def eval_vbond(pepsa0, pepsa, i, j, auxbond):
debug = False
# Sz*Sz
pepsb = peps.copy(pepsa)
pepsb[i, j] = einsum("pq,qludr->pludr", Sz, pepsa[i, j])
pepsb[i + 1, j] = einsum("pq,qludr->pludr", Sz, pepsa[i + 1, j])
valzz = peps.dot(pepsa0, pepsb, auxbond)
if debug: print(i, j), 'valzz=', valzz
# Sp*Sm
pepsb = peps.copy(pepsa)
pepsb[i, j] = einsum("xpq,qludr->plxudr", Sp,
pepsa[i, j]).merge_adjpair(2, 3)
pepsb[i + 1, j] = einsum("xpq,qludr->pluxdr", Sm,
pepsa[i + 1, j]).merge_adjpair(3, 4)
valpm = peps.dot(pepsa0, pepsb, auxbond)
if debug: print(i, j), 'valpm=', valpm
# Sm*Sp
pepsb = peps.copy(pepsa)
pepsb[i, j] = einsum("xpq,qludr->plxudr", Sm,
pepsa[i, j]).merge_adjpair(2, 3)
pepsb[i + 1, j] = einsum("xpq,qludr->pluxdr", Sp,
pepsa[i + 1, j]).merge_adjpair(3, 4)
valmp = peps.dot(pepsa0, pepsb, auxbond)
if debug: print(i, j), 'valmp=', valmp
return valzz + 0.5 * (valpm + valmp)
def test_conf():
np.random.seed(5)
nr = 3
nc = 3
pdim = 2
bond = 2
auxbond = 4
# Initialization:
# [[0 1 0 1]
# [1 0 1 0]
# [0 1 0 1]
# [1 0 1 0]
# [0 1 0 1]
# [1 0 1 0]]
configa = np.zeros([nr, nc], dtype=np.int)
for i in range(nr):
for j in range(nc):
configa[i, j] = (i + j) % 2
pepsa = peps.create(pdim, configa)
#for i in range(nr):
# for j in range(nc):
# print '(i,j)=',(i,j)
# pepsa[i,j].prt()
print "CEVAL =", peps.ceval(pepsa, configa, auxbond)
PP = peps.dot(pepsa, pepsa, None)
print "<P|P> =", PP
Sp = peps_h.get_Sp()
Sm = peps_h.get_Sm()
Sz = peps_h.get_Sz()
i = j = 0
# Sm*Sp
pepsb = peps.copy(pepsa)
pepsb[i, j] = einsum("xpq,qludr->plxudr", Sm,
pepsa[i, j]).merge_adjpair(2, 3)
pepsb[i, j].prt()
pepsb[i, j + 1] = einsum("xpq,qludr->pluxdr", Sp,
pepsa[i, j + 1]).merge_adjpair(3, 4)
valmp = peps.dot(pepsb, pepsa, auxbond)
print 'valmp=', valmp
# Sz*Sz
pepsb = peps.copy(pepsa)
pepsb[i, j] = einsum("pq,qludr->pludr", Sz, pepsa[i, j])
pepsb[i, j + 1] = einsum("pq,qludr->pludr", Sz, pepsa[i, j + 1])
valzz = peps.dot(pepsb, pepsa, auxbond)
print 'valzz=', valzz
# Sp*Sm
pepsb = peps.copy(pepsa)
pepsb[i, j] = einsum("xpq,qludr->plxudr", Sp,
pepsa[i, j]).merge_adjpair(2, 3)
pepsb[i, j + 1] = einsum("xpq,qludr->pluxdr", Sm,
pepsa[i, j + 1]).merge_adjpair(3, 4)
valpm = peps.dot(pepsb, pepsa, auxbond)
print 'valpm=', valpm
return 0
def eval_vbond(pepsa0, pepsa, i, j, auxbond):
pepsb = peps.copy(pepsa)
pepsb[i, j] = einsum("pq,qludr->pludr", Sz, pepsa[i, j])
pepsb[i + 1, j] = einsum("pq,qludr->pludr", Sz, pepsa[i + 1, j])
valzz = peps.dot(pepsa0, pepsb, auxbond)
pepsb = peps.copy(pepsa)
pepsb[i, j] = einsum("pq,qludr->pludr", Sp, pepsa[i, j])
pepsb[i + 1, j] = einsum("pq,qludr->pludr", Sm, pepsa[i + 1, j])
valpm = peps.dot(pepsa0, pepsb, auxbond)
pepsb = peps.copy(pepsa)
pepsb[i, j] = einsum("pq,qludr->pludr", Sm, pepsa[i, j])
pepsb[i + 1, j] = einsum("pq,qludr->pludr", Sp, pepsa[i + 1, j])
valmp = peps.dot(pepsa0, pepsb, auxbond)
return valzz + .5 * (valpm + valmp)
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():
pdim = 2
bond = 2
numpy.random.seed(5)
nr = 4
nc = 4
configs = spins.configs(nr * nc, pdim)
zpeps = peps.random([nr, nc], pdim, bond)
print zpeps
for i in range(nr):
for j in range(nc):
print np.linalg.norm(zpeps[i, j])
#auxbond = 2
# for config in configs:
# print config
# cpeps = peps.cpeps(zpeps,config)
# print "norms", np.linalg.norm(cpeps[0,0]), np.linalg.norm(cpeps[0,1]), np.linalg.norm(cpeps[1,0]), np.linalg.norm(cpeps[1,1])
# print peps.ceval(zpeps,config,auxbond)
php = peps_h.eval_heish(zpeps, None)
pp = peps.dot(zpeps, zpeps, None)
print pp
print numpy.random.random([1])
print "Expectation value", php, pp, 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 genWs(by):
cy = mc_helper.fromBits2Conf(by, nr, nc)
py = peps.create(pdim, cy)
wy = peps.dot(py, P, auxbond)
return wy
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)