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
