# Physique Numerique M1 : TD 2 - Exercice 3 ## Generate random

# Physique Numerique M1 : TD 2 - Exercice 3
## Generate random numbers with a Gaussian distribution
## using the Metropolis algorithm.
from pylab import *
def gauss(v): # Gaussian distribution
g=exp(-(v-mu)**2/(2*sig**2))/(sqrt(2*pi)*sig)
return g
def dist(a,b): # ratio of probabilities
c=gauss(a)/gauss(b)
return c
print "Entrer le nombre de pas pour la chaine de Markov:"
M = input()
print "Choisir le deplacement maximal (<=1) par pas:"
delta = input()
res=zeros([M])
sig=0.05
mu=0.5
# variance of the Gaussian distribution
# mean of the Gaussian distribution
x0=random() # start with a random number
res[0]=x0
counter=0.
for i in xrange(M):
xt=random() # choose another random number
x=x0+(2*xt-1.)*delta-floor(x0+(2*xt-1.)*delta)
# decide whether to ...
if dist(x,x0)>=random(): # ... accept the new number
res[i]=x
# & append to the list
x0=x
counter+=1.
# or ...
else:
res[i]=x0
# keep the old number
# & append to the list
t=arange(0,1,0.01)
plot(t,gauss(t))
# plot the Gaussian distribution
hist(res,bins=100,normed=True) # plot the histogram of the array of random numbers
show()
print 'moyenne:', sum(res)/M
print 'variance:', sqrt(sum(res**2)/M-(sum(res)/M)**2)
print 'pourcentage des pas acceptes:', counter/M*100