def eps_l_noop_inplace(x, A1, A2, out):
"""Implements the left epsilon map for a pre-exisiting output matrix.
The output must have shape (A1.shape[2], A2.shape[2]).
See eps_l_noop().
Parameters
----------
x : ndarray
The argument matrix.
A1: ndarray
The MPS ket tensor for the current site.
A2: ndarray
The MPS bra tensor for the current site.
out: ndarray
The output matrix (must have correct dimensions).
Returns
-------
res : ndarray
The resulting matrix.
"""
out.fill(0)
#Two extra temporaries required because scipy doesn't bother to provide full gemm functionality.
tmp_A1sh = np.empty((A1[0].shape[1], A1[0].shape[0]),
dtype=A1[0].dtype,
order='F')
tmp_xA2s = np.empty((x.shape[0], A2[0].shape[1]),
dtype=np.promote_types(x.dtype, A2[0].dtype))
out_s = np.empty_like(out, order='C')
for s in xrange(A1.shape[0]):
tmp_A1sh[:] = A1[s].T
np.conjugate(tmp_A1sh, out=tmp_A1sh)
tmp_xA2s = mm.dot_inplace(x, A2[s], tmp_xA2s)
out_s = np.dot(tmp_A1sh, tmp_xA2s,
out=out_s) #dot expects a C-ordered output array
out += out_s
return out
def eps_r_noop_inplace(x, A1, A2, out):
"""Implements the right epsilon map for a pre-exisiting output matrix.
The output must have shape (A1.shape[1], A2.shape[1]).
See eps_r_noop().
Parameters
----------
x : ndarray
The argument matrix.
A1: ndarray
The MPS ket tensor for the current site.
A2: ndarray
The MPS bra tensor for the current site.
out: ndarray
The output matrix (must have correct dimensions).
Returns
-------
res : ndarray
The resulting matrix.
"""
out.fill(0)
tmp_A1xs = np.empty((A1[0].shape[0], x.shape[1]),
dtype=np.promote_types(A1.dtype, x.dtype))
tmp_A2sh = np.empty((A2[0].shape[1], A2[0].shape[0]),
dtype=A2[0].dtype,
order='F')
out_s = np.empty_like(out, order='C')
for s in xrange(A1.shape[0]):
tmp_A1xs = mm.dot_inplace(A1[s], x, tmp_A1xs)
tmp_A2sh[:] = A2[s].T
np.conjugate(tmp_A2sh, out=tmp_A2sh)
out_s = np.dot(tmp_A1xs, tmp_A2sh, out=out_s)
out += out_s
return out
def eps_l_noop_inplace(x, A1, A2, out):
"""Implements the left epsilon map for a pre-exisiting output matrix.
The output must have shape (A1.shape[2], A2.shape[2]).
See eps_l_noop().
Parameters
----------
x : ndarray
The argument matrix.
A1: ndarray
The MPS ket tensor for the current site.
A2: ndarray
The MPS bra tensor for the current site.
out: ndarray
The output matrix (must have correct dimensions).
Returns
-------
res : ndarray
The resulting matrix.
"""
out.fill(0)
#Two extra temporaries required because scipy doesn't bother to provide full gemm functionality.
tmp_A1sh = np.empty((A1[0].shape[1], A1[0].shape[0]), dtype=A1[0].dtype, order='F')
tmp_xA2s = np.empty((x.shape[0], A2[0].shape[1]), dtype=np.promote_types(x.dtype, A2[0].dtype))
out_s = np.empty_like(out, order='C')
for s in xrange(A1.shape[0]):
tmp_A1sh[:] = A1[s].T
np.conjugate(tmp_A1sh, out=tmp_A1sh)
tmp_xA2s = mm.dot_inplace(x, A2[s], tmp_xA2s)
out_s = np.dot(tmp_A1sh, tmp_xA2s, out=out_s) #dot expects a C-ordered output array
out += out_s
return out
def eps_r_noop_inplace(x, A1, A2, out):
"""Implements the right epsilon map for a pre-exisiting output matrix.
The output must have shape (A1.shape[1], A2.shape[1]).
See eps_r_noop().
Parameters
----------
x : ndarray
The argument matrix.
A1: ndarray
The MPS ket tensor for the current site.
A2: ndarray
The MPS bra tensor for the current site.
out: ndarray
The output matrix (must have correct dimensions).
Returns
-------
res : ndarray
The resulting matrix.
"""
out.fill(0)
tmp_A1xs = np.empty((A1[0].shape[0], x.shape[1]), dtype=np.promote_types(A1.dtype, x.dtype))
tmp_A2sh = np.empty((A2[0].shape[1], A2[0].shape[0]), dtype=A2[0].dtype, order='F')
out_s = np.empty_like(out, order='C')
for s in xrange(A1.shape[0]):
tmp_A1xs = mm.dot_inplace(A1[s], x, tmp_A1xs)
tmp_A2sh[:] = A2[s].T
np.conjugate(tmp_A2sh, out=tmp_A2sh)
out_s = np.dot(tmp_A1xs, tmp_A2sh, out=out_s)
out += out_s
return out
def calc_BHB(self, x, p, tdvp, tdvp2, prereq,
M_prev=None, y_pi_prev=None, pinv_solver=None):
if pinv_solver is None:
pinv_solver = las.gmres
if self.ham_sites == 3:
return
else:
V_, AhlAo1, A_o2c, Ao1, Ao1c, A_Vr_ho2, A_A_o12c, rhs10, _ham_tp = prereq
A = tdvp.A[0]
A_ = tdvp2.A[0]
l = tdvp.l[0]
r_ = tdvp2.r[0]
l_sqrt = tdvp.l_sqrt[0]
l_sqrt_i = tdvp.l_sqrt_i[0]
r__sqrt = tdvp2.r_sqrt[0]
r__sqrt_i = tdvp2.r_sqrt_i[0]
K__r = tdvp2.K[0]
K_l = tdvp.K_left[0]
pseudo = tdvp2 is tdvp
B = tdvp2.get_B_from_x(x, tdvp2.Vsh[0], l_sqrt_i, r__sqrt_i)
#Skip zeros due to rank-deficiency
if la.norm(B) == 0:
return sp.zeros_like(x), M_prev, y_pi_prev
if self.sanity_checks:
tst = tm.eps_r_noop(r_, B, A_)
if not la.norm(tst) > self.sanity_tol:
log.warning("Sanity check failed: Gauge-fixing violation! "
+ str(la.norm(tst)))
if self.sanity_checks:
B2 = np.zeros_like(B)
for s in xrange(self.q):
B2[s] = l_sqrt_i.dot(x.dot(m.mmul(V_[s], r__sqrt_i)))
if la.norm(B - B2) / la.norm(B) > self.sanity_tol:
log.warning("Sanity Fail in calc_BHB! Bad Vri!")
y = tm.eps_l_noop(l, B, A)
# if pseudo:
# y = y - m.adot(r_, y) * l #should just = y due to gauge-fixing
M = pinv_1mE(y, [A_], [A], l, r_, p=-p, left=True, pseudo=pseudo,
out=M_prev, tol=self.pinv_tol, solver=pinv_solver,
use_CUDA=self.pinv_CUDA, CUDA_use_batch=self.pinv_CUDA_batch,
sanity_checks=self.sanity_checks, sc_data='M')
#print m.adot(r, M)
if self.sanity_checks:
y2 = M - sp.exp(+1.j * p) * tm.eps_l_noop(M, A_, A)
norm = la.norm(y.ravel())
if norm == 0:
norm = 1
tst = la.norm(y - y2) / norm
if tst > self.sanity_tol:
log.warning("Sanity Fail in calc_BHB! Bad M. Off by: %g", tst)
# if pseudo:
# M = M - l * m.adot(r_, M)
Mh = M.conj().T.copy(order='C')
res_ls = 0
res_lsi = 0
exp = sp.exp
if self.ham_sites == 3:
pass
else:
Bo1 = get_Aop(B, _ham_tp, 2, conj=False)
tmp = sp.empty((B.shape[1], V_.shape[1]), dtype=A.dtype, order='C')
tmp2 = sp.empty((A_.shape[1], A_o2c[0].shape[1]), dtype=A.dtype, order='C')
tmp3 = sp.empty_like(tmp2, order='C')
for al in xrange(len(Bo1)):
tmp3 = m.dot_inplace(tm.eps_r_noop_inplace(r_, A_, A_o2c[al], tmp2), r__sqrt_i, tmp3)
res_ls += tm.eps_r_noop_inplace(tmp3, Bo1[al], V_, tmp) #1
tmp3 = m.dot_inplace(tm.eps_r_noop_inplace(r_, B, A_o2c[al], tmp2), r__sqrt_i, tmp3)
tmp = tm.eps_r_noop_inplace(tmp3, Ao1[al], V_, tmp) #3
tmp *= exp(+1.j * p)
res_ls += tmp
del(tmp)
del(tmp2)
del(tmp3)
res_lsi += sp.exp(-1.j * p) * Mh.dot(rhs10) #10
if self.ham_sites == 3:
pass
else:
Bo2 = get_Aop(B, _ham_tp, 3, conj=False)
for al in xrange(len(AhlAo1)):
res_lsi += AhlAo1[al].dot(tm.eps_r_noop(r__sqrt, Bo2[al], V_)) #2
res_lsi += exp(-1.j * p) * tm.eps_l_noop(l, Ao1c[al], B).dot(A_Vr_ho2[al]) #4
res_lsi += exp(-2.j * p) * tm.eps_l_noop(Mh, Ao1c[al], A_).dot(A_Vr_ho2[al]) #12
K__rri = m.mmul(K__r, r__sqrt_i)
res_ls += tm.eps_r_noop(K__rri, B, V_) #5
res_lsi += K_l.dot(tm.eps_r_noop(r__sqrt, B, V_)) #6
res_lsi += sp.exp(-1.j * p) * Mh.dot(tm.eps_r_noop(K__rri, A_, V_)) #8
y1 = sp.exp(+1.j * p) * tm.eps_r_noop(K__r, B, A_) #7
if self.ham_sites == 3:
pass
elif self.ham_sites == 2:
tmp = 0
for al in xrange(len(A_A_o12c)):
tmp += sp.exp(+1.j * p) * tm.eps_r_noop(tm.eps_r_noop(r_, A_, A_A_o12c[al][1]), B, A_A_o12c[al][0]) #9
tmp += sp.exp(+2.j * p) * tm.eps_r_noop(tm.eps_r_noop(r_, B, A_A_o12c[al][1]), A, A_A_o12c[al][0]) #11
y = y1 + tmp #7, 9, 11
del(tmp)
if pseudo:
y = y - m.adot(l, y) * r_
y_pi = pinv_1mE(y, [A], [A_], l, r_, p=p, left=False,
pseudo=pseudo, out=y_pi_prev, tol=self.pinv_tol,
solver=pinv_solver, use_CUDA=self.pinv_CUDA,
CUDA_use_batch=self.pinv_CUDA_batch,
sanity_checks=self.sanity_checks, sc_data='y_pi')
#print m.adot(l, y_pi)
if self.sanity_checks:
z = y_pi - sp.exp(+1.j * p) * tm.eps_r_noop(y_pi, A, A_)
tst = la.norm((y - z).ravel()) / la.norm(y.ravel())
if tst > self.sanity_tol:
log.warning("Sanity Fail in calc_BHB! Bad x_pi. Off by: %g", tst)
res_ls += tm.eps_r_noop(m.mmul(y_pi, r__sqrt_i), A, V_)
res = l_sqrt.dot(res_ls)
res += l_sqrt_i.dot(res_lsi)
if self.sanity_checks:
expval = m.adot(x, res) / m.adot(x, x)
#print "expval = " + str(expval)
if expval < -self.sanity_tol:
log.warning("Sanity Fail in calc_BHB! H is not pos. semi-definite (%s)", expval)
if abs(expval.imag) > self.sanity_tol:
log.warning("Sanity Fail in calc_BHB! H is not Hermitian (%s)", expval)
return res, M, y_pi
def calc_BHB(self,
x,
p,
tdvp,
tdvp2,
prereq,
M_prev=None,
y_pi_prev=None,
pinv_solver=None):
if pinv_solver is None:
pinv_solver = las.gmres
if self.ham_sites == 3:
return
else:
V_, AhlAo1, A_o2c, Ao1, Ao1c, A_Vr_ho2, A_A_o12c, rhs10, _ham_tp = prereq
A = tdvp.A[0]
A_ = tdvp2.A[0]
l = tdvp.l[0]
r_ = tdvp2.r[0]
l_sqrt = tdvp.l_sqrt[0]
l_sqrt_i = tdvp.l_sqrt_i[0]
r__sqrt = tdvp2.r_sqrt[0]
r__sqrt_i = tdvp2.r_sqrt_i[0]
K__r = tdvp2.K[0]
K_l = tdvp.K_left[0]
pseudo = tdvp2 is tdvp
B = tdvp2.get_B_from_x(x, tdvp2.Vsh[0], l_sqrt_i, r__sqrt_i)
#Skip zeros due to rank-deficiency
if la.norm(B) == 0:
return sp.zeros_like(x), M_prev, y_pi_prev
if self.sanity_checks:
tst = tm.eps_r_noop(r_, B, A_)
if not la.norm(tst) > self.sanity_tol:
log.warning("Sanity check failed: Gauge-fixing violation! " +
str(la.norm(tst)))
if self.sanity_checks:
B2 = np.zeros_like(B)
for s in xrange(self.q):
B2[s] = l_sqrt_i.dot(x.dot(m.mmul(V_[s], r__sqrt_i)))
if la.norm(B - B2) / la.norm(B) > self.sanity_tol:
log.warning("Sanity Fail in calc_BHB! Bad Vri!")
y = tm.eps_l_noop(l, B, A)
# if pseudo:
# y = y - m.adot(r_, y) * l #should just = y due to gauge-fixing
M = pinv_1mE(y, [A_], [A],
l,
r_,
p=-p,
left=True,
pseudo=pseudo,
out=M_prev,
tol=self.pinv_tol,
solver=pinv_solver,
use_CUDA=self.pinv_CUDA,
CUDA_use_batch=self.pinv_CUDA_batch,
sanity_checks=self.sanity_checks,
sc_data='M')
#print m.adot(r, M)
if self.sanity_checks:
y2 = M - sp.exp(+1.j * p) * tm.eps_l_noop(M, A_, A)
norm = la.norm(y.ravel())
if norm == 0:
norm = 1
tst = la.norm(y - y2) / norm
if tst > self.sanity_tol:
log.warning("Sanity Fail in calc_BHB! Bad M. Off by: %g", tst)
# if pseudo:
# M = M - l * m.adot(r_, M)
Mh = M.conj().T.copy(order='C')
res_ls = 0
res_lsi = 0
exp = sp.exp
if self.ham_sites == 3:
pass
else:
Bo1 = get_Aop(B, _ham_tp, 2, conj=False)
tmp = sp.empty((B.shape[1], V_.shape[1]), dtype=A.dtype, order='C')
tmp2 = sp.empty((A_.shape[1], A_o2c[0].shape[1]),
dtype=A.dtype,
order='C')
tmp3 = sp.empty_like(tmp2, order='C')
for al in xrange(len(Bo1)):
tmp3 = m.dot_inplace(
tm.eps_r_noop_inplace(r_, A_, A_o2c[al], tmp2), r__sqrt_i,
tmp3)
res_ls += tm.eps_r_noop_inplace(tmp3, Bo1[al], V_, tmp) #1
tmp3 = m.dot_inplace(
tm.eps_r_noop_inplace(r_, B, A_o2c[al], tmp2), r__sqrt_i,
tmp3)
tmp = tm.eps_r_noop_inplace(tmp3, Ao1[al], V_, tmp) #3
tmp *= exp(+1.j * p)
res_ls += tmp
del (tmp)
del (tmp2)
del (tmp3)
res_lsi += sp.exp(-1.j * p) * Mh.dot(rhs10) #10
if self.ham_sites == 3:
pass
else:
Bo2 = get_Aop(B, _ham_tp, 3, conj=False)
for al in xrange(len(AhlAo1)):
res_lsi += AhlAo1[al].dot(tm.eps_r_noop(r__sqrt, Bo2[al],
V_)) #2
res_lsi += exp(-1.j * p) * tm.eps_l_noop(l, Ao1c[al], B).dot(
A_Vr_ho2[al]) #4
res_lsi += exp(-2.j * p) * tm.eps_l_noop(Mh, Ao1c[al], A_).dot(
A_Vr_ho2[al]) #12
K__rri = m.mmul(K__r, r__sqrt_i)
res_ls += tm.eps_r_noop(K__rri, B, V_) #5
res_lsi += K_l.dot(tm.eps_r_noop(r__sqrt, B, V_)) #6
res_lsi += sp.exp(-1.j * p) * Mh.dot(tm.eps_r_noop(K__rri, A_, V_)) #8
y1 = sp.exp(+1.j * p) * tm.eps_r_noop(K__r, B, A_) #7
if self.ham_sites == 3:
pass
elif self.ham_sites == 2:
tmp = 0
for al in xrange(len(A_A_o12c)):
tmp += sp.exp(+1.j * p) * tm.eps_r_noop(
tm.eps_r_noop(r_, A_, A_A_o12c[al][1]), B,
A_A_o12c[al][0]) #9
tmp += sp.exp(+2.j * p) * tm.eps_r_noop(
tm.eps_r_noop(r_, B, A_A_o12c[al][1]), A,
A_A_o12c[al][0]) #11
y = y1 + tmp #7, 9, 11
del (tmp)
if pseudo:
y = y - m.adot(l, y) * r_
y_pi = pinv_1mE(y, [A], [A_],
l,
r_,
p=p,
left=False,
pseudo=pseudo,
out=y_pi_prev,
tol=self.pinv_tol,
solver=pinv_solver,
use_CUDA=self.pinv_CUDA,
CUDA_use_batch=self.pinv_CUDA_batch,
sanity_checks=self.sanity_checks,
sc_data='y_pi')
#print m.adot(l, y_pi)
if self.sanity_checks:
z = y_pi - sp.exp(+1.j * p) * tm.eps_r_noop(y_pi, A, A_)
tst = la.norm((y - z).ravel()) / la.norm(y.ravel())
if tst > self.sanity_tol:
log.warning("Sanity Fail in calc_BHB! Bad x_pi. Off by: %g",
tst)
res_ls += tm.eps_r_noop(m.mmul(y_pi, r__sqrt_i), A, V_)
res = l_sqrt.dot(res_ls)
res += l_sqrt_i.dot(res_lsi)
if self.sanity_checks:
expval = m.adot(x, res) / m.adot(x, x)
#print "expval = " + str(expval)
if expval < -self.sanity_tol:
log.warning(
"Sanity Fail in calc_BHB! H is not pos. semi-definite (%s)",
expval)
if abs(expval.imag) > self.sanity_tol:
log.warning("Sanity Fail in calc_BHB! H is not Hermitian (%s)",
expval)
return res, M, y_pi