def MetropolisJsampling(J,B,alpha): # Metropolis sampling algorithm for Jars
Jmean=np.array([0]*len(J)) # declare a J mean.
#Jtemp=np.array([0]*len(J))
for i in range(1,1000): # run the iteration for 1000 times.
Jnew=b.Jrandom(J) # Randomize the Jar sequence Value
acceptance_ratio=b.PalphaJB(alpha,Jnew,B)/b.PalphaJB(alpha,J,B) # find Acceptance Ratio, which is division of probabilities with new vs old values
if random.uniform(0,1)<= acceptance_ratio: # choose a random number, if It is less than acceptance ratio
J[:]=Jnew[:] # if it is less than, then assign it to a temp varaibale
Jmean[:]=np.add(J[:],Jmean[:]) # add temp variable to Jmean entries
return [x/1000.0 for x in Jmean[:]] # return mean of all entries for J values.
def MetropolisAlphaSampling(J,B,alpha): # Metropolis Sampling Algorithm for alpha
alpha_mean=0.0 # declare a variable which will add all values of alpha, after sampling
alpha_collect=np.array([])
for i in range(1,3000): # run iterations till 3000
a1=b.PalphaJB(alpha,J,B)
alpha_new=b.Randomalpha(alpha) # find alpha randomly
b1=b.PalphaJB(alpha_new,J,B)
acceptance_ratio=b1/a1 # find Acceptance Ratio, which is division of probabilities with new vs old values
if np.random.rand()<= acceptance_ratio: # if random number found is less than accepatance ratio then assign alpha to new alpha
alpha=alpha_new
alpha_collect = np.append( alpha_collect , alpha )
alpha_mean+=alpha # add alpha values to alpha mean
return alpha_mean/3000,alpha_collect # return mean values of alpha_mean
def MetropolisAlphaJ(J,B,alpha): #Metropolis Algorithm for J and Alpha sampling
alpha_mean=0.0 # set a variable to 0, in which all alpha values will get accumulated
alpha_collect=np.array([])
Jmean=np.array([0]*len(J)) # set a variable to 0, in which all J values will get accumulated
for i in range(1,5000): # Iterate 5000 times
random_values=b.genalphaJ(alpha,J) # generate random values of both alpha and J
acceptance_ratio=b.PalphaJB(random_values[0],random_values[1],B)/b.PalphaJB(alpha,J,B) # generate acceptance ratio for alpha
if random.uniform(0,1)<= acceptance_ratio: # if randomly generated value is less than acceptance ratio, then assign random alpha to alpha.
alpha=random_values[0]
J[:]=random_values[1]
alpha_collect = np.append( alpha_collect , alpha )
alpha_mean+=alpha
# accumulate values of alpha to alpha_mean
Jmean[:]=np.add(J[:],Jmean[:]) # accumulate values of J, to Jmean numpy array.
return alpha_mean/5000, [x/5000.0 for x in Jmean[:]], alpha_collect # return both sampled alpha mean and Jmean
def MCAlphaExperiment(J, B,
alpha): #Metropolis Algorithm for J and Alpha sampling
alpha_mean = 0.0 # set a variable to 0, in which all alpha values will get accumulated
alpha_collect = np.array(
[]) # set a variable to 0, in which all J values will get accumulated
for i in range(1, 3000): # Iterate 5000 times
random_values = b.genalphaJ(
alpha, J) # generate random values of both alpha and J
acceptance_ratio = b.PalphaJB(
random_alpha_Experiment(alpha), J, B) / b.PalphaJB(
alpha, J, B) # generate acceptance ratio for alpha
if random.uniform(
0, 1
) <= acceptance_ratio: # if randomly generated value is less than acceptance ratio, then assign random alpha to alpha.
alpha = random_values[0]
alpha_collect = np.append(alpha_collect, alpha)
alpha_mean += alpha
# accumulate values of alpha to alpha_mean
return alpha_mean / 3000, alpha_collect # return both sampled alpha mean and Jmean
