def test_onsager(self):
size = 900
dbeta = 0.001
beta = _np.arange(0., 2., dbeta)
pf = logpf_ising_onsager(size, beta)
dpf = _np.diff(pf) / dbeta
d1beta = beta[1:]
d2pf = _np.diff(dpf) / dbeta
d2beta = beta[2:]
if self.plot:
import matplotlib.pyplot as plt
plt.figure()
plt.plot(beta, pf / size, label='logZ')
plt.plot(beta[1:], dpf / size, label='dlogZ')
plt.plot(beta[2:], d2pf / size, label='d2logZ')
plt.xlabel('beta')
plt.legend(loc='upper left')
plt.title('Log partition function per site and its derivatives'
'.\nObtained with Onsager equations')
figFn = os.path.join(self.outDir, figfn('logPF_onsager'))
plt.savefig(figFn)
# plt.show()
# critical value:
logger.info('critical beta: %f', d2beta[_np.argmax(d2pf)])
logger.info('beta grid precision: %f', dbeta)
assert _np.abs(d2beta[_np.argmax(d2pf)] - 0.88) <= 0.005
def test_extrapolation(self):
size = 900
shape = (int(size ** .5), int(size ** .5))
mask = _np.ones(shape, dtype=int) # full mask
g = graph_from_lattice(mask, kerMask=kerMask2D_4n)
pf, beta = Cpt_Vec_Estim_lnZ_Graph_fast(g, 2)
dbeta = beta[1] - beta[0]
dpf = _np.diff(pf) / dbeta
d1beta = beta[1:]
d2pf = _np.diff(dpf) / dbeta
d2beta = beta[2:]
if self.plot:
import matplotlib.pyplot as plt
plt.figure()
plt.plot(beta, pf / size, label='logZ')
plt.plot(beta[1:], dpf / size, label='dlogZ')
plt.plot(beta[2:], d2pf / size, label='d2logZ')
plt.xlabel('beta')
plt.legend(loc='upper left')
plt.title('Log partition function per site and its derivatives'
'.\nDiscretized using the Extrapolation Scheme.')
figFn = os.path.join(self.outDir, figfn('logPF_ES'))
plt.savefig(figFn)
# plt.show()
# critical value:
logger.info('critical beta: %f', d2beta[_np.argmax(d2pf)])
logger.info('beta grid precision: %f', dbeta)
assert _np.abs(d2beta[_np.argmax(d2pf)] - 0.88) <= 2 * dbeta
def test_extrapolation(self):
size = 900
shape = (int(size**.5), int(size**.5))
mask = _np.ones(shape, dtype=int) # full mask
g = graph_from_lattice(mask, kerMask=kerMask2D_4n)
pf, beta = Cpt_Vec_Estim_lnZ_Graph_fast(g, 2)
dbeta = beta[1] - beta[0]
dpf = _np.diff(pf) / dbeta
d1beta = beta[1:]
d2pf = _np.diff(dpf) / dbeta
d2beta = beta[2:]
if self.plot:
import matplotlib.pyplot as plt
plt.figure()
plt.plot(beta, pf / size, label='logZ')
plt.plot(beta[1:], dpf / size, label='dlogZ')
plt.plot(beta[2:], d2pf / size, label='d2logZ')
plt.xlabel('beta')
plt.legend(loc='upper left')
plt.title('Log partition function per site and its derivatives'
'.\nDiscretized using the Extrapolation Scheme.')
figFn = os.path.join(self.outDir, figfn('logPF_ES'))
plt.savefig(figFn)
# plt.show()
# critical value:
logger.info('critical beta: %f', d2beta[_np.argmax(d2pf)])
logger.info('beta grid precision: %f', dbeta)
assert _np.abs(d2beta[_np.argmax(d2pf)] - 0.88) <= 2 * dbeta
def test_path_sampling(self):
size = 900
shape = (int(size**.5), int(size**.5))
mask = _np.ones(shape, dtype=int) #full mask
g = graph_from_lattice(mask, kerMask=kerMask2D_4n)
pf, beta = Cpt_Vec_Estim_lnZ_Graph(g,2)
dbeta = beta[1]-beta[0]
dpf = _np.diff(pf)/dbeta
d1beta = beta[1:]
d2pf = _np.diff(dpf)/dbeta
d2beta = beta[2:]
if self.plot:
import matplotlib.pyplot as plt
plt.figure()
plt.plot(beta, pf/size, label='logZ')
plt.plot(beta[1:], dpf/size, label='dlogZ')
plt.plot(beta[2:], d2pf/size, label='d2logZ')
plt.xlabel('beta')
plt.legend(loc='upper left')
plt.title('Log partition function per site and its derivatives' \
'.\nDiscretized using Path Sampling')
#print '##### ',
figFn = os.path.join(self.outDir, figfn('logPF_PS'))
plt.savefig(figFn)
#plt.show()
#critical value:
if self.verbose:
print 'critical beta:', d2beta[_np.argmax(d2pf)]
print 'beta grid precision:', dbeta
assert _np.abs(d2beta[_np.argmax(d2pf)] - 0.88) <= dbeta
def test_onsager(self):
size = 900
dbeta = 0.001
beta = _np.arange(0., 2., dbeta)
pf = logpf_ising_onsager(size, beta)
dpf = _np.diff(pf) / dbeta
d1beta = beta[1:]
d2pf = _np.diff(dpf) / dbeta
d2beta = beta[2:]
if self.plot:
import matplotlib.pyplot as plt
plt.figure()
plt.plot(beta, pf / size, label='logZ')
plt.plot(beta[1:], dpf / size, label='dlogZ')
plt.plot(beta[2:], d2pf / size, label='d2logZ')
plt.xlabel('beta')
plt.legend(loc='upper left')
plt.title('Log partition function per site and its derivatives'
'.\nObtained with Onsager equations')
figFn = os.path.join(self.outDir, figfn('logPF_onsager'))
plt.savefig(figFn)
# plt.show()
# critical value:
logger.info('critical beta: %f', d2beta[_np.argmax(d2pf)])
logger.info('beta grid precision: %f', dbeta)
assert _np.abs(d2beta[_np.argmax(d2pf)] - 0.88) <= 0.005
def MC_comp_pfmethods_ML(self, shape):
mask = np.ones(shape, dtype=int) #full mask
g = graph_from_lattice(mask, kerMask=kerMask2D_4n, toroidal=True)
# Betas to iterate over ...
betaMax = 1.4
dbeta = .1
betas = np.arange(0., betaMax, dbeta)
# nb of monte carlo iterations
mcit = 40#100
# nb of classes
nbc = 2
# Path sampling:
mBePS, stdBePS, stdBeMCPS = cached_eval(test_beta_estim_obs_fields,
([g], betas, nbc, 'PS',
mcit), path=config.cacheDir,
prefix='pyhrf_',
new=False)
# Extrapolation scheme:
mBeES, stdBeES, stdBeMCES = cached_eval(test_beta_estim_obs_fields,
([g], betas, nbc, 'ES',
mcit), path=config.cacheDir,
prefix='pyhrf_',
new=False)
# Onsager:
#mBeON, stdBeON, stdBeMCON = cached_eval(test_beta_estim_obs_fields,
# ([g], betas, nbc, 'ONSAGER',
# mcit), path=config.cacheDir,
# prefix='pyhrf_',
# new=True)
if self.plot:
import matplotlib.pyplot as plt
plt.figure()
plt.errorbar(betas, mBeES, stdBeMCES, fmt='r', label='ES')
plt.errorbar(betas, mBePS, stdBeMCPS, fmt='b', label='PS')
#plt.errorbar(betas, mBeON, stdBeMCON, fmt='g', label='Onsager')
plt.plot(betas, betas, 'k', label='true')
#plt.xlabel('simulated beta')
#plt.ylabel('beta MAP')
plt.legend(loc='upper left')
plt.ylim((0.0,1.45))
#plt.title('MC validation (%d it) for beta estimation on '\
# ' observed fields.' %mcit)
#fn = 'comp_obs_field_MC_PS_ES_Onsager_%dx%d' %shape
fn = 'comp_obs_field_MC_PS_%dx%d' %shape
figFn = os.path.join(self.outDir, figfn(fn))
plt.savefig(figFn)
def test_SW_nrj_2C_3C(self):
size = 400
shape = (int(size**.5), int(size**.5))
mask = _np.ones(shape, dtype=int) # full mask
g = graph_from_lattice(mask, kerMask=kerMask2D_4n)
betas = _np.arange(0, 2.7, .2)
nitMC = 100
mU2C = _np.zeros(len(betas))
vU2C = _np.zeros(len(betas))
mU3C = _np.zeros(len(betas))
vU3C = _np.zeros(len(betas))
nrjCalc = field_energy_calculator(g)
# print "nbClasses = 2"
for ib, b in enumerate(betas):
# print ' MC for beta ', b
pottsGen = potts_generator(graph=g,
beta=b,
nbLabels=2,
method='SW')
mU2C[ib], vU2C[ib] = montecarlo(pottsGen, nrjCalc, nbit=nitMC)
# print ' mu2C=',mU2C
# print ' vU2C=',vU2C
# print "nbClasses = 3"
for ib, b in enumerate(betas):
# print ' MC for beta ', b
pottsGen = potts_generator(graph=g,
beta=b,
nbLabels=3,
method='SW')
mU3C[ib], vU3C[ib] = montecarlo(pottsGen, nrjCalc, nbit=nitMC)
# print ' mu3C=',mU3C
# print ' vU3C=',vU3C
if config.savePlots:
import matplotlib.pyplot as plt
plt.plot(betas, mU2C, 'b-', label="2C")
plt.errorbar(betas, mU2C, vU2C**.5, fmt=None, ecolor='b')
plt.plot(betas, mU3C, 'r-', label="3C")
plt.errorbar(betas, mU3C, vU3C**.5, fmt=None, ecolor='r')
plt.legend(loc='upper right')
plt.title(
'Mean energy in terms of beta \n for 2-color and 3-color Potts (SW sampling)'
)
plt.xlabel('beta')
plt.ylabel('mean U per site')
plt.xlim(betas[0] - .1, betas[-1] * 1.05)
figFn = os.path.join(self.outDir, figfn('potts_energy_2C_3C'))
# print figFn
plt.savefig(figFn)
def test_SW_nrj_2C_3C(self):
size = 400
shape = (int(size ** .5), int(size ** .5))
mask = _np.ones(shape, dtype=int) # full mask
g = graph_from_lattice(mask, kerMask=kerMask2D_4n)
betas = _np.arange(0, 2.7, .2)
nitMC = 100
mU2C = _np.zeros(len(betas))
vU2C = _np.zeros(len(betas))
mU3C = _np.zeros(len(betas))
vU3C = _np.zeros(len(betas))
nrjCalc = field_energy_calculator(g)
# print "nbClasses = 2"
for ib, b in enumerate(betas):
# print ' MC for beta ', b
pottsGen = potts_generator(graph=g, beta=b, nbLabels=2,
method='SW')
mU2C[ib], vU2C[ib] = montecarlo(pottsGen, nrjCalc, nbit=nitMC)
# print ' mu2C=',mU2C
# print ' vU2C=',vU2C
# print "nbClasses = 3"
for ib, b in enumerate(betas):
# print ' MC for beta ', b
pottsGen = potts_generator(graph=g, beta=b, nbLabels=3,
method='SW')
mU3C[ib], vU3C[ib] = montecarlo(pottsGen, nrjCalc, nbit=nitMC)
# print ' mu3C=',mU3C
# print ' vU3C=',vU3C
if config.savePlots:
import matplotlib.pyplot as plt
plt.plot(betas, mU2C, 'b-', label="2C")
plt.errorbar(betas, mU2C, vU2C ** .5, fmt=None, ecolor='b')
plt.plot(betas, mU3C, 'r-', label="3C")
plt.errorbar(betas, mU3C, vU3C ** .5, fmt=None, ecolor='r')
plt.legend(loc='upper right')
plt.title(
'Mean energy in terms of beta \n for 2-color and 3-color Potts (SW sampling)')
plt.xlabel('beta')
plt.ylabel('mean U per site')
plt.xlim(betas[0] - .1, betas[-1] * 1.05)
figFn = os.path.join(self.outDir, figfn('potts_energy_2C_3C'))
# print figFn
plt.savefig(figFn)
def test_comparison(self):
size = 1000
shape = (int(size ** .5), int(size ** .5))
mask = _np.ones(shape, dtype=int) # full mask
g = graph_from_lattice(mask, kerMask=kerMask2D_4n, toroidal=True)
dbeta = 0.05
# ES
pfES, betaES = Cpt_Vec_Estim_lnZ_Graph_fast3(g, 2, BetaStep=dbeta)
logger.info('betaES: %f', betaES)
pfES = pfES[:-1]
logger.info('pfES %d:', len(pfES))
dpfES = _np.diff(pfES) / dbeta
d2pfES = _np.diff(dpfES) / dbeta
# Path Sampling
pfPS, beta = Cpt_Vec_Estim_lnZ_Graph(
g, 2, BetaStep=dbeta, SamplesNb=30)
logger.info('beta grid from PS: %f', beta)
dpfPS = _np.diff(pfPS) / dbeta
d1beta = beta[1:]
d2pfPS = _np.diff(dpfPS) / dbeta
d2beta = beta[2:]
# Onsager
logger.info('Onsager ...')
pfOns = logpf_ising_onsager(size, beta) * .96
dpfOns = _np.diff(pfOns) / dbeta
d2pfOns = _np.diff(dpfOns) / dbeta
if self.plot:
logger.info('Plots ...')
import matplotlib.pyplot as plt
# PF plots
plt.figure()
plt.plot(beta, pfES, 'r-+', label='logZ-ES')
plt.plot(beta, pfPS, 'b', label='logZ-PS')
plt.plot(beta, pfOns, 'g', label='logZ-Onsager')
# plt.xlabel('beta')
#plt.legend(loc='upper left')
#plt.title('Log partition function per site - comparison')
figFn = os.path.join(self.outDir, figfn('logPF_ES_PS_Ons'))
print 'saved:', figFn
plt.savefig(figFn)
plt.figure()
plt.plot(d1beta, dpfES / size, 'r-+', label='dlogZ-ES')
plt.plot(d1beta, dpfPS / size, 'b', label='dlogZ-PS')
plt.plot(d1beta, dpfOns / size, 'g', label='dlogZ-Onsager')
plt.xlabel('beta')
plt.legend(loc='upper left')
plt.title('dLog partition function per site - comparison')
figFn = os.path.join(self.outDir, figfn('dlogPF_ES_PS_Ons'))
print 'saved:', figFn
plt.savefig(figFn)
plt.figure()
plt.plot(d2beta, d2pfES / size, 'r-+', label='d2logZ-ES')
plt.plot(d2beta, d2pfPS / size, 'b', label='d2logZ-PS')
plt.plot(d2beta, d2pfOns / size, 'g', label='d2logZ-Onsager')
plt.xlabel('beta')
plt.legend(loc='upper left')
plt.title('d2Log partition function per site - comparison')
figFn = os.path.join(self.outDir, figfn('d2logPF_ES_PS_Ons'))
print 'saved:', figFn
plt.savefig(figFn)
plt.figure()
plt.plot(beta, _np.abs(pfES - pfOns) / size, 'r-+',
label='|logZ_ES-logZ-Ons|')
plt.plot(beta, _np.abs(pfPS - pfOns) / size, 'b',
label='|logZ_PS-logZ-Ons|')
plt.xlabel('beta')
plt.legend(loc='upper left')
plt.title('Error of Log partition function per site')
figFn = os.path.join(self.outDir, figfn('logPF_error_ES_PS'))
print 'saved:', figFn
plt.savefig(figFn)
def test_onsager(self):
size = 900
dbeta = 0.001
beta = _np.arange(0., 2., dbeta)
pf = logpf_ising_onsager(size, beta)
dpf = _np.diff(pf)/dbeta
d1beta = beta[1:]
d2pf = _np.diff(dpf)/dbeta
d2beta = beta[2:]
if self.plot:
import matplotlib.pyplot as plt
plt.figure()
plt.plot(beta, pf/size, label='logZ')
plt.plot(beta[1:], dpf/size, label='dlogZ')
plt.plot(beta[2:], d2pf/size, label='d2logZ')
plt.xlabel('beta')
plt.legend(loc='upper left')
plt.title('Log partition function per site and its derivatives' \
'.\nObtained with Onsager equations')
figFn = os.path.join(self.outDir, figfn('logPF_onsager'))
plt.savefig(figFn)
#plt.show()
#critical value:
if self.verbose:
#print 'critical beta:', d2beta[_np.argmax(d2pf)]
#print 'beta grid precision:', dbeta
assert _np.abs(d2beta[_np.argmax(d2pf)] - 0.88) <= 0.005
def test_path_sampling(self):
size = 900
shape = (int(size**.5), int(size**.5))
mask = _np.ones(shape, dtype=int) #full mask
g = graph_from_lattice(mask, kerMask=kerMask2D_4n)
pf, beta = Cpt_Vec_Estim_lnZ_Graph(g,2)
dbeta = beta[1]-beta[0]
dpf = _np.diff(pf)/dbeta
d1beta = beta[1:]
d2pf = _np.diff(dpf)/dbeta
d2beta = beta[2:]
if self.plot:
import matplotlib.pyplot as plt
plt.figure()
plt.plot(beta, pf/size, label='logZ')
plt.plot(beta[1:], dpf/size, label='dlogZ')
plt.plot(beta[2:], d2pf/size, label='d2logZ')
plt.xlabel('beta')
plt.legend(loc='upper left')
plt.title('Log partition function per site and its derivatives' \
'.\nDiscretized using Path Sampling')
#print '##### ',
figFn = os.path.join(self.outDir, figfn('logPF_PS'))
plt.savefig(figFn)
#plt.show()
#critical value:
if self.verbose:
print 'critical beta:', d2beta[_np.argmax(d2pf)]
print 'beta grid precision:', dbeta
assert _np.abs(d2beta[_np.argmax(d2pf)] - 0.88) <= dbeta
def test_extrapolation(self):
size = 900
shape = (int(size**.5), int(size**.5))
mask = _np.ones(shape, dtype=int) #full mask
g = graph_from_lattice(mask, kerMask=kerMask2D_4n)
pf, beta = Cpt_Vec_Estim_lnZ_Graph_fast(g,2)
dbeta = beta[1]-beta[0]
dpf = _np.diff(pf)/dbeta
d1beta = beta[1:]
d2pf = _np.diff(dpf)/dbeta
d2beta = beta[2:]
if self.plot:
import matplotlib.pyplot as plt
plt.figure()
plt.plot(beta, pf/size, label='logZ')
plt.plot(beta[1:], dpf/size, label='dlogZ')
plt.plot(beta[2:], d2pf/size, label='d2logZ')
plt.xlabel('beta')
plt.legend(loc='upper left')
plt.title('Log partition function per site and its derivatives' \
'.\nDiscretized using the Extrapolation Scheme.')
figFn = os.path.join(self.outDir, figfn('logPF_ES'))
plt.savefig(figFn)
#plt.show()
#critical value:
if self.verbose:
print 'critical beta:', d2beta[_np.argmax(d2pf)]
print 'beta grid precision:', dbeta
assert _np.abs(d2beta[_np.argmax(d2pf)] - 0.88) <= dbeta
def test_comparison(self):
size = 1000
shape = (int(size**.5), int(size**.5))
mask = _np.ones(shape, dtype=int) #full mask
g = graph_from_lattice(mask, kerMask=kerMask2D_4n,toroidal=True)
dbeta = 0.05
# ES
pfES, betaES = Cpt_Vec_Estim_lnZ_Graph_fast3(g,2,BetaStep=dbeta)
if self.verbose:
print 'betaES:', betaES
pfES = pfES[:-1]
if self.verbose:
print 'pfES:', len(pfES)
#print pfES
dpfES = _np.diff(pfES)/dbeta
#print 'dpfES:'
#print _np.diff(pfES)
d2pfES = _np.diff(dpfES)/dbeta
# Path Sampling
pfPS, beta = Cpt_Vec_Estim_lnZ_Graph(g,2,BetaStep=dbeta,SamplesNb=30)
if self.verbose:
print 'beta grid from PS:', beta
dpfPS = _np.diff(pfPS)/dbeta
d1beta = beta[1:]
d2pfPS = _np.diff(dpfPS)/dbeta
d2beta = beta[2:]
# Onsager
if self.verbose: print 'Onsager ...'
pfOns = logpf_ising_onsager(size, beta)*.96
dpfOns = _np.diff(pfOns)/dbeta
d2pfOns = _np.diff(dpfOns)/dbeta
if self.plot:
if self.verbose: print 'Plots ...'
import matplotlib.pyplot as plt
# PF plots
plt.figure()
plt.plot(beta, pfES, 'r-+', label='logZ-ES')
plt.plot(beta, pfPS, 'b', label='logZ-PS')
plt.plot(beta, pfOns,'g', label='logZ-Onsager')
#plt.xlabel('beta')
#plt.legend(loc='upper left')
#plt.title('Log partition function per site - comparison')
figFn = os.path.join(self.outDir, figfn('logPF_ES_PS_Ons'))
print 'saved:', figFn
plt.savefig(figFn)
plt.figure()
plt.plot(d1beta, dpfES/size, 'r-+', label='dlogZ-ES')
plt.plot(d1beta, dpfPS/size, 'b', label='dlogZ-PS')
plt.plot(d1beta, dpfOns/size,'g', label='dlogZ-Onsager')
plt.xlabel('beta')
plt.legend(loc='upper left')
plt.title('dLog partition function per site - comparison')
figFn = os.path.join(self.outDir, figfn('dlogPF_ES_PS_Ons'))
print 'saved:', figFn
plt.savefig(figFn)
plt.figure()
plt.plot(d2beta, d2pfES/size, 'r-+', label='d2logZ-ES')
plt.plot(d2beta, d2pfPS/size, 'b', label='d2logZ-PS')
plt.plot(d2beta, d2pfOns/size,'g', label='d2logZ-Onsager')
plt.xlabel('beta')
plt.legend(loc='upper left')
plt.title('d2Log partition function per site - comparison')
figFn = os.path.join(self.outDir, figfn('d2logPF_ES_PS_Ons'))
print 'saved:', figFn
plt.savefig(figFn)
plt.figure()
plt.plot(beta, _np.abs(pfES-pfOns)/size, 'r-+',
label='|logZ_ES-logZ-Ons|')
plt.plot(beta, _np.abs(pfPS-pfOns)/size, 'b',
label='|logZ_PS-logZ-Ons|')
plt.xlabel('beta')
plt.legend(loc='upper left')
plt.title('Error of Log partition function per site')
figFn = os.path.join(self.outDir, figfn('logPF_error_ES_PS'))
print 'saved:', figFn
plt.savefig(figFn)
def MC_comp_pfmethods_ML_3C(self, shape):
newEval = config.updateCache
mask = np.ones(shape, dtype=int) #full mask
g = graph_from_lattice(mask, kerMask=kerMask2D_4n, toroidal=True)
# Betas to iterate over ...
betaMax = 1.4
dbeta = .1
betas = np.arange(0., betaMax, dbeta)
# nb of monte carlo iterations
mcit = 100#100
# nb of classes
nbc = 3
# Path sampling:
mBePS, stdBePS, stdBeMCPS = cached_eval(test_beta_estim_obs_fields,
([g], betas, nbc, 'PS',
mcit), path=config.cacheDir,
prefix=pyhrf.tmpPrefix,
new=False)
# Extrapolation scheme:
mBeES, stdBeES, stdBeMCES = cached_eval(test_beta_estim_obs_fields,
([g], betas, nbc, 'ES',
mcit), path=config.cacheDir,
prefix=pyhrf.tmpPrefix,
new=False)
# Onsager:
#mBeON, stdBeON, stdBeMCON = cached_eval(test_beta_estim_obs_fields,
# ([g], betas, nbc, 'ONSAGER',
# mcit), path=config.cacheDir,
# prefix=pyhrf.tmpPrefix,
# new=True)
if self.plot:
import plt
plt.figure()
plt.errorbar(betas, mBeES, stdBeMCES, fmt='r', label='ES')
plt.errorbar(betas, mBePS, stdBeMCPS, fmt='b', label='PS')
#plt.errorbar(betas, mBeON, stdBeMCON, fmt='g', label='Onsager')
plt.plot(betas, betas, 'k', label='true')
#plt.xlabel('simulated beta')
#plt.ylabel('beta MAP')
plt.legend(loc='upper left')
#plt.title('MC validation (%d it) for beta estimation on '\
# ' observed fields.' %mcit)
fn = 'comp_obs_field_3class_MC_PS_ES_%dx%d' %shape
figFn = os.path.join(self.outDir, figfn(fn))
plt.savefig(figFn)
plt.figure()
grid = cached_eval(Cpt_Vec_Estim_lnZ_Graph_fast3, (g,nbc),
path=config.cacheDir, prefix=pyhrf.tmpPrefix)
lnzES, betas = (grid[0][:-1], grid[1][:-1])
lnzPS, betas = cached_eval(Cpt_Vec_Estim_lnZ_Graph, (g,nbc),
path=config.cacheDir, new=False,
prefix=pyhrf.tmpPrefix)
plt.plot(betas, lnzES, 'r', label='ES')
plt.plot(betas, lnzPS, 'b', label='PS')
fn = 'comp_PF_3class_PS_ES_%dx%d' %shape
figFn = os.path.join(self.outDir, figfn(fn))
plt.savefig(figFn)
def test_comparison(self):
size = 1000
shape = (int(size**.5), int(size**.5))
mask = _np.ones(shape, dtype=int) # full mask
g = graph_from_lattice(mask, kerMask=kerMask2D_4n, toroidal=True)
dbeta = 0.05
# ES
pfES, betaES = Cpt_Vec_Estim_lnZ_Graph_fast3(g, 2, BetaStep=dbeta)
logger.info('betaES: %f', betaES)
pfES = pfES[:-1]
logger.info('pfES %d:', len(pfES))
dpfES = _np.diff(pfES) / dbeta
d2pfES = _np.diff(dpfES) / dbeta
# Path Sampling
pfPS, beta = Cpt_Vec_Estim_lnZ_Graph(g,
2,
BetaStep=dbeta,
SamplesNb=30)
logger.info('beta grid from PS: %f', beta)
dpfPS = _np.diff(pfPS) / dbeta
d1beta = beta[1:]
d2pfPS = _np.diff(dpfPS) / dbeta
d2beta = beta[2:]
# Onsager
logger.info('Onsager ...')
pfOns = logpf_ising_onsager(size, beta) * .96
dpfOns = _np.diff(pfOns) / dbeta
d2pfOns = _np.diff(dpfOns) / dbeta
if self.plot:
logger.info('Plots ...')
import matplotlib.pyplot as plt
# PF plots
plt.figure()
plt.plot(beta, pfES, 'r-+', label='logZ-ES')
plt.plot(beta, pfPS, 'b', label='logZ-PS')
plt.plot(beta, pfOns, 'g', label='logZ-Onsager')
# plt.xlabel('beta')
#plt.legend(loc='upper left')
#plt.title('Log partition function per site - comparison')
figFn = os.path.join(self.outDir, figfn('logPF_ES_PS_Ons'))
print 'saved:', figFn
plt.savefig(figFn)
plt.figure()
plt.plot(d1beta, dpfES / size, 'r-+', label='dlogZ-ES')
plt.plot(d1beta, dpfPS / size, 'b', label='dlogZ-PS')
plt.plot(d1beta, dpfOns / size, 'g', label='dlogZ-Onsager')
plt.xlabel('beta')
plt.legend(loc='upper left')
plt.title('dLog partition function per site - comparison')
figFn = os.path.join(self.outDir, figfn('dlogPF_ES_PS_Ons'))
print 'saved:', figFn
plt.savefig(figFn)
plt.figure()
plt.plot(d2beta, d2pfES / size, 'r-+', label='d2logZ-ES')
plt.plot(d2beta, d2pfPS / size, 'b', label='d2logZ-PS')
plt.plot(d2beta, d2pfOns / size, 'g', label='d2logZ-Onsager')
plt.xlabel('beta')
plt.legend(loc='upper left')
plt.title('d2Log partition function per site - comparison')
figFn = os.path.join(self.outDir, figfn('d2logPF_ES_PS_Ons'))
print 'saved:', figFn
plt.savefig(figFn)
plt.figure()
plt.plot(beta,
_np.abs(pfES - pfOns) / size,
'r-+',
label='|logZ_ES-logZ-Ons|')
plt.plot(beta,
_np.abs(pfPS - pfOns) / size,
'b',
label='|logZ_PS-logZ-Ons|')
plt.xlabel('beta')
plt.legend(loc='upper left')
plt.title('Error of Log partition function per site')
figFn = os.path.join(self.outDir, figfn('logPF_error_ES_PS'))
print 'saved:', figFn
plt.savefig(figFn)
