def calc_BHB_prereq(self, tdvp, tdvp2):
"""Calculates prerequisites for the application of the effective Hamiltonian in terms of tangent vectors.
This is called (indirectly) by the self.excite.. functions.
Parameters
----------
tdvp2: EvoMPS_TDVP_Uniform
Second state (may be the same, or another ground state).
Returns
-------
A lot of stuff.
"""
l = tdvp.l[0]
r_ = tdvp2.r[0]
r__sqrt = tdvp2.r_sqrt[0]
r__sqrt_i = tdvp2.r_sqrt_i[0]
A = tdvp.A[0]
A_ = tdvp2.A[0]
AA = tdvp.AA[0]
AA_ = tdvp2.AA[0]
AAA_ = tdvp2.AAA[0]
eyed = np.eye(self.q**self.ham_sites)
eyed = eyed.reshape(tuple([self.q] * self.ham_sites * 2))
ham_ = self.ham - tdvp.h_expect.real * eyed
V_ = sp.transpose(tdvp2.Vsh[0], axes=(0, 2, 1)).conj().copy(order='C')
Vri_ = sp.zeros_like(V_)
try:
for s in xrange(self.q):
Vri_[s] = r__sqrt_i.dot_left(V_[s])
except AttributeError:
for s in xrange(self.q):
Vri_[s] = V_[s].dot(r__sqrt_i)
Vr_ = sp.zeros_like(V_)
try:
for s in xrange(self.q):
Vr_[s] = r__sqrt.dot_left(V_[s])
except AttributeError:
for s in xrange(self.q):
Vr_[s] = V_[s].dot(r__sqrt)
Vri_A_ = tm.calc_AA(Vri_, A_)
if self.ham_sites == 2:
_C_AhlA = np.empty((self.q, self.q, A.shape[2], A.shape[2]), dtype=tdvp.typ)
for u in xrange(self.q):
for s in xrange(self.q):
_C_AhlA[u, s] = A[u].conj().T.dot(l.dot(A[s]))
C_AhlA = sp.tensordot(ham_, _C_AhlA, ((0, 2), (0, 1)))
C_AhlA = sp.transpose(C_AhlA, axes=(1, 0, 2, 3)).copy(order='C')
_C_A_Vrh_ = tm.calc_AA(A_, sp.transpose(Vr_, axes=(0, 2, 1)).conj())
C_A_Vrh_ = sp.tensordot(ham_, _C_A_Vrh_, ((3, 1), (0, 1)))
C_A_Vrh_ = sp.transpose(C_A_Vrh_, axes=(1, 0, 2, 3)).copy(order='C')
C_Vri_A_conj = tm.calc_C_conj_mat_op_AA(ham_, Vri_A_).copy(order='C')
C_ = tm.calc_C_mat_op_AA(ham_, AA_).copy(order='C')
C_conj = tm.calc_C_conj_mat_op_AA(ham_, AA_).copy(order='C')
rhs10 = tm.eps_r_op_2s_AA12_C34(r_, AA_, C_Vri_A_conj)
return C_, C_conj, V_, Vr_, Vri_, C_Vri_A_conj, C_AhlA, C_A_Vrh_, rhs10
elif self.ham_sites == 3:
C_Vri_AA_ = np.empty((self.q, self.q, self.q, Vri_.shape[1], A_.shape[2]), dtype=tdvp.typ)
for s in xrange(self.q):
for t in xrange(self.q):
for u in xrange(self.q):
C_Vri_AA_[s, t, u] = Vri_[s].dot(AA_[t, u])
C_Vri_AA_ = sp.tensordot(ham_, C_Vri_AA_, ((3, 4, 5), (0, 1, 2))).copy(order='C')
C_AAA_r_Ah_Vrih = np.empty((self.q, self.q, self.q, self.q, self.q, #FIXME: could be too memory-intensive
A_.shape[1], Vri_.shape[1]),
dtype=tdvp.typ)
for s in xrange(self.q):
for t in xrange(self.q):
for u in xrange(self.q):
for k in xrange(self.q):
for j in xrange(self.q):
C_AAA_r_Ah_Vrih[s, t, u, k, j] = AAA_[s, t, u].dot(r_.dot(A_[k].conj().T)).dot(Vri_[j].conj().T)
C_AAA_r_Ah_Vrih = sp.tensordot(ham_, C_AAA_r_Ah_Vrih, ((3, 4, 5, 2, 1), (0, 1, 2, 3, 4))).copy(order='C')
C_AhAhlAA = np.empty((self.q, self.q, self.q, self.q,
A_.shape[2], A.shape[2]), dtype=tdvp.typ)
for t in xrange(self.q):
for j in xrange(self.q):
for i in xrange(self.q):
for s in xrange(self.q):
C_AhAhlAA[j, t, i, s] = AA[i, j].conj().T.dot(l.dot(AA[s, t]))
C_AhAhlAA = sp.tensordot(ham_, C_AhAhlAA, ((4, 1, 0, 3), (1, 0, 2, 3))).copy(order='C')
C_AA_r_Ah_Vrih_ = np.empty((self.q, self.q, self.q, self.q,
A_.shape[1], Vri_.shape[1]), dtype=tdvp.typ)
for t in xrange(self.q):
for u in xrange(self.q):
for k in xrange(self.q):
for j in xrange(self.q):
C_AA_r_Ah_Vrih_[u, t, k, j] = AA_[t, u].dot(r_.dot(A_[k].conj().T)).dot(Vri_[j].conj().T)
C_AA_r_Ah_Vrih_ = sp.tensordot(ham_, C_AA_r_Ah_Vrih_, ((4, 5, 2, 1), (1, 0, 2, 3))).copy(order='C')
C_AAA_Vrh_ = np.empty((self.q, self.q, self.q, self.q,
A_.shape[1], Vri_.shape[1]), dtype=tdvp.typ)
for s in xrange(self.q):
for t in xrange(self.q):
for u in xrange(self.q):
for k in xrange(self.q):
C_AAA_Vrh_[s, t, u, k] = AAA_[s, t, u].dot(Vr_[k].conj().T)
C_AAA_Vrh_ = sp.tensordot(ham_, C_AAA_Vrh_, ((3, 4, 5, 2), (0, 1, 2, 3))).copy(order='C')
C_Vri_A_r_Ah_ = np.empty((self.q, self.q, self.q,
A_.shape[2], Vri_.shape[1]), dtype=tdvp.typ)
for u in xrange(self.q):
for k in xrange(self.q):
for j in xrange(self.q):
C_Vri_A_r_Ah_[u, k, j] = Vri_[j].dot(A_[k]).dot(r_.dot(A_[u].conj().T))
C_Vri_A_r_Ah_ = sp.tensordot(ham_.conj(), C_Vri_A_r_Ah_, ((5, 2, 1), (0, 1, 2))).copy(order='C')
C_AhlAA = np.empty((self.q, self.q, self.q,
A_.shape[2], A.shape[2]), dtype=tdvp.typ)
for j in xrange(self.q):
for i in xrange(self.q):
for s in xrange(self.q):
C_AhlAA[j, i, s] = A[s].conj().T.dot(l.dot(AA[i, j]))
C_AhlAA_conj = sp.tensordot(ham_.conj(), C_AhlAA, ((1, 0, 3), (0, 1, 2))).copy(order='C')
C_AhlAA = sp.tensordot(ham_, C_AhlAA, ((4, 3, 0), (0, 1, 2)))
C_AhlAA = sp.transpose(C_AhlAA, axes=(2, 0, 1, 3, 4)).copy(order='C')
C_AA_Vrh = np.empty((self.q, self.q, self.q,
A_.shape[2], Vr_.shape[1]), dtype=tdvp.typ)
for t in xrange(self.q):
for u in xrange(self.q):
for k in xrange(self.q):
C_AA_Vrh[k, u, t] = AA_[t, u].dot(Vr_[k].conj().T)
C_AA_Vrh = sp.tensordot(ham_, C_AA_Vrh, ((4, 5, 2), (2, 1, 0))).copy(order='C')
C_ = sp.tensordot(ham_, AAA_, ((3, 4, 5), (0, 1, 2))).copy(order='C')
rhs10 = tm.eps_r_op_3s_C123_AAA456(r_, AAA_, C_Vri_AA_)
#NOTE: These C's are good as C12 or C34, but only because h is Hermitian!
#TODO: Make this consistent with the updated 2-site case above.
return V_, Vr_, Vri_, Vri_A_, C_, C_Vri_AA_, C_AAA_r_Ah_Vrih, C_AhAhlAA, C_AA_r_Ah_Vrih_, C_AAA_Vrh_, C_Vri_A_r_Ah_, C_AhlAA, C_AhlAA_conj, C_AA_Vrh, rhs10,
def calc_BHB_prereq(self, tdvp, tdvp2):
"""Calculates prerequisites for the application of the effective Hamiltonian in terms of tangent vectors.
This is called (indirectly) by the self.excite.. functions.
Parameters
----------
tdvp2: EvoMPS_TDVP_Uniform
Second state (may be the same, or another ground state).
Returns
-------
A lot of stuff.
"""
l = tdvp.l[0]
r_ = tdvp2.r[0]
r__sqrt = tdvp2.r_sqrt[0]
r__sqrt_i = tdvp2.r_sqrt_i[0]
A = tdvp.A[0]
A_ = tdvp2.A[0]
AA = tdvp.AA[0]
AA_ = tdvp2.AA[0]
AAA_ = tdvp2.AAA[0]
eyed = np.eye(self.q**self.ham_sites)
eyed = eyed.reshape(tuple([self.q] * self.ham_sites * 2))
ham_ = self.ham - tdvp.h_expect.real * eyed
V_ = sp.transpose(tdvp2.Vsh[0], axes=(0, 2, 1)).conj().copy(order='C')
Vri_ = sp.zeros_like(V_)
try:
for s in xrange(self.q):
Vri_[s] = r__sqrt_i.dot_left(V_[s])
except AttributeError:
for s in xrange(self.q):
Vri_[s] = V_[s].dot(r__sqrt_i)
Vr_ = sp.zeros_like(V_)
try:
for s in xrange(self.q):
Vr_[s] = r__sqrt.dot_left(V_[s])
except AttributeError:
for s in xrange(self.q):
Vr_[s] = V_[s].dot(r__sqrt)
Vri_A_ = tm.calc_AA(Vri_, A_)
if self.ham_sites == 2:
_C_AhlA = np.empty((self.q, self.q, A.shape[2], A.shape[2]),
dtype=tdvp.typ)
for u in xrange(self.q):
for s in xrange(self.q):
_C_AhlA[u, s] = A[u].conj().T.dot(l.dot(A[s]))
C_AhlA = sp.tensordot(ham_, _C_AhlA, ((0, 2), (0, 1)))
C_AhlA = sp.transpose(C_AhlA, axes=(1, 0, 2, 3)).copy(order='C')
_C_A_Vrh_ = tm.calc_AA(A_,
sp.transpose(Vr_, axes=(0, 2, 1)).conj())
C_A_Vrh_ = sp.tensordot(ham_, _C_A_Vrh_, ((3, 1), (0, 1)))
C_A_Vrh_ = sp.transpose(C_A_Vrh_,
axes=(1, 0, 2, 3)).copy(order='C')
C_Vri_A_conj = tm.calc_C_conj_mat_op_AA(ham_,
Vri_A_).copy(order='C')
C_ = tm.calc_C_mat_op_AA(ham_, AA_).copy(order='C')
C_conj = tm.calc_C_conj_mat_op_AA(ham_, AA_).copy(order='C')
rhs10 = tm.eps_r_op_2s_AA12_C34(r_, AA_, C_Vri_A_conj)
return C_, C_conj, V_, Vr_, Vri_, C_Vri_A_conj, C_AhlA, C_A_Vrh_, rhs10
elif self.ham_sites == 3:
C_Vri_AA_ = np.empty(
(self.q, self.q, self.q, Vri_.shape[1], A_.shape[2]),
dtype=tdvp.typ)
for s in xrange(self.q):
for t in xrange(self.q):
for u in xrange(self.q):
C_Vri_AA_[s, t, u] = Vri_[s].dot(AA_[t, u])
C_Vri_AA_ = sp.tensordot(ham_, C_Vri_AA_,
((3, 4, 5), (0, 1, 2))).copy(order='C')
C_AAA_r_Ah_Vrih = np.empty(
(
self.q,
self.q,
self.q,
self.q,
self.q, #FIXME: could be too memory-intensive
A_.shape[1],
Vri_.shape[1]),
dtype=tdvp.typ)
for s in xrange(self.q):
for t in xrange(self.q):
for u in xrange(self.q):
for k in xrange(self.q):
for j in xrange(self.q):
C_AAA_r_Ah_Vrih[s, t, u, k,
j] = AAA_[s, t, u].dot(
r_.dot(
A_[k].conj().T)).dot(
Vri_[j].conj().T)
C_AAA_r_Ah_Vrih = sp.tensordot(ham_, C_AAA_r_Ah_Vrih,
((3, 4, 5, 2, 1),
(0, 1, 2, 3, 4))).copy(order='C')
C_AhAhlAA = np.empty(
(self.q, self.q, self.q, self.q, A_.shape[2], A.shape[2]),
dtype=tdvp.typ)
for t in xrange(self.q):
for j in xrange(self.q):
for i in xrange(self.q):
for s in xrange(self.q):
C_AhAhlAA[j, t, i,
s] = AA[i,
j].conj().T.dot(l.dot(AA[s, t]))
C_AhAhlAA = sp.tensordot(ham_, C_AhAhlAA,
((4, 1, 0, 3),
(1, 0, 2, 3))).copy(order='C')
C_AA_r_Ah_Vrih_ = np.empty(
(self.q, self.q, self.q, self.q, A_.shape[1], Vri_.shape[1]),
dtype=tdvp.typ)
for t in xrange(self.q):
for u in xrange(self.q):
for k in xrange(self.q):
for j in xrange(self.q):
C_AA_r_Ah_Vrih_[u, t, k, j] = AA_[t, u].dot(
r_.dot(A_[k].conj().T)).dot(Vri_[j].conj().T)
C_AA_r_Ah_Vrih_ = sp.tensordot(ham_, C_AA_r_Ah_Vrih_,
((4, 5, 2, 1),
(1, 0, 2, 3))).copy(order='C')
C_AAA_Vrh_ = np.empty(
(self.q, self.q, self.q, self.q, A_.shape[1], Vri_.shape[1]),
dtype=tdvp.typ)
for s in xrange(self.q):
for t in xrange(self.q):
for u in xrange(self.q):
for k in xrange(self.q):
C_AAA_Vrh_[s, t, u,
k] = AAA_[s, t, u].dot(Vr_[k].conj().T)
C_AAA_Vrh_ = sp.tensordot(ham_, C_AAA_Vrh_,
((3, 4, 5, 2),
(0, 1, 2, 3))).copy(order='C')
C_Vri_A_r_Ah_ = np.empty(
(self.q, self.q, self.q, A_.shape[2], Vri_.shape[1]),
dtype=tdvp.typ)
for u in xrange(self.q):
for k in xrange(self.q):
for j in xrange(self.q):
C_Vri_A_r_Ah_[u, k, j] = Vri_[j].dot(A_[k]).dot(
r_.dot(A_[u].conj().T))
C_Vri_A_r_Ah_ = sp.tensordot(ham_.conj(), C_Vri_A_r_Ah_,
((5, 2, 1),
(0, 1, 2))).copy(order='C')
C_AhlAA = np.empty(
(self.q, self.q, self.q, A_.shape[2], A.shape[2]),
dtype=tdvp.typ)
for j in xrange(self.q):
for i in xrange(self.q):
for s in xrange(self.q):
C_AhlAA[j, i, s] = A[s].conj().T.dot(l.dot(AA[i, j]))
C_AhlAA_conj = sp.tensordot(ham_.conj(), C_AhlAA,
((1, 0, 3), (0, 1, 2))).copy(order='C')
C_AhlAA = sp.tensordot(ham_, C_AhlAA, ((4, 3, 0), (0, 1, 2)))
C_AhlAA = sp.transpose(C_AhlAA,
axes=(2, 0, 1, 3, 4)).copy(order='C')
C_AA_Vrh = np.empty(
(self.q, self.q, self.q, A_.shape[2], Vr_.shape[1]),
dtype=tdvp.typ)
for t in xrange(self.q):
for u in xrange(self.q):
for k in xrange(self.q):
C_AA_Vrh[k, u, t] = AA_[t, u].dot(Vr_[k].conj().T)
C_AA_Vrh = sp.tensordot(ham_, C_AA_Vrh,
((4, 5, 2), (2, 1, 0))).copy(order='C')
C_ = sp.tensordot(ham_, AAA_,
((3, 4, 5), (0, 1, 2))).copy(order='C')
rhs10 = tm.eps_r_op_3s_C123_AAA456(r_, AAA_, C_Vri_AA_)
#NOTE: These C's are good as C12 or C34, but only because h is Hermitian!
#TODO: Make this consistent with the updated 2-site case above.
return V_, Vr_, Vri_, Vri_A_, C_, C_Vri_AA_, C_AAA_r_Ah_Vrih, C_AhAhlAA, C_AA_r_Ah_Vrih_, C_AAA_Vrh_, C_Vri_A_r_Ah_, C_AhlAA, C_AhlAA_conj, C_AA_Vrh, rhs10,
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:
V_, Vr_, Vri_, Vri_A_, C_, C_Vri_AA_, C_AAA_r_Ah_Vrih, \
C_AhAhlAA, C_AA_r_Ah_Vrih_, C_AAA_Vrh_, C_Vri_A_r_Ah_, \
C_AhlAA, C_AhlAA_conj, C_AA_Vrh, rhs10 = prereq
else:
C_, C_conj, V_, Vr_, Vri_, C_Vri_A_conj, C_AhlA, C_A_Vrh_, rhs10 = prereq
A = tdvp.A[0]
A_ = tdvp2.A[0]
AA = tdvp.AA[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(Vri_[s]))
if la.norm(B - B2) / la.norm(B) > self.sanity_tol:
log.warning("Sanity Fail in calc_BHB! Bad Vri!")
BA_ = tm.calc_AA(B, A_)
AB = tm.calc_AA(A, B)
if self.ham_sites == 3:
BAA_ = tm.calc_AAA_AA(BA_, A_)
ABA_ = tm.calc_AAA_AA(AB, A_)
AAB = tm.calc_AAA_AA(AA, B)
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')
if self.ham_sites == 3:
tmp = BAA_ + sp.exp(+1.j * p) * ABA_ + sp.exp(+2.j * p) * AAB
res = l_sqrt.dot(tm.eps_r_op_3s_C123_AAA456(r_, tmp, C_Vri_AA_)) #1 1D, #3, #3c
else:
tmp = BA_ + sp.exp(+1.j * p) * AB
res = l_sqrt.dot(tm.eps_r_op_2s_AA12_C34(r_, tmp, C_Vri_A_conj)) #1, #3 OK
res += sp.exp(-1.j * p) * l_sqrt_i.dot(Mh.dot(rhs10)) #10
exp = sp.exp
subres = sp.zeros_like(res)
eye = m.eyemat(C_.shape[2], dtype=tdvp.typ)
eye2 = m.eyemat(A.shape[2], dtype=tdvp.typ)
if self.ham_sites == 3:
subres += exp(-2.j * p) * tm.eps_l_noop(Mh, A, C_AAA_r_Ah_Vrih) #12
subres += exp(-3.j * p) * tm.eps_l_op_2s_AA12_C34(Mh, AA, C_AAA_Vrh_) #12b
for s in xrange(self.q):
#subres += exp(-2.j * p) * A[s].conj().T.dot(Mh.dot(C_AAA_r_Ah_Vrih[s])) #12
subres += tm.eps_r_noop(B[s], C_AhAhlAA[s, :], Vr_) #2b
subres += exp(-1.j * p) * tm.eps_l_noop(l.dot(B[s]), A, C_AA_r_Ah_Vrih_[s, :]) #4
subres += A[s].conj().T.dot(l.dot(tm.eps_r_op_2s_AA12_C34(eye2, AB, C_Vri_A_r_Ah_[s, :, :]))) #2 -ive of that it should be....
subres += exp(-1.j * p) * tm.eps_l_op_2s_AA12_C34(eye2, C_AhlAA_conj[s, :, :], BA_).dot(Vr_[s].conj().T) #4b
subres += exp(-2.j * p) * tm.eps_l_op_2s_AA12_C34(l.dot(B[s]), AA, C_AA_Vrh[s, :, :]) #4c
subres += exp(+1.j * p) * tm.eps_r_op_2s_AA12_C34(r_.dot_left(B[s]), C_AhlAA[s, :, :], Vri_A_) #3b
#for t in xrange(self.q):
#subres += (C_AhAhlAA[t, s].dot(B[s]).dot(Vr_[t].conj().T)) #2b
#subres += (exp(-1.j * p) * A[s].conj().T.dot(l.dot(B[t])).dot(C_AA_r_Ah_Vrih_[s, t])) #4
#subres += (exp(-3.j * p) * AA[t, s].conj().T.dot(Mh).dot(C_AAA_Vrh_[t, s])) #12b
#for u in xrange(self.q):
#subres += A[s].conj().T.dot(l.dot(AB[t, u]).dot(C_A_r_Ah_Vrih[s, t, u])) #2 -ive of that it should be....
#subres += (exp(+1.j * p) * C_AhlAA[t, s, s].dot(B[u]).dot(r_.dot(A_[u].conj().T)).dot(Vri_[t].conj().T)) #3b
#subres += (exp(-1.j * p) * C_AhAhlA[s, t, u].dot(BA_[t, u]).dot(Vr_[s].conj().T)) #4b
#subres += (exp(-2.j * p) * AA[t, s].conj().T.dot(l.dot(B[u])).dot(C_AA_Vrh[t, s, u])) #4c
else:
for s in xrange(self.q):
#subres += C_AhlA[s, t].dot(B[s]).dot(Vr_[t].conj().T) #2 OK
subres += tm.eps_r_noop(B[s], C_AhlA[s, :], Vr_) #2
#+ exp(-1.j * p) * A[t].conj().T.dot(l.dot(B[s])).dot(C_A_Vrh_[t, s]) #4 OK with 3
subres += exp(-1.j * p) * tm.eps_l_noop(l.dot(B[s]), A, C_A_Vrh_[s, :]) #4
#+ exp(-2.j * p) * A[s].conj().T.dot(Mh.dot(C_[s, t])).dot(Vr_[t].conj().T)) #12
subres += exp(-2.j * p) * A[s].conj().T.dot(Mh).dot(tm.eps_r_noop(eye, C_[s, :], Vr_)) #12
res += l_sqrt_i.dot(subres)
res += l_sqrt.dot(tm.eps_r_noop(K__r, B, Vri_)) #5
res += l_sqrt_i.dot(K_l.dot(tm.eps_r_noop(r__sqrt, B, V_))) #6
res += sp.exp(-1.j * p) * l_sqrt_i.dot(Mh.dot(tm.eps_r_noop(K__r, A_, Vri_))) #8
y1 = sp.exp(+1.j * p) * tm.eps_r_noop(K__r, B, A_) #7
if self.ham_sites == 3:
tmp = sp.exp(+1.j * p) * BAA_ + sp.exp(+2.j * p) * ABA_ + sp.exp(+3.j * p) * AAB #9, #11, #11b
y = y1 + tm.eps_r_op_3s_C123_AAA456(r_, tmp, C_)
elif self.ham_sites == 2:
tmp = sp.exp(+1.j * p) * BA_ + sp.exp(+2.j * p) * AB #9, #11
y = y1 + tm.eps_r_op_2s_AA12_C34(r_, tmp, C_conj)
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 += l_sqrt.dot(tm.eps_r_noop(y_pi, A, Vri_))
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:
V_, Vr_, Vri_, Vri_A_, C_, C_Vri_AA_, C_AAA_r_Ah_Vrih, \
C_AhAhlAA, C_AA_r_Ah_Vrih_, C_AAA_Vrh_, C_Vri_A_r_Ah_, \
C_AhlAA, C_AhlAA_conj, C_AA_Vrh, rhs10 = prereq
else:
C_, C_conj, V_, Vr_, Vri_, C_Vri_A_conj, C_AhlA, C_A_Vrh_, rhs10 = prereq
A = tdvp.A[0]
A_ = tdvp2.A[0]
AA = tdvp.AA[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(Vri_[s]))
if la.norm(B - B2) / la.norm(B) > self.sanity_tol:
log.warning("Sanity Fail in calc_BHB! Bad Vri!")
BA_ = tm.calc_AA(B, A_)
AB = tm.calc_AA(A, B)
if self.ham_sites == 3:
BAA_ = tm.calc_AAA_AA(BA_, A_)
ABA_ = tm.calc_AAA_AA(AB, A_)
AAB = tm.calc_AAA_AA(AA, B)
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')
if self.ham_sites == 3:
tmp = BAA_ + sp.exp(+1.j * p) * ABA_ + sp.exp(+2.j * p) * AAB
res = l_sqrt.dot(tm.eps_r_op_3s_C123_AAA456(
r_, tmp, C_Vri_AA_)) #1 1D, #3, #3c
else:
tmp = BA_ + sp.exp(+1.j * p) * AB
res = l_sqrt.dot(tm.eps_r_op_2s_AA12_C34(r_, tmp,
C_Vri_A_conj)) #1, #3 OK
res += sp.exp(-1.j * p) * l_sqrt_i.dot(Mh.dot(rhs10)) #10
exp = sp.exp
subres = sp.zeros_like(res)
eye = m.eyemat(C_.shape[2], dtype=tdvp.typ)
eye2 = m.eyemat(A.shape[2], dtype=tdvp.typ)
if self.ham_sites == 3:
subres += exp(-2.j * p) * tm.eps_l_noop(Mh, A,
C_AAA_r_Ah_Vrih) #12
subres += exp(-3.j * p) * tm.eps_l_op_2s_AA12_C34(
Mh, AA, C_AAA_Vrh_) #12b
for s in xrange(self.q):
#subres += exp(-2.j * p) * A[s].conj().T.dot(Mh.dot(C_AAA_r_Ah_Vrih[s])) #12
subres += tm.eps_r_noop(B[s], C_AhAhlAA[s, :], Vr_) #2b
subres += exp(-1.j * p) * tm.eps_l_noop(
l.dot(B[s]), A, C_AA_r_Ah_Vrih_[s, :]) #4
subres += A[s].conj().T.dot(
l.dot(
tm.eps_r_op_2s_AA12_C34(eye2, AB, C_Vri_A_r_Ah_[
s, :, :]))) #2 -ive of that it should be....
subres += exp(-1.j * p) * tm.eps_l_op_2s_AA12_C34(
eye2, C_AhlAA_conj[s, :, :], BA_).dot(Vr_[s].conj().T) #4b
subres += exp(-2.j * p) * tm.eps_l_op_2s_AA12_C34(
l.dot(B[s]), AA, C_AA_Vrh[s, :, :]) #4c
subres += exp(+1.j * p) * tm.eps_r_op_2s_AA12_C34(
r_.dot_left(B[s]), C_AhlAA[s, :, :], Vri_A_) #3b
#for t in xrange(self.q):
#subres += (C_AhAhlAA[t, s].dot(B[s]).dot(Vr_[t].conj().T)) #2b
#subres += (exp(-1.j * p) * A[s].conj().T.dot(l.dot(B[t])).dot(C_AA_r_Ah_Vrih_[s, t])) #4
#subres += (exp(-3.j * p) * AA[t, s].conj().T.dot(Mh).dot(C_AAA_Vrh_[t, s])) #12b
#for u in xrange(self.q):
#subres += A[s].conj().T.dot(l.dot(AB[t, u]).dot(C_A_r_Ah_Vrih[s, t, u])) #2 -ive of that it should be....
#subres += (exp(+1.j * p) * C_AhlAA[t, s, s].dot(B[u]).dot(r_.dot(A_[u].conj().T)).dot(Vri_[t].conj().T)) #3b
#subres += (exp(-1.j * p) * C_AhAhlA[s, t, u].dot(BA_[t, u]).dot(Vr_[s].conj().T)) #4b
#subres += (exp(-2.j * p) * AA[t, s].conj().T.dot(l.dot(B[u])).dot(C_AA_Vrh[t, s, u])) #4c
else:
for s in xrange(self.q):
#subres += C_AhlA[s, t].dot(B[s]).dot(Vr_[t].conj().T) #2 OK
subres += tm.eps_r_noop(B[s], C_AhlA[s, :], Vr_) #2
#+ exp(-1.j * p) * A[t].conj().T.dot(l.dot(B[s])).dot(C_A_Vrh_[t, s]) #4 OK with 3
subres += exp(-1.j * p) * tm.eps_l_noop(
l.dot(B[s]), A, C_A_Vrh_[s, :]) #4
#+ exp(-2.j * p) * A[s].conj().T.dot(Mh.dot(C_[s, t])).dot(Vr_[t].conj().T)) #12
subres += exp(-2.j * p) * A[s].conj().T.dot(Mh).dot(
tm.eps_r_noop(eye, C_[s, :], Vr_)) #12
res += l_sqrt_i.dot(subres)
res += l_sqrt.dot(tm.eps_r_noop(K__r, B, Vri_)) #5
res += l_sqrt_i.dot(K_l.dot(tm.eps_r_noop(r__sqrt, B, V_))) #6
res += sp.exp(-1.j * p) * l_sqrt_i.dot(
Mh.dot(tm.eps_r_noop(K__r, A_, Vri_))) #8
y1 = sp.exp(+1.j * p) * tm.eps_r_noop(K__r, B, A_) #7
if self.ham_sites == 3:
tmp = sp.exp(+1.j * p) * BAA_ + sp.exp(+2.j * p) * ABA_ + sp.exp(
+3.j * p) * AAB #9, #11, #11b
y = y1 + tm.eps_r_op_3s_C123_AAA456(r_, tmp, C_)
elif self.ham_sites == 2:
tmp = sp.exp(+1.j * p) * BA_ + sp.exp(+2.j * p) * AB #9, #11
y = y1 + tm.eps_r_op_2s_AA12_C34(r_, tmp, C_conj)
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 += l_sqrt.dot(tm.eps_r_noop(y_pi, A, Vri_))
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
