def test_nonint(self):
#get the exact solution.
h_exact=self.model_exact.hgen.H()
E_excit=eigvalsh(h_exact)
Emin_exact=sum(E_excit[E_excit<0])
#the solution in occupation representation.
h_occ=self.model_occ.hgen.H()
Emin=eigsh(h_occ,which='SA',k=1)[0]
print 'The Ground State Energy for hexagon(t = %s, t2 = %s) is %s, tolerence %s.'%(self.t,self.t2,Emin,Emin-Emin_exact)
assert_almost_equal(Emin_exact,Emin)
#the solution through updates
H_serial=op2collection(op=self.model_occ.hgen.get_opH())
H=get_H(H=H_serial,hgen=self.expander)
H2,bm2=get_H_bm(H=H_serial,hgen=self.expander2,bstr='QM')
Emin=eigsh(H,k=1,which='SA')[0]
Emin2=eigsh(H2,k=1,which='SA')[0]
print 'The Ground State Energy is %s, tolerence %s.'%(Emin,Emin-Emin2)
assert_almost_equal(Emin_exact,Emin)
assert_almost_equal(Emin_exact,Emin2)
#the solution through dmrg.
bmgen=get_bmgen(self.expander3.spaceconfig,'QM')
dmrgegn=DMRGEngine(hchain=H_serial,hgen=self.expander3,tol=0,bmg=bmgen,symmetric=True)
EG2=dmrgegn.run_finite(endpoint=(5,'<-',0),maxN=[10,20,30,40,40],tol=0)[-1]
assert_almost_equal(Emin_exact,EG2*H_serial.nsite,decimal=4)
def test_nonint(self):
#get the exact solution.
spaceconfig = self.spaceconfig1
self.set_params(U=0., t=1., mu=0.2, t2=0., nsite=6)
h_exact = self.model_exact.hgen.H()
E_excit = eigvalsh(h_exact)
Emin_exact = sum(E_excit[E_excit < 0])
#the solution in occupation representation.
h_occ = self.model_occ.hgen.H()
Emin, Vmin1 = eigsh(h_occ, which='SA', k=1)
print 'The Ground State Energy for hexagon(t = %s, t2 = %s) is %s, tolerence %s.' % (
self.t, self.t2, Emin, Emin - Emin_exact)
assert_almost_equal(Emin_exact, Emin)
#the solution through updates
H_serial = op2collection(op=self.model_occ.hgen.get_opH())
H_serial_Z = copy.copy(H_serial)
H_serial_Z.insert_Zs(spaceconfig=spaceconfig)
expander = ExpandGenerator(spaceconfig=spaceconfig,
H=H_serial_Z,
evolutor_type='null',
use_zstring=True)
H = get_H(hgen=expander)
expander2 = ExpandGenerator(spaceconfig=spaceconfig,
H=H_serial_Z,
evolutor_type='normal',
use_zstring=True)
H2, bm2 = get_H_bm(hgen=expander2, bstr='QM')
Emin = eigsh(H, k=1, which='SA')[0]
Emin2 = eigsh(H2, k=1, which='SA')[0]
print 'The Ground State Energy is %s, tolerence %s.' % (Emin,
Emin - Emin2)
assert_almost_equal(Emin_exact, Emin)
assert_almost_equal(Emin_exact, Emin2)
#the solution through dmrg.
expander3 = ExpandGenerator(spaceconfig=spaceconfig,
H=H_serial,
evolutor_type='masked',
use_zstring=True)
dmrgegn = DMRGEngine(hgen=expander3, tol=0, reflect=False)
dmrgegn.use_U1_symmetry('QM', target_block=(0, 0))
EG2, Vmin2 = dmrgegn.run_finite(endpoint=(5, '<-', 0),
maxN=[10, 30, 60, 100, 100],
tol=0)
Vmin2 = fix_tail(Vmin2, expander3.spaceconfig, 0)
#check for states.
assert_almost_equal(Emin_exact, EG2, decimal=4)
Vmin1 = Vmin1[:, 0]
assert_almost_equal(abs(Vmin2.state), abs(Vmin1), decimal=3)
print(Vmin2.state / Vmin1)[abs(Vmin1) > 1e-2]
pdb.set_trace()
def test_lanczos(self):
'''test for directly construct and solve the ground state energy.'''
model=self.get_model(10,1)
hgen1=RGHGen(spaceconfig=SpinSpaceConfig([2,1]),H=model.H_serial,evolutor_type='null')
hgen2=RGHGen(spaceconfig=SpinSpaceConfig([2,1]),H=model.H_serial,evolutor_type='normal')
dmrgegn=DMRGEngine(hgen=hgen1,tol=0)
H=get_H(hgen=hgen1)
H2,bm2=get_H_bm(hgen=hgen2,bstr='M')
Emin=eigsh(H,k=1)[0]
Emin2=eigsh(bm2.lextract_block(H2,(0.,0,)),k=1)[0]
print 'The Ground State Energy is %s, tolerence %s.'%(Emin,Emin-Emin2)
assert_almost_equal(Emin,Emin2)
def test_lanczos(self):
'''test for directly construct and solve the ground state energy.'''
model=self.get_model(10,1)
hgen1=SpinHGen(spaceconfig=SpinSpaceConfig([2,1]),evolutor=NullEvolutor(hndim=2))
hgen2=SpinHGen(spaceconfig=SpinSpaceConfig([2,1]),evolutor=Evolutor(hndim=2))
dmrgegn=DMRGEngine(hchain=model.H_serial,hgen=hgen1,tol=0)
H=get_H(H=model.H_serial,hgen=hgen1)
H2,bm2=get_H_bm(H=model.H_serial,hgen=hgen2,bstr='M')
Emin=eigsh(H,k=1)[0]
Emin2=eigsh(bm2.lextract_block(H2,0.),k=1)[0]
print 'The Ground State Energy is %s, tolerence %s.'%(Emin,Emin-Emin2)
assert_almost_equal(Emin,Emin2)
def test_dmrg_finite(self):
'''
Run iDMFT for heisenberg model.
'''
nsite=10
model=self.get_model(nsite,1)
hgen1=RGHGen(spaceconfig=SpinSpaceConfig([2,1]),H=model.H_serial,evolutor_type='null')
hgen2=RGHGen(spaceconfig=SpinSpaceConfig([2,1]),H=model.H_serial,evolutor_type='masked')
H=get_H(hgen1)
EG1=eigsh(H,k=1,which='SA')[0]
dmrgegn=DMRGEngine(hgen=hgen2,tol=0,reflect=True)
dmrgegn.use_U1_symmetry('M',target_block=0)
EG2=dmrgegn.run_finite(endpoint=(5,'<-',0),maxN=[10,20,30,40,40],tol=0)[0]
assert_almost_equal(EG1,EG2,decimal=4)
def get_even_eop(self,spaceconfig):
'''Get the evolution operator collection for even bonds.'''
nsite=self.opc.nsite
#query even bonds, like 1-2 or 1.
res=None
for i in xrange(1,nsite,2):
bop=self.opc.query(i,i+1)
sop=self.opc.query(i)
op=bop+sop
#get the hamiltonian
hgen=ExpandGenerator(spaceconfig=spaceconfig,H=op,evolutor_type='null')
H=get_H(hgen)
#get the evolution matrix, exponential of H
expH=expm(H)
#SVD decompose to make it into .
return res
def test_lanczos(self):
'''test for directly construct and solve the ground state energy.'''
model = self.get_model(10, 1)
hgen1 = ExpandGenerator(spaceconfig=SpinSpaceConfig([1, 2]),
H=model.H_serial,
evolutor_type='null')
hgen2 = ExpandGenerator(spaceconfig=SpinSpaceConfig([1, 2]),
H=model.H_serial,
evolutor_type='normal')
dmrgegn = DMRGEngine(hgen=hgen1, tol=0, iprint=10)
H = get_H(hgen=hgen1)
H2, bm2 = get_H_bm(hgen=hgen2, bstr='M')
Emin = eigsh(H, k=1)[0]
Emin2 = eigsh(bm2.extract_block(H2, (zeros(1), zeros(1)),
uselabel=True),
k=1)[0]
print 'The Ground State Energy is %s, tolerence %s.' % (Emin,
Emin - Emin2)
assert_almost_equal(Emin, Emin2)
def test_dmrg_finite(self):
'''
Run iDMFT for heisenberg model.
'''
nsite = 10
model = self.get_model(nsite, 1)
hgen1 = ExpandGenerator(spaceconfig=SpinSpaceConfig([1, 2]),
H=model.H_serial,
evolutor_type='null')
hgen2 = ExpandGenerator(spaceconfig=SpinSpaceConfig([1, 2]),
H=model.H_serial,
evolutor_type='masked')
H = get_H(hgen1)
EG1 = eigsh(H, k=1, which='SA')[0]
dmrgegn = DMRGEngine(hgen=hgen2, tol=0, reflect=True)
dmrgegn.use_U1_symmetry('M', target_block=zeros(1))
EG2 = dmrgegn.run_finite(endpoint=(5, '<-', 0),
maxN=[10, 20, 40, 40, 40],
tol=0)[0]
assert_almost_equal(EG1, EG2, decimal=4)