i, 0] = output[0]
store_array[i, 1] = output[1]
print(sum(store_array[:, 0]) / chain_L)
import matplotlib.pyplot as plt
plt.plot(range(0, chain_L), store_array[:, 1], 'ro')
plt.show()
#exit()
# RW Metropolis Sampling
temp_f = lambda x: post1.log_lik(x)
RW_sampler = metropolis(numpy.array([0.05]), 3.21, temp_f, chain_L)
RW_sampler.sample()
print(sum(RW_sampler.store_matrix[:, 0]) / chain_L)
plt.plot(range(0, chain_L), RW_sampler.store_matrix[:, 1], 'ro')
plt.show()
lcir = int(log10(ncir)) + 1
dpath = 'data/'
ddir = dpath + datname(T,h.g) + '/'
print 'data stored in', ddir
try:
mkdir(dpath)
except:
print dpath,'exist'
try:
mkdir(ddir)
except:
raise OSError('Directory ' + ddir + ' exists.')
mt = metropolis(h,T=T*RT,cutoff=cutoff)
for i in xrange(ncir):
df = open(ddir + 'c' + str(i).zfill(lcir) + '.dat', 'w')
d, n, en, a = mt.next()
dump((i,d,n,en,a), df, -1)
print ''
print '*****************'
print ' Cycle %s ' % (i)
print '*****************'
print ''
print 'Acceptance rate:', a
print ''
print 'Average energies:', en
print ''
df.close()
y = data[:, 1]
# choix des paramètres initiaux
p_init = [1000, 25e3, 2e3]
plt.subplot(221)
plt.plot(x, y, 'o')
x_ = np.linspace(np.min(x), np.max(x), 1000)
plt.plot(x_, model(p_init, x_), '-')
plt.title("initial guess")
# p_var : in python, this parameter is only used to initialize the walkers.
# then you can put small values when you are sure about the p_init.
p_var = [500, 1e3, 0.2e3]
# fit :
p = metropolis(model, x, y, p_init, p_var, 2000)
# moyennes et écarts types :
w0 = np.mean(p[:, 1])
dw0 = np.std(p[:, 1])
print "pulsation propre = {} +- {} rad/s".format(w0, dw0)
# plots
plt.subplot(222)
plt.plot(x, y, 'o')
x_ = np.linspace(np.min(x), np.max(x), 1000)
plt.plot(x_, model(np.mean(p, axis=0), x_), '-')
plt.title("fit")
plt.subplot(223)
from metropolis import metropolis
import numpy as np
import matplotlib.pyplot as plt
# création du modèle :
def model(p, x):
return p[0] * x + p[1]
# génération aléatoire des données :
x = np.linspace(-5, 15, 30)
y = 4.5 * x + 12 + 2 * np.random.randn(len(x))
# fit :
p = metropolis(model, x, y, [5, 10], [0.5, 1])
# moyennes et écarts types :
a = np.mean(p[:, 0], axis=0)
da = np.std(p[:, 0], axis=0)
b = np.mean(p[:, 1], axis=0)
db = np.std(p[:, 1], axis=0)
print "pente = {} +- {}".format(a, da)
print "ordonnée à l'origine = {} +- {}".format(b, db)
# plots
plt.figure()
plt.plot(x, y, 'o')
x_ = np.linspace(-6, 16, 1000)
plt.plot(x_, model(np.mean(p, axis=0), x_), '-')
from hamiltonian import ham
from metropolis import metropolis
cutoff = 0.003
h = ham(length=5, width=4, holes=[[2, 1]])
mt = metropolis(h, cutoff=cutoff)
for i in xrange(10):
d, n, en, a = mt.next()
print ""
print "*****************"
print " Cycle %s " % (i)
print "*****************"
print ""
print "Acceptance rate:", a
print ""
print "Average particle densities:"
print n
print ""
print "Average displacements:"
print d
lcir = int(log10(ncir)) + 1
dpath = 'data/'
ddir = dpath + datname(T, h.g) + '/'
print 'data stored in', ddir
try:
mkdir(dpath)
except:
print dpath, 'exist'
try:
mkdir(ddir)
except:
raise OSError('Directory ' + ddir + ' exists.')
mt = metropolis(h, T=T * RT, cutoff=cutoff)
for i in xrange(ncir):
df = open(ddir + 'c' + str(i).zfill(lcir) + '.dat', 'w')
d, n, en, a = mt.next()
dump((i, d, n, en, a), df, -1)
print ''
print '*****************'
print ' Cycle %s ' % (i)
print '*****************'
print ''
print 'Acceptance rate:', a
print ''
print 'Average energies:', en
print ''
df.close()
# -*- coding: utf-8 -*-
# plot de la marche aléatoire
from metropolis import metropolis
import numpy as np
import matplotlib.pyplot as plt
# création du modèle :
def model(param, x):
return param[0] * x + param[1]
# génération des données :
x = np.linspace(-5, 15, 120)
y = 4.5 * x + 12 + 5 * np.random.randn(len(x))
# fit :
p = metropolis(model, x, y, [5, 10], [0.1, 0.2], 5000, 500, 20)
# plot de la marche aléatoire
plt.figure()
plt.plot(p[:, 0], p[:, 1], 'x')
plt.title("{} points".format(p.shape[0]))
plt.xlabel("slope")
plt.ylabel("intercept")
plt.show()
# ce plot permet d'observer la correlation entre les paramètres
from hamiltonian import ham from metropolis import metropolis cutoff=0.003 h = ham(length=5,width=4,holes=[[2,1]]) mt = metropolis(h,cutoff=cutoff) for i in xrange(10): d, n, en, a = mt.next() print '' print '*****************' print ' Cycle %s ' % (i) print '*****************' print '' print 'Acceptance rate:', a print '' print 'Average particle densities:' print n print '' print 'Average displacements:' print d
