from tqdm import tqdm " " " Implementation of Hopfield Network to calculate the simulated error probability for a network initialised at corrupted memory. The result is then compared to the values obtained from the analytical expression for the error probability." " " # CONSTANTS N = 100 # number of neurons in network M_an = np.array(range( 2 , 1001 )) # number of memories for analytical values of p_e # number of memories for simulated values of p_e M_sim = [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 15 , 20 , 25 , 30 , 35 , 40 , 45 , 50 , 55 , 60 , 65 , 70 , 75 , 80 , 85 , 90 , 95 , 100 , 125 , 150 , 175 , 200 , 225 , 250 , 275 , 300 , 325 , 350 , 375 , 400 , 425 , 450 , 475 , 500 , 525 , 550 , 575 , 600 , 625 , 650 , 675 , 700 , 725 , 750 , 775 , 800 , 825 , 850 , 875 , 900 , 925 , 950 , 975 , 1000 # input noises (i.e. probability of flipping a bit # of original memory in initial state) input_noise = [0, 0 . 01 , 0 . 02 , 0 . 05 , 0 . 1 , 0 . 2 , 0 . 5 , 0 . 8 , 0 . 9 , 1] # placeholder for simulated error probabilities error_probs = np.zeros([len(input_noise), len(M_sim)]) # SIMULATION AND ERROR PROBABILITY for noise in tqdm(range(len(input_noise))): # counting variable for indexing error_probs index = 0 # loop over number of memories for m in M_sim: n_errors= 0 index += 1 # increase counting variable # for 50 different collections of memories for n in range( 50 ): # initialise empty memory array mem_array = np.zeros([m, N]) # generate random memories (i.e. bit patterns) for i in range(m): mem = random.randint( 0 , 2**N - 1 ) mem_bin = BitArray( uint =mem, length=N) mem_array[i] = mem_bin # calculate weight matrix W = np.matmul(np.transpose(mem_array)-0. 5 , mem_array-0. 5 ) np.fill_diagonal(W, 0 ) # choose initial memory states orig_mems = mem_array[np.random.choice(range(m), 50 )] # average over chosen memory states for orig_mem in orig_mems: # average over 50 memory state corruptions for each # selected memory for i in range( 50 ): # flip the bits according to the input noise mask = np.random.binomial( 1 , input_noise[noise], N) r = np.logical_xor(orig_mem, mask) # asynchronous update from Equation 1 . 1 . 2 r_new = np.matmul(W, r) # implementation of step function applied # to the input for the first neuron new_val = 0 if r_new[0]<0 else r[0] if r_new[0]== 0 else 1 n_errors += 1 if new_val != orig_mem[0] else 0 # calculate probability as proportion of changes prop_errors = n_errors/(50*50*len(orig_mems)) # populate error probability array error_probs[noise, index-1] = prop_errors # PLOTTING # plot of simulated values fig = plt.figure() ax = fig.add_subplot( 111 ) sim_error_0, = ax.plot(M_sim, error_probs[0], linestyle = ' --' , color = ' k' ) ax.plot(M_sim, error_probs[1], linestyle = ' --' , color = ' b' ) ax.plot(M_sim, error_probs[2], linestyle = ' --' , color = ' m' ) ax.plot(M_sim, error_probs[3], linestyle = ' --' , color = ' g' ) ax.plot(M_sim, error_probs[4], linestyle = ' --' , color = ' c' ) ax.plot(M_sim, error_probs[5], linestyle = ' --' , color = ' r' ) ax.plot(M_sim, error_probs[6], linestyle = ' --' , color = ' brown' ) ax.plot(M_sim, error_probs[7], linestyle = ' --' , color = ' olive' ) ax.plot(M_sim, error_probs[8], linestyle = ' --' , color = ' orange' ) ax.plot(M_sim, error_probs[9], linestyle = ' --' , color = ' darkgray' ) # calculate analytical values of the error probability p_e_0 = norm.cdf(-np.sqrt((N-1)/(2*(M_an-1)))) p_e_0_01 = norm.cdf((2*0.01-1)*np.sqrt((N-1)/(2*(M_an-1)))) p_e_0_02 = norm.cdf((2*0.02-1)*np.sqrt((N-1)/(2*(M_an-1)))) p_e_0_05 = norm.cdf((2*0.05-1)*np.sqrt((N-1)/(2*(M_an-1)))) p_e_0_1 = norm.cdf((2*0.1-1)*np.sqrt((N-1)/(2*(M_an-1)))) p_e_0_2 = norm.cdf((2*0.2-1)*np.sqrt((N-1)/(2*(M_an-1)))) p_e_0_5 = norm.cdf((2*0.5-1)*np.sqrt((N-1)/(2*(M_an-1)))) p_e_0_8 = norm.cdf((2*0.8-1)*np.sqrt((N-1)/(2*(M_an-1)))) p_e_0_9 = norm.cdf((2*0.9-1)*np.sqrt((N-1)/(2*(M_an-1)))) p_e_1 = norm.cdf((2-1)*np.sqrt((N-1)/(2*(M_an-1)))) # plot analytical values of the error probability analytical_error_0, = ax.plot(M_an, p_e_0, label = ' $p_{noise} = 0$' , color = ' k' ) ax.plot(M_an, p_e_0_01, label = ' $p_{noise} = 0.01$' , color = ' b' ) ax.plot(M_an, p_e_0_02, label = ' $p_{noise} = 0.02$' , color = ' m' ) ax.plot(M_an, p_e_0_05, label = ' $p_{noise} = 0.05$' , color = ' g' ) ax.plot(M_an, p_e_0_1, label = ' $p_{noise} = 0.1$' , color = ' c' ) ax.plot(M_an, p_e_0_2, label = ' $p_{noise} = 0.2$' , color = ' r' ) ax.plot(M_an, p_e_0_5, label = ' $p_{noise} = 0.5$' , color = ' brown' ) ax.plot(M_an, p_e_0_8, label = ' $p_{noise} = 0.8$' , color = ' olive' ) ax.plot(M_an, p_e_0_9, label = ' $p_{noise} = 0.9$' , color = ' orange' ) ax.plot(M_an, p_e_1, label = ' $p_{noise} = 1.0$' , color = ' darkgray' ) # settings for x and y labels and ticks and legend ax.set_xlabel( ' Number of Memories (M)' , size = 15 ) ax.set_ylabel( ' Probability of Error ($p_e$)' , size = 15 ) ax.tick_params(labelsize= 15 ) leg1 = ax.legend(prop={ ' size' : 15 }) # ensuring that the x-axis is logarithmic plt.xscale( ' log' ) # add two legends (one for an/sim and one for input noise level) leg2 = ax.legend([sim_error_0, analytical_error_0],[ ' Simulated' , ' Analytical' ], loc= ' upper left' , prop={ ' size' : 15 }) ax.add_artist(leg1) plt.show()
What I have tried:
-progress bar " 0%| | 0/10 [00:00<?, ?it/s] " appears and stays at 0 .
I believe that somethings wrong with the for loops but i dont know what.. Im running the code with Python 3 . 8 . 10 from idle or cmd panel

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