def energy_fn(vec, pdim, bond):
P = peps.aspeps(vec, (nr, nc), pdim, bond)
PHP = peps_h.eval_heish(P, P, auxbond)
PP = peps.dot(P, P, auxbond)
e = PHP / PP
print ' PHP,PP,PHP/PP,eav=', PHP, PP, e, e / (nr * nc)
return PHP / PP
def test_basic(vec, nr, nc, pdim, bond):
P = peps.aspeps(vec, (nr, nc), pdim, bond)
# Initialization
auxbond = 16
configa = np.zeros([nr, nc], dtype=np.int)
configb = np.zeros([nr, nc], dtype=np.int)
for i in range(nr):
for j in range(nc):
configa[i, j] = (i + j) % 2
configb[i, j] = (i + j + 1) % 2
assert np.sum(configa) % 2 == 0
assert np.sum(configb) % 2 == 0
x = mc_helper.fromConf2Bits(configa)
print configa
print x, bin(x)
conf = mc_helper.fromBits2Conf(x, nr, nc)
print conf
print
configb = configa.copy()
configb[1, 1] = 1
configb[1, 2] = 0
y = mc_helper.fromConf2Bits(configb)
print configb
print y, bin(y)
Pa = peps.create(pdim, configa)
Pb = peps.create(pdim, configb)
print '<Pa|P>=', peps.dot(Pa, P, auxbond)
print '<Pb|P>=', peps.dot(Pb, P, auxbond)
print
print ' configa=\n', configa
print ' configb=\n', configb
#peps_h.eval_hbond(Pa, Pb, 1, 1, auxbond)
Hab = peps_h.eval_heish(Pa, Pb, auxbond)
print ' Hab=', Hab
assert abs(Hab - 0.5) < 1.e-10
Haa = peps_h.eval_heish(Pa, Pa, auxbond)
print ' Haa=', Haa
assert abs(Haa + 6.0) < 1.e-10
Hbb = peps_h.eval_heish(Pb, Pb, auxbond)
print ' Hbb=', Hbb
assert abs(Hbb + 3.0) < 1.e-10
return 0
def test_mc(vec, nr, nc, pdim, bond):
P = peps.aspeps(vec, (nr, nc), pdim, bond)
# Initialization
auxbond = 20
configa = np.zeros([nr, nc], dtype=np.int)
configb = np.zeros([nr, nc], dtype=np.int)
for i in range(nr):
for j in range(nc):
configa[i, j] = (i + j) % 2
configb[i, j] = (i + j + 1) % 2
assert np.sum(configa) % 2 == 0
assert np.sum(configb) % 2 == 0
def genWs(by):
cy = mc_helper.fromBits2Conf(by, nr, nc)
py = peps.create(pdim, cy)
wy = peps.dot(py, P, auxbond)
return wy
mtx = mc_helper.genHeisenbergHlst(nr, nc)
x = mc_helper.fromConf2Bits(configa)
wsx = genWs(x)
nsample = 10000
maxiter = 30
sample = [x] * nsample
ws = np.array([wsx] * nsample)
iop = 1
for niter in range(maxiter):
print '\nniter=', niter
for i in range(nsample):
bx = sample[i]
wx = ws[i]
by = mc_helper.genHeisenbergMove(bx, nr, nc)
wy = genWs(by)
if niter == 0: # accept all
print 'i=', i, bin(by)
sample[i] = by
ws[i] = wy
else:
prob = min([1, (wy / wx)**2])
rand = np.random.rand()
if prob > rand:
sample[i] = by
ws[i] = wy
else:
sample[i] = bx
ws[i] = wx
print 'i=', i, prob, rand, 'accept=', prob > rand
# Compute energy
z = np.sum(ws**2)
eloc = np.zeros(nsample)
# E = 1/Z*sum_S |<P|S>|^2*Eloc
if iop == 0:
# Eloc = <P|H|S>/<P|S> (Variational?)
for i in range(nsample):
by = sample[i]
cy = mc_helper.fromBits2Conf(by, nr, nc)
py = peps.create(pdim, cy)
PHP = peps_h.eval_heish(P, py, auxbond)
eloc[i] = PHP / ws[i]
print 'i=', i, eloc[i]
else:
# Eloc = sum_S' <P|S'><S'|H|S>/<P|S>
# We need a way to generate S' from <S'|H|S>
for i in range(nsample):
sample2 = mc_helper.genHeisenbergConnected(sample[i], nr, nc)
hs = map(
lambda s1: mc_helper.genHeisenbergHmn(s1, sample[i], mtx),
sample2)
wsp = map(lambda s1: genWs(s1), sample2)
eloc[i] = np.dot(wsp, hs) / ws[i]
print 'i=', i, eloc[i]
#
# THIS IS WRONG !!! SIMPLE AVERAGE IS OK.
#
esum = np.dot(eloc, ws**2) / z
print 'etot=', esum, ' e_per_site=', esum / (nr * nc)
return 0
def test_min():
np.random.seed(5)
nr = 4
nc = 4
pdim = 2
bond = 2
auxbond = 4 # None - PHP,PP,PHP/PP,eav= -6.0 1.0 -6.0 -0.375
def energy_fn(vec, pdim, bond):
P = peps.aspeps(vec, (nr, nc), pdim, bond)
PHP = peps_h.eval_heish(P, P, auxbond)
PP = peps.dot(P, P, auxbond)
e = PHP / PP
print ' PHP,PP,PHP/PP,eav=', PHP, PP, e, e / (nr * nc)
return PHP / PP
# Initialization
configa = np.zeros([nr, nc], dtype=np.int)
configb = np.zeros([nr, nc], dtype=np.int)
for i in range(nr):
for j in range(nc):
configa[i, j] = (i + j) % 2
configb[i, j] = (i + j + 1) % 2
assert np.sum(configa) % 2 == 0
assert np.sum(configb) % 2 == 0
pepsa = peps.create(pdim, configa)
pepsb = peps.create(pdim, configb)
# AUTOGRAD
pepsc = peps.random(pepsa.shape, pdim, bond - 1, fac=1.e-2)
peps0 = peps.add(pepsa, pepsc)
peps0 = peps.add_noise(peps0, fac=1.e-1)
vec = peps.flatten(peps0)
import scipy.optimize
import autograd
def bound_energy_fn(vec):
return energy_fn(vec, pdim, bond)
deriv = autograd.grad(bound_energy_fn)
print 'nparams=', len(vec)
#print bound_energy_fn(vec)
#print deriv(vec)
def save_vec(vec):
fname = 'peps_vec1'
np.save(fname, vec)
print ' --- save vec into fname=', fname
return 0
#vec = np.load('peps_vec.npy')
#peps0 = peps.aspeps(vec, (nr,nc), pdim, bond)
#peps0 = peps.add_noise(peps0,fac=5.e-1)
#vec = peps.flatten(peps0)
# Optimize
result = scipy.optimize.minimize(bound_energy_fn, jac=deriv, x0=vec,\
tol=1.e-4, callback=save_vec)
P0 = peps.aspeps(result.x, (nr, nc), pdim, bond)
print "final =", energy_fn(peps.flatten(P0), pdim, bond)
return 0
def energy_fn(vec, pdim, bond):
P = peps.aspeps(vec, (nr, nc), pdim, bond)
PHP = peps_h.eval_heish(P, auxbond)
PP = peps.dot(P, P, auxbond)
print PHP, PP, PHP / PP
return PHP / PP
def test_min():
numpy.random.seed(5)
nr = 6
nc = 4
auxbond = 8
def energy_fn(vec, pdim, bond):
P = peps.aspeps(vec, (nr, nc), pdim, bond)
PHP = peps_h.eval_heish(P, auxbond)
PP = peps.dot(P, P, auxbond)
print PHP, PP, PHP / PP
return PHP / PP
afma = np.zeros([nr * nc])
configa = np.zeros([nr, nc], dtype=np.int)
configb = np.zeros([nr, nc], dtype=np.int)
for i in range(nr):
for j in range(nc):
configa[i, j] = (i + j) % 2
configb[i, j] = (i + j + 1) % 2
#print afma
#print afmb
pdim = 2
pepsa = peps.create((nr, nc), pdim, configa)
pepsb = peps.create((nr, nc), pdim, configb)
print peps.dot(pepsa, pepsa, None)
print peps.dot(pepsb, pepsb, None)
print peps.dot(pepsa, pepsb, None)
PHP = peps_h.eval_heish(pepsa, None)
#print "config", configa[0,0], configa[0,1]
print "PHP energy", PHP
print "PP", peps.dot(pepsa, pepsa, None)
# flata = peps.flatten(pepsa)
# pepsA = peps.aspeps(flata, (nr,nc), pdim, bond=1)
# print "reconstituted dot", peps.dot(pepsA,pepsa,None)
# print pepsa
# print pepsA
print "A energy", energy_fn(peps.flatten(pepsa), pdim, bond=1)
print "B energy", energy_fn(peps.flatten(pepsb), pdim, bond=1)
print "---start opt-----"
pdim = 2
bond = 2
peps0 = peps.add(pepsa, pepsb) # this has bond=2
pepsc = peps.zeros(pepsa.shape, pdim,
bond - 2) # add some zeros to make up full bond
peps0 = peps.add(peps0, pepsc)
peps0 = add_noise(peps0, 0.1)
print energy_fn(peps.flatten(peps0), pdim, bond)
#vec = 0.3*np.random.random(nparam)
vec = peps.flatten(peps0)
#0.3*np.random.random(nparam)
def bound_energy_fn(vec):
return energy_fn(vec, pdim, bond)
deriv = autograd.grad(bound_energy_fn)
d = deriv(vec)
print bound_energy_fn(vec)
result = scipy.optimize.minimize(bound_energy_fn, jac=deriv, x0=vec)
print "max value", np.max(result.x)
P0 = peps.aspeps(result.x, (nr, nc), pdim, bond)