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tn_np.py
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tn_np.py
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"""
Tensor network class
TODO:
1. estimate error made in SVD
2. remove graphx dependences in Tensor_Network class
3. replace dictionary tensors{} to array
"""
import numpy as np
import math
import networkx as nx
from scipy.linalg import sqrtm
import time
import sys
import mps_node_np
from npsvd import svd, rsvd
from args import args
class Tensor_Network_np:
""" Tensor network for the graphical model.
Storage: The data are stored in a dictionary *tensors*, each of which is a Node class.
"""
def __init__(self, n, edges, weights, fields, beta, seed=1, mydevice='cpu', maxdim=30, verbose=-1, Dmax=12, chi=32,
node_type="np", norm_method=1, svdopt=True, swapopt=True, reverse=True, bins=20,select=1):
self.norm_method = norm_method
self.reverse = reverse
self.sign = 1
self.bins = bins
self.beta = beta
self.weights = weights
self.fields = fields
self.n = n
self.select=select
self.print_interval = self.n // self.bins
self.svdopt = svdopt
self.swapopt = swapopt
self.edges = edges
self.G = nx.MultiGraph()
self.node_type = node_type
self.chi = chi
self.device = mydevice
self.verbose = verbose
np.random.seed(seed)
self.maxdim = maxdim
self.Dmax = Dmax # maximum bond dimension
self.cutoff = 1.0e-15
self.G.add_nodes_from(np.arange(self.n))
self.G.add_edges_from(set([tuple(sorted(a)) for a in edges]))
self.m = len(self.G.edges)
self.maxdim_intermediate = -1
self.max_degree = max(np.array(self.G.degree)[:, 1])
self.num_isolated = sum((np.array(self.G.degree)[:, 1]) == 0)
print("totally", self.n, "nodes,", self.m, "edges,", "maximum degree=", self.max_degree,
", number of isolated nodes=", self.num_isolated)
# print(edges)
# print("degree",self.G.degree)
# print("G.edges",self.G.edges)
'''
self.tensors = {}.fromkeys(np.arange(self.n))
for key in self.tensors.keys():
tensor = tensors[key]
self.tensors[key] = mps_node_np.MPSNode(tensor, key, list(labels[key]), self.chi, self.cutoff,
self.norm_method, self.svdopt, self.swapopt)
self.tensors[key].left_canonical()
'''
self.construct_tensor()
self.select_edge_init()
def construct_tensor(self, pos1=None, val1=None, pos2=None, val2=None):
Is = [np.array([])]
for i in range(1, self.max_degree + 2):
tensor = np.zeros(2 ** i, dtype=np.float64)
tensor[0] = 1
tensor[-1] = 1
Is.append(tensor.reshape([2] * i))
self.tensors = {}.fromkeys(np.arange(self.n))
# self.tensors = []
for key in range(self.n):
self.tensors[key]= mps_node_np.MPSNode(np.array([], dtype=np.float64),
key,
[],
self.chi,swapopt=self.swapopt)
self.tensors[key].mps = []
spin = np.array([1, -1], dtype=np.float64)
for edge in range(len(self.edges)):
i, j = self.edges[edge]
spini = spin.copy()
spinj = spin.copy()
if i == pos1:
spini[val1] = 0
elif i == pos2:
spini[val2] = 0
if j == pos1:
spinj[val1] = 0
elif j == pos2:
spinj[val2] = 0
M_ij = spini.reshape(2, 1) @ spinj.reshape(1, 2)
if len(self.weights[edge].shape) == 0: # a number, simply weight
# B = np.exp(self.weights[edge] * self.beta * np.tensor([[1, -1], [-1, 1]],
# dtype=np.float64, device=self.device))
B = np.exp(self.weights[edge] * self.beta * M_ij)
elif len(self.weights[edge].shape) == 2 and self.weights[edge].shape[1] > 1: # factor matrix
# B = weights[edge] * np.tensor([1], dtype=np.float64, device=self.device)
B = self.weights[edge]
else:
print("weight data structure not understood")
sys.exit(-7)
# U, s, V = svd(B)
# s = np.diag(np.sqrt(s))
Q = B # U @ s
R = np.eye(len(B), dtype=np.float64) # V @ s
# Q=np.tensor(sqrtm([[np.exp(beta), np.exp(-beta)], [np.exp(-beta), np.exp(beta)]]),dtype=np.float64,device=self.device)
# R=Q
nodei = self.tensors[i]
# fieldi = np.diag(
# np.exp(self.fields[i] * np.tensor([1, -1], dtype=np.float64, device=self.device)))
fieldi = np.diag(np.exp(self.fields[i] * spini))
if self.G.degree(i) == 1:
mat = (fieldi @ Q)
mat = mat.sum(0)
nodei.mps.append(mat.reshape([1, 2, 1]))
else:
if len(nodei.neighbor) == 0:
# Q.shape[0] is the internal dimension chi, the rank, that is, the dimension of the identity matrix.
# Q.shape[1] is the physical dimesion d, could be arbitrary
mat = (fieldi @ Q).transpose() # notice that the physical dimension could have lower or higher dimension, but the inner dimension should be 2
nodei.mps.append(mat.reshape([1, 2, 2]))
elif len(nodei.neighbor) == self.G.degree(i) - 1:
mat = Q
nodei.mps.append(mat.reshape([2, 2, 1]))
else:
t3 = np.zeros([2, 2, 2], dtype=np.float64)
mat0 = np.diag(Q[:, 0]) # chi x chi
mat1 = np.diag(Q[:, 1]) # chi x chi
t3[:, 0, :] = mat0
t3[:, 1, :] = mat1
nodei.mps.append(t3)
nodei.neighbor.append(j)
nodej = self.tensors[j]
# fieldj = np.diag(
# np.exp(self.fields[j] * np.tensor([1, -1], dtype=np.float64, device=self.device)))
fieldj = np.diag(np.exp(self.fields[j] * spinj))
if self.G.degree(j) == 1:
mat = (fieldj @ R)
mat = mat.sum(0)
nodej.mps.append(mat.reshape([1, 2, 1]))
else:
if len(nodej.neighbor) == 0:
mat = (fieldj @ R).transpose()
nodej.mps.append(mat.reshape([1, 2, 2]))
elif len(nodej.neighbor) == self.G.degree(j) - 1:
mat = R
nodej.mps.append(mat.reshape([2, 2, 1]))
else:
t3 = np.zeros([2, 2, 2], dtype=np.float64)
mat0 = np.diag(R[:, 0])
mat1 = np.diag(R[:, 1])
t3[:, 0, :] = mat0
t3[:, 1, :] = mat1
nodej.mps.append(t3)
nodej.neighbor.append(i)
def dim_after_merge(self,i,j):
nodei = self.tensors[i]
nodej = self.tensors[j]
idx_j_in_i=nodei.find_neighbor(j)
di = nodei.logdim()
dj = nodej.logdim()
d=nodei.logdim(idx_j_in_i)
return round(di+dj-d*2)
def select_edge_total_dimension(self):
edge = np.array(list(self.G.edges()))
minidx=0
mind=math.inf
for i,j in edge:
count = self.dim_after_merge(i,j)
if count<mind:
mind = count
myi,myj=i,j
if(mind>self.maxdim_intermediate):
self.maxdim_intermediate=mind
if(mind>self.maxdim):
print("Tring to contract tensor",i, "and tensor",j,"intermediate tensor dimension",mind)
nodei = self.tensors[i]
nodej = self.tensors[j]
print(i,nodei.shape(),nodei.neighbor)
print(j,nodej.shape(),nodej.neighbor)
print("The intermediate tensor is larger than maximum dimension")
self.print_all_tensor_shape()
sys.exit(1)
return myi,myj
def select_edge_min_dim(self):
count = min([i if len(self.edge_count[i]) > 0 else math.inf for i in self.edge_count.keys()])
if(count>self.maxdim_intermediate):
self.maxdim_intermediate = count
return self.edge_count[count][0]
def select_edge_min_dim_triangle(self):
count = min([i if len(self.edge_count[i]) > 0 else math.inf for i in self.edge_count.keys()])
if(count>self.maxdim_intermediate):
self.maxdim_intermediate = count
# print(self.edge_count[count])
x = np.random.randint(len(self.edge_count[count]))
# print("count=",count)
# print(self.edge_count[count])
triangle_count = []
# for i,j in self.edge_count[count]:
for a in range(len(self.edge_count[count])):
i,j = self.edge_count[count][a]
neigh1 = self.tensors[i].neighbor
neigh2 = self.tensors[j].neighbor
idx_i_in_j=np.argwhere(neigh2==i)[0][0]
both = 0
for l in range(len(neigh2)):
if l != idx_i_in_j:
k=neigh2[l]
idx_i_in_k = self.tensors[k].find_neighbor(i)
if(idx_i_in_k > -1): # i already in k
both = both+1
triangle_count.append(both)
# print(triangle_count)
x = np.array(triangle_count).argmax()
# print(triangle_count[x])
return self.edge_count[count][x]
def count_add_nodes(self,nodes):
edges = []
for i in nodes:
edges = edges + [tuple(sorted([i,j])) for j in self.tensors[i].neighbor]
self.count_add_edges(set(edges))
def count_add_edges(self,edges):
""" Notice that two end nodes of each edge should sorted, and edges should be unique """
for i,j in edges:
count = self.dim_after_merge(i,j)
if count in self.edge_count.keys():
self.edge_count[count].append(sorted([i,j]))
else:
self.edge_count[count]=[sorted([i,j])]
def select_edge_init(self):
self.edge_count = {}
self.count_add_edges(set([tuple(sorted(a)) for a in self.G.edges()]))
def count_remove_nodes(self,nodes):
for j in nodes:
for i in self.tensors[j].neighbor:
count = self.dim_after_merge(i,j)
if(sorted([i,j]) in self.edge_count[count]):
self.edge_count[count].remove(sorted([i,j]))
def print_all_tensor_shape(self):
for i,t in self.tensors.items():
if(t.shape() != []):
print(i,t.shape(),t.neighbor)
def find_low_rank_all_edges(self):
if(self.verbose >= 1):
print("Finding low rank structures...");
error=0
for i in range(self.n):
if(len(self.tensors[i].neighbor) <=1 ):
continue
for idxj in range(len(self.tensors[i].neighbor)):
j = self.tensors[i].neighbor[idxj]
if(len(self.tensors[j].mps) <=1 ):
continue
if self.svdopt:
error = error + self.cut_bondim_opt(i,idxj)
else:
error = error + self.cut_bondim(i,idxj)
if(self.verbose >= 1):
print("done")
return error
def select_edge_sequentially(self):
edge = np.array(list(self.G.edges()))
sum_edge=edge[:,0]+edge[:,1]
#print(sum_edge)
index=np.argmin(sum_edge)
# i, j = pool[np.random.choice(np.where(count == count.max())[0])]
#print(edge)
#print(index)
i, j = edge[index]
return i, j
def contraction(self):
error = 0
self.psi = 1
self.lnZ = np.log(np.array([2]).astype(self.tensors[0].dtype)) * self.num_isolated
t_select=0
t_contract=0
t_svd=0
#self.find_low_rank_all_edges()
while self.G.number_of_edges() > 0:
t0 =time.time()
if(self.select == 0):
i,j = self.select_edge_min_dim()
elif(self.select == 1):
i,j = self.select_edge_min_dim_triangle()
elif(self.select ==2):
i,j =self.select_edge_sequentially()
else:
print("wrong choice for args.select")
sys.exit(10)
if(self.tensors[j].order() > self.tensors[i].order()):
i,j = j,i # this is to ensure that node i has larger degree than node j
print(i,j)
orderi = self.tensors[i].order()
orderj = self.tensors[j].order()
logdimi = self.tensors[i].logdim()
logdimj = self.tensors[j].logdim()
self.count_remove_nodes([i, j] + list(self.tensors[i].neighbor) + list(self.tensors[j].neighbor)) # take care of the count dictionary first because it depends on shape of tensors
t_select += time.time() - t0
neigh1 = self.tensors[i].neighbor
neigh2 = self.tensors[j].neighbor
idx_j_in_i = np.argwhere(neigh1 == j)[0][0]
idx_i_in_j = np.argwhere(neigh2 == i)[0][0]
if(self.reverse):
if(idx_j_in_i < len(self.tensors[i].neighbor)//2):
# print("idx_j ",idx_j_in_i)
print("inverse")
self.tensors[i].reverse()
neigh1 = self.tensors[i].neighbor
idx_j_in_i=np.argwhere(neigh1==j)[0][0]
# print("idx_j ",idx_j_in_i)
if(idx_i_in_j >= len(self.tensors[j].neighbor)//2):
# print("idx_i ",idx_i_in_j)
print("inverse")
self.tensors[j].reverse()
neigh2 = self.tensors[j].neighbor
idx_i_in_j=np.argwhere(neigh2==i)[0][0]
# print("idx_i ",idx_i_in_j)
t1=time.time()
self.tensors[i].delete_neighbor(j)
duplicate=[]
for l in range(len(neigh2)):
# arrange neighbors
if l != idx_i_in_j:
k=neigh2[l]
idx_k_in_i = self.tensors[i].find_neighbor(k)
self.tensors[i].add_neighbor(k)# append the new neighbor to the neighbor list
self.G.add_edge(i, k)
idx_i_in_k = self.tensors[k].find_neighbor(i)
idx_j_in_k = self.tensors[k].delete_neighbor(j)
self.tensors[k].add_neighbor(i, idx_j_in_k) # add i to k's neighbor list, replacing j
if(idx_i_in_k > -1): # i already in k
duplicate.append(k)
if(self.verbose >= 1):
sys.stdout.write("merging %d %d ..."%(k,i));sys.stdout.flush()
error = error + self.tensors[k].merge(i,cross=idx_i_in_k > idx_j_in_k)
if(self.verbose >= 1):
print("done")
old_shapei = self.tensors[i].shape()
old_shapej = self.tensors[j].shape()
if(self.verbose >= 1):
sys.stdout.write("eating %d %d ..."%(i,j));sys.stdout.flush()
lognorm,err,psi = self.tensors[i].eat(self.tensors[j],idx_j_in_i,idx_i_in_j)
if(self.verbose >= 1):
print("done")
error = error+err
self.psi = self.psi*psi
self.lnZ += lognorm
for k in duplicate:
if(self.verbose >= 1):
sys.stdout.write("merging %d %d ..."%(i,k));sys.stdout.flush()
self.tensors[i].merge(k,cross=False)
if(self.verbose >= 1):
print("done")
idx_k_in_i = self.tensors[i].find_neighbor(k)
if(self.verbose >= 1):
#sys.stdout.write("cutting %d %d ..."%(i,k));sys.stdout.flush()
print("cutting %d %d ..."%(i,k))
if self.svdopt:
if args.cut_bond:
error = error + self.cut_bondim_opt(i,idx_k_in_i)
else:
if self.tensors[i].mps[idx_k_in_i].shape[1] > self.Dmax and self.Dmax>0:
error = error + self.cut_bondim_opt(i,idx_k_in_i)
else:
if args.cut_bond:
error = error + self.cut_bondim_opt(i,idx_k_in_i)
else:
if self.tensors[i].mps[idx_k_in_i].shape[1] > self.Dmax and self.Dmax>0:
error = error + self.cut_bondim_opt(i,idx_k_in_i)
self.tensors[j].clear()
self.G.remove_node(j)
t_contract += time.time()-t1
t0=time.time()
if args.compress:
if(self.verbose >= 1):
sys.stdout.write("compressing...");sys.stdout.flush()
if self.svdopt:
self.tensors[i].compress_opt()
else:
self.tensors[i].compress()
if(self.verbose >= 1):
print("done")
"""
#The code below tries to find low-rank structures after compression. However in practice it can not find any low-rank structures.
if(self.verbose >= 1):
#sys.stdout.write("check low-rank again...");sys.stdout.flush()
print("check low-rank again...")
for idxj in range(len(self.tensors[i].neighbor)):
j = self.tensors[i].neighbor[idxj]
if(len(self.tensors[j].mps) <=1 ):
continue
if self.svdopt:
error = error + self.cut_bondim_opt(i,idxj)
else:
error = error + self.cut_bondim(i,idxj)
if(self.verbose >= 1):
print("done")
"""
edges=np.array(list(self.G.edges))
m_left=0
if(len(edges)>0):
edges = edges[:,:2]
m_left=len(np.unique(edges,axis=0))
# if(m_left>2 and self.Dmax>0):
# error = error + self.low_rank_approx_site(i)
t_svd += time.time()-t0
n_left=self.num_tensor_remain()
duplicate_str = " ".join([str(ii) for ii in duplicate])
if(self.verbose < 1):
if(m_left< 100 or (n_left % self.print_interval == 0)):
print("%d/%d"%(m_left,self.m),"%d/%d"%(n_left,len(self.tensors)),"err=%.3e"%np.abs(error),"lnZ=%.3e"%np.real(self.lnZ),"%d, %d -> %d"%(orderi,orderj,self.tensors[i].order()), "\t%.2f"%(time.time()-t1),"Sec.")
else:
print("%d/%d"%(m_left,self.m),"%d/%d"%(n_left,len(self.tensors)),"(%d,%d)"%(i,j),"err=%.3e"%np.abs(error),"lnZ=%.3e"%np.real(self.lnZ),"%d, %d -> %d [%s],"%(orderi,orderj,self.tensors[i].order(),duplicate_str),"%.1f %.1f %.1f"%(logdimi,logdimj,self.tensors[i].logdim()), "\t%.2f"%(time.time()-t1),"Sec.")
#print([str(i) for i in self.tensors[i].logdim()])
# print(self.tensors[i].logdim())
self.count_add_nodes([i]+list(self.tensors[i].neighbor))
lognorm,self.sign = self.lognorm()
self.lnZ = self.lnZ + lognorm
return self.lnZ,error,self.psi
def lognorm(self):
lognorm = np.array(0).astype(self.tensors[0].dtype)
for i in self.tensors.keys():
lognormi,sign = self.tensors[i].lognorm()
lognorm = lognorm + lognormi
return lognorm,sign
def low_rank_approx_site(self,i):
""" Try to do low-dimensional approximations to large bond fo site i"""
error = 0
if(self.tensors[i].shape() == []):
return 0
t=self.tensors[i]
try:
if(t.order()==0):
return 0
except:
print("error in low_rank_approximate(",i,")","tensor")
print(t.tensor)
sys.exit(2)
while max(self.tensors[i].shape()) > self.Dmax:
if self.svdopt:
error = error + self.cut_bondim_opt(i,np.array(self.tensors[i].shape()).argmax())
else:
error = error + self.cut_bondim(i,np.array(self.tensors[i].shape()).argmax())
return error
def cut_bondim(self,i,idx_j_in_i):
error = 0
j=self.tensors[i].neighbor[idx_j_in_i]
idx_i_in_j = self.tensors[j].find_neighbor(i)
if(self.verbose >=1):
sys.stdout.write(" %s,%s --->"%(str(list(self.tensors[i].mps[idx_j_in_i].shape)),str(list(self.tensors[j].mps[idx_i_in_j].shape))));
sys.stdout.flush()
da_l = self.tensors[i].mps[idx_j_in_i].shape[0]
da_r = self.tensors[i].mps[idx_j_in_i].shape[2]
d = self.tensors[i].mps[idx_j_in_i].shape[1]
db_l = self.tensors[j].mps[idx_i_in_j].shape[0]
db_r = self.tensors[j].mps[idx_i_in_j].shape[2]
mati = self.tensors[i].mps[idx_j_in_i].transpose([0,2,1]).reshape(-1,d)
matj = self.tensors[j].mps[idx_i_in_j].transpose([0,2,1]).reshape(-1,d)
merged_matrix = [email protected]
try:
[U,s,V] = svd(merged_matrix)
except:
print("SVD failed: shape of merged_matrix",merged_matrix.shape)
sys.exit(-1)
s_eff = s[s>self.cutoff]
if(len(s_eff) == 0):
s_eff = s[:1]
error += s[len(s_eff):].sum()
myd = min(len(s_eff),self.Dmax)
if(myd == 0):
print("Warning: encountered ZERO matrix in cut_bondim()")
myd = 1
mati=(U[:,0]*s[0])[:,None]
matj = ((s[0]*V[:,0].T).T)[:,None]
else:
error = error + s_eff[myd:].sum()
s_eff=s_eff[:myd]
s=np.diag(np.sqrt(s_eff))
U=U[:,:myd]
V=V[:,:myd]
mati=U@s
matj = ([email protected]).T
mati = mati.reshape(da_l,da_r,mati.shape[1]).transpose([0,2,1])
self.tensors[i].mps[idx_j_in_i] = mati
matj = matj.reshape(db_l,db_r,matj.shape[1]).transpose([0,2,1])
self.tensors[j].mps[idx_i_in_j] = matj
print(list(self.tensors[i].mps[idx_j_in_i].shape),list(self.tensors[j].mps[idx_i_in_j].shape));
return error
def cut_bondim_opt2(self,i,idx_j_in_i):
error = 0
j=self.tensors[i].neighbor[idx_j_in_i]
idx_i_in_j = self.tensors[j].find_neighbor(i)
self.tensors[i].cano_to(idx_j_in_i)
self.tensors[j].cano_to(idx_i_in_j)
# print("cano_i",self.tensors[i].cano,idx_j_in_i)
# print("cano_j",self.tensors[j].cano,idx_i_in_j)
if(self.verbose >=1):
sys.stdout.write(" %s,%s --->"%(str(list(self.tensors[i].mps[idx_j_in_i].shape)),str(list(self.tensors[j].mps[idx_i_in_j].shape))));
sys.stdout.flush()
da_l = self.tensors[i].mps[idx_j_in_i].shape[0]
da_r = self.tensors[i].mps[idx_j_in_i].shape[2]
d = self.tensors[i].mps[idx_j_in_i].shape[1]
db_l = self.tensors[j].mps[idx_i_in_j].shape[0]
db_r = self.tensors[j].mps[idx_i_in_j].shape[2]
mati = self.tensors[i].mps[idx_j_in_i].transpose([0,2,1]).reshape(da_l*da_r,d)
matj = self.tensors[j].mps[idx_i_in_j].transpose([0,2,1]).reshape(db_l*db_r,d)
flag = False
#if(mati.shape[0]*matj.shape[0] < mati.shape[1]*matj.shape[1]):
if(1==2):
merged_matrix = [email protected]
else:
flag=True
qi,ri = np.linalg.qr(mati)
qj,rj = np.linalg.qr(matj)
merged_matrix = [email protected]
[U,s,V] = svd(merged_matrix)
s_eff = s[s>self.cutoff]
if(len(s_eff) == 0):
s_eff = s[:1]
error = error + s[len(s_err):].sum()
myd = min(len(s_eff),self.Dmax)
if(myd == 0):
print("Warning: encountered ZERO matrix in cut_bondim()")
myd = 1
mati=(U[:,0]*s[0])[:,None]
matj = ((s[0]*V[:,0].T).T)[:,None]
else:
error = error + s_eff[myd:].sum()
s_eff=s_eff[:myd]
s=np.diag(np.sqrt(s_eff))
U=U[:,:myd]
V=V[:,:myd]
mati = U@s
matj = ([email protected]).T
if flag:
mati = qi @ mati
matj = qj @ matj
mati = mati.reshape(da_l,da_r,mati.shape[1]).transpose([0,2,1])
self.tensors[i].mps[idx_j_in_i] = mati
matj = matj.reshape(db_l,db_r,matj.shape[1]).transpose([0,2,1])
self.tensors[j].mps[idx_i_in_j] = matj
if(self.verbose >=1):
print(list(self.tensors[i].mps[idx_j_in_i].shape),list(self.tensors[j].mps[idx_i_in_j].shape));
return error
def cut_bondim_opt(self,i,idx_j_in_i):
error = 0
j=self.tensors[i].neighbor[idx_j_in_i]
idx_i_in_j = self.tensors[j].find_neighbor(i)
self.tensors[i].cano_to(idx_j_in_i)
self.tensors[j].cano_to(idx_i_in_j)
# print("cano_i",self.tensors[i].cano,idx_j_in_i)
# print("cano_j",self.tensors[j].cano,idx_i_in_j)
Dold = self.tensors[i].mps[idx_j_in_i].shape[1]
if(self.verbose >=1):
sys.stdout.write(" %s,%s ---> "%(str(list(self.tensors[i].mps[idx_j_in_i].shape)),str(list(self.tensors[j].mps[idx_i_in_j].shape))));
sys.stdout.flush()
da_l = self.tensors[i].mps[idx_j_in_i].shape[0]
da_r = self.tensors[i].mps[idx_j_in_i].shape[2]
d = self.tensors[i].mps[idx_j_in_i].shape[1]
db_l = self.tensors[j].mps[idx_i_in_j].shape[0]
db_r = self.tensors[j].mps[idx_i_in_j].shape[2]
mati = self.tensors[i].mps[idx_j_in_i].transpose([0,2,1]).reshape(da_l*da_r,d)
matj = self.tensors[j].mps[idx_i_in_j].transpose([0,2,1]).reshape(db_l*db_r,d)
flag = False
#if(mati.shape[0]*matj.shape[0] < mati.shape[1]*matj.shape[1]):
# if(1==2):
# merged_matrix = [email protected]
# else:
# flag=True
# qi,ri = np.linalg.qr(mati)
# qj,rj = np.linalg.qr(matj)
# merged_matrix = [email protected]
#
flag_left = False
if(mati.shape[0] > mati.shape[1]):
qi,ri = np.linalg.qr(mati)
flag_left = True
else:
ri = mati
flag_right = False
if(matj.shape[0] > matj.shape[1]):
qj,rj = np.linalg.qr(matj)
flag_right = True
else:
rj = matj
merged_matrix = [email protected]
[U,s,V] = svd(merged_matrix)
# s_str = str(["%.3f"%t for t in s])
s_bak = s
s_eff = s[s>self.cutoff]
if(len(s_eff) == 0):
s_eff = s[:1]
error = error + s[len(s_eff):].sum()
myd = min(len(s_eff),self.Dmax)
if(myd == 0):
print("Warning: encountered ZERO matrix in cut_bondim()")
myd = 1
mati=(U[:,0]*s[0])[:,None]
matj = ((s[0]*V[:,0].T).T)[:,None]
else:
error = error + s[myd:].sum()
s_eff=s_eff[:myd]
s=np.diag(np.sqrt(s_eff))
U=U[:,:myd]
V=V[:,:myd]
mati = U@s
matj = ([email protected]).T
# if flag:
# mati = qi @ mati
# matj = qj @ matj
if flag_left:
mati = qi @ mati
if flag_right:
matj = qj @ matj
mati = mati.reshape(da_l,da_r,mati.shape[1]).transpose([0,2,1])
self.tensors[i].mps[idx_j_in_i] = mati
matj = matj.reshape(db_l,db_r,matj.shape[1]).transpose([0,2,1])
self.tensors[j].mps[idx_i_in_j] = matj
if(self.verbose >=1):
if(self.tensors[i].mps[idx_j_in_i].shape[1] < Dold):
sys.stdout.write(str([list(self.tensors[i].mps[idx_j_in_i].shape),list(self.tensors[j].mps[idx_i_in_j].shape)]));
# sys.stdout.write(" %s"%s_str)
# print(s_bak)
print(" ")
else:
print(" ")
return error
def num_tensor_remain(self):
return np.sum(np.array([1 if len(self.tensors[i].mps)>0 else 0 for i in self.tensors.keys()]))
def resources_remain(self):
#return 2**(np.sum(np.array([self.tensors[i].logdim() for i in self.tensors.keys()]))-30)
return (np.sum(np.array([self.tensors[i].logdim() for i in self.tensors.keys()]))-30)