def impsgrowth(self, sites, bonds, osvs, qn=0, ttype=None):
'''
Infinite MPS growth.
Parameters
----------
sites,bonds : list of Label/str
The site/bond labels/identifiers of the new mps.
osvs : 1d ndarray
The old singular values.
qn : QuantumNumber, optional
The injected quantum number of the new mps.
ttype : NOne/'D'/'S', optional
Tensor type. 'D' for dense, 'S' for sparse and None for automatic.
Returns
-------
MPS
The imps after growth.
'''
if self.nsite > 0:
assert self.cut == self.nsite // 2 and self.nsite % 2 == 0 and len(
sites) + 1 == len(bonds)
ob, nb = self.nsite // 2 + 1, (len(bonds) + 1) // 2
ns = nb - ob
cms = self[ob - ns - 1:ob + ns - 1].impsprediction(
sites[ob - 1:2 * nb - ob - 1],
bonds[ob - 1:2 * nb - ob],
osvs,
qn=qn,
ttype=ttype)
lms = MPS([copy(self[pos]) for pos in range(0, self.cut)])
rms = MPS([copy(self[pos]) for pos in range(self.cut, self.nsite)])
lms.relabel(sites[:ob - 1], bonds[:ob])
rms.relabel(sites[-ob + 1:], bonds[-ob:])
rms.qninject(qn)
result = MPS(it.chain(lms, cms, rms),
Lambda=cms.Lambda,
cut=nb - 1,
ttype=ttype)
else:
bonds = copy(bonds)
iqns, oqns = (QNS.mono(qn.zero()),
QNS.mono(qn)) if isinstance(qn, QN) else (1, 1)
bonds[+0] = bonds[+0].replace(qns=iqns) if isinstance(
bonds[+0], Label) else Label(bonds[+0], qns=iqns, flow=None)
bonds[-1] = bonds[-1].replace(qns=oqns) if isinstance(
bonds[-1], Label) else Label(bonds[-1], qns=oqns, flow=None)
result = MPS.random(sites,
bonds=bonds,
cut=len(sites) // 2,
nmax=10,
ttype=ttype or 'D')
return result
def impsgrowth(self,sites,bonds,osvs,qn=0,ttype=None):
'''
Infinite MPS growth.
Parameters
----------
sites,bonds : list of Label/str
The site/bond labels/identifiers of the new mps.
osvs : 1d ndarray
The old singular values.
qn : QuantumNumber, optional
The injected quantum number of the new mps.
ttype : NOne/'D'/'S', optional
Tensor type. 'D' for dense, 'S' for sparse and None for automatic.
Returns
-------
MPS
The imps after growth.
'''
if self.nsite>0:
assert self.cut==self.nsite//2 and self.nsite%2==0 and len(sites)+1==len(bonds)
ob,nb=self.nsite//2+1,(len(bonds)+1)//2
ns=nb-ob
cms=self[ob-ns-1:ob+ns-1].impsprediction(sites[ob-1:2*nb-ob-1],bonds[ob-1:2*nb-ob],osvs,qn=qn,ttype=ttype)
lms=MPS([copy(self[pos]) for pos in range(0,self.cut)])
rms=MPS([copy(self[pos]) for pos in range(self.cut,self.nsite)])
lms.relabel(sites[:ob-1],bonds[:ob])
rms.relabel(sites[-ob+1:],bonds[-ob:])
rms.qninject(qn)
result=MPS(it.chain(lms,cms,rms),Lambda=cms.Lambda,cut=nb-1,ttype=ttype)
else:
bonds=copy(bonds)
iqns,oqns=(QNS.mono(qn.zero()),QNS.mono(qn)) if isinstance(qn,QN) else (1,1)
bonds[+0]=bonds[+0].replace(qns=iqns) if isinstance(bonds[+0],Label) else Label(bonds[+0],qns=iqns,flow=None)
bonds[-1]=bonds[-1].replace(qns=oqns) if isinstance(bonds[-1],Label) else Label(bonds[-1],qns=oqns,flow=None)
result=MPS.random(sites,bonds=bonds,cut=len(sites)//2,nmax=10,ttype=ttype or 'D')
return result
def tompo(self, ttype='D', **karg):
'''
Convert to the tensor-formatted mpo.
Parameters
----------
ttype : 'D'/'S', optional
Tensor type. 'D' for dense and 'S' for sparse.
karg : dict with keys containing 'nsweep','method' and 'options'
Please see MPO.compress for details.
Returns
-------
MPO
The corresponding tensor-formatted MPO.
'''
Ms = []
type = self[0][0, 0].site.qns.type if isinstance(
self[0][0, 0].site.qns, QuantumNumbers) else None
for pos, m in enumerate(self):
dim = self.sites[pos].dim
L = Label(self.bonds[pos], qns=m.shape[0], flow=0)
U = self.sites[pos].replace(prime=True, qns=dim, flow=0)
D = self.sites[pos].replace(qns=dim, flow=0)
R = Label(self.bonds[pos + 1], qns=m.shape[1], flow=0)
Ms.append(
DTensor(np.zeros((m.shape[0], dim, dim, m.shape[1]),
dtype=self.dtype),
labels=[L, U, D, R]))
for i, j in it.product(range(m.shape[0]), range(m.shape[1])):
Ms[-1].data[i, :, :, j] = m[i, j].matrix
result = MPO(Ms)
result.compress(**karg)
if type is not None:
for pos in range(len(result)):
lqns, sqns = QuantumNumbers.mono(
type.zero()) if pos == 0 else result[pos - 1].labels[
MPO.R].qns, self.sites[pos].qns
result[pos].qngenerate(flow=-1,
axes=[MPO.L, MPO.U, MPO.D],
qnses=[lqns, sqns, sqns],
flows=[1, 1, -1])
if ttype == 'S':
assert issubclass(type, QuantumNumber)
for i, m in enumerate(result):
m.qnsort()
result[i] = m.tostensor()
return result
def tompo(self,degfres,ttype='D'):
'''
Convert an optstr to the full-formatted mpo.
Parameters
----------
degfres : DegFreTree
The tree of the site degrees of freedom.
ttype : 'D'/'S', optional
Tensor type. 'D' for dense and 'S' for sparse.
Returns
-------
MPO
The corresponding MPO.
'''
index=self[0].site.identifier
type,layer=degfres.dtype,degfres.layers[degfres.level(index)-1]
table,sites,bonds=degfres.table(layer),degfres.labels('S',layer),degfres.labels('O',layer)
poses,matrices=set(table[opt.site.identifier] for opt in self),[opt.matrix for opt in self]
ms,count=[],0
for pos in range(len(sites)):
ndegfre=sites[pos].dim
if issubclass(type,QuantumNumbers):
L=Label(bonds[pos],qns=QuantumNumbers.mono(type.zero()) if pos==0 else ms[-1].labels[MPO.R].qns,flow=None)
U=sites[pos].P
D=copy(sites[pos])
R=Label(bonds[pos+1],qns=1,flow=None)
else:
L=Label(bonds[pos],qns=1,flow=0)
U=sites[pos].P.replace(flow=0)
D=sites[pos].replace(flow=0)
R=Label(bonds[pos+1],qns=1,flow=0)
if pos in poses:
ms.append(DTensor(np.asarray(matrices[count],dtype=self.dtype).reshape((1,ndegfre,ndegfre,1)),labels=[L,U,D,R]))
count+=1
else:
ms.append(DTensor(np.identity(ndegfre,dtype=self.dtype).reshape((1,ndegfre,ndegfre,1)),labels=[L,U,D,R]))
if issubclass(type,QuantumNumbers): ms[-1].qngenerate(flow=-1,axes=[MPO.L,MPO.U,MPO.D],qnses=[L.qns,U.qns,D.qns],flows=[1,1,-1])
if ttype=='S':
assert issubclass(type,QuantumNumbers)
for m in ms: m.qnsort()
ms=[m.tostensor() for m in ms]
return MPO(ms)
def tompo(self,ttype='D',**karg):
'''
Convert to the tensor-formatted mpo.
Parameters
----------
ttype : 'D'/'S', optional
Tensor type. 'D' for dense and 'S' for sparse.
karg : dict with keys containing 'nsweep','method' and 'options'
Please see MPO.compress for details.
Returns
-------
MPO
The corresponding tensor-formatted MPO.
'''
Ms=[]
type=self[0][0,0].site.qns.type if isinstance(self[0][0,0].site.qns,QuantumNumbers) else None
for pos,m in enumerate(self):
dim=self.sites[pos].dim
L=Label(self.bonds[pos],qns=m.shape[0],flow=0)
U=self.sites[pos].replace(prime=True,qns=dim,flow=0)
D=self.sites[pos].replace(qns=dim,flow=0)
R=Label(self.bonds[pos+1],qns=m.shape[1],flow=0)
Ms.append(DTensor(np.zeros((m.shape[0],dim,dim,m.shape[1]),dtype=self.dtype),labels=[L,U,D,R]))
for i,j in it.product(range(m.shape[0]),range(m.shape[1])):
Ms[-1].data[i,:,:,j]=m[i,j].matrix
result=MPO(Ms)
result.compress(**karg)
if type is not None:
for pos in range(len(result)):
lqns,sqns=QuantumNumbers.mono(type.zero()) if pos==0 else result[pos-1].labels[MPO.R].qns,self.sites[pos].qns
result[pos].qngenerate(flow=-1,axes=[MPO.L,MPO.U,MPO.D],qnses=[lqns,sqns,sqns],flows=[1,1,-1])
if ttype=='S':
assert issubclass(type,QuantumNumber)
for i,m in enumerate(result):
m.qnsort()
result[i]=m.tostensor()
return result
def to_mpo(self,**karg):
'''
Convert to the tensor-formatted mpo.
Parameters
----------
karg : dict with keys containing 'nsweep','method' and 'options'
Please see MPO.compress for details.
Returns
-------
MPO
The corresponding tensor-formatted MPO.
'''
Ms=[]
type=self[0][0,0].site.qns.type if isinstance(self[0][0,0].site.qns,QuantumNumbers) else None
for pos,m in enumerate(self):
dim=self.sites[pos].dim
if type is None:
L=self.bonds[pos].replace(qns=m.shape[0],flow=0)
U=self.sites[pos].replace(prime=True,flow=0)
D=self.sites[pos].replace(flow=0)
R=self.bonds[pos+1].replace(qns=m.shape[1],flow=0)
else:
L=copy(self.bonds[pos])
U=self.sites[pos].P
D=self.sites[pos]
R=copy(self.bonds[pos+1])
Ms.append(DTensor(np.zeros((m.shape[0],dim,dim,m.shape[1]),dtype=dtype),labels=[L,U,D,R]))
for i,j in it.product(xrange(m.shape[0]),xrange(m.shape[1])):
Ms[-1][i,:,:,j]=m[i,j].matrix
result=MPO(Ms)
result.compress(**karg)
if type is not None:
for pos in xrange(len(result)):
lqns,sqns=QuantumNumbers.mono(type.zero()) if pos==0 else result[pos-1].labels[MPO.R].qns,self.sites[pos].qns
result[pos].qngenerate(flow=-1,axes=[MPO.L,MPO.U,MPO.D],qnses=[lqns,sqns,sqns],flows=[1,1,-1])
return result
def to_mpo(self,degfres):
'''
Convert an optstr to the full-formatted mpo.
Parameters
----------
degfres : DegFreTree
The tree of the site degrees of freedom.
Returns
-------
MPO
The corresponding MPO.
'''
index=self[0].site.identifier
type,layer=degfres[index].type if degfres.mode=='QN' else None,degfres.layers[degfres.level(index)-1]
table,sites,bonds=degfres.table(layer),degfres.labels('S',layer),degfres.labels('O',layer)
poses,matrices=set(table[opt.site.identifier] for opt in self),[opt.matrix for opt in self]
ms,count=[],0
for pos in xrange(len(sites)):
ndegfre=sites[pos].dim
if degfres.mode=='QN':
L=bonds[pos].replace(qns=QuantumNumbers.mono(type.zero()) if pos==0 else ms[-1].labels[MPO.R].qns)
U=sites[pos].P
D=copy(sites[pos])
R=bonds[pos+1].replace(qns=1)
else:
L=bonds[pos].replace(qns=1,flow=0)
U=sites[pos].P.replace(flow=0)
D=sites[pos].replace(flow=0)
R=bonds[pos+1].replace(qns=1,flow=0)
if pos in poses:
ms.append(DTensor(np.asarray(matrices[count],dtype=self.dtype).reshape((1,ndegfre,ndegfre,1)),labels=[L,U,D,R]))
count+=1
else:
ms.append(DTensor(np.identity(ndegfre,dtype=self.dtype).reshape((1,ndegfre,ndegfre,1)),labels=[L,U,D,R]))
if degfres.mode=='QN': ms[-1].qngenerate(flow=-1,axes=[MPO.L,MPO.U,MPO.D],qnses=[L.qns,U.qns,D.qns],flows=[1,1,-1])
return MPO(ms)
def random(sites, bonds=None, cut=None, nmax=None, dtype=np.float64):
'''
Generate a random mps.
Parameters
----------
sites : list of Label/int/QuantumNumbers
The labels/number-of-degrees-of-freedom/quantum-numbers of the physical legs.
bonds : optional
* list of Label
The labels of the virtual legs.
* 2-list of QuantumNumber
The quantum number of the first and last virtual legs.
cut : int, optional
The index of the connecting link.
nmax : int, optional
The maximum number of singular values to be kept.
dtype : np.float64, np.complex128, optional
The data type of the random mps.
Returns
-------
MPS
The random mixed-canonical mps.
'''
np.random.seed()
sites = [
site if isinstance(site, Label) else Label(
'__MPS_RANDOM_S_%s__' % i, qns=site)
for i, site in enumerate(sites)
]
if bonds is not None and all(
isinstance(bond, Label) for bond in bonds):
assert len(bonds) == len(sites) + 1
else:
if bonds is not None:
assert len(bonds) == 2 and isinstance(
bonds[0], QN) and isinstance(bonds[1], QN)
iqns, oqns = (QNS.mono(bonds[0]),
QNS.mono(bonds[1])) if bonds is not None else (1, 1)
bonds = [
Label(
'__MPS_RANDOM_B_%s__' % i,
qns=iqns if i == 0 else oqns if i == len(sites) else None)
for i in xrange(len(sites) + 1)
]
mode, shape = 'QN' if next(iter(sites)).qnon else 'NB', tuple(
[site.dim for site in sites])
if mode == 'QN':
result = 0
if dtype in (np.float32, np.float64):
coeffs = np.random.random(nmax)
else:
coeffs = np.random.random(nmax) + 1j * np.random.random(nmax)
for k, indices in enumerate(
QNS.decomposition([site.qns for site in sites],
bonds[-1].qns[0] - bonds[0].qns[0],
method='monte carlo',
nmax=nmax)):
ms = [
np.array(
[1.0 if i == index else 0.0 for i in xrange(site.dim)],
dtype=dtype) for site, index in zip(sites, indices)
]
result += MPS.productstate(ms, sites, copy(bonds)) * coeffs[k]
else:
ms = []
for i in xrange(len(sites)):
if dtype in (np.float32, np.float64):
ms.append(np.random.random((nmax, shape[i], nmax)))
else:
ms.append(
np.random.random((nmax, shape[i], nmax)) +
1j * np.random.random((nmax, shape[i], nmax)))
result = MPS(mode=mode, ms=ms, sites=sites, bonds=bonds)
if cut is None:
result.canonicalize(cut=len(sites) / 2, nmax=nmax)
result._merge_ABL_()
else:
result.canonicalize(cut=cut, nmax=nmax)
return result
def random(sites,
bonds=None,
cut=None,
nmax=None,
ttype='D',
dtype=np.float64):
'''
Generate a random mps.
Parameters
----------
sites : list of Label/int/QuantumNumbers
The labels/number-of-degrees-of-freedom/quantum-numbers of the physical legs.
bonds : optional
* list of Label/str
The labels/identifiers of the virtual legs.
* 2-list of QuantumNumber
The quantum number of the first and last virtual legs.
cut : int, optional
The index of the connecting link.
nmax : int, optional
The maximum number of singular values to be kept.
ttype : 'D'/'S', optional
Tensor type. 'D' for dense and 'S' for sparse.
dtype : np.float64, np.complex128, optional
The data type of the random mps.
Returns
-------
MPS
The random mixed-canonical mps.
'''
np.random.seed()
sites = [
site if isinstance(site, Label) else Label(
'__MPS_RANDOM_S_%s__' % i, qns=site)
for i, site in enumerate(sites)
]
if bonds is None or not isinstance(bonds[+0], Label) or not isinstance(
bonds[-1], Label):
if bonds is not None:
iqns = bonds[+0].qns if isinstance(
bonds[+0], Label) else bonds[+0] if isinstance(
bonds[+0], QNS) else QNS.mono(bonds[+0]) if isinstance(
bonds[+0], QN) else 1
oqns = bonds[-1].qns if isinstance(
bonds[-1], Label) else bonds[-1] if isinstance(
bonds[-1], QNS) else QNS.mono(bonds[-1]) if isinstance(
bonds[-1], QN) else 1
else:
iqns, oqns = 1, 1
bonds = [
Label('__MPS_RANDOM_B_%s__' % i, None, None)
for i in range(len(sites) + 1)
]
bonds[+0] = bonds[+0].replace(qns=iqns)
bonds[-1] = bonds[-1].replace(qns=oqns)
else:
assert len(bonds) == len(sites) + 1
bonds = [
bond if isinstance(bond, Label) else Label(bond, None, None)
for bond in bonds
]
qnon, shape = next(iter(sites)).qnon, tuple(
[site.dim for site in sites])
if ttype == 'S': assert qnon
if qnon:
result = 0
if dtype in (np.float32, np.float64):
coeffs = np.random.random(nmax)
else:
coeffs = np.random.random(nmax) + 1j * np.random.random(nmax)
for k, indices in enumerate(
QNS.decomposition([site.qns for site in sites],
bonds[-1].qns[0] - bonds[+0].qns[0],
method='monte carlo',
nmax=nmax)):
ms = [
np.array(
[1.0 if i == index else 0.0 for i in range(site.dim)],
dtype=dtype) for site, index in zip(sites, indices)
]
result += MPS.productstate(ms, sites, copy(bonds)) * coeffs[k]
if ttype == 'S':
for m in result:
m.qnsort()
result = result.tosparse()
else:
ms = []
for i in range(len(sites)):
if dtype in (np.float32, np.float64):
ms.append(np.random.random((nmax, shape[i], nmax)))
else:
ms.append(
np.random.random((nmax, shape[i], nmax)) +
1j * np.random.random((nmax, shape[i], nmax)))
result = MPS.compose(ms=ms, sites=sites, bonds=bonds)
if cut is None:
result.canonicalize(cut=len(sites) / 2, nmax=nmax)
result._merge_ABL_()
else:
result.canonicalize(cut=cut, nmax=nmax)
return result
def random(sites,bonds=None,cut=None,nmax=None,ttype='D',dtype=np.float64):
'''
Generate a random mps.
Parameters
----------
sites : list of Label/int/QuantumNumbers
The labels/number-of-degrees-of-freedom/quantum-numbers of the physical legs.
bonds : optional
* list of Label/str
The labels/identifiers of the virtual legs.
* 2-list of QuantumNumber
The quantum number of the first and last virtual legs.
cut : int, optional
The index of the connecting link.
nmax : int, optional
The maximum number of singular values to be kept.
ttype : 'D'/'S', optional
Tensor type. 'D' for dense and 'S' for sparse.
dtype : np.float64, np.complex128, optional
The data type of the random mps.
Returns
-------
MPS
The random mixed-canonical mps.
'''
np.random.seed()
sites=[site if isinstance(site,Label) else Label('__MPS_RANDOM_S_%s__'%i,qns=site) for i,site in enumerate(sites)]
if bonds is None or not isinstance(bonds[+0],Label) or not isinstance(bonds[-1],Label):
if bonds is not None:
iqns=bonds[+0].qns if isinstance(bonds[+0],Label) else bonds[+0] if isinstance(bonds[+0],QNS) else QNS.mono(bonds[+0]) if isinstance(bonds[+0],QN) else 1
oqns=bonds[-1].qns if isinstance(bonds[-1],Label) else bonds[-1] if isinstance(bonds[-1],QNS) else QNS.mono(bonds[-1]) if isinstance(bonds[-1],QN) else 1
else:
iqns,oqns=1,1
bonds=[Label('__MPS_RANDOM_B_%s__'%i,None,None) for i in range(len(sites)+1)]
bonds[+0]=bonds[+0].replace(qns=iqns)
bonds[-1]=bonds[-1].replace(qns=oqns)
else:
assert len(bonds)==len(sites)+1
bonds=[bond if isinstance(bond,Label) else Label(bond,None,None) for bond in bonds]
qnon,shape=next(iter(sites)).qnon,tuple([site.dim for site in sites])
if ttype=='S': assert qnon
if qnon:
result=0
if dtype in (np.float32,np.float64):
coeffs=np.random.random(nmax)
else:
coeffs=np.random.random(nmax)+1j*np.random.random(nmax)
for k,indices in enumerate(QNS.decomposition([site.qns for site in sites],bonds[-1].qns[0]-bonds[+0].qns[0],method='monte carlo',nmax=nmax)):
ms=[np.array([1.0 if i==index else 0.0 for i in range(site.dim)],dtype=dtype) for site,index in zip(sites,indices)]
result+=MPS.productstate(ms,sites,copy(bonds))*coeffs[k]
if ttype=='S':
for m in result: m.qnsort()
result=result.tosparse()
else:
ms=[]
for i in range(len(sites)):
if dtype in (np.float32,np.float64):
ms.append(np.random.random((nmax,shape[i],nmax)))
else:
ms.append(np.random.random((nmax,shape[i],nmax))+1j*np.random.random((nmax,shape[i],nmax)))
result=MPS.compose(ms=ms,sites=sites,bonds=bonds)
if cut is None:
result.canonicalize(cut=len(sites)/2,nmax=nmax)
result._merge_ABL_()
else:
result.canonicalize(cut=cut,nmax=nmax)
return result
def tompo(self, degfres, ttype='D'):
'''
Convert an optstr to the full-formatted mpo.
Parameters
----------
degfres : DegFreTree
The tree of the site degrees of freedom.
ttype : 'D'/'S', optional
Tensor type. 'D' for dense and 'S' for sparse.
Returns
-------
MPO
The corresponding MPO.
'''
index = self[0].site.identifier
type, layer = degfres.dtype, degfres.layers[degfres.level(index) - 1]
table, sites, bonds = degfres.table(layer), degfres.labels(
'S', layer), degfres.labels('O', layer)
poses, matrices = set(table[opt.site.identifier]
for opt in self), [opt.matrix for opt in self]
ms, count = [], 0
for pos in range(len(sites)):
ndegfre = sites[pos].dim
if issubclass(type, QuantumNumbers):
L = Label(bonds[pos],
qns=QuantumNumbers.mono(type.zero())
if pos == 0 else ms[-1].labels[MPO.R].qns,
flow=None)
U = sites[pos].P
D = copy(sites[pos])
R = Label(bonds[pos + 1], qns=1, flow=None)
else:
L = Label(bonds[pos], qns=1, flow=0)
U = sites[pos].P.replace(flow=0)
D = sites[pos].replace(flow=0)
R = Label(bonds[pos + 1], qns=1, flow=0)
if pos in poses:
ms.append(
DTensor(np.asarray(matrices[count],
dtype=self.dtype).reshape(
(1, ndegfre, ndegfre, 1)),
labels=[L, U, D, R]))
count += 1
else:
ms.append(
DTensor(np.identity(ndegfre, dtype=self.dtype).reshape(
(1, ndegfre, ndegfre, 1)),
labels=[L, U, D, R]))
if issubclass(type, QuantumNumbers):
ms[-1].qngenerate(flow=-1,
axes=[MPO.L, MPO.U, MPO.D],
qnses=[L.qns, U.qns, D.qns],
flows=[1, 1, -1])
if ttype == 'S':
assert issubclass(type, QuantumNumbers)
for m in ms:
m.qnsort()
ms = [m.tostensor() for m in ms]
return MPO(ms)