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utils.py
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utils.py
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import numpy as np
import tensorflow as tf
import pickle
import matplotlib.pyplot as plt
def periodic_padding(x, padding=1):
p = padding
top_left = x[:, -p:, -p:, :] # top left
top_center = x[:, -p:, :, :] # top center
top_right = x[:, -p:, :p, :] # top right
middle_left = x[:, :, -p:,:] # middle left
middle_center = x # middle center
middle_right = x[:, :, :p, :] # middle right
bottom_left = x[:, :p, -p:, :] # bottom left
bottom_center = x[:, :p, :, :] # bottom center
bottom_right = x[:, :p, :p, :] # bottom right
top = tf.concat([top_left, top_center, top_right], axis=2)
middle = tf.concat([middle_left, middle_center, middle_right], axis=2)
bottom = tf.concat([bottom_left, bottom_center, bottom_right], axis=2)
padded_x = tf.concat([top, middle, bottom], axis=1)
return padded_x
def calculate_energy(lattices,J=1,K=1):
x = lattices.shape[1]
y = lattices.shape[2]
L = np.reshape(lattices,(-1,x,y))
H = np.zeros(L.shape)
for i in range(x):
for j in range(y):
H[:,i,j] -= 0.50*J*np.cos(2 * np.pi * ( L[:,i,j] - L[:,i,(j+1)%y]))
H[:,i,j] -= 0.50*J*np.cos(2 * np.pi * ( L[:,i,j] - L[:,i,(j-1)%y]))
H[:,i,j] -= 0.50*J*np.cos(2 * np.pi * ( L[:,i,j] - L[:,(i+1)%x,j]))
H[:,i,j] -= 0.50*J*np.cos(2 * np.pi * ( L[:,i,j] - L[:,(i-1)%x,j]))
H[:,i,j] -= 0.25*K*np.cos(2 * np.pi * ( L[:,i,j] + L[:,(i-1)%x,(j-1)%y] - L[:,i,(j-1)%y] - L[:,(i-1)%x,j]))
H[:,i,j] -= 0.25*K*np.cos(2 * np.pi * ( L[:,i,j] + L[:,(i-1)%x,(j+1)%y] - L[:,i,(j+1)%y] - L[:,(i-1)%x,j]))
H[:,i,j] -= 0.25*K*np.cos(2 * np.pi * ( L[:,i,j] + L[:,(i+1)%x,(j-1)%y] - L[:,i,(j-1)%y] - L[:,(i+1)%x,j]))
H[:,i,j] -= 0.25*K*np.cos(2 * np.pi * ( L[:,i,j] + L[:,(i+1)%x,(j+1)%y] - L[:,i,(j+1)%y] - L[:,(i+1)%x,j]))
return H
def get_energy(lattices,J,K):
H = calculate_energy(lattices,J=J,K=K)
energy = (tf.reduce_mean(H,axis=[1,2]))
mean_energy = tf.reduce_mean(energy)
var_energy = tf.math.reduce_std(energy)
return [energy,mean_energy,var_energy]
def calculate_magnetization(lattices):
[n,x,y,channels] = lattices.shape
if channels==1:
mag_cos = tf.reduce_mean(tf.reshape(tf.math.cos(2*np.pi*lattices),
shape=[n,x,y]),axis=[1,2])
mag_sin = tf.reduce_mean(tf.reshape(tf.math.sin(2*np.pi*lattices),
shape=[n,x,y]),axis=[1,2])
else:
mag_cos = tf.reduce_mean(lattices[:,:,:,0],axis=[1,2])
mag_sin = tf.reduce_mean(lattices[:,:,:,1],axis=[1,2])
mag = tf.math.sqrt(mag_cos**2 + mag_sin**2)
mean_mag_cos = tf.reduce_mean(mag_cos)
mean_mag_sin = tf.reduce_mean(mag_sin)
mean_mag = tf.math.sqrt(mean_mag_cos**2 + mean_mag_sin**2)
mean_mag1 = tf.reduce_mean(mag)
mag_susceptibility = tf.math.reduce_std(mag)
return [mag,mean_mag,mean_mag1,mag_susceptibility]
def calculate_specific_heat(lattices,T,J,K):
[energy,mean_energy,var_energy] = get_energy(lattices,J,K)
specific_heat = var_energy**2/((T**2)*64)
return specific_heat
def observable_plot(lattices,samples,min_t,max_t,temp_len,J=1,K=1,name= 'xy_ring'):
index_set = np.arange(temp_len)
T_vals = np.linspace(min_t,max_t,temp_len)
#Empty arrays for holding lattices1 and lattices2 energy , specific heat, magnetization,
#Magnetization Variance, Mean Energy and Varaiance
lattices_energy = []
lattices_sp_heat = []
lattices_mag = []
lattices_mean_mag = []
lattices_mean_energy = []
lattices_var_energy = []
lattices_mag_susceptibility = []
for i in index_set:
[energy,mean_energy,var_energy] = get_energy(lattices[samples*i:samples*(i+1)],J,K)
specific_heat = calculate_specific_heat(lattices[samples*i:samples*(i+1)],T_vals[i],J,K)
[mag,mean_mag,mean_new,mag_susceptibility] = calculate_magnetization(lattices[samples*i:samples*(i+1)])
lattices_energy.append(energy)
lattices_mean_energy.append(mean_energy)
lattices_var_energy.append(var_energy)
lattices_sp_heat.append(specific_heat)
lattices_mag.append(mag)
lattices_mag_susceptibility.append(mag_susceptibility)
lattices_mean_mag.append(mean_new)
lower_limit_energy = list(np.array(lattices_mean_energy) - np.array(lattices_var_energy))
upper_limit_energy = list(np.array(lattices_mean_energy) + np.array(lattices_var_energy))
lower_limit_mag = list(np.array(lattices_mean_mag) - np.array(lattices_mag_susceptibility))
upper_limit_mag = list(np.array(lattices_mean_mag) + np.array(lattices_mag_susceptibility))
fig, axs = plt.subplots(3,figsize=(7,15))
#Plot of Specific Heat
axs[0].plot(T_vals,lattices_sp_heat,'r',marker='o')
axs[0].set_xlabel('Temperature')
axs[0].set_ylabel('Specific Heat')
#Plot of Mean Energy
axs[1].plot(T_vals,lattices_mean_energy,'r',marker='o')
axs[1].fill_between(T_vals,lower_limit_energy,upper_limit_energy,color='red', alpha=0.1)
axs[1].set_xlabel('Temperature')
axs[1].set_ylabel('Mean Energy')
#Plot of Mean Magnetization.
axs[2].plot(T_vals,lattices_mean_mag,'r',marker='o')
axs[2].fill_between(T_vals,lower_limit_mag,upper_limit_mag,color='red', alpha=0.1)
axs[2].set_xlabel('Temperature')
axs[2].set_ylabel('Mean Magnetization')
fig.savefig(name +'.png')
def comparison_plot(lattices1,lattices2,samples,min_t,max_t,temp_len,J=1,K=1,name='comparison_plot'):
index_set = np.arange(temp_len)
T_vals = np.linspace(min_t,max_t,temp_len)
#Empty arrays for holding lattices1 and lattices2 energy , specific heat, magnetization,
#Magnetization Variance, Mean Energy and Varaiance
lattices1_energy = []
lattices2_energy = []
lattices1_sp_heat = []
lattices2_sp_heat = []
lattices1_mag = []
lattices2_mag = []
lattices1_mean_mag = []
lattices2_mean_mag = []
lattices1_mean_energy = []
lattices2_mean_energy = []
lattices1_var_energy = []
lattices2_var_energy = []
lattices1_mag_susceptibility = []
lattices2_mag_susceptibility = []
for i in index_set:
[energy1,mean_energy1,var_energy1] = get_energy(lattices1[samples*i:samples*(i+1)],J,K)
[energy2,mean_energy2,var_energy2] = get_energy(lattices2[samples*i:samples*(i+1)],J,K)
specific_heat1 = calculate_specific_heat(lattices1[samples*i:samples*(i+1)],T_vals[i],J,K)
specific_heat2 = calculate_specific_heat(lattices2[samples*i:samples*(i+1)],T_vals[i],J,K)
[mag1,mean_mag1,mean_new1,mag_susceptibility1] = calculate_magnetization(lattices1[samples*i:samples*(i+1)])
[mag2,mean_mag2,mean_new2,mag_susceptibility2] = calculate_magnetization(lattices2[samples*i:samples*(i+1)])
lattices1_energy.append(energy1)
lattices2_energy.append(energy2)
lattices1_mean_energy.append(mean_energy1)
lattices2_mean_energy.append(mean_energy2)
lattices1_var_energy.append(var_energy1)
lattices2_var_energy.append(var_energy2)
lattices1_sp_heat.append(specific_heat1)
lattices2_sp_heat.append(specific_heat2)
lattices1_mag.append(mag1)
lattices2_mag.append(mag2)
lattices1_mag_susceptibility.append(mag_susceptibility1)
lattices2_mag_susceptibility.append(mag_susceptibility2)
lattices1_mean_mag.append(mean_new1)
lattices2_mean_mag.append(mean_new2)
lower_limit1_energy = list(np.array(lattices1_mean_energy)-np.array(lattices1_var_energy))
lower_limit2_energy = list(np.array(lattices2_mean_energy)-np.array(lattices2_var_energy))
upper_limit1_energy = list(np.array(lattices1_mean_energy)+np.array(lattices1_var_energy))
upper_limit2_energy = list(np.array(lattices2_mean_energy)+np.array(lattices2_var_energy))
lower_limit1_mag = list(np.array(lattices1_mean_mag)-np.array(lattices1_mag_susceptibility))
lower_limit2_mag = list(np.array(lattices2_mean_mag)-np.array(lattices2_mag_susceptibility))
upper_limit1_mag = list(np.array(lattices1_mean_mag)+np.array(lattices1_mag_susceptibility))
upper_limit2_mag = list(np.array(lattices2_mean_mag)+np.array(lattices2_mag_susceptibility))
fig, axs = plt.subplots(3,figsize=(7,15))
#Plot of Specific Heat
axs[0].plot(T_vals,lattices1_sp_heat,'r',marker='o')
axs[0].plot(T_vals,lattices2_sp_heat,'g',marker='^')
axs[0].set_xlabel('Temperature')
axs[0].set_ylabel('Specific Heat')
axs[0].legend(['MCMC Samples','Generated Samples'])
#plt.savefig('./cgan_samples/sp_heat_epoch_%s.png'%(epoch))
#plt.show()
#Plot of Mean Energy
axs[1].plot(T_vals,lattices1_mean_energy,'r',marker='o')
axs[1].fill_between(T_vals,lower_limit1_energy,upper_limit1_energy,color='red', alpha=0.1)
axs[1].plot(T_vals,lattices2_mean_energy,'g',marker='o')
axs[1].fill_between(T_vals,lower_limit2_energy,upper_limit2_energy,color='green', alpha=0.1)
axs[1].set_xlabel('Temperature')
axs[1].set_ylabel('Mean Energy')
axs[1].legend(['MCMC Samples','Generated Samples'])
#plt.savefig('./cgan_samples/mean_energy_epoch_%s.png'%(epoch))
#plt.show()
#Plot of Mean Magnetization.
axs[2].plot(T_vals,lattices1_mean_mag,'r',marker='o')
axs[2].fill_between(T_vals,lower_limit1_mag,upper_limit1_mag,color='red', alpha=0.1)
axs[2].plot(T_vals,lattices2_mean_mag,'g',marker='o')
axs[2].fill_between(T_vals,lower_limit2_mag,upper_limit2_mag,color='green', alpha=0.1)
axs[2].set_xlabel('Temperature')
axs[2].set_ylabel('Mean Magnetization')
axs[2].legend(['MCMC Samples','Generated Samples'])
fig.savefig(name +'.png')
#plt.show()
def earth_mover_distance(A,B):
n = len(A)
dist = np.zeros(n)
for i in range(1,n):
dist[i] = A[i-1]-B[i-1]+dist[i-1]
return np.sum(abs(dist))/(n*1000)
def percent_overlap(hist_1, hist_2):# For evaluation : Calculates the % Overlap between two Histograms
overlap_each_bin = np.minimum(hist_1, hist_2)
total_overlap = np.true_divide(np.sum(overlap_each_bin), np.sum(hist_2))
return total_overlap*100
def evaluation_metrics(lattices1,lattices2,J=1,K=1):
nsamples = 1000
index_set = np.arange(32)
T_vals = np.linspace(0.05,2.05,32)
#Empty arrays for holding lattices1 and lattices2 energy
lattices1_energy = []
lattices2_energy = []
lattices1_mag = []
lattices2_mag = []
overlap_energy = []
overlap_mag = []
EMD_energy = []
EMD_mag = []
for i in index_set:
[energy1,mean_energy1,var_energy1] = get_energy(lattices1[1000*i:1000*(i+1)],J,K)
[energy2,mean_energy2,var_energy2] = get_energy(lattices2[1000*i:1000*(i+1)],J,K)
hist1_energy,bin1_energy = np.histogram(np.array(energy1),bins =80,range=[-2, 0])
hist2_energy,bin2_energy = np.histogram(np.array(energy2),bins =80,range=[-2, 0])
[mag1,mean_mag1,mean_new1,mag_susceptibility1] = calculate_magnetization(lattices1[1000*i:1000*(i+1)])
[mag2,mean_mag2,mean_new2,mag_susceptibility2] = calculate_magnetization(lattices2[1000*i:1000*(i+1)])
hist1_mag,bin1_mag = np.histogram(mag1,bins =40,range=[0, 1])
hist2_mag,bin2_mag = np.histogram(mag2,bins =40,range=[0, 1])
overlap_energy.append(percent_overlap(hist1_energy,hist2_energy))
overlap_mag.append(percent_overlap(hist1_mag,hist2_mag))
EMD_energy.append(earth_mover_distance(hist2_energy,hist1_energy))
EMD_mag.append(earth_mover_distance(hist2_mag,hist1_mag))
Energy_overlap = [np.mean(np.array(overlap_energy)),np.std(np.array(overlap_energy))]
Magnetization_overlap = [np.mean(np.array(overlap_mag)),np.std(np.array(overlap_mag))]
Energy_wass_dist = [np.mean(np.array(EMD_energy)),np.std(np.array(EMD_energy))]
Magnetization_wass_dist= [np.mean(np.array(EMD_mag)),np.std(np.array(EMD_mag))]
return [Energy_overlap,Magnetization_overlap,Energy_wass_dist,Magnetization_wass_dist]
def multi_lattice_comparison_plot(lattices1,lattices2,lattices3,samples,min_t,max_t,temp_len,J=1,K=1,name = 'multi_lattice_plot'):
index_set = np.arange(temp_len)
T_vals = np.linspace(min_t,max_t,temp_len)
#Empty arrays for holding lattices1 and lattices2 energy , specific heat, magnetization,
#Magnetization Variance, Mean Energy and Varaiance
lattices1_energy = []
lattices2_energy = []
lattices3_energy = []
lattices1_sp_heat = []
lattices2_sp_heat = []
lattices3_sp_heat = []
lattices1_mag = []
lattices2_mag = []
lattices3_mag = []
lattices1_mean_mag = []
lattices2_mean_mag = []
lattices3_mean_mag = []
lattices1_mean_energy = []
lattices2_mean_energy = []
lattices3_mean_energy = []
lattices1_var_energy = []
lattices2_var_energy = []
lattices3_var_energy = []
lattices1_mag_susceptibility = []
lattices2_mag_susceptibility = []
lattices3_mag_susceptibility = []
for i in index_set:
[energy1,mean_energy1,var_energy1] = get_energy(lattices1[samples*i:samples*(i+1)],J,K)
[energy2,mean_energy2,var_energy2] = get_energy(lattices2[samples*i:samples*(i+1)],J,K)
[energy3,mean_energy3,var_energy3] = get_energy(lattices3[samples*i:samples*(i+1)],J,K)
specific_heat1 = calculate_specific_heat(lattices1[samples*i:samples*(i+1)],T_vals[i],J,K)
specific_heat2 = calculate_specific_heat(lattices2[samples*i:samples*(i+1)],T_vals[i],J,K)
specific_heat3 = calculate_specific_heat(lattices3[samples*i:samples*(i+1)],T_vals[i],J,K)
[mag1,mean_mag1,mean_new1,mag_susceptibility1] = calculate_magnetization(lattices1[samples*i:samples*(i+1)])
[mag2,mean_mag2,mean_new2,mag_susceptibility2] = calculate_magnetization(lattices2[samples*i:samples*(i+1)])
[mag3,mean_mag3,mean_new3,mag_susceptibility3] = calculate_magnetization(lattices3[samples*i:samples*(i+1)])
lattices1_energy.append(energy1)
lattices2_energy.append(energy2)
lattices3_energy.append(energy3)
lattices1_mean_energy.append(mean_energy1)
lattices2_mean_energy.append(mean_energy2)
lattices3_mean_energy.append(mean_energy3)
lattices1_var_energy.append(var_energy1)
lattices2_var_energy.append(var_energy2)
lattices3_var_energy.append(var_energy3)
lattices1_sp_heat.append(specific_heat1)
lattices2_sp_heat.append(specific_heat2)
lattices3_sp_heat.append(specific_heat3)
lattices1_mag.append(mag1)
lattices2_mag.append(mag2)
lattices3_mag.append(mag3)
lattices1_mag_susceptibility.append(mag_susceptibility1)
lattices2_mag_susceptibility.append(mag_susceptibility2)
lattices3_mag_susceptibility.append(mag_susceptibility3)
lattices1_mean_mag.append(mean_new1)
lattices2_mean_mag.append(mean_new2)
lattices3_mean_mag.append(mean_new3)
lower_limit1_energy = list(np.array(lattices1_mean_energy)-np.array(lattices1_var_energy))
lower_limit2_energy = list(np.array(lattices2_mean_energy)-np.array(lattices2_var_energy))
lower_limit3_energy = list(np.array(lattices3_mean_energy)-np.array(lattices3_var_energy))
upper_limit1_energy = list(np.array(lattices1_mean_energy)+np.array(lattices1_var_energy))
upper_limit2_energy = list(np.array(lattices2_mean_energy)+np.array(lattices2_var_energy))
upper_limit3_energy = list(np.array(lattices3_mean_energy)+np.array(lattices3_var_energy))
lower_limit1_mag = list(np.array(lattices1_mean_mag)-np.array(lattices1_mag_susceptibility))
lower_limit2_mag = list(np.array(lattices2_mean_mag)-np.array(lattices2_mag_susceptibility))
lower_limit3_mag = list(np.array(lattices3_mean_mag)-np.array(lattices3_mag_susceptibility))
upper_limit1_mag = list(np.array(lattices1_mean_mag)+np.array(lattices1_mag_susceptibility))
upper_limit2_mag = list(np.array(lattices2_mean_mag)+np.array(lattices2_mag_susceptibility))
upper_limit3_mag = list(np.array(lattices3_mean_mag)+np.array(lattices3_mag_susceptibility))
fig, axs = plt.subplots(3,figsize=(7,15))
#Plot of Specific Heat
axs[0].plot(T_vals,lattices1_sp_heat,'r',marker='o')
axs[0].plot(T_vals,lattices2_sp_heat,'g',marker='^')
axs[0].plot(T_vals,lattices3_sp_heat,'b',marker='*')
axs[0].set_xlabel('Temperature')
axs[0].set_ylabel('Specific Heat')
axs[0].legend(['MCMC Samples','Generated Samples','MH-Model'])
#Plot of Mean Energy
axs[1].plot(T_vals,lattices1_mean_energy,'r',marker='o')
axs[1].fill_between(T_vals,lower_limit1_energy,upper_limit1_energy,color='red', alpha=0.1)
axs[1].plot(T_vals,lattices2_mean_energy,'g',marker='o')
axs[1].fill_between(T_vals,lower_limit2_energy,upper_limit2_energy,color='green', alpha=0.1)
axs[1].plot(T_vals,lattices3_mean_energy,'b',marker='o')
axs[1].fill_between(T_vals,lower_limit3_energy,upper_limit3_energy,color='blue', alpha=0.1)
axs[1].set_xlabel('Temperature')
axs[1].set_ylabel('Mean Energy')
axs[1].legend(['MCMC Samples','Generated Samples','MH-Model'])
#Plot of Mean Magnetization.
axs[2].plot(T_vals,lattices1_mean_mag,'r',marker='o')
axs[2].fill_between(T_vals,lower_limit1_mag,upper_limit1_mag,color='red', alpha=0.1)
axs[2].plot(T_vals,lattices2_mean_mag,'g',marker='o')
axs[2].fill_between(T_vals,lower_limit2_mag,upper_limit2_mag,color='green', alpha=0.1)
axs[2].plot(T_vals,lattices3_mean_mag,'b',marker='o')
axs[2].fill_between(T_vals,lower_limit3_mag,upper_limit3_mag,color='blue', alpha=0.1)
axs[2].set_xlabel('Temperature')
axs[2].set_ylabel('Mean Magnetization')
axs[2].legend(['MCMC Samples','Generated Samples','MH-Model'])
fig.savefig(name +'.png')
#plt.show()