def configure(self,
H_sys,
coup_op,
coup_strength,
temperature,
N_cut,
N_exp,
cut_freq,
planck=None,
boltzmann=None,
renorm=None,
bnd_cut_approx=None,
options=None,
progress_bar=None,
stats=None):
"""
Calls configure from :class:`HEOMSolver` and sets any attributes
that are specific to this subclass
"""
start_config = timeit.default_timer()
HEOMSolver.configure(self,
H_sys,
coup_op,
coup_strength,
temperature,
N_cut,
N_exp,
planck=planck,
boltzmann=boltzmann,
options=options,
progress_bar=progress_bar,
stats=stats)
self.cut_freq = cut_freq
if renorm is not None: self.renorm = renorm
if bnd_cut_approx is not None: self.bnd_cut_approx = bnd_cut_approx
# Load local values for optional parameters
# Constants and Hamiltonian.
hbar = self.planck
options = self.options
progress_bar = self.progress_bar
stats = self.stats
if stats:
ss_conf = stats.sections.get('config')
if ss_conf is None:
ss_conf = stats.add_section('config')
c, nu = self._calc_matsubara_params()
if renorm:
norm_plus, norm_minus = self._calc_renorm_factors()
if stats:
stats.add_message('options', 'renormalisation', ss_conf)
# Dimensions et by system
sup_dim = H_sys.dims[0][0]**2
unit_sys = qeye(H_sys.dims[0])
# Use shorthands (mainly as in referenced PRL)
lam0 = self.coup_strength
gam = self.cut_freq
N_c = self.N_cut
N_m = self.N_exp
Q = coup_op # Q as shorthand for coupling operator
beta = 1.0 / (self.boltzmann * self.temperature)
# Ntot is the total number of ancillary elements in the hierarchy
# Ntot = factorial(N_c + N_m) / (factorial(N_c)*factorial(N_m))
# Turns out to be the same as nstates from state_number_enumerate
N_he, he2idx, idx2he = enr_state_dictionaries([N_c + 1] * N_m, N_c)
unit_helems = fast_identity(N_he)
if self.bnd_cut_approx:
# the Tanimura boundary cut off operator
if stats:
stats.add_message('options', 'boundary cutoff approx', ss_conf)
op = -2 * spre(Q) * spost(Q.dag()) + spre(Q.dag() * Q) + spost(
Q.dag() * Q)
approx_factr = ((2 * lam0 /
(beta * gam * hbar)) - 1j * lam0) / hbar
for k in range(N_m):
approx_factr -= (c[k] / nu[k])
L_bnd = -approx_factr * op.data
L_helems = zcsr_kron(unit_helems, L_bnd)
else:
L_helems = fast_csr_matrix(shape=(N_he * sup_dim, N_he * sup_dim))
# Build the hierarchy element interaction matrix
if stats: start_helem_constr = timeit.default_timer()
unit_sup = spre(unit_sys).data
spreQ = spre(Q).data
spostQ = spost(Q).data
commQ = (spre(Q) - spost(Q)).data
N_he_interact = 0
for he_idx in range(N_he):
he_state = list(idx2he[he_idx])
n_excite = sum(he_state)
# The diagonal elements for the hierarchy operator
# coeff for diagonal elements
sum_n_m_freq = 0.0
for k in range(N_m):
sum_n_m_freq += he_state[k] * nu[k]
op = -sum_n_m_freq * unit_sup
L_he = cy_pad_csr(op, N_he, N_he, he_idx, he_idx)
L_helems += L_he
# Add the neighour interations
he_state_neigh = copy(he_state)
for k in range(N_m):
n_k = he_state[k]
if n_k >= 1:
# find the hierarchy element index of the neighbour before
# this element, for this Matsubara term
he_state_neigh[k] = n_k - 1
he_idx_neigh = he2idx[tuple(he_state_neigh)]
op = c[k] * spreQ - np.conj(c[k]) * spostQ
if renorm:
op = -1j * norm_minus[n_k, k] * op
else:
op = -1j * n_k * op
L_he = cy_pad_csr(op, N_he, N_he, he_idx, he_idx_neigh)
L_helems += L_he
N_he_interact += 1
he_state_neigh[k] = n_k
if n_excite <= N_c - 1:
# find the hierarchy element index of the neighbour after
# this element, for this Matsubara term
he_state_neigh[k] = n_k + 1
he_idx_neigh = he2idx[tuple(he_state_neigh)]
op = commQ
if renorm:
op = -1j * norm_plus[n_k, k] * op
else:
op = -1j * op
L_he = cy_pad_csr(op, N_he, N_he, he_idx, he_idx_neigh)
L_helems += L_he
N_he_interact += 1
he_state_neigh[k] = n_k
if stats:
stats.add_timing('hierarchy contruct',
timeit.default_timer() - start_helem_constr,
ss_conf)
stats.add_count('Num hierarchy elements', N_he, ss_conf)
stats.add_count('Num he interactions', N_he_interact, ss_conf)
# Setup Liouvillian
if stats:
start_louvillian = timeit.default_timer()
H_he = zcsr_kron(unit_helems, liouvillian(H_sys).data)
L_helems += H_he
if stats:
stats.add_timing('Liouvillian contruct',
timeit.default_timer() - start_louvillian,
ss_conf)
if stats: start_integ_conf = timeit.default_timer()
r = scipy.integrate.ode(cy_ode_rhs)
r.set_f_params(L_helems.data, L_helems.indices, L_helems.indptr)
r.set_integrator('zvode',
method=options.method,
order=options.order,
atol=options.atol,
rtol=options.rtol,
nsteps=options.nsteps,
first_step=options.first_step,
min_step=options.min_step,
max_step=options.max_step)
if stats:
time_now = timeit.default_timer()
stats.add_timing('Liouvillian contruct',
time_now - start_integ_conf, ss_conf)
if ss_conf.total_time is None:
ss_conf.total_time = time_now - start_config
else:
ss_conf.total_time += time_now - start_config
self._ode = r
self._N_he = N_he
self._sup_dim = sup_dim
self._configured = True
def configure(self, H_sys, coup_op, coup_strength, temperature,
N_cut, N_exp, cut_freq, planck=None, boltzmann=None,
renorm=None, bnd_cut_approx=None,
options=None, progress_bar=None, stats=None):
"""
Calls configure from :class:`HEOMSolver` and sets any attributes
that are specific to this subclass
"""
start_config = timeit.default_timer()
HEOMSolver.configure(self, H_sys, coup_op, coup_strength,
temperature, N_cut, N_exp,
planck=planck, boltzmann=boltzmann,
options=options, progress_bar=progress_bar, stats=stats)
self.cut_freq = cut_freq
if renorm is not None: self.renorm = renorm
if bnd_cut_approx is not None: self.bnd_cut_approx = bnd_cut_approx
# Load local values for optional parameters
# Constants and Hamiltonian.
hbar = self.planck
options = self.options
progress_bar = self.progress_bar
stats = self.stats
if stats:
ss_conf = stats.sections.get('config')
if ss_conf is None:
ss_conf = stats.add_section('config')
c, nu = self._calc_matsubara_params()
if renorm:
norm_plus, norm_minus = self._calc_renorm_factors()
if stats:
stats.add_message('options', 'renormalisation', ss_conf)
# Dimensions et by system
N_temp = 1
for i in H_sys.dims[0]:
N_temp *= i
sup_dim = N_temp**2
unit_sys = qeye(N_temp)
# Use shorthands (mainly as in referenced PRL)
lam0 = self.coup_strength
gam = self.cut_freq
N_c = self.N_cut
N_m = self.N_exp
Q = coup_op # Q as shorthand for coupling operator
beta = 1.0/(self.boltzmann*self.temperature)
# Ntot is the total number of ancillary elements in the hierarchy
# Ntot = factorial(N_c + N_m) / (factorial(N_c)*factorial(N_m))
# Turns out to be the same as nstates from state_number_enumerate
N_he, he2idx, idx2he = enr_state_dictionaries([N_c + 1]*N_m , N_c)
unit_helems = fast_identity(N_he)
if self.bnd_cut_approx:
# the Tanimura boundary cut off operator
if stats:
stats.add_message('options', 'boundary cutoff approx', ss_conf)
op = -2*spre(Q)*spost(Q.dag()) + spre(Q.dag()*Q) + spost(Q.dag()*Q)
approx_factr = ((2*lam0 / (beta*gam*hbar)) - 1j*lam0) / hbar
for k in range(N_m):
approx_factr -= (c[k] / nu[k])
L_bnd = -approx_factr*op.data
L_helems = zcsr_kron(unit_helems, L_bnd)
else:
L_helems = fast_csr_matrix(shape=(N_he*sup_dim, N_he*sup_dim))
# Build the hierarchy element interaction matrix
if stats: start_helem_constr = timeit.default_timer()
unit_sup = spre(unit_sys).data
spreQ = spre(Q).data
spostQ = spost(Q).data
commQ = (spre(Q) - spost(Q)).data
N_he_interact = 0
for he_idx in range(N_he):
he_state = list(idx2he[he_idx])
n_excite = sum(he_state)
# The diagonal elements for the hierarchy operator
# coeff for diagonal elements
sum_n_m_freq = 0.0
for k in range(N_m):
sum_n_m_freq += he_state[k]*nu[k]
op = -sum_n_m_freq*unit_sup
L_he = cy_pad_csr(op, N_he, N_he, he_idx, he_idx)
L_helems += L_he
# Add the neighour interations
he_state_neigh = copy(he_state)
for k in range(N_m):
n_k = he_state[k]
if n_k >= 1:
# find the hierarchy element index of the neighbour before
# this element, for this Matsubara term
he_state_neigh[k] = n_k - 1
he_idx_neigh = he2idx[tuple(he_state_neigh)]
op = c[k]*spreQ - np.conj(c[k])*spostQ
if renorm:
op = -1j*norm_minus[n_k, k]*op
else:
op = -1j*n_k*op
L_he = cy_pad_csr(op, N_he, N_he, he_idx, he_idx_neigh)
L_helems += L_he
N_he_interact += 1
he_state_neigh[k] = n_k
if n_excite <= N_c - 1:
# find the hierarchy element index of the neighbour after
# this element, for this Matsubara term
he_state_neigh[k] = n_k + 1
he_idx_neigh = he2idx[tuple(he_state_neigh)]
op = commQ
if renorm:
op = -1j*norm_plus[n_k, k]*op
else:
op = -1j*op
L_he = cy_pad_csr(op, N_he, N_he, he_idx, he_idx_neigh)
L_helems += L_he
N_he_interact += 1
he_state_neigh[k] = n_k
if stats:
stats.add_timing('hierarchy contruct',
timeit.default_timer() - start_helem_constr,
ss_conf)
stats.add_count('Num hierarchy elements', N_he, ss_conf)
stats.add_count('Num he interactions', N_he_interact, ss_conf)
# Setup Liouvillian
if stats:
start_louvillian = timeit.default_timer()
H_he = zcsr_kron(unit_helems, liouvillian(H_sys).data)
L_helems += H_he
if stats:
stats.add_timing('Liouvillian contruct',
timeit.default_timer() - start_louvillian,
ss_conf)
if stats: start_integ_conf = timeit.default_timer()
r = scipy.integrate.ode(cy_ode_rhs)
r.set_f_params(L_helems.data, L_helems.indices, L_helems.indptr)
r.set_integrator('zvode', method=options.method, order=options.order,
atol=options.atol, rtol=options.rtol,
nsteps=options.nsteps, first_step=options.first_step,
min_step=options.min_step, max_step=options.max_step)
if stats:
time_now = timeit.default_timer()
stats.add_timing('Liouvillian contruct',
time_now - start_integ_conf,
ss_conf)
if ss_conf.total_time is None:
ss_conf.total_time = time_now - start_config
else:
ss_conf.total_time += time_now - start_config
self._ode = r
self._N_he = N_he
self._sup_dim = sup_dim
self._configured = True