def energy2(vec, bond):
P = peps.aspeps(vec, (nr, nc), pdim, bond)
PHP = spepo_hlr.eval_heish(P, P, iop)
PP = peps.dot(P, P, auxbond)
e = PHP / PP
print ' PHP,PP,PHP/PP,eav=', PHP, PP, e, e / (nr * nc)
return e
def save_vec(vec):
print '\ncallback...'
fname = 'peps_vec1'
energy = bound_energy_fn(vec) / (nr * nc)
peps_v = peps.aspeps(vec, (nr, nc), pdim, bond)
PP = peps.dot(peps_v, peps_v, auxbond)
nvec = vec * np.power(PP, -0.5 / (nr * nc))
np.save(fname, nvec)
print ' --- save vec into fname=', fname, ' eav=', energy
print
return nvec
def test_min():
np.random.seed(0)
nr = 4
nc = 4
pdim = 2
bond = 1
auxbond = bond**2
# interface to autograd:
def energy1(vec, bond):
P = peps.aspeps(vec, (nr, nc), pdim, bond)
PHP = peps_hlr.eval_heish(P, P, auxbond, iop)
PP = peps.dot(P, P, auxbond)
e = PHP / PP
print ' PHP,PP,PHP/PP,eav=', PHP, PP, e, e / (nr * nc)
return e
# dlog<P|1+tH+t^2+...|P>/dt|(t=0) = Energy
def energy2(vec, bond):
P = peps.aspeps(vec, (nr, nc), pdim, bond)
PHP = spepo_hlr.eval_heish(P, P, iop)
PP = peps.dot(P, P, auxbond)
e = PHP / PP
print ' PHP,PP,PHP/PP,eav=', PHP, PP, e, e / (nr * nc)
return e
bound_energy_fn = lambda x: energy1(x, bond)
deriv = autograd.grad(bound_energy_fn)
ifload = False
if not ifload:
# 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
# initial guess by AFM
pepsa = peps.create((nr, nc), pdim, configa)
pepsb = peps.create((nr, nc), pdim, configb)
if bond == 1:
peps0 = pepsa
else:
peps0 = peps.add(pepsa, pepsb) # this has bond=2
#pepsc = peps.random(peps0.shape, pdim, 1, 0.01)
#peps0 = peps.add(peps0, pepsc)
peps0 = peps.add_noise(peps0, pdim, bond, fac=0.1)
vec = peps.flatten(peps0)
# test
print 'energy1=', energy1(vec, bond)
print 'energy2=', energy2(vec, bond)
print 'nparams=', len(vec)
exit()
print 'test energy'
print bound_energy_fn(vec)
print 'test grad'
d = deriv(vec)
else:
print 'load guess...'
vec = np.load('peps_vec2.npy')
D0 = 2
peps_v = peps.aspeps(vec, (nr, nc), pdim, D0)
PP = peps.dot(peps_v, peps_v, auxbond)
vec = vec * np.power(PP, -0.5 / (nr * nc))
# Add noise
if bond > D0:
peps_v = peps.aspeps(vec, (nr, nc), pdim, D0)
peps_c = peps.random(peps_v.shape, pdim, bond - D0, 1.0)
peps_t = peps.add(peps_v, peps_c)
peps_t = peps.add_noise(peps_t, pdim, bond, fac=0.1)
PP = peps.dot(peps_t, peps_t, auxbond)
vec = peps.flatten(peps_t) * np.power(PP, -0.5 / (nr * nc))
print '<v|v>=', peps.dot(peps_v, peps_v, auxbond)
print '<v|c>=', peps.dot(peps_v, peps_c, auxbond)
print '<c|c>=', peps.dot(peps_c, peps_c, auxbond)
print '<t|t>=', peps.dot(peps_t, peps_t, auxbond)
print '<t|v>=', peps.dot(peps_t, peps_v, auxbond)
print '<t|c>=', peps.dot(peps_t, peps_c, auxbond)
print 'e_v=', energy1(peps.flatten(peps_v), 2)
print 'e_c=', energy1(peps.flatten(peps_c), 1)
print 'e_t=', energy1(peps.flatten(peps_t), 3)
energy = bound_energy_fn(vec) / (nr * nc)
print 'PP =', PP, ' eav =', energy
def save_vec(vec):
print '\ncallback...'
fname = 'peps_vec1'
energy = bound_energy_fn(vec) / (nr * nc)
peps_v = peps.aspeps(vec, (nr, nc), pdim, bond)
PP = peps.dot(peps_v, peps_v, auxbond)
nvec = vec * np.power(PP, -0.5 / (nr * nc))
np.save(fname, nvec)
print ' --- save vec into fname=', fname, ' eav=', energy
print
return nvec
# optimize
step = 1.0
for i in range(3):
g = deriv(vec)
print 'i=', i, np.linalg.norm(g)
vec = vec - step * g
print '\nStart optimization...'
result = scipy.optimize.minimize(bound_energy_fn, jac=deriv, x0=vec,\
options={'maxiter':10},callback=save_vec)
P0 = peps.aspeps(result.x, (nr, nc), pdim, bond)
print "final eav =", bound_energy_fn(peps.flatten(P0)) / (nr * nc)
return 0