def cano_to(self, idx):
"""
move canonical position to i
"""
if (idx == -1):
idx = len(self.mps) - 1
if (self.cano == idx): # there is nothing to do
return
if (self.cano < idx):
for i in range(self.cano, idx):
dl = self.mps[i].shape[0]
d = self.mps[i].shape[1]
#Q,R = torch.qr(self.mps[i].reshape(dl * d,-1))
#U,s,V = torch.svd(self.mps[i].reshape(dl * d,-1))
U, s, V = svd(self.mps[i].reshape(dl * d, -1))
#Q=U
#R=torch.diag(s)@V.t()
seff = s[s > self.cutoff]
myd = seff.shape[0]
if (myd == 0):
myd = U.shape[1]
else:
s = seff
Q = U[:, :myd]
R = np.diag(s) @ (V[:, :myd]).T
self.mps[i] = Q.reshape(dl, d, -1)
self.mps[i + 1] = np.einsum("ij,jab->iab", R, self.mps[i + 1])
self.cano = i + 1
else:
for i in range(self.cano, idx, -1):
dr = self.mps[i].shape[2]
d = self.mps[i].shape[1]
#Q,R = torch.qr(self.mps[i].reshape(-1,d*dr).t())
#U,s,V = torch.svd(self.mps[i].reshape(-1,d*dr).t())
U, s, V = svd(self.mps[i].reshape(-1, d * dr).T)
#Q=U
#R=torch.diag(s)@V.t()
seff = s[s > self.cutoff]
myd = seff.shape[0]
if (myd == 0):
myd = U.shape[1]
else:
s = seff
Q = U[:, :myd]
R = np.diag(s) @ (V[:, :myd].T)
self.mps[i] = Q.T.reshape(-1, d, dr)
self.mps[i - 1] = np.einsum("abc,ci->abi", self.mps[i - 1],
R.T)
self.cano = i - 1
return 0
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 = mati @ matj.T
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 = (s @ V.T).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 compress(self):
"""
Compress the whole mps.
First, do left canonicalization to move self.cano to -1.
Second, do two-site merging-splitting, for moving self.cano back to 0.
"""
error = 0
if len(self.mps) == 0:
return error
self.left_canonical() # now self.cano is at the bottom (right)
for j in range(len(self.mps) - 1, 0, -1):
i = j - 1
tl = self.mps[i]
tr = self.mps[j]
d0 = tl.shape[0]
d1 = tl.shape[1]
d2 = tr.shape[1]
d3 = tr.shape[2] # notice the difference to self.swap()
mat = np.einsum("ijk,kab->ijab", tl, tr).reshape(
d0 * d1, d2 * d3) # notice the difference to self. swap()
[U, s, V] = svd(mat)
s_eff = s[s > self.cutoff]
myd = min(len(s_eff), self.chi)
if (myd == 0):
print(
"Warning in swap(), probably a zero matrix is encountered !!! myd=",
myd)
sys.exit(-8)
s_eff = s_eff[:myd]
error = error + s[myd:].sum()
U = U[:, :myd]
V = V[:, :myd]
s = np.diag(s_eff)
U = U @ s
self.mps[i] = U.reshape(d0, d1, myd)
self.mps[j] = V.T.reshape(myd, d2, d3)
self.cano = 0
def raw2mps(self, tensor):
if (len(tensor.shape) == 0): # scalar, a isolated node
return []
shape = [1] + list(tensor.shape) + [1]
if (len(tensor.shape) == 1): # degree 1, leaf
return [tensor.reshape(shape)]
order = len(tensor.shape)
tensor = tensor.reshape(1, -1)
mps = []
for i in range(order - 1):
dleft = tensor.shape[0]
tensor = tensor.reshape(dleft * shape[i + 1], -1)
[U, s, V] = svd(tensor)
s_eff = s[s > self.cutoff]
myd = min(len(s_eff), self.chi)
s_eff = s_eff[:myd]
U = U[:, :myd]
V = V[:, :myd]
s = np.diag(s_eff)
mps.append(U.reshape(dleft, shape[i + 1], myd))
tensor = s @ V.T
mps.append(tensor.reshape(myd, shape[order], 1))
self.cano = order - 1 # left canonical
return mps
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 = ri @ rj.T
[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 = (s @ V.T).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 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 = mati @ matj.T
else:
flag = True
qi, ri = np.linalg.qr(mati)
qj, rj = np.linalg.qr(matj)
merged_matrix = ri @ rj.T
[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 = (s @ V.T).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 swap(self, i, j):
"""
swap index i and index j in mps, i and j must be consecutive indices
Assuming that canonical form is maintained.
Default direction is i \to j, that is the canonical position will be j after swap
The canonicalization is maintained.
"""
error = 0
# sys.stdout.write(" swap %d %d cano=%d "%(i,j,self.cano));sys.stdout.flush()
if (j < 0 or j > len(self.mps)):
return
# print("in swap(), move cano")
if (self.cano != i and self.cano != j):
self.cano_to(i if abs(self.cano - i) < abs(self.cano - j) else j)
if (abs(i - j) != 1):
print(
"swap(): i and j must be consecutive indices, there must be something wrong"
)
sys.exit(3)
if (i < j):
tl = self.mps[i]
tr = self.mps[j]
else:
tl = self.mps[j]
tr = self.mps[i]
d0 = tl.shape[0]
d1 = tr.shape[1]
d2 = tl.shape[1]
d3 = tr.shape[2]
mat = np.einsum("ijk,kab->iajb", tl, tr).reshape(d0 * d1,
d2 * d3) # swaped
if (self.swapopt and ((mat.shape[0] > 7000 and mat.shape[1] > 7000) or
(mat.shape[0] > 20000 or mat.shape[1] > 20000))):
[U, s, V] = rsvd(mat, self.chi, 10, 10)
else:
[U, s, V] = svd(mat)
s_eff = s[s > self.cutoff]
if (len(s_eff) == 0):
s_eff = s[:1]
myd = min(len(s_eff), self.chi)
if (myd == 0):
print(
"Warning in swap(), probably a zero matrix is encountered !!! myd=",
myd)
sys.exit(-7)
s_eff = s_eff[:myd]
error = error + s[myd:].sum()
U = U[:, :myd]
V = V[:, :myd]
s = np.diag(s_eff)
if (i < j): #going right
V = s @ V.T
self.mps[i] = U.reshape(d0, d1, myd)
self.mps[j] = V.reshape(myd, d2, d3)
else: # going left
U = U @ s
self.mps[j] = U.reshape(d0, d1, myd)
self.mps[i] = V.T.reshape(myd, d2, d3)
self.cano = j
return error
def compress_opt(self):
"""
Compress the whole mps.
First, do left canonicalization to move self.cano to -1.
Second, do two-site merging-splitting, for moving self.cano back to 0.
Do qr before SVD
"""
error = 0
if len(self.mps) == 0:
return error
self.left_canonical() # now self.cano is at the bottom (right)
for j in range(len(self.mps) - 1, 0, -1):
i = j - 1
tl = self.mps[i]
tr = self.mps[j]
d0 = tl.shape[0]
d1 = tl.shape[1]
d2 = tr.shape[1]
d3 = tr.shape[2] # notice the difference to self.swap()
dd = tl.shape[2]
assert (dd == tr.shape[0])
# mat = torch.einsum("ijk,kab->ijab",tl,tr).reshape(d0*d1,d2*d3) # notice the difference to self. swap()
matl = tl.reshape(d0 * d1, dd)
matr = tr.reshape(dd, d2 * d3)
# flag=False
#if(matl.shape[0]*matr.shape[1] > dd*dd):
# if(1==1):
# flag=True
# Ql,Rl = np.linalg.qr(matl)
# Qr,Rr = np.linalg.qr(matr.T)
# mat = [email protected]
# else:
# mat = matl@matr
flag_left = False
flag_right = False
if (matl.shape[0] > matl.shape[1]):
flag_left = True
Ql, Rl = np.linalg.qr(matl)
else:
Rl = matl
if (matr.shape[0] < matr.shape[1]):
flag_right = True
Qr, Rr = np.linalg.qr(matr.T)
else:
Rr = matr.T
mat = Rl @ Rr.T
[U, s, V] = svd(mat)
s_eff = s[s > self.cutoff]
if (len(s_eff) == 0):
s_eff = s[:1]
myd = min(len(s_eff), self.chi)
if (myd == 0):
print(
"Warning in swap(), probably a zero matrix is encountered !!! myd=",
myd)
sys.exit(-8)
s_eff = s_eff[:myd]
error = error + s[myd:].sum()
U = U[:, :myd]
V = V[:, :myd]
s = np.diag(s_eff)
U = U @ s
# if flag:
# U = Ql @ U
# V = Qr @ V
if flag_left:
U = Ql @ U
if flag_right:
V = Qr @ V
self.mps[i] = U.reshape(d0, d1, myd)
self.mps[j] = V.T.reshape(myd, d2, d3)
# print("correct after swap:, error=",self.check_mps())
self.cano = 0