def _propagate_SExp_RTOp_ReSymK_Re_pytorch(self,
rhoi,
Ham,
RT,
dt,
use_gpu=False,
L=4):
"""Integration by short exponentional expansion
Integration by expanding exponential (_SExp_) to Lth order.
This is a PyTorch (_pytorch) implementation with real (_Re_) matrices
for a system part of the system-bath interaction operator ``K``
in a form of real symmetric operator (ReSymK). The relaxation tensor
is assumed in form of a set of operators (_RTOp_)
"""
Nref = self.Nref
Nt = self.Nt
verbose = self.verbose
timea = self.TimeAxis
prop_name = self.propagation_name
try:
import torch
except:
raise Exception("PyTorch not installed")
# no self beyond this point
qr.log_detail("PROPAGATION (short exponential with " +
"relaxation in operator form): order ",
L,
verbose=verbose)
qr.log_detail("Using pytorch implementation")
qr.log_detail("Using GPU: ", use_gpu & torch.cuda.is_available())
pr = ReducedDensityMatrixEvolution(timea, rhoi, name=prop_name)
rho1_r = torch.from_numpy(numpy.real(rhoi.data))
rho2_r = torch.from_numpy(numpy.real(rhoi.data))
rho1_i = torch.from_numpy(numpy.imag(rhoi.data))
rho2_i = torch.from_numpy(numpy.imag(rhoi.data))
HH = torch.from_numpy(Ham.data)
try:
Km = torch.from_numpy(RT.Km) #self.RelaxationTensor.Km # real
Lm_r = torch.from_numpy(numpy.real(
RT.Lm)) #self.RelaxationTensor.Lm) # complex
Lm_i = torch.from_numpy(numpy.imag(
RT.Lm)) #self.RelaxationTensor.Lm)
Nm = RT.Km.shape[0]
except:
raise Exception("Tensor is not in operator form")
if use_gpu & torch.cuda.is_available():
rho1_r = rho1_r.cuda()
rho2_r = rho1_r
rho1_i = rho1_i.cuda()
rho2_i = rho1_i
HH = HH.cuda()
Km = Km.cuda()
Lm_r = Lm_r.cuda()
Lm_i = Lm_i.cuda()
indx = 1
# verbosity inside loops
levs = [qr.LOG_QUICK]
verb = qr.loglevels2bool(levs)
# loop over time
for ii in range(1, Nt):
qr.printlog(" time step ",
ii,
"of",
Nt,
verbose=verb[0],
loglevel=levs[0])
# steps in between saving the results
for jj in range(Nref):
# L interations to get short exponential expansion
for ll in range(1, L + 1):
A = torch.matmul(HH, rho1_i)
B = torch.matmul(HH, rho1_r)
rhoY_r = torch.mul(A + torch.transpose(A, 0, 1), dt / ll)
rhoY_i = torch.mul(B - torch.transpose(B, 0, 1), -dt / ll)
for mm in range(Nm):
a = torch.matmul(Lm_r[mm, :, :], rho1_r)
A = a - torch.transpose(a, 0, 1)
b = torch.matmul(Lm_i[mm, :, :], rho1_i)
B = b - torch.transpose(b, 0, 1)
c = torch.matmul(Lm_r[mm, :, :], rho1_i)
C = -(c + torch.transpose(c, 0, 1))
d = torch.matmul(Lm_i[mm, :, :], rho1_r)
D = d + torch.transpose(d, 0, 1)
E = B - A
F = C - D
A = torch.matmul(Km[mm, :, :], E)
B = torch.matmul(Km[mm, :, :], F)
rhoY_r += torch.mul(A + torch.transpose(A, 0, 1),
dt / ll)
rhoY_i += torch.mul(B - torch.transpose(B, 0, 1),
dt / ll)
rho1_r = rhoY_r
rho1_i = rhoY_i
rho2_r += rho1_r
rho2_i += rho1_i
rho1_r = rho2_r
rho1_i = rho2_i
if use_gpu & torch.cuda.is_available():
rho2_sr = rho2_r.cpu()
rho2_si = rho2_i.cpu()
else:
rho2_sr = rho2_r
rho2_si = rho2_i
pr.data[indx, :, :] = rho2_sr.numpy() + 1j * rho2_si.numpy()
indx += 1
qr.log_detail("...DONE")
return pr
def _implementation(self, ham, sbi):
""" Reference implementation, completely in Python
Implementation of Redfield relaxation tensor according to
V. May and O. Kuehn, Charge and Energy Transfer Dynamics in Molecular
System, Wiley-VCH, Berlin, 2000, 1st edition, chapter 3.8.2.
In particular we refer to Eq. (3.8.13) on page 132
We assume the system-bath interaction operator in form of Eq. (3.5.30)
with the bath part specified through two-point correlation functions.
We construct operators K_{m} introduced in Eq. (3.5.30) and
operators \Lambda_{m} of Eq. (3.8.11).
We do not delete the imaginary part of the tensor (as is done later
in Section 3.8.3 to get the so-called "Multi-level Redfield
Equations"). Such a deletion can be done later manually.
"""
qr.log_detail("Reference time-independent Redfield tensor calculation")
#print("Reference Redfield implementation ...")
#
# dimension of the Hamiltonian (includes excitons
# with all multiplicities specified at its creation)
#
Na = ham.dim #data.shape[0]
# time axis
ta = sbi.TimeAxis
#
# is this beyond single excitation band?
#
multi_ex = False
# figure out if the aggregate specifies more than one exciton band
if sbi.aggregate is not None:
agg = sbi.aggregate
if agg.mult > 1:
multi_ex = True
#
# shorten the interval of integration if a cut-off time is set
#
if self._has_cutoff_time:
# index of the cut-off time on the time axis
tcut = ta.nearest(self.cutoff_time)
# select the section of the time axis up to the cut-off time
tm = ta.data[0:tcut]
# length of the section corresponds to the index of cut-off time
length = tcut
else:
# if cut-off time is not set then we take the whole time axis
tm = ta.data
# and the length corresponds to the length of the time axis
length = ta.length
#
# Get eigenenergies and transformation matrix of the Hamiltonian
#
if True:
# FIXME: here we need to access ham._data (we want to protect basis)
#
# THIS ASSUMES WE ARE IN SITE BASIS
# FIXME: devise a mechanism to ensure this!!!!
#
hD, SS = numpy.linalg.eigh(ham.data)
#
# Find all transition frequencies
#
Om = numpy.zeros((Na, Na))
for a in range(Na):
for b in range(Na):
Om[a,b] = hD[a] - hD[b]
# number of baths - one per monomer
Nb = sbi.N
#
# Site K_m operators
#
Km = numpy.zeros((Nb, Na, Na), dtype=numpy.float64)
# Transform site operators
S1 = scipy.linalg.inv(SS)
#FIXME: SBI should also be basis controlled
for ns in range(Nb):
Km[ns,:,:] = numpy.dot(S1, numpy.dot(sbi.KK[ns,:,:],SS))
#
# \Lambda_m operator
#
# Integrals of correlation functions from the set
Lm = numpy.zeros((Nb, Na, Na), dtype=numpy.complex128)
#######################################################################
# PARALLELIZATION
#######################################################################
start_parallel_region()
for ms in block_distributed_range(0, Nb): #range(Nb):
qr.log_quick("Calculating bath component", ms, "of", Nb, end="\r")
#print(ms, "of", Nb)
#for ns in range(Nb):
if not multi_ex:
ns = ms
# correlation function of site ns (if ns == ms)
# or a cross-correlation function of sites ns and ms
#FIXME: reaching correct correlation function is a nightmare!!!
rc1 = sbi.CC.get_coft(ms, ns)
self._guts_Cmplx_Splines(ms, Lm, Km, Na, Om, length, rc1, tm)
# perform reduction of Lm
qr.log_quick()
distributed_configuration().allreduce(Lm, operation="sum")
close_parallel_region()
#######################################################################
# END PARALLELIZATION
#######################################################################
# create the Hermite conjuged version of \Lamnda_m
Ld = numpy.zeros((Nb, Na, Na), dtype=numpy.complex128)
for ms in range(Nb):
Ld[ms, :, :] += numpy.conj(numpy.transpose(Lm[ms,:,:]))
self._post_implementation(Km, Lm, Ld)
qr.log_detail("... Redfield done")
def __propagate_short_exp_with_rel_operators(self, rhoi, L=4):
"""Integration by short exponentional expansion
Integration by expanding exponential to Lth order.
"""
mana = Manager()
save_pytorch = None
legacy = mana.gen_conf.legacy_relaxation
if mana.num_conf.gpu_acceleration:
save_pytorch = mana.num_conf.enable_pytorch
mana.num_conf.enable_pytorch = True
if mana.num_conf.enable_pytorch and (not legacy):
ret = self._propagate_SExp_RTOp_ReSymK_Re_pytorch(
rhoi,
self.Hamiltonian,
self.RelaxationTensor,
self.dt,
use_gpu=mana.num_conf.gpu_acceleration,
L=L)
if save_pytorch is not None:
mana.num_conf.enable_pytorch = save_pytorch
return ret
elif not legacy:
return self._propagate_SExp_RTOp_ReSymK_Re_numpy(
rhoi, self.Hamiltonian, self.RelaxationTensor, self.dt, L=L)
#
# legacy version
#
pr = ReducedDensityMatrixEvolution(self.TimeAxis,
rhoi,
name=self.propagation_name)
rho1 = rhoi.data
rho2 = rhoi.data
#
# RWA is applied here
#
if self.Hamiltonian.has_rwa:
HH = self.Hamiltonian.get_RWA_data() #data - self.HOmega
else:
HH = self.Hamiltonian.data
qr.log_detail("PROPAGATION (short exponential with " +
"relaxation in operator form): order ",
L,
verbose=self.verbose)
qr.log_detail("Using complex numpy implementation")
try:
Km = self.RelaxationTensor.Km # real
Lm = self.RelaxationTensor.Lm # complex
Ld = self.RelaxationTensor.Ld # complex - get by transposition
Kd = numpy.zeros(Km.shape, dtype=numpy.float64)
Nm = Km.shape[0]
for m in range(Nm):
Kd[m, :, :] = numpy.transpose(Km[m, :, :])
except:
raise Exception("Tensor is not in operator form")
indx = 1
levs = [qr.LOG_QUICK] #, 8]
verb = qr.loglevels2bool(levs)
# after each step we apply pure dephasing (if present)
if self.has_PDeph:
if self.PDeph.dtype == "Lorentzian":
expo = numpy.exp(-self.PDeph.data * self.dt)
t0 = 0.0
elif self.PDeph.dtype == "Gaussian":
expo = numpy.exp(-self.PDeph.data * (self.dt**2) / 2.0)
t0 = self.PDeph.data * self.dt
# loop over time
for ii in range(1, self.Nt):
qr.printlog(" time step ",
ii,
"of",
self.Nt,
verbose=verb[0],
loglevel=levs[0])
# time at the beginning of the step
tNt = self.TimeAxis.data[indx - 1]
#print("tNt = ", tNt)
# steps in between saving the results
for jj in range(0, self.Nref):
tt = tNt + jj * self.dt # time right now
# L interations to get short exponential expansion
for ll in range(1, L + 1):
rhoY = -(1j * self.dt / ll) * (numpy.dot(HH, rho1) -
numpy.dot(rho1, HH))
#rhoX = numpy.zeros(rho1.shape, dtype=numpy.complex128)
for mm in range(Nm):
rhoY += (self.dt / ll) * (
numpy.dot(Km[mm, :, :],
numpy.dot(rho1, Ld[mm, :, :])) +
numpy.dot(Lm[mm, :, :],
numpy.dot(rho1, Kd[mm, :, :])) -
numpy.dot(
numpy.dot(Kd[mm, :, :], Lm[mm, :, :]),
rho1) - numpy.dot(
rho1,
numpy.dot(Ld[mm, :, :], Km[mm, :, :])))
rho1 = rhoY #+ rhoX
rho2 = rho2 + rho1
# pure dephasing is added here
rho2 = rho2 * expo * numpy.exp(-t0 * tt)
rho1 = rho2
pr.data[indx, :, :] = rho2
indx += 1
# no extra dephasing
else:
# loop over time
for ii in range(1, self.Nt):
qr.printlog(" time step ",
ii,
"of",
self.Nt,
verbose=verb[0],
loglevel=levs[0])
# steps in between saving the results
for jj in range(0, self.Nref):
# L interations to get short exponential expansion
for ll in range(1, L + 1):
rhoY = -(1j * self.dt / ll) * (numpy.dot(HH, rho1) -
numpy.dot(rho1, HH))
#rhoX = numpy.zeros(rho1.shape, dtype=numpy.complex128)
for mm in range(Nm):
rhoY += (self.dt / ll) * (
numpy.dot(Km[mm, :, :],
numpy.dot(rho1, Ld[mm, :, :])) +
numpy.dot(Lm[mm, :, :],
numpy.dot(rho1, Kd[mm, :, :])) -
numpy.dot(
numpy.dot(Kd[mm, :, :], Lm[mm, :, :]),
rho1) - numpy.dot(
rho1,
numpy.dot(Ld[mm, :, :], Km[mm, :, :])))
rho1 = rhoY #+ rhoX
rho2 = rho2 + rho1
rho1 = rho2
pr.data[indx, :, :] = rho2
indx += 1
qr.log_detail("...DONE")
if self.Hamiltonian.has_rwa:
pr.is_in_rwa = True
return pr
def _propagate_SExp_RTOp_ReSymK_Re_numpy(self, rhoi, Ham, RT, dt, L=4):
"""Integration by short exponentional expansion
Integration by expanding exponential (_SExp_) to Lth order.
This is a numpy (_numpy) implementation with real (_Re_) matrices
for a system part of the system-bath interaction operator ``K``
in a form of real symmetric operator (ReSymK). The relaxation tensor
is assumed in form of a set of operators (_RTOp_)
"""
Nref = self.Nref
Nt = self.Nt
verbose = self.verbose
timea = self.TimeAxis
prop_name = self.propagation_name
# no self beyond this point
qr.log_detail("PROPAGATION (short exponential with " +
"relaxation in operator form): order ",
L,
verbose=verbose)
qr.log_detail("Using real valued numpy implementation")
pr = ReducedDensityMatrixEvolution(timea, rhoi, name=prop_name)
rho1_r = numpy.real(rhoi.data)
rho2_r = numpy.real(rhoi.data)
rho1_i = numpy.imag(rhoi.data)
rho2_i = numpy.imag(rhoi.data)
HH = Ham.data
try:
Km = RT.Km #self.RelaxationTensor.Km # real
Lm_r = numpy.real(RT.Lm) #self.RelaxationTensor.Lm) # complex
Lm_i = numpy.imag(RT.Lm) #self.RelaxationTensor.Lm)
Nm = Km.shape[0]
except:
raise Exception("Tensor is not in operator form")
indx = 1
# verbosity inside loops
levs = [qr.LOG_QUICK]
verb = qr.loglevels2bool(levs, verbose=self.verbose)
# after each step we apply pure dephasing (if present)
if self.has_PDeph:
# loop over time
for ii in range(1, Nt):
qr.printlog("time step ",
ii,
"of",
Nt,
verbose=verb[0],
loglevel=levs[0],
end="\r")
# steps in between saving the results
for jj in range(Nref):
# L interations to get short exponential expansion
for ll in range(1, L + 1):
A = numpy.dot(HH, rho1_i)
B = numpy.dot(HH, rho1_r)
rhoY_r = (dt / ll) * (A + numpy.transpose(A))
rhoY_i = -(dt / ll) * (B - numpy.transpose(B))
for mm in range(Nm):
a = numpy.dot(Lm_r[mm, :, :], rho1_r)
A = a - numpy.transpose(a)
b = numpy.dot(Lm_i[mm, :, :], rho1_i)
B = b - numpy.transpose(b)
c = numpy.dot(Lm_r[mm, :, :], rho1_i)
C = -(c + numpy.transpose(c))
d = numpy.dot(Lm_i[mm, :, :], rho1_r)
D = d + numpy.transpose(d)
E = B - A
F = C - D
A = numpy.dot(Km[mm, :, :], E)
B = numpy.dot(Km[mm, :, :], F)
rhoY_r += (dt / ll) * (A + numpy.transpose(A))
rhoY_i += (dt / ll) * (B - numpy.transpose(B))
rho1_r = rhoY_r
rho1_i = rhoY_i
rho2_r += rho1_r
rho2_i += rho1_i
rho2_r = rho2_r * numpy.exp(-self.PDeph.data * dt)
rho2_i = rho2_i * numpy.exp(-self.PDeph.data * dt)
rho1_r = rho2_r
rho1_i = rho2_i
pr.data[indx, :, :] = rho2_r + 1j * rho2_i
indx += 1
# propagatiomn with no extra dephasing
else:
# loop over time
for ii in range(1, Nt):
qr.printlog("time step ",
ii,
"of",
Nt,
verbose=verb[0],
loglevel=levs[0],
end="\r")
# steps in between saving the results
for jj in range(Nref):
# L interations to get short exponential expansion
for ll in range(1, L + 1):
A = numpy.dot(HH, rho1_i)
B = numpy.dot(HH, rho1_r)
rhoY_r = (dt / ll) * (A + numpy.transpose(A))
rhoY_i = -(dt / ll) * (B - numpy.transpose(B))
for mm in range(Nm):
a = numpy.dot(Lm_r[mm, :, :], rho1_r)
A = a - numpy.transpose(a)
b = numpy.dot(Lm_i[mm, :, :], rho1_i)
B = b - numpy.transpose(b)
c = numpy.dot(Lm_r[mm, :, :], rho1_i)
C = -(c + numpy.transpose(c))
d = numpy.dot(Lm_i[mm, :, :], rho1_r)
D = d + numpy.transpose(d)
E = B - A
F = C - D
A = numpy.dot(Km[mm, :, :], E)
B = numpy.dot(Km[mm, :, :], F)
rhoY_r += (dt / ll) * (A + numpy.transpose(A))
rhoY_i += (dt / ll) * (B - numpy.transpose(B))
rho1_r = rhoY_r
rho1_i = rhoY_i
rho2_r += rho1_r
rho2_i += rho1_i
rho1_r = rho2_r
rho1_i = rho2_i
pr.data[indx, :, :] = rho2_r + 1j * rho2_i
indx += 1
qr.log_detail()
qr.log_detail("...DONE")
return pr
# set bath correlation functions to the molecules
for i_m in range(N_molecules):
mols[i_m].set_transition_environment((0, 1), cf)
# aggregate of molecules
agg = qr.Aggregate(mols)
agg.set_coupling_by_dipole_dipole()
# Building the aggregate
qr.log_report("Building aggregate")
agg.build()
qr.log_report("...done")
qr.log_detail("Resonance coupling matrix: ")
qr.log_detail(qr.convert(agg.resonance_coupling, "int", "1/cm"),
use_indent=False)
# Dimension of the problem
HH = agg.get_Hamiltonian()
Nr = HH.dim
qr.log_detail("Hamiltonian has a rank:", Nr)
benchmark_report["Dimension"] = Nr
qr.log_report("Calculating Relaxation tensor:")
t1 = time.time()
(RT, ham) = agg.get_RelaxationTensor(timea,
relaxation_theory="standard_Redfield",
as_operators=True)
# set bath correlation functions to the molecules
for i_m in range(N_molecules):
mols[i_m].set_transition_environment((0, 1), cf)
# aggregate of molecules
agg = qr.Aggregate(mols)
agg.set_coupling_by_dipole_dipole()
# Building the aggregate
qr.log_report("Building aggregate")
agg.build()
qr.log_report("...done")
qr.log_detail("Resonance coupling matrix: ")
qr.log_detail(qr.convert(agg.resonance_coupling, "int", "1/cm"),
use_indent=False)
# Dimension of the problem
HH = agg.get_Hamiltonian()
Nr = HH.dim
qr.log_detail("Hamiltonian has a rank:", Nr)
benchmark_report["Dimension"] = Nr
qr.log_report("Calculating Relaxation tensor:")
t1 = time.time()
(RT, ham) = agg.get_RelaxationTensor(timea,
relaxation_theory="standard_Redfield",
as_operators=True)
def _propagate_SExp_RTOp_ReSymK_Re_pytorch(self, rhoi, Ham, RT, dt,
use_gpu=False, L=4):
"""Integration by short exponentional expansion
Integration by expanding exponential (_SExp_) to Lth order.
This is a PyTorch (_pytorch) implementation with real (_Re_) matrices
for a system part of the system-bath interaction operator ``K``
in a form of real symmetric operator (ReSymK). The relaxation tensor
is assumed in form of a set of operators (_RTOp_)
"""
Nref = self.Nref
Nt = self.Nt
verbose = self.verbose
timea = self.TimeAxis
prop_name = self.propagation_name
try:
import torch
except:
raise Exception("PyTorch not installed")
# no self beyond this point
qr.log_detail("PROPAGATION (short exponential with "+
"relaxation in operator form): order ", L,
verbose=verbose)
qr.log_detail("Using pytorch implementation")
qr.log_detail("Using GPU: ", use_gpu & torch.cuda.is_available())
pr = ReducedDensityMatrixEvolution(timea, rhoi,
name=prop_name)
rho1_r = torch.from_numpy(numpy.real(rhoi.data))
rho2_r = torch.from_numpy(numpy.real(rhoi.data))
rho1_i = torch.from_numpy(numpy.imag(rhoi.data))
rho2_i = torch.from_numpy(numpy.imag(rhoi.data))
HH = torch.from_numpy(Ham.data)
try:
Km = torch.from_numpy(RT.Km) #self.RelaxationTensor.Km # real
Lm_r = torch.from_numpy(numpy.real(RT.Lm)) #self.RelaxationTensor.Lm) # complex
Lm_i = torch.from_numpy(numpy.imag(RT.Lm)) #self.RelaxationTensor.Lm)
Nm = RT.Km.shape[0]
except:
raise Exception("Tensor is not in operator form")
if use_gpu & torch.cuda.is_available():
rho1_r = rho1_r.cuda()
rho2_r = rho1_r
rho1_i = rho1_i.cuda()
rho2_i = rho1_i
HH = HH.cuda()
Km = Km.cuda()
Lm_r = Lm_r.cuda()
Lm_i = Lm_i.cuda()
indx = 1
# verbosity inside loops
levs = [qr.LOG_QUICK]
verb = qr.loglevels2bool(levs)
# loop over time
for ii in range(1, Nt):
qr.printlog(" time step ", ii, "of", Nt,
verbose=verb[0], loglevel=levs[0])
# steps in between saving the results
for jj in range(Nref):
# L interations to get short exponential expansion
for ll in range(1, L+1):
A = torch.matmul(HH,rho1_i)
B = torch.matmul(HH,rho1_r)
rhoY_r = torch.mul(A + torch.transpose(A, 0, 1), dt/ll)
rhoY_i = torch.mul(B - torch.transpose(B, 0, 1), -dt/ll)
for mm in range(Nm):
a = torch.matmul(Lm_r[mm,:,:], rho1_r)
A = a - torch.transpose(a, 0, 1)
b = torch.matmul(Lm_i[mm,:,:], rho1_i)
B = b - torch.transpose(b, 0, 1)
c = torch.matmul(Lm_r[mm,:,:], rho1_i)
C = -(c + torch.transpose(c, 0, 1))
d = torch.matmul(Lm_i[mm,:,:], rho1_r)
D = d + torch.transpose(d, 0, 1)
E = B - A
F = C - D
A = torch.matmul(Km[mm,:,:], E)
B = torch.matmul(Km[mm,:,:], F)
rhoY_r += torch.mul(A + torch.transpose(A, 0, 1),dt/ll)
rhoY_i += torch.mul(B - torch.transpose(B, 0, 1),dt/ll)
rho1_r = rhoY_r
rho1_i = rhoY_i
rho2_r += rho1_r
rho2_i += rho1_i
rho1_r = rho2_r
rho1_i = rho2_i
if use_gpu & torch.cuda.is_available():
rho2_sr = rho2_r.cpu()
rho2_si = rho2_i.cpu()
else:
rho2_sr = rho2_r
rho2_si = rho2_i
pr.data[indx,:,:] = rho2_sr.numpy() + 1j*rho2_si.numpy()
indx += 1
qr.log_detail("...DONE")
return pr
def _propagate_SExp_RTOp_ReSymK_Re_numpy(self, rhoi, Ham, RT, dt, L=4):
"""Integration by short exponentional expansion
Integration by expanding exponential (_SExp_) to Lth order.
This is a numpy (_numpy) implementation with real (_Re_) matrices
for a system part of the system-bath interaction operator ``K``
in a form of real symmetric operator (ReSymK). The relaxation tensor
is assumed in form of a set of operators (_RTOp_)
"""
Nref = self.Nref
Nt = self.Nt
verbose = self.verbose
timea = self.TimeAxis
prop_name = self.propagation_name
# no self beyond this point
qr.log_detail("PROPAGATION (short exponential with "+
"relaxation in operator form): order ", L,
verbose=verbose)
qr.log_detail("Using real valued numpy implementation")
pr = ReducedDensityMatrixEvolution(timea, rhoi,
name=prop_name)
rho1_r = numpy.real(rhoi.data)
rho2_r = numpy.real(rhoi.data)
rho1_i = numpy.imag(rhoi.data)
rho2_i = numpy.imag(rhoi.data)
HH = Ham.data
try:
Km = RT.Km #self.RelaxationTensor.Km # real
Lm_r = numpy.real(RT.Lm) #self.RelaxationTensor.Lm) # complex
Lm_i = numpy.imag(RT.Lm) #self.RelaxationTensor.Lm)
Nm = Km.shape[0]
except:
raise Exception("Tensor is not in operator form")
indx = 1
# verbosity inside loops
levs = [qr.LOG_QUICK]
verb = qr.loglevels2bool(levs, verbose=self.verbose)
# after each step we apply pure dephasing (if present)
if self.has_PDeph:
# loop over time
for ii in range(1, Nt):
qr.printlog("time step ", ii, "of", Nt,
verbose=verb[0], loglevel=levs[0], end="\r")
# steps in between saving the results
for jj in range(Nref):
# L interations to get short exponential expansion
for ll in range(1, L+1):
A = numpy.dot(HH,rho1_i)
B = numpy.dot(HH,rho1_r)
rhoY_r = (dt/ll)*(A + numpy.transpose(A))
rhoY_i = -(dt/ll)*(B - numpy.transpose(B))
for mm in range(Nm):
a = numpy.dot(Lm_r[mm,:,:], rho1_r)
A = a - numpy.transpose(a)
b = numpy.dot(Lm_i[mm,:,:], rho1_i)
B = b - numpy.transpose(b)
c = numpy.dot(Lm_r[mm,:,:], rho1_i)
C = -(c + numpy.transpose(c))
d = numpy.dot(Lm_i[mm,:,:], rho1_r)
D = d + numpy.transpose(d)
E = B - A
F = C - D
A = numpy.dot(Km[mm,:,:], E)
B = numpy.dot(Km[mm,:,:], F)
rhoY_r += (dt/ll)*(A + numpy.transpose(A))
rhoY_i += (dt/ll)*(B - numpy.transpose(B))
rho1_r = rhoY_r
rho1_i = rhoY_i
rho2_r += rho1_r
rho2_i += rho1_i
rho2_r = rho2_r*numpy.exp(-self.PDeph.data*dt)
rho2_i = rho2_i*numpy.exp(-self.PDeph.data*dt)
rho1_r = rho2_r
rho1_i = rho2_i
pr.data[indx,:,:] = rho2_r + 1j*rho2_i
indx += 1
# propagatiomn with no extra dephasing
else:
# loop over time
for ii in range(1, Nt):
qr.printlog("time step ", ii, "of", Nt,
verbose=verb[0], loglevel=levs[0], end="\r")
# steps in between saving the results
for jj in range(Nref):
# L interations to get short exponential expansion
for ll in range(1, L+1):
A = numpy.dot(HH,rho1_i)
B = numpy.dot(HH,rho1_r)
rhoY_r = (dt/ll)*(A + numpy.transpose(A))
rhoY_i = -(dt/ll)*(B - numpy.transpose(B))
for mm in range(Nm):
a = numpy.dot(Lm_r[mm,:,:], rho1_r)
A = a - numpy.transpose(a)
b = numpy.dot(Lm_i[mm,:,:], rho1_i)
B = b - numpy.transpose(b)
c = numpy.dot(Lm_r[mm,:,:], rho1_i)
C = -(c + numpy.transpose(c))
d = numpy.dot(Lm_i[mm,:,:], rho1_r)
D = d + numpy.transpose(d)
E = B - A
F = C - D
A = numpy.dot(Km[mm,:,:], E)
B = numpy.dot(Km[mm,:,:], F)
rhoY_r += (dt/ll)*(A + numpy.transpose(A))
rhoY_i += (dt/ll)*(B - numpy.transpose(B))
rho1_r = rhoY_r
rho1_i = rhoY_i
rho2_r += rho1_r
rho2_i += rho1_i
rho1_r = rho2_r
rho1_i = rho2_i
pr.data[indx,:,:] = rho2_r + 1j*rho2_i
indx += 1
qr.log_detail()
qr.log_detail("...DONE")
return pr
def __propagate_short_exp_with_rel_operators(self, rhoi, L=4):
"""Integration by short exponentional expansion
Integration by expanding exponential to Lth order.
"""
mana = Manager()
save_pytorch = None
legacy = mana.gen_conf.legacy_relaxation
if mana.num_conf.gpu_acceleration:
save_pytorch = mana.num_conf.enable_pytorch
mana.num_conf.enable_pytorch = True
if mana.num_conf.enable_pytorch and (not legacy):
ret = self._propagate_SExp_RTOp_ReSymK_Re_pytorch(rhoi,
self.Hamiltonian,
self.RelaxationTensor,
self.dt,
use_gpu=mana.num_conf.gpu_acceleration,
L=L)
if save_pytorch is not None:
mana.num_conf.enable_pytorch = save_pytorch
return ret
elif not legacy:
return self._propagate_SExp_RTOp_ReSymK_Re_numpy(rhoi,
self.Hamiltonian,
self.RelaxationTensor,
self.dt, L=L)
#
# legacy version
#
pr = ReducedDensityMatrixEvolution(self.TimeAxis, rhoi,
name=self.propagation_name)
rho1 = rhoi.data
rho2 = rhoi.data
#
# RWA is applied here
#
if self.Hamiltonian.has_rwa:
HH = self.Hamiltonian.data - self.HOmega
else:
HH = self.Hamiltonian.data
qr.log_detail("PROPAGATION (short exponential with "+
"relaxation in operator form): order ", L,
verbose=self.verbose)
qr.log_detail("Using complex numpy implementation")
try:
Km = self.RelaxationTensor.Km # real
Lm = self.RelaxationTensor.Lm # complex
Ld = self.RelaxationTensor.Ld # complex - get by transposition
Kd = numpy.zeros(Km.shape, dtype=numpy.float64)
Nm = Km.shape[0]
for m in range(Nm):
Kd[m, :, :] = numpy.transpose(Km[m, :, :])
except:
raise Exception("Tensor is not in operator form")
indx = 1
levs = [qr.LOG_QUICK] #, 8]
verb = qr.loglevels2bool(levs)
# after each step we apply pure dephasing (if present)
if self.has_PDeph:
if self.PDeph.dtype == "Lorentzian":
expo = numpy.exp(-self.PDeph.data*self.dt)
t0 = 0.0
elif self.PDeph.dtype == "Gaussian":
expo = numpy.exp(-self.PDeph.data*(self.dt**2)/2.0)
t0 = self.PDeph.data*self.dt
# loop over time
for ii in range(1, self.Nt):
qr.printlog(" time step ", ii, "of", self.Nt,
verbose=verb[0], loglevel=levs[0])
# time at the beginning of the step
tNt = self.TimeAxis.data[indx-1]
#print("tNt = ", tNt)
# steps in between saving the results
for jj in range(0, self.Nref):
tt = tNt + jj*self.dt # time right now
# L interations to get short exponential expansion
for ll in range(1, L+1):
rhoY = - (1j*self.dt/ll)*(numpy.dot(HH,rho1)
- numpy.dot(rho1,HH))
#rhoX = numpy.zeros(rho1.shape, dtype=numpy.complex128)
for mm in range(Nm):
rhoY += (self.dt/ll)*(
numpy.dot(Km[mm,:,:],numpy.dot(rho1, Ld[mm,:,:]))
+numpy.dot(Lm[mm,:,:],numpy.dot(rho1, Kd[mm,:,:]))
-numpy.dot(numpy.dot(Kd[mm,:,:],Lm[mm,:,:]), rho1)
-numpy.dot(rho1, numpy.dot(Ld[mm,:,:],Km[mm,:,:]))
)
rho1 = rhoY #+ rhoX
rho2 = rho2 + rho1
# pure dephasing is added here
rho2 = rho2*expo*numpy.exp(-t0*tt)
rho1 = rho2
pr.data[indx,:,:] = rho2
indx += 1
# no extra dephasing
else:
# loop over time
for ii in range(1, self.Nt):
qr.printlog(" time step ", ii, "of", self.Nt,
verbose=verb[0], loglevel=levs[0])
# steps in between saving the results
for jj in range(0, self.Nref):
# L interations to get short exponential expansion
for ll in range(1, L+1):
rhoY = - (1j*self.dt/ll)*(numpy.dot(HH,rho1)
- numpy.dot(rho1,HH))
#rhoX = numpy.zeros(rho1.shape, dtype=numpy.complex128)
for mm in range(Nm):
rhoY += (self.dt/ll)*(
numpy.dot(Km[mm,:,:],numpy.dot(rho1, Ld[mm,:,:]))
+numpy.dot(Lm[mm,:,:],numpy.dot(rho1, Kd[mm,:,:]))
-numpy.dot(numpy.dot(Kd[mm,:,:],Lm[mm,:,:]), rho1)
-numpy.dot(rho1, numpy.dot(Ld[mm,:,:],Km[mm,:,:]))
)
rho1 = rhoY #+ rhoX
rho2 = rho2 + rho1
rho1 = rho2
pr.data[indx,:,:] = rho2
indx += 1
qr.log_detail("...DONE")
return pr