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HOTRGZ2.py
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HOTRGZ2.py
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import torch
from tqdm.auto import tqdm as tqdm
from opt_einsum import contract
import torch.utils.checkpoint
import itertools as itt
import functools
from collections import namedtuple
from dataclasses import dataclass
import math
import numpy as np
import copy
def _toN(t):
if isinstance(t,list):
return [_toN(tt) for tt in t]
elif isinstance(t,torch.Tensor):
return t.detach().cpu().tolist()
else:
return t
def _toP(t):
if isinstance(t,list):
return [_toP(tt) for tt in t]
elif isinstance(t,torch.Tensor):
return t.detach().cpu().numpy()
else:
return t
#from safe_svd import svd,sqrt # TODO is it necessary???
from torch.linalg import svd
#======================== Z2 =================================
def RepDim(dimV1R1,dimV1R2,dimV2R1,dimV2R2):
return (dimV1R1*dimV2R1+dimV1R2*dimV2R2,dimV1R1*dimV2R2+dimV1R2*dimV2R1)
def RepMat(dimV1R1,dimV1R2,dimV2R1,dimV2R2):
dimV1=dimV1R1+dimV1R2
dimV2=dimV2R1+dimV2R2
P=torch.zeros([dimV1*dimV2,dimV1,dimV2])
counter=0
for i in range(dimV1R1):
for j in range(dimV2R1):
P[counter,i,j]=1
counter+=1
for i in range(dimV1R2):
for j in range(dimV2R2):
P[counter,dimV1R1+i,dimV2R1+j]=1
counter+=1
for i in range(dimV1R1):
for j in range(dimV2R2):
P[counter,i,dimV2R1+j]=1
counter+=1
for i in range(dimV1R2):
for j in range(dimV2R1):
P[counter,dimV1R1+i,j]=1
counter+=1
return P
def _RepMat(a,b):
return RepMat(a,b,a,b)
def Z2_sectors(T,dimR):
if len(T.shape)==2*len(dimR): dimR=[d for d in dimR for _ in range(2)]
assert len(T.shape)==len(dimR) and all(i==sum(j) for i,j in zip(T.shape,dimR))
for sector in itt.product(range(2),repeat=len(dimR)):
begin=[sum(dimR[leg][:rep]) for leg,rep in enumerate(sector)]
end=[sum(dimR[leg][:rep+1]) for leg,rep in enumerate(sector)]
slices=[slice(b,e) for b,e in zip(begin,end)]
yield sector,slices
def Z2_sector_norm(T,dimR):
sqrnorm=torch.zeros(2)
for sector,slices in Z2_sectors(T,dimR):
sqrnorm[sum(sector)%2]+=T[slices].norm()**2
return sqrnorm**.5
def project_Z2(T,dimR,weights=[1,0],tolerance=float('inf')):
Tn=torch.zeros(T.shape)
sqrnorm=torch.zeros(2)
for sector,slices in Z2_sectors(T,dimR):
sqrnorm[sum(sector)%2]+=T[slices].norm()**2
Tn[slices]=T[slices]*weights[sum(sector)%2]
norm=sqrnorm**.5
assert not(weights[1]==0 and norm[1]>norm[0]*tolerance)
assert not(weights[0]==0 and norm[0]>norm[1]*tolerance)
return Tn
#============================= Forward Layers ======================================
def is_isometry(g):
return torch.isclose([email protected](),torch.eye(g.shape[0])).all()
@dataclass
class HOTRGLayer:
tensor_shape:'tuple(int)'
ww:'list[torch.Tensor]'
dimR:'tuple[tuple[int]]'=None
dimR_next:'tuple[tuple[int]]'=None
gg:'list[list[torch.Tensor]]'=None
hh:'list[list[torch.Tensor]]'=None
_gg1=None
def _gg(self,iNode,iLeg):
# if self._gg1 is None and BypassGilt.v[iNode]:
# self.prepare_bypass_gilt()
# return self._gg1[iNode][iLeg] if BypassGilt.v[iNode] else self.gg[iNode][iLeg]
return self.gg[iNode][iLeg]
def make_gg_isometric(self):
if self.gg is None: return
def make_isometric(g):
u,s,vh=svd(g)
g=u@vh
assert is_isometry(g)
return g
for i in range(len(self.gg)):
for j in range(0,len(self.gg[i]),2):
self.gg[i][j]=make_isometric(self.gg[i][j])
# self.gg[i][j+1]=make_isometric(self.gg[i][j+1])
self.gg[i][j+1]=self.gg[i][j].conj() # not quite correct, since w depends on g[i][j+1], but we erased it
assert torch.isclose(self.gg[i][j]@self.gg[i][j+1].T.conj(),torch.eye(self.gg[i][j].shape[0])).all()
# self.gg=[[make_isometric(g) for g in gg] for gg in self.gg]
# self.gg=None
def get_isometry(self,i):
# h0
# g00
# /g02-Ta-g03\ 0 2
#h2-w0 |g.. w0-h3 2T3 -> 0T'1
# \g12-Tb-g13/ 1 3
# g11
# h1
iAxis=i//2
if iAxis==0: #first virtual leg
w=torch.eye(self.tensor_shape[i])
if self.gg:
w=self._gg(i,i)@w
if self.hh:
w=self.hh[i]@w
elif iAxis<len(self.tensor_shape)//2: #other virtual legs
w=self.ww[iAxis-1]
if self.dimR:
P=_RepMat(self.dimR[iAxis][0],self.dimR[iAxis][1])
w=contract('ab,bij->aij',w,P)
else:
w=w.reshape(-1,self.tensor_shape[i],self.tensor_shape[i])
if i%2==1:
w=w.conj()
if self.gg:
w=contract('aij,iI,jJ->aIJ',w,self._gg(0,i),self._gg(1,i))
if self.hh:
w=contract('aij,Aa->Aij',w,self.hh[i])
else: #physical leg
w=self.ww[iAxis-1]
if self.dimR:
P=_RepMat(self.dimR[iAxis][0],self.dimR[iAxis][1])
w=contract('ab,bij->aij',w,P)
else:
w=w.reshape(-1,self.tensor_shape[i],self.tensor_shape[i])
return w
def get_insertion(self):
if self.gg:
return self._gg(0,1).T@self._gg(1,0)
else:
return torch.eye(self.tensor_shape[0])
def delete_PEPS_(self):
if(len(self.tensor_shape)%2==0):
print('Warning! Theres no PEPS.')
return
self.tensor_shape=self.tensor_shape[:-1]
self.ww=self.ww[:-1]
if self.dimR:
self.dimR=self.dimR[:-1]
self.dimR_next=self.dimR_next[:-1]
# def prepare_bypass_gilt(self):
# self._gg1=[[to_unitary(g) for g in ggg]for ggg in self.gg]
# class BypassGilt:
# v=[False,False]
# def __init__(self,*v):
# self.u=v
# def __enter__(self):
# BypassGilt.v,self.u=self.u,BypassGilt.v
# def __exit__(self, exc_type, exc_value, exc_tb):
# BypassGilt.v,self.u=self.u,BypassGilt.v
def _forward_layer(Ta,Tb,layer:HOTRGLayer):
assert layer.tensor_shape==Ta.shape and layer.tensor_shape==Tb.shape
isometries=[layer.get_isometry(i) for i in range(len(layer.tensor_shape))]
insertion=layer.get_insertion()
eq={4:'ijkl,Jmno,jJ,xi,ym,akn,blo->abxy',
5:'ijklA,JmnoB,jJ,xi,ym,akn,blo,CAB->abxyC',
6:'ijklmn,Jopqrs,jJ,xi,yo,akp,blq,cmr,dns->abcdxy',
}[len(layer.tensor_shape)]
T=contract(eq,Ta,Tb,insertion,*isometries)
return T
# def _forward_layer_2D(Ta,Tb,layer:HOTRGLayer):
# # h0
# # g00
# # /g02-Ta-g03\ 0 2
# #h2-w |g w-h3 2T3 -> 0T'1
# # \g12-Tb-g13/ 1 3
# # g11
# # h1
# ww,dimR,gg,hh,T0Shape=layer.ww,layer.dimR,layer.gg,layer.hh,layer.tensor_shape
# assert T0Shape==Ta.shape and T0Shape==Tb.shape
# if gg:
# Ta=contract('ijkl,Ii,Jj,Kk,Ll->IJKL',Ta,*gg[0])
# Tb=contract('ijkl,Ii,Jj,Kk,Ll->IJKL',Tb,*gg[1])
# if dimR:
# P=RepMat(dimR[1][0],dimR[1][1],dimR[1][0],dimR[1][1])
# wP=contract('ab,bij->aij',ww[0],P)
# else:
# wP=ww[0].reshape(-1,Ta.shape[2],Tb.shape[2])
# Tn=contract('ijkl,jmno,akn,blo->imab',Ta,Tb,wP,wP.conj())
# if hh:
# Tn=contract('ijkl,Ii,Jj,Kk,Ll->IJKL',Tn,*hh)
# Tn=contract('ijab->abij',Tn)
# return Tn
# def _forward_layer_3D(Ta,Tb,layer:HOTRGLayer):
# # g| 5--6
# # /g-T1-g\ 50 34 |1--2
# # h-w g|g w-h 2T3 -> 0T'1 7| 8|
# # \g-T2-g/ 14 52 3--4
# # |g
# ww,dimR,gg,hh,T0Shape=layer.ww,layer.dimR,layer.gg,layer.hh,layer.tensor_shape
# assert T0Shape==Ta.shape and T0Shape==Tb.shape
# if gg:
# Ta=contract('ijklmn,Ii,Jj,Kk,Ll,Mm,Nn->IJKLMN',Ta,*gg[0])
# Tb=contract('ijklmn,Ii,Jj,Kk,Ll,Mm,Nn->IJKLMN',Tb,*gg[1])
# if dimR:
# P1=RepMat(dimR[1][0],dimR[1][1],dimR[1][0],dimR[1][1])
# wP1=contract('ab,bij->aij',ww[0],P1)
# P2=RepMat(dimR[2][0],dimR[2][1],dimR[2][0],dimR[2][1])
# wP2=contract('ab,bij->aij',ww[1],P2)
# else:
# wP1=ww[0].reshape(-1,Ta.shape[2],Tb.shape[2])
# wP2=ww[1].reshape(-1,Ta.shape[4],Tb.shape[4])
# Tn=contract('ijklmn,jopqrs,akp,blq,cmr,dns->ioabcd',Ta,Tb,wP1,wP1.conj(),wP2,wP2.conj())
# if hh:
# Tn=contract('ijklmn,Ii,Jj,Kk,Ll,Mm,Nn->IJKLMN',Tn,*hh)
# Tn=contract('ijabcd->abcdij')
# return Tn
def _checkpoint(function,args,args1,use_checkpoint=True):
if use_checkpoint and any(x.requires_grad for x in args):
def wrapper(*args):
return function(*args,**args1)
return torch.utils.checkpoint.checkpoint(wrapper,*args)
else:
return function(*args,**args1)
def forward_layer(Ta,Tb,layer:HOTRGLayer,use_checkpoint=False)->torch.Tensor:
#_forward_layer={4:_forward_layer_2D,6:_forward_layer_3D}[len(Ta.shape)]
return _checkpoint(_forward_layer,[Ta,Tb],{'layer':layer},use_checkpoint=use_checkpoint)
def gauge_invariant_norm(T):
contract_path={4:'iijj->',5:'iijjk->k',6:'iijjkk->',7:'iijjkkl->l'}[len(T.shape)]
norm=contract(contract_path,T).norm()
if norm<1e-6:#fallback
norm=T.norm()
#norm=T.norm()
#print(norm)
return norm
def to_unitary(g):
u,s,vh=svd(g)
return u@vh
def forward_tensor(T0,layers:'list[HOTRGLayer]',use_checkpoint=False,return_layers=False):
T,logTotal=T0,0
if return_layers:
Ts,logTotals=[T],[0]
for layer in tqdm(layers,leave=False):
norm=gauge_invariant_norm(T)
T=T/norm
logTotal=2*(logTotal+norm.log())
T=forward_layer(T,T,layer=layer,use_checkpoint=use_checkpoint)
if return_layers:
Ts.append(T);logTotals.append(logTotal)
return (Ts,logTotals) if return_layers else (T,logTotal)
def forward_observable_tensor(T0,T0_op,layers:'list[HOTRGLayer]',
start_layer=0,checkerboard=False,use_checkpoint=False,return_layers=False,cached_Ts=None):
spacial_dim=len(T0.shape)//2
T,logTotal=forward_tensor(T0,layers=layers[:start_layer],use_checkpoint=use_checkpoint,return_layers=return_layers)
T_op=T0_op
if return_layers:
Ts,T,logTotals,logTotal=T,T[-1],logTotal,logTotal[-1]
T_ops=[None]*start_layer+[T_op]
for ilayer,layer in tqdm(list(enumerate(layers))[start_layer:],leave=False):
norm=gauge_invariant_norm(T)
T,T_op=T/norm,T_op/norm
logTotal=2*(logTotal+norm.log())
if cached_Ts:
T1=cached_Ts[ilayer+1]
else:
T1=forward_layer(T,T,layer=layer,use_checkpoint=use_checkpoint)
#with BypassGilt(False,True):
T2=forward_layer(T,T_op,layer=layer,use_checkpoint=use_checkpoint)
#with BypassGilt(True,False):
T3=forward_layer(T_op,T,layer=layer,use_checkpoint=use_checkpoint)
T3=-T3 if (checkerboard and ilayer<spacial_dim) else T3
T,T_op=T1,(T2+T3)/2
if return_layers:
Ts.append(T);T_ops.append(T_op);logTotals.append(logTotal)
return (Ts,T_ops,logTotals) if return_layers else (T,T_op,logTotal)
def forward_observalbe_tensor_moments(T0_moments:'list[torch.Tensor]',layers:'list[HOTRGLayer]',
checkerboard=False,use_checkpoint=False,return_layers=False,cached_Ts=None):
print('WARNING NOT TESTED')
# -T'[OO]- = -T[OO]-T[1]- + 2 -T[O]-T[O]- + -T[1]-T[OO]-
spacial_dim=len(T0_moments[0].shape)//2
logTotal=0
Tms=T0_moments.copy()
if return_layers:
Tmss,logTotals=[Tms],[logTotal]
for ilayer,layer in tqdm(list(enumerate(layers)),leave=False):
norm=gauge_invariant_norm(Tms[0])
logTotal=2*(logTotal+norm.log())
Tms=[x/norm for x in Tms]
Tms1=[torch.zeros_like(Tms[0])]*len(Tms)
for a in range(len(Tms)):
for b in range(len(Tms)):
if a+b<len(Tms1):
if a+b==0 and cached_Ts:
Tms1[a+b]=cached_Ts[ilayer+1]
else:
Tms1[a+b]=math.comb(a+b,b)\
*forward_layer(Tms[a],Tms[b],layer=layer,use_checkpoint=use_checkpoint)
Tms=Tms1
if return_layers:
Tmss.append(Tms);logTotals.append(logTotal)
return (Tmss,logTotals) if return_layers else (Tms,logTotal)
def get_lattice_size(nLayers,spacial_dim):
return tuple(2**(nLayers//spacial_dim+(1 if i<nLayers%spacial_dim else 0)) for i in range(spacial_dim))
def get_dist_2D(x,y):
return (x**2+y**2)**.5
def get_dist_torus_2D(x,y,lattice_size):
# modulus but return positive numers
x,y=x%lattice_size[0],y%lattice_size[1]
d1=x**2+y**2
d2=(lattice_size[0]-x)**2+y**2
d3=x**2+(lattice_size[1]-y)**2
d4=(lattice_size[0]-x)**2+(lattice_size[1]-y)**2
return functools.reduce(np.minimum,[d1,d2,d3,d4])**.5
def forward_coordinate(coords):
return coords[1:]+(coords[0]//2,)
def forward_observable_tensors(T0,T0_ops:list,positions:'list[tuple[int]]',
layers:'list[HOTRGLayer]',checkerboard=False,use_checkpoint=False,cached_Ts=None,user_tqdm=True):
spacial_dim=len(T0.shape)//2
nLayers=len(layers)
lattice_size=get_lattice_size(nLayers,spacial_dim=spacial_dim)
assert all(isinstance(c,int) and 0<=c and c<s for coords in positions for c,s in zip(coords,lattice_size)),"coordinates must be integers in the range [0,lattice_size)\n"+str(positions)+" "+str(lattice_size)
assert all(positions[i]!=positions[j] for i,j in itt.combinations(range(len(positions)),2))
assert len(positions)==len(T0_ops)
T,T_ops,logTotal=T0,T0_ops.copy(),0
_tqdm=tqdm if user_tqdm else lambda x,leave:x
for ilayer,layer in _tqdm(list(enumerate(layers)),leave=False):
norm=gauge_invariant_norm(T)
logTotal=2*(logTotal+norm.log())
T,T_ops=T/norm,[T_op/norm for T_op in T_ops]
# check if any two points are going to merge
iRemoved=[]
T_ops_new,positions_new=[],[]
for i,j in itt.combinations(range(len(positions)),2):
if forward_coordinate(positions[i])==forward_coordinate(positions[j]):
i,j=(i,j) if positions[i][0]%2==0 else (j,i)
#print(positions[i],positions[j])
assert positions[i][0]%2==0 and positions[j][0]%2==1
#with BypassGilt(True,True):
T_op_new=forward_layer(T_ops[i],T_ops[j],layer,use_checkpoint=use_checkpoint)
if checkerboard and ilayer<spacial_dim:
T_op_new=-T_op_new
T_ops_new.append(T_op_new)
positions_new.append(forward_coordinate(positions[i]))
assert (not i in iRemoved) and (not j in iRemoved)
iRemoved.extend([i,j])
# forward other points with T
for i in range(len(positions)):
if i not in iRemoved:
if positions[i][0]%2==0:
#with BypassGilt(False,True):
T_op_new=forward_layer(T_ops[i],T,layer,use_checkpoint=use_checkpoint)
else:
#with BypassGilt(True,False):
T_op_new=forward_layer(T,T_ops[i],layer,use_checkpoint=use_checkpoint)
if checkerboard and ilayer<spacial_dim:
T_op_new=-T_op_new
T_ops_new.append(T_op_new)
positions_new.append(forward_coordinate(positions[i]))
# forward T
if cached_Ts:
T_new=cached_Ts[ilayer+1]
else:
T_new=forward_layer(T,T,layer=layer,use_checkpoint=use_checkpoint)
T,T_ops,positions=T_new,T_ops_new,positions_new
if len(positions)==0:
return T,T,logTotal
else:
assert len(positions)==1
return T,T_ops[0],logTotal
def trace_tensor(T):
eq={4:'aabb->',6:'aabbcc->'}[len(T.shape)]
return contract(eq,T)
def trace_two_tensors(T,T1=None):
T1=T if T1 is None else T1
eq={4:'abcc,badd->',6:'abccdd,baeeff->'}[len(T.shape)]
return contract(eq,T,T)
def reflect_tensor_axis(T):
Ai=[2*i+j for i in range(len(T.shape)//2) for j in range(2)]
Bi=[2*i+1-j for i in range(len(T.shape)//2) for j in range(2)]
return contract(T,Ai,Bi)
def permute_tensor_axis(T):
Ai=[*range(len(T.shape))]
Bi=Ai[2:]+Ai[:2]
return contract(T,Ai,Bi)
#==================
import importlib
import HOSVD,GILT,fix_gauge
importlib.reload(HOSVD)
importlib.reload(GILT)
importlib.reload(fix_gauge)
from HOSVD import HOSVD_layer
from GILT import GILT_HOTRG,GILT_options
from fix_gauge import minimal_canonical_form,fix_unitary_gauge,fix_phase,MCF_options
def HOTRG_layer(T1,T2,max_dim,dimR=None,options:dict={},Tref=None):
T1old,T2old=T1,T2
gilt_options=GILT_options(**{k[5:]:v for k,v in options.items() if k[:5]=='gilt_'})
mcf_options=MCF_options(**{k[4:]:v for k,v in options.items() if k[:4]=='mcf_'})
if options.get('gilt_enabled',False):
assert not dimR
T1,T2,gg=GILT_HOTRG(T1,T2,options=gilt_options)
else:
gg=None
Tn,layer=HOSVD_layer(T1,T2,max_dim=max_dim,dimR=dimR)
layer.gg=gg
if options.get('gilt_make_isometric',False):
layer.make_gg_isometric()
Tn= forward_layer(T1old,T2old,layer)
if options.get('mcf_enabled',False):
assert not dimR
Tn,hh=minimal_canonical_form(Tn,options=mcf_options)
if Tref is not None and Tn.shape==Tref.shape:
Tn,hh1=fix_phase(Tn,Tref)
hh=[h1@h for h1,h in zip(hh1,hh)]
if options.get('mcf_enabled_unitary',False):
Tn,hh1=fix_unitary_gauge(Tn,Tref)
hh=[h1@h for h1,h in zip(hh1,hh)]
else:
# still fix the phase
if Tref is not None and Tn.shape==Tref.shape:
Tn,hh=fix_phase(Tn,Tref)
else:
hh=None
if hh is not None:
hh=hh[-2:]+hh[:-2] # why?
layer.hh=hh
if options.get('hotrg_sanity_check'):
Tn1= forward_layer(T1old,T2old,layer)
assert (Tn-Tn1).abs().max()<1e-6
return Tn,layer
def HOTRG_layers(T0,max_dim,nLayers,
dimR:"tuple[tuple[int]]"=None,
options:dict={},
return_tensors=False):
print('Generating HOTRG layers')
spacial_dim=len(T0.shape)//2
stride=spacial_dim
T,logTotal=T0,0
Ts,logTotals=[T],[0]
layers=[]
for iLayer in tqdm(list(range(nLayers)),leave=False):
norm=gauge_invariant_norm(T)
T=T/norm
logTotal=2*(logTotal+norm.log())
Tref=Ts[iLayer+1-stride] if iLayer+1-stride>=0 else None
Told=T
T,layer=HOTRG_layer(T,T,max_dim=max_dim,dimR=dimR,Tref=Tref,options=options)
dimR=layer.dimR_next
if options.get('hotrg_sanity_check',False):
assert ((forward_layer(Told,Told,layer)-T).norm()/T.norm()<=options.get('hotrg_sanity_check_tol',1e-7))
layers.append(layer)
Ts.append(T);logTotals.append(logTotal)
print('HOTRG layers generated')
return (layers,Ts,logTotals) if return_tensors else layers
#==================
'''
def get_w_random(dimRn0,dimRn1,max_dim):
max_dim-=max_dim%2
dimRnn0,dimRnn1=max_dim//2,max_dim-max_dim//2
w=torch.zeros((max_dim,dimRn0+dimRn1))
w[:dimRnn0,:dimRn0]=generate_random_isometry(dimRnn0,dimRn0)
w[dimRnn0:,dimRn0:]=generate_random_isometry(dimRnn1,dimRn1)
return w,dimRnn0,dimRnn1
def generate_random_isometry(dim0,dim1):
dim=max(dim0,dim1)
A=torch.randn(dim,dim)
U=torch.matrix_exp(A-A.t())
U=U[:dim0,:dim1]
return U
def generate_isometries_random(dimR:"tuple[tuple[int]]",max_dim,nLayers):
layers=[]
spacial_dim=len(dimR)
for iLayer in range(nLayers):
ww=[]
dimRn=(dimR[-1],)
for i in range(1,spacial_dim):
w,dimR0,dimR1=get_w_random(dimR[i][0],dimR[i][1],max_dim)
ww.append(w)
dimRn.append([dimR0,dimR1])
dimRn+=((dimR0,dimR1),)
Tshape=(sum(x) for x in dimR) #todo not sure
layers.append(HOTRGLayer(T0shape=Tshape,ww=ww,dimR=dimR,dimR_next=dimRn))
dimR=dimRn
return layers
'''
'''
def forward_two_observable_tensors(T0,T0_op1,T0_op2,coords:"tuple[int]",layers:'list[HOTRGLayer]',checkerboard=False,use_checkpoint=False,cached_Ts=None):
spacial_dim=len(T0.shape)//2
nLayers=len(layers)
lattice_size=get_lattice_size(nLayers,spacial_dim=spacial_dim)
#print(coords,lattice_size)
assert all(isinstance(c,int) and 0<=c and c<s for c,s in zip(coords,lattice_size))
assert not all(c==0 for c in coords)
T,T_op1,T_op2,T_op12,logTotal=T0,T0_op1,T0_op2,None,0
for ilayer,layer in tqdm(list(enumerate(layers)),leave=False):
norm=gauge_invariant_norm(T)
logTotal=2*(logTotal+norm.log())
T,T_op1,T_op2,T_op12=(t/norm if t is not None else None for t in (T,T_op1,T_op2,T_op12))
#Evolve vacuum T
if cached_Ts:
T1=cached_Ts[ilayer+1]
else:
T1=forward_layer(T,T,layer=layer,use_checkpoint=use_checkpoint)
#Evolve defected T depends on whether the two defects are in the same coarse-grained block
#print(coords)
if coords==(0,)*spacial_dim:
T2=forward_layer(T_op12,T,layer=layer,use_checkpoint=use_checkpoint)
T,T_op12=T1,T2
elif coords==(1,)+(0,)*(spacial_dim-1):
T2=forward_layer(T_op1,T_op2,layer=layer,use_checkpoint=use_checkpoint)
T2=-T2 if checkerboard and ilayer<spacial_dim else T2
T,T_op12,T_op1,T_op2=T1,T2,None,None
else:
c=coords[0]%2
T2=forward_layer(T_op1,T,layer=layer,use_checkpoint=use_checkpoint)
if c==0:
T3=forward_layer(T_op2,T,layer=layer,use_checkpoint=use_checkpoint)
elif c==1:
T3=forward_layer(T,T_op2,layer=layer,use_checkpoint=use_checkpoint)
T3=-T3 if checkerboard and ilayer<spacial_dim else T3
T,T_op1,T_op2=T1,T2,T3
coords=forward_coordinate(coords)
assert coords==(0,)*spacial_dim
return T,T_op12,logTotal
'''