def get_from_chain_stepwise_convergence(J,
domain,
nof_coefficients,
disc_type='sp_quad',
interval_type='log',
mapping_type='sp_hes',
permute=None,
residual=True,
low_memory=True,
stable=False,
min_ncap=10,
max_ncap=2000,
step_ncap=1,
stop_rel=1e-10,
stop_abs=1e-10,
get_trafo=False,
force_sp=False,
mp_dps=30,
sort_by=None,
**kwargs):
"""
Returns star coefficients, constructed from chain coefficients via diagonalization
see chain.get_from_stepwise_convergence and convert_chain_to_star for an explanation of the arguments.
Sort_by sorts the couplings and energies (if passed and not None), see utils.sorting.sort_star_coefficients
for details on the parameters.
Defaults to logarithmic intervals for the direct discretization
:returns: gamma (couplings), xi (energies), info dict from both the conversion and the chain mapping
if get_trafo is set True, the dict only contains the latest transformation (from chain to star here)
"""
c0, omega, t, info = get_from_stepwise_convergence(
J,
domain,
nof_coefficients,
disc_type=disc_type,
interval_type=interval_type,
mapping_type=mapping_type,
permute=permute,
residual=residual,
low_memory=low_memory,
stable=stable,
min_ncap=min_ncap,
max_ncap=max_ncap,
step_ncap=step_ncap,
stop_rel=stop_rel,
stop_abs=stop_abs,
get_trafo=False,
**kwargs)
gamma, xi, trafo_info = convert_chain_to_star(c0,
omega,
t,
force_sp=force_sp,
mp_dps=mp_dps,
get_trafo=get_trafo)
gamma, xi = sort_star_coefficients(gamma, xi, sort_by)
return gamma, xi, info.update(trafo_info)
def get_from_hr_star_stepwise_convergence(discretized_bath,
nof_coefficients,
mapping_type='sp_hes',
permute=None,
residual=True,
low_memory=True,
stable=False,
min_ncap=10,
max_ncap=2000,
step_ncap=1,
stop_rel=1e-10,
stop_abs=1e-10,
get_trafo=False,
force_sp=False,
mp_dps=30,
sort_by=None):
"""
Returns star coefficients, constructed from chain coefficients via diagonalization using a pre-
constructed discretized bath as 'high-resolution' star, which is mapped to chain, truncated and
then mapped back,
see chain.from_bath_from_stepwise_convergence and convert_chain_to_star for an explanation of the arguments.
Sort_by sorts the couplings and energies (if passed and not None), see utils.sorting.sort_star_coefficients
for details on the parameters.
:returns: gamma (couplings), xi (energies), info dict from both the conversion and the chain mapping
if get_trafo is set True, the dict only contains the latest transformation (from chain to star here)
"""
c0, omega, t, info = from_bath_from_stepwise_convergence(
discretized_bath,
nof_coefficients,
mapping_type=mapping_type,
permute=permute,
residual=residual,
low_memory=low_memory,
stable=stable,
min_ncap=min_ncap,
max_ncap=max_ncap,
step_ncap=step_ncap,
stop_rel=stop_rel,
stop_abs=stop_abs,
get_trafo=get_trafo)
gamma, xi, trafo_info = convert_chain_to_star(c0,
omega,
t,
force_sp=force_sp,
mp_dps=mp_dps,
get_trafo=get_trafo)
gamma, xi = sort_star_coefficients(gamma, xi, sort_by)
return gamma, xi, info.update(trafo_info)
def get_star_coefficients_from_chain(self,
get_trafo=False,
force_sp=False,
mp_dps=30):
"""
Calculates the equivalent star coefficients of the currently calculated chain coefficients.
Returns None if none have been calculated so far
See utils.convert.convert_chain_to_star for an explanation of the parameters
:return: star couplings gamma, star energies xi, info dict from conversion
(see utils.convert.convert_chain_to_star)
"""
if self.nof_calculated_coefficients == 0:
return None, None, None
else:
return convert_chain_to_star(self.c0,
self.omega,
self.t,
get_trafo=get_trafo,
force_sp=force_sp,
mp_dps=mp_dps)
def get_discretized_bath_from_chain(self,
get_trafo=False,
force_sp=False,
mp_dps=30):
"""
Calculates the equivalent discretized bath of the currently calculated chain coefficients.
Returns None if none have been calculated so far
See utils.convert.convert_chain_to_star for an explanation of the parameters.
:return: discretized bath object, info dict from conversion (see utils.convert.convert_chain_to_star)
"""
if self.nof_calculated_coefficients == 0:
return None, None
else:
gamma, xi = convert_chain_to_star(self.c0,
self.omega,
self.t,
get_trafo=get_trafo,
force_sp=force_sp,
mp_dps=mp_dps)
return DiscretizedBath(gamma, xi)
def __init__(self, J, domain, max_nof_coefficients=100, **kwargs):
"""
Generates BSDO coefficients from a spectral density J, by diagonalizing the tridiagonal matrix
of polynomial recurrence coefficients
:param J: Spectral density. A function defined on 'domain', must be >0 in the inner part of domain
:param domain: List/tuple of two elements for the left and right boundary of the domain of J
:param max_nof_coefficients: Size of the buffers which hold gamma and xi coefficients (maximum number of
these coefficients that can be calculated)
:param kwargs: may contain 'orthpol_ncap' to change the internal discretization of orthpol, default is 60000
'mp_dps' to change the number o decimals with which the diagonalization is performed
defult is 30
'force_sp' forces scipy eigh for the diagonalization, default is False
"""
self.J = J
try:
orthpol_ncap = kwargs['orthpol_ncap']
except KeyError:
orthpol_ncap = 60000
try:
mp_dps = kwargs['mp_dps']
except KeyError:
mp_dps = 30
try:
force_sp = kwargs['force_sp']
except KeyError:
force_sp = False
try:
get_trafo = kwargs['get_trafo']
except KeyError:
get_trafo = False
super().__init__(self.compute_coefficients, max_nof_coefficients=max_nof_coefficients)
# Preallocate arrays for the coefficients
alpha, beta = self.get_monic_recurrence(max_nof_coefficients, domain, J, orthpol_ncap)
self._eta_0 = beta[0]
self.gamma_buf[:], self.xi_buf[:], info = \
convert_chain_to_star(np.sqrt(beta[0]), alpha, np.sqrt(beta[1::]), force_sp=force_sp, mp_dps=mp_dps,
sort_by=None, get_trafo=get_trafo)
self.info = info
self._set_next_n(max_nof_coefficients)