def fx(xdata, mps, rfun, args=None, dtype=numpy.complex_):
nsite = mps.nsite
sites1 = mps.torank2()
ydata = numpy.zeros(xdata.shape, dtype=dtype)
for i, x in enumerate(xdata):
sites2 = []
for isite in range(nsite):
if args is None:
ntmp = rfun(x)
else:
occ = [args[2 * isite], args[2 * isite + 1]]
ntmp = rfun(x, occ)
if isite == 0:
#tmp = numpy.einsum('ij,ja->ia',ntmp,sites1[isite])
tmp = numpy.dot(ntmp, sites1[isite])
elif isite == nsite - 1:
#tmp = numpy.einsum('ij,aj->ai',ntmp,sites1[isite])
tmp = numpy.dot(sites1[isite], ntmp.T)
else:
#tmp = numpy.einsum('ij,ajb->aib',ntmp,sites1[isite])
# ajb,ij->abi
tmp = numpy.tensordot(sites1[isite],
ntmp,
axes=([1], [1]))
# abi->aib
tmp = tmp.transpose(0, 2, 1).copy()
sites2.append(tmp)
ydata[i] = mpslib.mps_dot(sites1, sites2)
return ydata
def makeRDM1(mps):
nb = len(mps)
rdm1 = numpy.zeros((nb, nb))
for i in range(nb):
for j in range(nb):
print 'rdm[i,j] (i,j)=', i, j
ci = mpo_r1(nb, i, 1)
aj = mpo_r1(nb, j, 0)
Aij = mpo_r1mul(ci, aj)
op = class_mpo(nb)
op.fromRank1(Aij)
rdm1[i, j] = mpslib.mps_dot(mps, op.dot(mps))
print 'Hermicity=', numpy.linalg.norm(rdm1 - rdm1.T)
return rdm1
def fx(x, mps, refdet, n):
global icounter
icounter += 1
nsite = len(refdet)
sites1 = mps.torank2()
sites2 = []
for isite in range(nsite):
if refdet[isite] == 0:
ntmp = numpy.array([[1., 0.], [0., cmath.exp(1.j * x)]])
else:
ntmp = numpy.array([[cmath.exp(1.j * x), 0.], [0., 1.]])
if isite == 0:
tmp = numpy.einsum('ij,ja->ia', ntmp, sites1[isite])
elif isite == nsite - 1:
tmp = numpy.einsum('ij,aj->ai', ntmp, sites1[isite])
else:
tmp = numpy.einsum('ij,ajb->aib', ntmp, sites1[isite])
sites2.append(tmp)
val = mpslib.mps_dot(sites1, sites2)
val = val * cmath.exp(-1.j * n * x) / (2.0 * numpy.pi)
val = val.real
return val
def makeRDM1q(self):
mps = self.torank2()
nb = len(mps)
rdm1 = numpy.zeros((4, nb, nb))
types = [[1, 0], [1, 1], [0, 1], [0, 0]]
for i in range(nb):
for j in range(nb):
print 'rdm[i,j] (i,j)=', i, j
for ijtp in range(4):
itp, jtp = types[ijtp]
ci = mpo_class.mpo_r1(nb, i, itp)
cj = mpo_class.mpo_r1(nb, j, jtp)
Aij = mpo_class.mpo_r1mul(ci, cj)
op = mpo_class.class_mpo(nb)
op.fromRank1(Aij)
rdm1[ijtp, i, j] = mpslib.mps_dot(mps, op.dot(mps))
rdm1q = numpy.zeros((2 * nb, 2 * nb))
rdm1q[:nb, :nb] = rdm1[0]
rdm1q[:nb, nb:] = rdm1[1]
rdm1q[nb:, :nb] = rdm1[2]
rdm1q[nb:, nb:] = rdm1[3]
print 'Hermicity=', numpy.linalg.norm(rdm1q - rdm1q.T)
return rdm1q
def fx(xdata, mps, refdet):
global icounter
icounter += 1
nsite = len(refdet)
sites1 = mps.torank2()
ydata = numpy.zeros(xdata.shape, dtype=numpy.complex_)
for i, x in enumerate(xdata):
sites2 = []
for isite in range(nsite):
if refdet[isite] == 0:
ntmp = numpy.array([[1., 0.], [0.,
cmath.exp(1.j * x)]])
else:
ntmp = numpy.array([[cmath.exp(1.j * x), 0.], [0.,
1.]])
if isite == 0:
tmp = numpy.einsum('ij,ja->ia', ntmp, sites1[isite])
elif isite == nsite - 1:
tmp = numpy.einsum('ij,aj->ai', ntmp, sites1[isite])
else:
tmp = numpy.einsum('ij,ajb->aib', ntmp, sites1[isite])
sites2.append(tmp)
ydata[i] = mpslib.mps_dot(sites1, sites2) / (2.0 * numpy.pi)
return ydata
def dot(self, other):
mps1 = self.torank2()
mps2 = other.torank2()
return mpslib.mps_dot(mps1, mps2)
def testDet(nb=12, nelec=6):
import jacobi
print '\n[testDet]'
# Init
numpy.random.seed(2)
h = numpy.random.uniform(-1, 1, nb * nb)
h = h.reshape(nb, nb)
h = 0.5 * (h + h.T)
e1, v1, givens = jacobi.jacobi(h, ifswap=False)
vmat1 = v1[:, :nelec].copy()
mps = detToMPS(vmat1)
bdim0 = mpslib.mps_bdim(mps)
rdm1 = makeRDM1(mps)
diff = numpy.linalg.norm(rdm1 - vmat1.dot(vmat1.T))
print 'RDMdiff=', diff
if diff > 1.e-10: exit()
#-----------------------------------------------------#
# Try to convert MPS(in AO basis) to MPS(in MO basis) #
# by applying the unitary transformation gates. #
#-----------------------------------------------------#
ngivens = len(givens)
mps1 = copy.deepcopy(mps)
for idx, rot in enumerate(givens):
k, l, arg = rot
if abs(arg) < 1.e-10: continue
print '>>> idx=', idx, '/', ngivens, ' arg=', arg, math.cos(
arg), math.sin(arg)
umpo = genU1mpo(nb, k, l, -arg)
mps1 = copy.deepcopy(umpo.dot(mps1))
print 'mps.bdim = ', mpslib.mps_bdim(mps1)
mpslib.mps_compress(mps1)
# Print
bdim0 = mpslib.mps_bdim(mps)
bdim1 = mpslib.mps_bdim(mps1)
print 'bdim0', bdim0
print 'bdim1', bdim1
# Comparison
dmps = mpslib.detmps(nb, nelec)
rr = mpslib.mps_diff(dmps, mps1, iprt=1)
print 'diff=', rr
nmpo = occmpo(nb)
nelec1 = mpslib.mps_dot(dmps, nmpo.dot(dmps))
nelec2 = mpslib.mps_dot(mps1, nmpo.dot(mps1))
print 'Check nelec:'
print 'nelec =', nelec
print 'nelec1=', nelec1
print 'nelec2=', nelec2
#
# bdim0 [2, 4, 8, 16, 32, 64, 128, 256, 128, 64, 32, 16, 8, 4, 2]
# bdim1 [2, 3, 3, 3, 3, 3, 4, 4, 4, 3, 2, 2, 2, 1, 1]
# [mps_diff]
# rr=0.00000e+00
# pp=1.00000
# pq=1.00000
# qp=1.00000
# qq=1.00000
# diff= 0.0
# Check nelec:
# nelec = 8
# nelec1= 8.0
# nelec2= 8.00000000001
#
return 0