def svd(tensor,row,new,col,nmax=None,tol=None,returnerr=False,**karg):
'''
Perform the svd.
Parameters
----------
tensor : DTensor/STensor
The tensor to be svded.
row,col : list of Label or int
The labels or axes to be merged as the row/column during the svd.
new : Label
The label for the singular values.
nmax,tol,returnerr :
Please refer to HamiltonianPy.Misc.Linalg.truncatedsvd for details.
Returns
-------
U,S,V : DTensor/STensor
The result tensor.
err : float, optional
The truncation error.
'''
assert len(row)+len(col)==tensor.ndim
row=[r if isinstance(r,Label) else tensor.label(r) for r in row]
col=[c if isinstance(c,Label) else tensor.label(c) for c in col]
if isinstance(tensor,STensor):
rowlabel,rowrecord=Label.union(row,'__TENSOR_SVD_ROW__',+1,mode=2)
collabel,colrecord=Label.union(col,'__TENSOR_SVD_COL__',-1,mode=2)
m=tensor.merge((row,rowlabel,rowrecord),(col,collabel,colrecord)).data
us,ss,vs,qns=[],[],[],[]
for (rowqn,colqn),block in m.items():
assert rowqn==colqn
u,s,v=sl.svd(block,full_matrices=False,lapack_driver='gesvd')[0:3]
us.append(u)
ss.append(s)
vs.append(v)
qns.append(rowqn)
temp=np.sort(np.concatenate([-s for s in ss]))
nmax=len(temp) if nmax is None else min(nmax,len(temp))
tol=temp[nmax-1] if tol is None else min(-tol,temp[nmax-1])
Us,Ss,Vs,contents={},[],{},([],[])
for u,s,v,qn in zip(us,ss,vs,qns):
cut=np.searchsorted(-s,tol,side='right')
if cut>0:
Us[(qn,qn)]=u[:,0:cut]
Ss.append(s[0:cut])
Vs[(qn,qn)]=v[0:cut,:]
contents[0].append(qn)
contents[1].append(cut)
new=new.replace(qns=QuantumNumbers('U',contents,protocol=QuantumNumbers.COUNTS),flow=None)
U=STensor(Us,labels=[rowlabel,new.replace(flow=-1)]).split((rowlabel,row,rowrecord))
S=DTensor(np.concatenate(Ss),labels=[new])
V=STensor(Vs,labels=[new.replace(flow=+1),collabel]).split((collabel,col,colrecord))
if returnerr: err=(temp[nmax:]**2).sum()
elif tensor.qnon:
rowlabel,rowpermutation=Label.union(row,'__TENSOR_SVD_ROW__',+1,mode=1)
collabel,colpermutation=Label.union(col,'__TENSOR_SVD_COL__',-1,mode=1)
m=tensor.merge((row,rowlabel,rowpermutation),(col,collabel,colpermutation)).data
rowod,colod=rowlabel.qns.toordereddict(),collabel.qns.toordereddict()
us,ss,vs,qns=[],[],[],[]
for qn in filter(lambda key: key in rowod,colod):
u,s,v=sl.svd(m[rowod[qn],colod[qn]],full_matrices=False,lapack_driver='gesvd')[0:3]
us.append(u)
ss.append(s)
vs.append(v)
qns.append(qn)
temp=np.sort(np.concatenate([-s for s in ss]))
nmax=len(temp) if nmax is None else min(nmax,len(temp))
tol=temp[nmax-1] if tol is None else min(-tol,temp[nmax-1])
Us,Ss,Vs,contents=[],[],[],([],[])
for u,s,v,qn in zip(us,ss,vs,qns):
cut=np.searchsorted(-s,tol,side='right')
if cut>0:
Us.append(u[:,0:cut])
Ss.append(s[0:cut])
Vs.append(v[0:cut,:])
contents[0].append(qn)
contents[1].append(cut)
S=np.concatenate(Ss)
new=new.replace(qns=QuantumNumbers('U',contents,protocol=QuantumNumbers.COUNTS),flow=None)
od=new.qns.toordereddict()
U=np.zeros((rowlabel.dim,new.dim),dtype=tensor.dtype)
V=np.zeros((new.dim,collabel.dim),dtype=tensor.dtype)
for u,v,qn in zip(Us,Vs,od):
U[rowod[qn],od[qn]]=u
V[od[qn],colod[qn]]=v
U=DTensor(U,labels=[rowlabel,new.replace(flow=-1)]).split((rowlabel,row,np.argsort(rowpermutation)))
S=DTensor(S,labels=[new])
V=DTensor(V,labels=[new.replace(flow=+1),collabel]).split((collabel,col,np.argsort(colpermutation)))
if returnerr: err=(temp[nmax:]**2).sum()
else:
rowlabel=Label('__TENSOR_SVD_ROW__',qns=np.product([label.dim for label in row]))
collabel=Label('__TENSOR_SVD_COL__',qns=np.product([label.dim for label in col]))
m=tensor.merge((row,rowlabel),(col,collabel)).data
temp=hm.truncatedsvd(m,full_matrices=False,nmax=nmax,tol=tol,returnerr=returnerr,**karg)
u,s,v=temp[0],temp[1],temp[2]
new=new.replace(qns=len(s),flow=None)
U=DTensor(u,labels=[rowlabel,new.replace(flow=0)]).split((rowlabel,row))
S=DTensor(s,labels=[new])
V=DTensor(v,labels=[new.replace(flow=0),collabel]).split((collabel,col))
if returnerr: err=temp[3]
return (U,S,V,err) if returnerr else (U,S,V)
def partitionedsvd(tensor,L,new,R,nmax=None,tol=None,ttype='D',returnerr=False):
'''
Partition a 1d-tensor according to L and R and then perform the Schmitt decomposition.
Parameters
----------
tensor : DTensor
The tensor to be partitioned svded.
L,R : Label
The left/right part of the partition.
new : Label
The label for the singular values.
ttype : 'D'/'S', optional
Tensor type. 'D' for dense and 'S' for sparse.
nmax,tol,returnerr :
Please refer to HamiltonianPy.Misc.Linalg.truncatedsvd for details.
Returns
-------
U,S,V : DTensor/STensor
The Schmitt decomposition of the 1d tensor.
err : float, optional
The truncation error.
'''
assert tensor.ndim==1 and ttype in 'DS'
if tensor.qnon:
data,qns=tensor.data,tensor.labels[0].qns
assert qns.num==1 and sl.norm(qns.contents)<10**-6
lod,rod=L.qns.toordereddict(),R.qns.toordereddict()
us,ss,vs,qns,count=[],[],[],[],0
for qn in filter(lambda key: key in lod,rod):
s1,s2=lod[qn],rod[qn]
n1,n2=s1.stop-s1.start,s2.stop-s2.start
u,s,v=sl.svd(data[count:count+n1*n2].reshape((n1,n2)),full_matrices=False,lapack_driver='gesvd')[0:3]
us.append(u)
ss.append(s)
vs.append(v)
qns.append(qn)
count+=n1*n2
temp=np.sort(np.concatenate([-s for s in ss]))
nmax=len(temp) if nmax is None else min(nmax,len(temp))
tol=temp[nmax-1] if tol is None else min(-tol,temp[nmax-1])
if ttype=='D':
Us,Ss,Vs,contents=[],[],[],([],[])
for u,s,v,qn in zip(us,ss,vs,qns):
cut=np.searchsorted(-s,tol,side='right')
if cut>0:
Us.append(u[:,0:cut])
Ss.append(s[0:cut])
Vs.append(v[0:cut,:])
contents[0].append(qn)
contents[1].append(cut)
new=new.replace(qns=QuantumNumbers('U',contents,QuantumNumbers.COUNTS),flow=None)
nod=new.qns.toordereddict()
U=np.zeros((L.dim,new.dim),dtype=tensor.dtype)
S=np.concatenate(Ss)
V=np.zeros((new.dim,R.dim),dtype=tensor.dtype)
for u,v,qn in zip(Us,Vs,nod):
U[lod[qn],nod[qn]]=u
V[nod[qn],rod[qn]]=v
U=DTensor(U,labels=[L,new.replace(flow=-1)])
S=DTensor(S,labels=[new])
V=DTensor(V,labels=[new.replace(flow=+1),R])
else:
Us,Ss,Vs,contents={},[],{},([],[])
for u,s,v,qn in zip(us,ss,vs,qns):
cut=np.searchsorted(-s,tol,side='right')
if cut>0:
Us[(qn,qn)]=u[:,0:cut]
Ss.append(s[0:cut])
Vs[(qn,qn)]=v[0:cut,:]
contents[0].append(qn)
contents[1].append(cut)
new=new.replace(qns=QuantumNumbers('U',contents,QuantumNumbers.COUNTS),flow=None)
U=STensor(Us,labels=[L,new.replace(flow=-1)])
S=DTensor(np.concatenate(Ss),labels=[new])
V=STensor(Vs,labels=[new.replace(flow=+1),R])
if returnerr: err=(temp[nmax:]**2).sum()
else:
m=tensor.data.reshape((L.dim,R.dim))
data=hm.truncatedsvd(m,full_matrices=False,nmax=nmax,tol=tol,returnerr=returnerr)
new=new.replace(qns=len(data[1]),flow=None)
U=DTensor(data[0],labels=[L,new.replace(flow=0)])
S=DTensor(data[1],labels=[new])
V=DTensor(data[2],labels=[new.replace(flow=0),R])
if returnerr: err=data[3]
return (U,S,V,err) if returnerr else (U,S,V)
