def Training_Data(size, temp, K, length, number, type='1d'):
if type == '1d':
data = np.zeros((number, size))
if type == '2d':
data = np.zeros((number, size**2))
if type == '3d':
data = np.zeros((number, size**3))
for num in range(number):
Initial = lattice.Initialise_Random_State(size, temp, K, type=type)
for i in range(length):
Initial.metropolis()
if type == '1d':
spins = np.reshape(Initial.get_spins(), size)
for i in range(size):
if (spins[i] == -1.0):
spins[i] = 0
elif type == '2d':
spins = np.reshape(Initial.get_spins(), size**2)
for i in range(size**2):
if (spins[i] == -1.0):
spins[i] = 0
elif type == '3d':
spins = np.reshape(Initial.get_spins(), size**3)
for i in range(size**3):
if (spins[i] == -1.0):
spins[i] = 0
data[num, :] = spins[:]
#print(data)
return data
def Converged_SHeat_Susept(size, temp, K, length, samples, type='1d'):
Initial = lattice.Initialise_Random_State(size, temp, K, type=type)
mean_M = 0.0
mean_M_squared = 0.0
mean_E = 0.0
mean_E_squared = 0.0
const = 0
if temp == 0:
temp = 0.001
for i in range(length + samples):
Initial.metropolis()
if i > length:
m = Initial.magnetisation()
en = Initial.energy()
mean_M += m
mean_M_squared += m**2
mean_E += en
mean_E_squared += en**2
mean_M = np.abs(mean_M / samples)
mean_M_squared = mean_M_squared / samples
susept = np.abs(mean_M_squared - mean_M**2) / (temp)
mean_E = mean_E / samples
mean_E_squared = mean_E_squared / samples
specific_heat = np.abs(mean_E_squared - mean_E**2) / (temp**2)
return Initial, specific_heat, susept
def Energy_Magnetization(size, temp, K, length, type='1d', show=True):
num = []
final_E = []
final_M = []
Initial = lattice.Initialise_Random_State(size, temp, K, type=type)
for i in range(length):
Initial.metropolis()
num.append(i)
final_E.append(Initial.energy())
final_M.append(np.abs(Initial.magnetisation()))
if show == True:
fig, ax = plt.subplots()
plt.plot(num, final_E, marker='.', label='Energy')
plt.legend()
plt.xlabel('Iterations of Metropolis Algorithm')
plt.ylabel('Average Energy per cell')
fig, ax = plt.subplots()
plt.plot(num, final_M, marker='.', label='Mag')
plt.legend()
plt.xlabel('Iterations of Metropolis Algorithm')
plt.ylabel('Average Magnetisation per cell')
plt.show()
def Test_Generated(data, size, temp, K, type=type, autocorrelation=1):
(num_samples, num_sites) = data.shape
num_samples = int(num_samples / autocorrelation)
mean_M = 0
mean_E = 0
mean_M_squared = 0
mean_E_squared = 0
# Should only take one in every few.. correlations between adjacent values = ?
for i in range(num_samples * autocorrelation):
if (i % autocorrelation == 0):
Initial = lattice.Initialise_Random_State(size, temp, K, type=type)
#print(size,data[i].shape)
Initial.set_spins(data[i])
m = np.abs(Initial.magnetisation())
en = Initial.energy()
mean_M += m
mean_M_squared += m**2
mean_E += en
mean_E_squared += en**2
mean_M = mean_M / float(num_samples)
mean_M_squared = mean_M_squared / float(num_samples)
susept = np.abs(mean_M_squared - mean_M**2) / (temp)
mean_E = mean_E / float(num_samples - 1)
mean_E_squared = mean_E_squared / float(num_samples - 1)
specific_heat = np.abs(mean_E_squared - mean_E**2) / (temp**2)
return mean_M, mean_E, susept, specific_heat
def Converged_E_M(size, temp, K, length, samples, type='1d'):
final_E = []
final_M = []
if temp == 0:
temp = 0.00001
Initial = lattice.Initialise_Random_State(size, temp, K, type=type)
for i in range(length):
Initial.metropolis()
for sample in range(samples):
for i in range(length):
Initial.metropolis()
final_E.append(Initial.energy())
final_M.append(np.abs(Initial.magnetisation()))
E = np.sum(final_E) / samples
M = np.sum(final_M) / samples
return Initial, E, M
def SHeat_Susept(size,
min_temp,
max_temp,
number_temps,
length,
samples,
K,
type='1d',
plot=True,
analytic_compare=False):
final_T = []
final_M = []
final_E = []
final_X = []
final_SH = []
if min_temp == 0:
min_temp = 0.0001
temperatures = np.linspace(min_temp, max_temp, number_temps)
for temp in temperatures:
mean_M = 0.0
mean_M_squared = 0.0
mean_E = 0.0
mean_E_squared = 0.0
const = 0
Initial = lattice.Initialise_Random_State(size, temp, K, type=type)
for i in range(length + samples):
Initial.metropolis()
if i > length:
for n in range(length):
Initial.metropolis()
m = Initial.magnetisation()
en = Initial.energy()
mean_M += np.abs(m)
mean_M_squared += m**2
mean_E += en
mean_E_squared += en**2
mean_M = mean_M / float(samples)
mean_M_squared = mean_M_squared / float(samples)
susept = np.abs(mean_M_squared - mean_M**2) / (temp)
mean_E = mean_E / float(samples)
mean_E_squared = mean_E_squared / float(samples)
specific_heat = np.abs(mean_E_squared - mean_E**2) / (temp**2)
final_T.append(temp)
final_M.append(mean_M)
final_E.append(mean_E)
final_X.append(susept)
final_SH.append(specific_heat)
print(temp)
'''deriving Curie temp from M and E'''
smoothed_e = gaussian_filter(final_E, 3.)
smoothed_m = gaussian_filter(final_M, 3.)
dx = np.diff(final_T)
dy_e = np.diff(smoothed_e)
dy_m = np.diff(smoothed_m)
slope_e = (dy_e / dx)
slope_m = (dy_m / dx)
max_slope_e = (max(slope_e))
min_slope_m = (min(slope_m))
Curie_e = 0.0
Curie_m = 0.0
for i in range(len(final_T) - 1):
if slope_e[i] == max_slope_e:
Curie_e = final_T[i]
if slope_m[i] == min_slope_m:
Curie_m = final_T[i]
print('Curie temperature from energy is', Curie_e)
print('Curie temperature from magnetisation is', Curie_m)
'''saving data and graphing'''
#mag_data = np.concatenate((np.array([final_T]).T,np.array([final_M]).T),axis=1)
#np.savetxt("magnetization3.csv",mag_data)
if plot == True:
def analytic_energy(temp):
return -K * np.tanh(temp**(-1) * K)
def analytic_Cv(temp):
return spc.k * (temp**(-1) * K)**2 * (np.cosh(
temp**(-1) * K))**(-2)
fig, ax = plt.subplots()
plt.plot(final_T, final_E, '.', label='Metropolis')
plt.plot(np.array(final_T),
analytic_energy(np.array(final_T)),
'.',
label='Exact')
plt.title('Energy')
plt.legend()
plt.xlabel('Fundamental Temperature')
plt.ylabel('Average Energy per cell after Convergence')
fig, ax = plt.subplots()
plt.plot(final_T, final_M, '.', label='Mag-Temp')
plt.legend()
plt.xlabel('Fundamental Temperature')
plt.ylabel('Average Magnetisation per cell after Convergence')
fig, ax = plt.subplots()
plt.plot(final_T, final_X, '.', label='Suseptibility')
plt.legend()
plt.xlabel('Fundamental Temperature')
plt.ylabel('Suseptibility')
fig, ax = plt.subplots()
plt.plot(final_T, final_SH, '.', label='Metropolis')
plt.plot(np.array(final_T),
analytic_Cv(np.array(final_T)),
'.',
label='Exact')
plt.title('Specific Heat')
plt.legend()
plt.xlabel('Fundamental Temperature')
plt.ylabel('Specific Heat')
plt.show()
return final_T, final_E, final_M, final_X, final_SH
def Energy_Magnetization_Temp(size,
min_temp,
max_temp,
number_temps,
K,
length,
type='1d'):
final_T = []
final_E = []
final_M = []
temperatures = np.log(
np.linspace(np.exp(min_temp), np.exp(max_temp), number_temps))
for temp in temperatures:
n_trials = 10
energies = np.zeros(n_trials)
mags = np.zeros(n_trials)
for n in range(n_trials):
if temp == 0:
temp = 0.0001
Initial = lattice.Initialise_Random_State(size, temp, K, type=type)
for i in range(length):
Initial.metropolis()
energies[n] = Initial.energy()
mags[n] = np.abs(Initial.magnetisation())
final_T.append(temp)
final_E.append(np.median(energies))
final_M.append(np.median(mags))
print(temp)
smoothed_e = gaussian_filter(final_E, 3.)
smoothed_m = gaussian_filter(final_M, 3.)
dx = np.diff(final_T)
dy_e = np.diff(smoothed_e)
dy_m = np.diff(smoothed_m)
slope_e = (dy_e / dx)
slope_m = (dy_m / dx)
max_slope_e = (max(slope_e))
min_slope_m = (min(slope_m))
Curie_e = 0.0
Curie_m = 0.0
for i in range(len(final_T) - 1):
if slope_e[i] == max_slope_e:
Curie_e = final_T[i]
if slope_m[i] == min_slope_m:
Curie_m = final_T[i]
print('Curie temperature from energy is', Curie_e)
print('Curie temperature from magnetisation is', Curie_m)
mag_data = np.concatenate((np.array([final_T]).T, np.array([final_M]).T),
axis=1)
np.savetxt("magnetization3.csv", mag_data)
fig, ax = plt.subplots()
plt.plot(final_T, final_E, '.', label='Energy-Temp')
plt.legend()
plt.xlabel('Fundamental Temperature')
plt.ylabel('Average Energy per cell after Convergence')
fig, ax = plt.subplots()
plt.plot(final_T, final_M, '.', label='Mag-Temp')
plt.legend()
plt.xlabel('Fundamental Temperature')
plt.ylabel('Average Magnetisation per cell after Convergence')
plt.show()
def Autocorrelations_in_generated(size,
K,
max_binsize,
min_samples,
temp,
type='1d',
plot=True,
epochs=100,
stacked=False,
k=1):
ratio_hidden = 0.5
gen_data = []
if type == '1d':
vis = size
hid = int(vis * ratio_hidden)
if type == '2d':
vis = size**2
if type == '3d':
vis = size**3
hid = int(vis * ratio_hidden)
if stacked == True:
second_hid = int(hid * ratio_hidden)
r = rbm.Stacked_RBM(num_visible=vis,
num_first_hidden=hid,
num_second_hidden=second_hid)
else:
r = rbm.RBM(num_visible=vis, num_hidden=hid)
training_data_sample = np.loadtxt('training_data_temp%s.txt' % temp)
r.train(training_data_sample,
epochs=int(epochs),
learning_rate=0.1,
batch_size=100,
k=k)
number_gen = max_binsize * min_samples
gen_data = r.daydream(number_gen, training_data_sample[0])
binsizes = np.arange(1, max_binsize + 1)
magnetisations = []
standard_dev_magnetisations = []
for binsize_index in range(max_binsize):
samples = int(number_gen / binsizes[binsize_index])
bin_magnetizations = np.zeros((samples))
for sample in range(samples):
for i in range(binsizes[binsize_index]):
Ising_lattice = lattice.Initialise_Random_State(size,
temp,
K,
type=type)
Ising_lattice.set_spins(
gen_data[sample * binsizes[binsize_index] + i])
bin_magnetizations[sample] += np.abs(
Ising_lattice.magnetisation())
bin_magnetizations[
sample] = bin_magnetizations[sample] / binsizes[binsize_index]
mean = np.mean(bin_magnetizations)
magnetisations.append(mean)
difference_from_mean = np.sum(np.square(bin_magnetizations - mean))
st_dev = (difference_from_mean / (samples * (samples - 1)))**0.5
standard_dev_magnetisations.append(st_dev)
fig, ax = plt.subplots()
ax.errorbar(binsizes,
magnetisations,
fmt='-o',
yerr=standard_dev_magnetisations)
plt.title('Determining Autocorrelations')
plt.xlabel('Binsizes')
plt.ylabel('Magnetization')
plt.show()