def persistent_compute(mi_mats, max_dim, bg, time_stamp, basename, tmpdir,
process_id, tlabel):
# Compute persistent entropy and save to temporary file
N = len(mi_mats)
if os.path.isdir(tmpdir) == False:
os.mkdir(tmpdir)
outfile = os.path.join(tmpdir, basename)
outstr = defaultdict(list)
stats = defaultdict(list)
for i in range(N):
mimat = mi_mats[i]
idx = bg + i
# Calculate distance matrix
#print(process_id, i, bg, idx, mimat[3][26])
if tlabel == 'MI':
netmeasures = nm.pearson(mimat)
dist = np.sqrt(1.0 - netmeasures[0]**2)
for j in range(dist.shape[0]):
dist[j, j] = 0
else:
# trace dist, bures_dist, bures_angle
dist = dm.compute_distance(mimat, tlabel)
dgms = ph.compute_ph_unit(dist, max_dim=max_dim)
for j, dgm in enumerate(dgms):
for pt in dgm:
outstr[j].append('{} {} {} {}'.format(pt[0], pt[1], 1, idx))
npent, pent, pnorm, maxnorm = ph.measure_diagram(dgm, p=2)
stats[j].append('{} {} {} {} {}'.format(idx, npent, pent, pnorm,
maxnorm))
# Save diagrams to file txt
for j, ostr in outstr.items():
with open('{}_ph_dim_{}_{}.txt'.format(outfile, j, process_id),
'w') as file_hdl:
file_hdl.write('\n'.join(ostr))
# Save stats to file txt
for j, ostr in stats.items():
with open('{}_stats_dim_{}_{}.txt'.format(outfile, j, process_id),
'w') as file_hdl:
file_hdl.write('\n'.join(ostr))
print('Finished process {} with bg={}, ed={}, outfile={}'.format(
process_id, bg, bg + N, outfile))
def main(PostProcess=False, ShowPlots=True, Persistent=False, pdim=0, L=30):
"""
Introductory example for openMPS to simulate the finite size statics of
the transverse Ising model. Two modes are available when running the
example from command line:
* ``python IsingStatics.py --PostProcess=F`` : runs the MPSFortLib to
determine the ground state statics of the Ising model. (default if
``--PostProcess`` not present.)
* ``python IsingStatics.py --PostProcess=T`` : plotting the results of the
simulation run before.
* The option ``--ShowPlots=T`` (``--ShowPlots=F``) lets you turn on (off)
the GUI windows with the plots. Default to on if not passed to the
command line.
"""
# Build spin operators for spin-1/2 system
# Transform to perserve Z2 symmetry
Operators = mps.BuildSpinOperators(0.5)
Operators['sigmax'] = 2 * Operators['sz']
Operators['sigmaz'] = (Operators['splus'] + Operators['sminus'])
Operators['gen'] = np.array([[0, 0], [0, 1.]])
# Define Hamiltonian of transverse Ising model
H = mps.MPO(Operators)
# Note the J parameter in the transverse Ising Hamiltonian
# has been set to 1, we are modelling a ferromagnetic chain.
H.AddMPOTerm('bond', ['sigmaz', 'sigmaz'], hparam='J', weight=-1.0)
H.AddMPOTerm('site', 'sigmax', hparam='g', weight=-1.0)
# Observables and convergence parameters
myObservables = mps.Observables(Operators)
#myObservables.AddObservable('corr', ['sigmaz', 'sigmaz'], 'zz')
#myObservables.AddObservable('DensityMatrix_i', [])
#myObservables.AddObservable('DensityMatrix_ij', [])
myObservables.AddObservable('MI', True)
myConv = mps.MPSConvParam(max_bond_dimension=200,
variance_tol=1E-10,
local_tol=1E-10,
max_num_sweeps=6)
#modparam = ['max_bond_dimension', 'max_num_sweeps']
#myConv.AddModifiedConvergenceParameters(0, modparam, [80, 4])
# Specify constants and parameter lists
J = 1.0
glist = np.linspace(0.1, 2.1, 41)
parameters = []
for g in glist:
parameters.append({
'simtype':
'Finite',
# Directories
'job_ID':
'Ising_Statics',
'unique_ID':
'g_' + str(g),
'Write_Directory':
'TMP_ISING_01_L_{}/'.format(L),
'Output_Directory':
'OUTPUTS_ISING_01_L_{}/'.format(L),
# System size and Hamiltonian parameters
'L':
L,
'J':
J,
'g':
g,
# ObservablesConvergence parameters
'verbose':
1,
'MPSObservables':
myObservables,
'MPSConvergenceParameters':
myConv,
'logfile':
True,
# Z2 symmetry
'Discrete_generators': ['gen'],
'Discrete_quantum_numbers': [0]
})
# Write Fortran-readable main files
MainFiles = mps.WriteFiles(parameters,
Operators,
H,
PostProcess=PostProcess)
# Run the simulations and quit if we are not just Post
if (not PostProcess):
if os.path.isfile('./Execute_MPSMain'):
RunDir = './'
else:
RunDir = None
mps.runMPS(MainFiles, RunDir=RunDir)
return
# PostProcess
# -----------
dmat_list = []
MI_list = []
Outputs = mps.ReadStaticObservables(parameters)
for Output in Outputs:
print(Output['converged'])
if Persistent:
netmeasures = nm.pearson(Output['MI'])
dist = 1.0 - np.abs(netmeasures[0])
for i in range(L):
dist[i, i] = 0.0
dmat_list.append(dist)
MI_list.append(Output['MI'][3][26])
plt.style.use('seaborn-colorblind')
#plt.style.use('seaborn-whitegrid')
plt.rc('font', family='serif')
plt.rc('mathtext', fontset='cm')
timestamp = int(time.time() * 1000.0)
if (not Persistent):
plt.scatter(glist, MI_list)
plt.xlabel(r"transverse field coupling " r"$g$", fontsize=16)
plt.ylabel(r"Mutual information (4,27)", fontsize=16)
plt.savefig('MI_L_{}_{}.pdf'.format(L, timestamp), bbox_inches='tight')
plt.show()
return
npent_list, pent_list, pnorm_list = ph.compute_ph(
out_path='./diagrams_{}_{}'.format(L, timestamp),
fig_path='./figs_{}_{}'.format(L, timestamp),
basename='ising',
dmat_list=dmat_list,
plot=True,
pdim=pdim)
# Save txt
np.savetxt('stats_L_{}_{}.txt'.format(L, timestamp),
list(zip(glist, npent_list, pent_list, pnorm_list)),
fmt='%.18g')
# Plot
fig, ax1 = plt.subplots()
ax1.scatter(glist, pnorm_list, c='red')
ax1.set_xlabel(r"transverse field coupling " r"$g$", fontsize=16)
ax1.set_ylabel(r"p-norm persistence", fontsize=16)
ax2 = ax1.twinx()
ax2.set_ylabel('normalize persistent entropy', fontsize=16)
ax2.scatter(glist, npent_list, c='blue')
#plt.xlim((0, 2))
#plt.ylim((0, 1))
if (ShowPlots):
plt.savefig('IsingStatic_L_{}_ph_dim_{}_{}.pdf'.format(
L, pdim, timestamp),
bbox_inches='tight')
plt.show()
return