def _mul_mps_(self,other):
'''
The multiplication of an mpo and an mps.
Parameters
----------
other : MPS
The mps.
Returns
-------
MPS
The product.
'''
assert self.nsite==other.nsite
u,Lambda=other._merge_ABL_()
ms=[]
for i,(m1,m2) in enumerate(zip(self,other)):
L1,U1,D1,R1=m1.labels
L2,S,R2=m2.labels
assert S==D1
L=L2.replace(qns=QuantumNumbers.kron([L1.qns,L2.qns]) if L1.qnon else L1.qns*L2.qns)
R=R2.replace(qns=QuantumNumbers.kron([R1.qns,R2.qns]) if R1.qnon else R1.qns*R2.qns)
m=(m1*m2).transpose((L1,L2,U1,R1,R2)).merge(([L1,L2],L),([R1,R2],R))
m.relabel(olds=[U1],news=[S])
ms.append(m)
other._set_ABL_(u,Lambda)
return MPS(mode=other.mode,ms=ms)
def _mul_mpo_(self,other):
'''
The multiplication of two mpos.
Parameters
----------
other : MPO
The other mpo.
Returns
-------
MPO
The product.
'''
assert self.nsite==other.nsite
ms=[]
for i,(m1,m2) in enumerate(zip(self,other)):
assert m1.labels==m2.labels
m1,m2=copy(m1),copy(m2)
L1,U1,D1,R1=m1.labels
L2,U2,D2,R2=m2.labels
L=L1.replace(qns=QuantumNumbers.kron([L1.qns,L2.qns]) if L1.qnon else L1.qns*L2.qns)
R=R1.replace(qns=QuantumNumbers.kron([R1.qns,R2.qns]) if R1.qnon else R1.qns*R2.qns)
s=Label('__MPO_MUL__',qns=U1.qns)
l1,r1=Label('__MPO_MUL_L1__',qns=L1.qns,flow=L1.flow),Label('__MPO_MUL_R1__',qns=R1.qns,flow=R1.flow)
l2,r2=Label('__MPO_MUL_L2__',qns=L2.qns,flow=L2.flow),Label('__MPO_MUL_R2__',qns=R2.qns,flow=R2.flow)
m1.relabel(olds=[L1,D1,R1],news=[l1,s.replace(flow=D1.flow),r1])
m2.relabel(olds=[L2,U2,R2],news=[l2,s.replace(flow=U2.flow),r2])
ms.append((m1*m2).transpose((l1,l2,U1,D2,r1,r2)).merge(([l1,l2],L),([r1,r2],R)))
return MPO(ms)
def reset(self,
mode=None,
layers=None,
priority=None,
leaves=(),
map=None):
'''
Reset the DegFreTree.
Parameters
----------
mode,layers,priority,leaves,map :
Please see DegFreTree.__init__ for details.
'''
self.clear()
Tree.__init__(self)
assert mode in (None, 'QN', 'NB')
if mode is not None: self.mode = mode
if layers is not None: self.layers = layers
if priority is not None: self.priority = priority
if map is not None: self.map = map
self.cache = {}
if len(leaves) > 0:
temp = [key for layer in self.layers for key in layer]
assert set(range(len(PID._fields))) == set(
[temp.index(key) for key in PID._fields])
temp = set(temp)
self.add_leaf(parent=None,
leaf=tuple([None] * len(leaves[0])),
data=None)
for layer in self.layers:
temp -= set(layer)
indices = set([
index.replace(**{key: None
for key in temp}) for index in leaves
])
self.cache[('indices', layer)] = sorted(
indices,
key=lambda index: index.to_tuple(priority=self.priority))
self.cache[('table', layer)] = Table(self.indices(layer=layer))
for index in self.indices(layer=layer):
self.add_leaf(
parent=index.replace(**{key: None
for key in layer}),
leaf=index,
data=None)
for i, layer in enumerate(reversed(self.layers)):
if i == 0:
for index in self.indices(layer):
self[index] = self.map(index)
else:
for index in self.indices(layer):
if self.mode == 'QN':
self[index] = QuantumNumbers.kron([
self[child] for child in self.children(index)
])
else:
self[index] = np.product([
self[child] for child in self.children(index)
])
def union(labels, identifier, flow=0, prime=False, mode=0):
'''
The union of a set of labels as a new label.
Parameters
----------
labels : list of Label
The set of labels.
identifier : any hashale object
The identifier of the union.
flow : -1/0/+1/None
The flow of the union.
prime : logical, optional
When True, the union is in the prime form; otherwise not.
mode : -2/-1/0/+1/+2, optional
* 0: When qnon, use QuantumNumbers.kron to get the qns of the union, no sorting and no returning the permutation array
* -1: When qnon, use QuantumNumbers.kron to get the qns of the union with sorting but without returning the permutation array
* +1: When qnon, use QuantumNumbers.kron to get the qns of the union with sorting and with returning the permutation array
* -2: When qnon, use QuantumNumbers.ukron to get the qns of the union without returning the record dict
* +2: When qnon, use QuantumNumbers.ukron to get the qns of the union with returning the record dict
Returns
-------
result : Label
The union of the input set of labels.
permutation/record : 1d-ndarray-of-int/dict, optional
The permutation/record of the quantum numbers of the union.
'''
qnon = labels[0].qnon
assert all(label.qnon == qnon
for label in labels[1:]) and mode in {-2, -1, 0, 1, 2}
if qnon:
assert flow in {-1, 1}
qnses, signs = [label.qns for label in labels], [
1 if label.flow == flow else -1 for label in labels
]
if mode in {-1, 0, +1}:
qns = QuantumNumbers.kron(qnses, signs=signs)
if mode == -1: qns = qns.sorted(history=False)
if mode == +1: qns, permutation = qns.sorted(history=True)
result = Label(identifier, qns, flow=flow, prime=prime)
return (result, permutation) if mode == 1 else result
else:
if mode == -2:
qns = QuantumNumbers.ukron(qnses,
signs=signs,
history=False)
if mode == +2:
qns, record = QuantumNumbers.ukron(qnses,
signs=signs,
history=True)
result = Label(identifier, qns, flow=flow, prime=prime)
return (result, record) if mode == 2 else result
else:
result = Label(identifier,
np.product([label.qns for label in labels]),
flow=None if flow is None else 0,
prime=prime)
return (result, None) if mode in (1, 2) else result
def union(labels,identifier,flow=0,prime=False,mode=0):
'''
The union of a set of labels as a new label.
Parameters
----------
labels : list of Label
The set of labels.
identifier : any hashale object
The identifier of the union.
flow : -1/0/+1/None
The flow of the union.
prime : logical, optional
When True, the union is in the prime form; otherwise not.
mode : -2/-1/0/+1/+2, optional
* 0: When qnon, use QuantumNumbers.kron to get the qns of the union, no sorting and no returning the permutation array
* -1: When qnon, use QuantumNumbers.kron to get the qns of the union with sorting but without returning the permutation array
* +1: When qnon, use QuantumNumbers.kron to get the qns of the union with sorting and with returning the permutation array
* -2: When qnon, use QuantumNumbers.ukron to get the qns of the union without returning the record dict
* +2: When qnon, use QuantumNumbers.ukron to get the qns of the union with returning the record dict
Returns
-------
result : Label
The union of the input set of labels.
permutation/record : 1d-ndarray-of-int/dict, optional
The permutation/record of the quantum numbers of the union.
'''
qnon=labels[0].qnon
assert all(label.qnon==qnon for label in labels[1:]) and mode in {-2,-1,0,1,2}
if qnon:
assert flow in {-1,1}
qnses,signs=[label.qns for label in labels],[1 if label.flow==flow else -1 for label in labels]
if mode in {-1,0,+1}:
qns=QuantumNumbers.kron(qnses,signs=signs)
if mode==-1: qns=qns.sorted(history=False)
if mode==+1: qns,permutation=qns.sorted(history=True)
result=Label(identifier,qns,flow=flow,prime=prime)
return (result,permutation) if mode==1 else result
else:
if mode==-2: qns=QuantumNumbers.ukron(qnses,signs=signs,history=False)
if mode==+2: qns,record=QuantumNumbers.ukron(qnses,signs=signs,history=True)
result=Label(identifier,qns,flow=flow,prime=prime)
return (result,record) if mode==2 else result
else:
result=Label(identifier,np.product([label.qns for label in labels]),flow=None if flow is None else 0,prime=prime)
return (result,None) if mode in (1,2) else result
def relayer(self,degfres,layer,nmax=None,tol=None):
'''
Construct a new mpo with the site labels living on a specific layer of degfres.
Parameters
----------
degfres : DegFreTree
The tree of the site degrees of freedom.
layer : int/tuple-of-str
The layer where the site labels live.
nmax : int, optional
The maximum number of singular values to be kept.
tol : np.float64, optional
The tolerance of the singular values.
Returns
-------
MPO
The new mpo.
'''
assert all(isinstance(m,DTensor) for m in self)
new=layer if type(layer) is int else degfres.layers.index(layer)
old=degfres.level(next(iter(self)).labels[MPO.U].identifier)-1
assert 0<=new<len(degfres.layers)
if new==old:
return copy(self)
else:
olayer,nlayer=degfres.layers[old],degfres.layers[new]
sites,bonds=[site.replace(flow=-1 if site.qnon else 0) for site in degfres.labels('S',nlayer)],degfres.labels('O',nlayer)
Ms=[]
if new<old:
table=degfres.table(olayer)
for i,site in enumerate(sites):
ms,ups,dws=[],[],[]
for index in degfres.descendants(site.identifier,generation=old-new):
m=self[table[index]]
ms.append(m)
ups.append(m.labels[MPO.U])
dws.append(m.labels[MPO.D])
M=np.product(ms)
o1,o2=M.labels[0],M.labels[-1]
n1,n2=o1.replace(identifier=bonds[i]),o2.replace(identifier=bonds[i+1])
M.relabel(olds=[o1,o2],news=[n1,n2])
Ms.append(M.transpose([n1]+ups+dws+[n2]).merge((ups,site.P),(dws,site)))
else:
table,s,v=degfres.table(nlayer),1.0,1.0
for i,m in enumerate(self):
m=s*v*m
L,U,D,R=m.labels
indices=degfres.descendants(D.identifier,generation=new-old)
start,stop=table[indices[0]],table[indices[-1]]+1
ups,dws,orders,labels,qnses=[],[],[],[],[]
for j,site in enumerate(sites[start:stop]):
ups.append(site.P)
dws.append(site)
orders.append(ups[-1])
orders.append(dws[-1])
qns=QuantumNumbers.kron([site.qns]*2,signs=(+1,-1)) if site.qnon else site.dim**2
labels.append(Label('__MPO_RELAYER_%s__'%j,qns=qns,flow=+1 if site.qnon else 0))
qnses.append(qns)
S=Label('__MPO_RELAYER__',qns=(QuantumNumbers.kron if U.qnon else np.product)(qnses),flow=+1 if U.qnon else 0)
m=m.split((U,ups),(D,dws)).transpose([L]+orders+[R]).merge((orders,S))
us,s,v=expandedsvd(m,L=[L],S=S,R=[R],E=labels,I=[Label(bond,None,None) for bond in bonds[start+1:stop+1]],cut=stop-start,nmax=nmax,tol=tol)
for u,up,dw,label in zip(us,ups,dws,labels):
Ms.append(u.split((label,[up,dw])))
Ms[-1]=Ms[-1]*s*v
Ms[+0].relabel(olds=[MPO.L],news=[Ms[+0].labels[MPO.L].replace(identifier=bonds[+0])])
Ms[-1].relabel(olds=[MPO.R],news=[Ms[-1].labels[MPO.R].replace(identifier=bonds[-1])])
return MPO(Ms)
def relayer(self,degfres,layer,nmax=None,tol=None):
'''
Construct a new mpo with the site labels living on a specific layer of degfres.
Parameters
----------
degfres : DegFreTree
The tree of the site degrees of freedom.
layer : int/tuple-of-str
The layer where the site labels live.
nmax : int, optional
The maximum number of singular values to be kept.
tol : np.float64, optional
The tolerance of the singular values.
Returns
-------
MPO
The new mpo.
'''
new=layer if type(layer) in (int,long) else degfres.layers.index(layer)
old=degfres.level(next(iter(self)).labels[MPO.U].identifier)-1
assert 0<=new<len(degfres.layers)
if new==old:
return copy(self)
else:
olayer,nlayer=degfres.layers[old],degfres.layers[new]
sites,bonds=[site.replace(flow=-1 if site.qnon else 0) for site in degfres.labels('S',nlayer)],degfres.labels('O',nlayer)
Ms=[]
if new<old:
table=degfres.table(olayer)
for i,site in enumerate(sites):
ms,ups,dws=[],[],[]
for index in degfres.descendants(site.identifier,generation=old-new):
m=self[table[index]]
ms.append(m)
ups.append(m.labels[MPO.U])
dws.append(m.labels[MPO.D])
M=np.product(ms)
o1,o2=M.labels[0],M.labels[-1]
n1,n2=bonds[i].replace(qns=o1.qns,flow=o1.flow),bonds[i+1].replace(qns=o2.qns,flow=o2.flow)
M.relabel(olds=[o1,o2],news=[n1,n2])
Ms.append(M.transpose([n1]+ups+dws+[n2]).merge((ups,site.P),(dws,site)))
else:
table=degfres.table(nlayer)
for i,m in enumerate(self):
if i>0: m=s*v*m
L,U,D,R=m.labels
indices=degfres.descendants(D.identifier,generation=new-old)
start,stop=table[indices[0]],table[indices[-1]]+1
ups,dws,orders,labels,qnses=[],[],[],[],[]
for j,site in enumerate(sites[start:stop]):
ups.append(site.P)
dws.append(site)
orders.append(ups[-1])
orders.append(dws[-1])
qns=QuantumNumbers.kron([site.qns]*2,signs=(+1,-1)) if site.qnon else site.dim**2
labels.append(Label('__MPO_RELAYER_%s__'%j,qns=qns,flow=+1 if site.qnon else 0))
qnses.append(qns)
S=Label('__MPO_RELAYER__',qns=(QuantumNumbers.kron if U.qnon else np.product)(qnses),flow=+1 if U.qnon else 0)
m=m.split((U,ups),(D,dws)).transpose([L]+orders+[R]).merge((orders,S))
us,s,v=expanded_svd(m,L=[L],S=S,R=[R],E=labels,I=bonds[start+1:stop+1],cut=stop-start,nmax=nmax,tol=tol)
for u,up,dw,label in zip(us,ups,dws,labels):
Ms.append(u.split((label,[up,dw])))
Ms[-1]=Ms[-1]*s*v
Ms[+0].relabel(olds=[MPO.L],news=[Ms[+0].labels[MPO.L].replace(identifier=bonds[+0].identifier)])
Ms[-1].relabel(olds=[MPO.R],news=[Ms[-1].labels[MPO.R].replace(identifier=bonds[-1].identifier)])
return MPO(Ms)