def _excite_correlation_1s_1s(AL, AR, B, lL, rR, op1, op2, d, g):
pseudo = AL is AR
BBL = pinv_1mE(tm.eps_l_noop(lL, B, B), [AR], [AR], lL, rR, p=0,
left=True, pseudo=True)
B1L = pinv_1mE(tm.eps_l_noop(lL, B, AL), [AR], [AL], lL, rR, p=0,
left=True, pseudo=pseudo)
B2L = pinv_1mE(tm.eps_l_noop(lL, AL, B), [AL], [AR], lL, rR, p=0,
left=True, pseudo=pseudo)
B1B2L = pinv_1mE(tm.eps_l_noop(B1L, AR, B), [AR], [AR], lL, rR, p=0,
left=True, pseudo=True)
B2B1L = pinv_1mE(tm.eps_l_noop(B2L, B, AR), [AR], [AR], lL, rR, p=0,
left=True, pseudo=True)
BBR = pinv_1mE(tm.eps_r_noop(rR, B, B), [AL], [AL], lL, rR, p=0,
left=False, pseudo=True)
print "gauge fixing:", la.norm(tm.eps_r_noop(rR, B, AR))
res = [0.] * (d + 1)
#B's on the left terms (0, 1, 2, 5)
res[0] += m.adot(tm.eps_l_op_1s(BBL + B1B2L + B2B1L, AR, AR, op1.dot(op2) - g[0] * sp.eye(len(op1))), rR)
res[0] += m.adot(tm.eps_l_op_1s(B1L, AR, B, op1.dot(op2)), rR)
res[0] += m.adot(tm.eps_l_op_1s(B2L, B, AR, op1.dot(op2)), rR)
res[0] += m.adot(tm.eps_l_op_1s(lL, B, B, op1.dot(op2) - g[0] * sp.eye(len(op1))), rR)
l1 = tm.eps_l_op_1s(BBL + B1B2L + B2B1L, AR, AR, op1)
l1 += tm.eps_l_op_1s(B1L, AR, B, op1)
l1 += tm.eps_l_op_1s(B2L, B, AR, op1)
l1 += tm.eps_l_op_1s(lL, B, B, op1)
for n in xrange(1, d + 1):
res[n] += m.adot(l1, tm.eps_r_op_1s(rR, AR, AR, op2))
res[n] -= 2 * g[n]
if n == d:
break
l1 = tm.eps_l_noop(l1, AR, AR)
print 1, res
#Terms 3, 4, 6, 7, a
ls = [None] * (d + 1)
ls[0] = tm.eps_l_op_1s(B1L, AR, AL, op1) + tm.eps_l_op_1s(lL, B, AL, op1)
for k in xrange(1, d + 1):
ls[k] = tm.eps_l_noop(ls[k - 1], AR, AL)
rs = [None] * (d + 1)
rs[d - 1] = tm.eps_r_op_1s(rR, AR, AR, op2)
for k in xrange(d - 1, 0, -1):
rs[k - 1] = tm.eps_r_noop(rs[k], AR, AR)
for n in xrange(2, d + 1):
for k in xrange(2, n):
res[n] += m.adot(ls[k - 1], tm.eps_r_noop(rs[-(n + 1):][k], AR, B))
res[n] += m.adot(ls[n - 1], tm.eps_r_op_1s(rR, AR, B, op2))
print 2, res
#Terms 3, 4, 6, 7, b
ls = [None] * (d + 1)
ls[0] = tm.eps_l_op_1s(B2L, AL, AR, op1) + tm.eps_l_op_1s(lL, AL, B, op1)
for k in xrange(1, d + 1):
ls[k] = tm.eps_l_noop(ls[k - 1], AL, AR)
for n in xrange(2, d + 1):
for k in xrange(2, n):
res[n] += m.adot(ls[k - 1], tm.eps_r_noop(rs[-(n + 1):][k], B, AR))
res[n] += m.adot(ls[n - 1], tm.eps_r_op_1s(rR, B, AR, op2))
print 3, res
#Term 8
ls = [None] * (d + 1)
ls[0] = tm.eps_l_op_1s(lL, AL, AL, op1)
for k in xrange(1, d + 1):
ls[k] = tm.eps_l_noop(ls[k - 1], AL, AL)
for n in xrange(2, d + 1):
for k in xrange(2, n):
res[n] += m.adot(ls[k - 1], tm.eps_r_noop(rs[-(n + 1):][k], B, B))
res[n] -= g[n]
print 4, res
#Terms 9 and 10
for n in xrange(2, d + 1):
for k in xrange(2, n):
lj = tm.eps_l_noop(ls[k - 1], AL, B)
for j in xrange(k + 1, n):
res[n] += m.adot(lj, tm.eps_r_noop(rs[-(n + 1):][j], B, AR))
lj = tm.eps_l_noop(lj, AL, AR)
res[n] += m.adot(lj, tm.eps_r_op_1s(rR, B, AR, op2))
lj = tm.eps_l_noop(ls[k - 1], B, AL)
for j in xrange(k + 1, n):
res[n] += m.adot(lj, tm.eps_r_noop(rs[-(n + 1):][j], AR, B))
lj = tm.eps_l_noop(lj, AL, AR)
res[n] += m.adot(lj, tm.eps_r_op_1s(rR, AR, B, op2))
print 5, res
#Term 11
res[0] += m.adot(tm.eps_l_op_1s(lL, AL, AL, op1.dot(op2) - g[0] * sp.eye(len(op1))), BBR)
for n in xrange(1, d + 1):
res[n] += m.adot(tm.eps_l_op_1s(ls[n - 1], AL, AL, op2), BBR)
res[n] -= g[n]
return res
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:
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 _excite_correlation_1s_1s(AL, AR, B, lL, rR, op1, op2, d, g):
pseudo = AL is AR
BBL = pinv_1mE(tm.eps_l_noop(lL, B, B), [AR], [AR],
lL,
rR,
p=0,
left=True,
pseudo=True)
B1L = pinv_1mE(tm.eps_l_noop(lL, B, AL), [AR], [AL],
lL,
rR,
p=0,
left=True,
pseudo=pseudo)
B2L = pinv_1mE(tm.eps_l_noop(lL, AL, B), [AL], [AR],
lL,
rR,
p=0,
left=True,
pseudo=pseudo)
B1B2L = pinv_1mE(tm.eps_l_noop(B1L, AR, B), [AR], [AR],
lL,
rR,
p=0,
left=True,
pseudo=True)
B2B1L = pinv_1mE(tm.eps_l_noop(B2L, B, AR), [AR], [AR],
lL,
rR,
p=0,
left=True,
pseudo=True)
BBR = pinv_1mE(tm.eps_r_noop(rR, B, B), [AL], [AL],
lL,
rR,
p=0,
left=False,
pseudo=True)
print "gauge fixing:", la.norm(tm.eps_r_noop(rR, B, AR))
res = [0.] * (d + 1)
#B's on the left terms (0, 1, 2, 5)
res[0] += m.adot(
tm.eps_l_op_1s(BBL + B1B2L + B2B1L, AR, AR,
op1.dot(op2) - g[0] * sp.eye(len(op1))), rR)
res[0] += m.adot(tm.eps_l_op_1s(B1L, AR, B, op1.dot(op2)), rR)
res[0] += m.adot(tm.eps_l_op_1s(B2L, B, AR, op1.dot(op2)), rR)
res[0] += m.adot(
tm.eps_l_op_1s(lL, B, B,
op1.dot(op2) - g[0] * sp.eye(len(op1))), rR)
l1 = tm.eps_l_op_1s(BBL + B1B2L + B2B1L, AR, AR, op1)
l1 += tm.eps_l_op_1s(B1L, AR, B, op1)
l1 += tm.eps_l_op_1s(B2L, B, AR, op1)
l1 += tm.eps_l_op_1s(lL, B, B, op1)
for n in xrange(1, d + 1):
res[n] += m.adot(l1, tm.eps_r_op_1s(rR, AR, AR, op2))
res[n] -= 2 * g[n]
if n == d:
break
l1 = tm.eps_l_noop(l1, AR, AR)
print 1, res
#Terms 3, 4, 6, 7, a
ls = [None] * (d + 1)
ls[0] = tm.eps_l_op_1s(B1L, AR, AL, op1) + tm.eps_l_op_1s(lL, B, AL, op1)
for k in xrange(1, d + 1):
ls[k] = tm.eps_l_noop(ls[k - 1], AR, AL)
rs = [None] * (d + 1)
rs[d - 1] = tm.eps_r_op_1s(rR, AR, AR, op2)
for k in xrange(d - 1, 0, -1):
rs[k - 1] = tm.eps_r_noop(rs[k], AR, AR)
for n in xrange(2, d + 1):
for k in xrange(2, n):
res[n] += m.adot(ls[k - 1], tm.eps_r_noop(rs[-(n + 1):][k], AR, B))
res[n] += m.adot(ls[n - 1], tm.eps_r_op_1s(rR, AR, B, op2))
print 2, res
#Terms 3, 4, 6, 7, b
ls = [None] * (d + 1)
ls[0] = tm.eps_l_op_1s(B2L, AL, AR, op1) + tm.eps_l_op_1s(lL, AL, B, op1)
for k in xrange(1, d + 1):
ls[k] = tm.eps_l_noop(ls[k - 1], AL, AR)
for n in xrange(2, d + 1):
for k in xrange(2, n):
res[n] += m.adot(ls[k - 1], tm.eps_r_noop(rs[-(n + 1):][k], B, AR))
res[n] += m.adot(ls[n - 1], tm.eps_r_op_1s(rR, B, AR, op2))
print 3, res
#Term 8
ls = [None] * (d + 1)
ls[0] = tm.eps_l_op_1s(lL, AL, AL, op1)
for k in xrange(1, d + 1):
ls[k] = tm.eps_l_noop(ls[k - 1], AL, AL)
for n in xrange(2, d + 1):
for k in xrange(2, n):
res[n] += m.adot(ls[k - 1], tm.eps_r_noop(rs[-(n + 1):][k], B, B))
res[n] -= g[n]
print 4, res
#Terms 9 and 10
for n in xrange(2, d + 1):
for k in xrange(2, n):
lj = tm.eps_l_noop(ls[k - 1], AL, B)
for j in xrange(k + 1, n):
res[n] += m.adot(lj, tm.eps_r_noop(rs[-(n + 1):][j], B, AR))
lj = tm.eps_l_noop(lj, AL, AR)
res[n] += m.adot(lj, tm.eps_r_op_1s(rR, B, AR, op2))
lj = tm.eps_l_noop(ls[k - 1], B, AL)
for j in xrange(k + 1, n):
res[n] += m.adot(lj, tm.eps_r_noop(rs[-(n + 1):][j], AR, B))
lj = tm.eps_l_noop(lj, AL, AR)
res[n] += m.adot(lj, tm.eps_r_op_1s(rR, AR, B, op2))
print 5, res
#Term 11
res[0] += m.adot(
tm.eps_l_op_1s(lL, AL, AL,
op1.dot(op2) - g[0] * sp.eye(len(op1))), BBR)
for n in xrange(1, d + 1):
res[n] += m.adot(tm.eps_l_op_1s(ls[n - 1], AL, AL, op2), BBR)
res[n] -= g[n]
return res
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:
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
