def _smepdpsolve_generic(sso, options, progress_bar):
"""
For internal use. See smepdpsolve.
"""
if debug:
logger.debug(inspect.stack()[0][3])
N_store = len(sso.times)
N_substeps = sso.nsubsteps
dt = (sso.times[1] - sso.times[0]) / N_substeps
nt = sso.ntraj
data = Result()
data.solver = "smepdpsolve"
data.times = sso.times
data.expect = np.zeros((len(sso.e_ops), N_store), dtype=complex)
data.jump_times = []
data.jump_op_idx = []
# Liouvillian for the deterministic part.
# needs to be modified for TD systems
L = liouvillian(sso.H, sso.c_ops)
progress_bar.start(sso.ntraj)
for n in range(sso.ntraj):
progress_bar.update(n)
rho_t = mat2vec(sso.rho0.full()).ravel()
states_list, jump_times, jump_op_idx = \
_smepdpsolve_single_trajectory(data, L, dt, sso.times,
N_store, N_substeps,
rho_t, sso.rho0.dims,
sso.c_ops, sso.e_ops)
data.states.append(states_list)
data.jump_times.append(jump_times)
data.jump_op_idx.append(jump_op_idx)
progress_bar.finished()
# average density matrices
if options.average_states and np.any(data.states):
data.states = [
sum([data.states[m][n] for m in range(nt)]).unit()
for n in range(len(data.times))
]
# average
data.expect = data.expect / sso.ntraj
# standard error
if nt > 1:
data.se = (data.ss - nt * (data.expect**2)) / (nt * (nt - 1))
else:
data.se = None
return data
def solve(self, rho0, tlist, options=None, progress=None):
"""
Solve the Hierarchy equations of motion for the given initial
density matrix and time.
"""
if options is None:
options = Options()
output = Result()
output.solver = "hsolve"
output.times = tlist
output.states = []
output.states.append(Qobj(rho0))
dt = np.diff(tlist)
rho_he = np.zeros(self.hshape, dtype=np.complex)
rho_he[0] = rho0.full().ravel("F")
rho_he = rho_he.flatten()
self.rhs()
L_helems = self.L_helems.asformat("csr")
r = 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,
)
r.set_initial_value(rho_he, tlist[0])
dt = np.diff(tlist)
n_tsteps = len(tlist)
if progress:
bar = progress(total=n_tsteps - 1)
for t_idx, t in enumerate(tlist):
if t_idx < n_tsteps - 1:
r.integrate(r.t + dt[t_idx])
r1 = r.y.reshape(self.hshape)
r0 = r1[0].reshape(self.N, self.N).T
output.states.append(Qobj(r0))
r_heom = r.y.reshape(self.hshape)
self.full_hierarchy.append(r_heom)
if progress:
bar.update()
return output
def run(self, rho0, tlist):
"""
Function to solve for an open quantum system using the
HEOM model.
Parameters
----------
rho0 : Qobj
Initial state (density matrix) of the system.
tlist : list
Time over which system evolves.
Returns
-------
results : :class:`qutip.solver.Result`
Object storing all results from the simulation.
"""
sup_dim = self._sup_dim
solver = self._ode
if not self._configured:
raise RuntimeError("Solver must be configured before it is run")
output = Result()
output.solver = "hsolve"
output.times = tlist
output.states = []
output.states.append(Qobj(rho0))
rho0_flat = rho0.full().ravel('F')
rho0_he = np.zeros([sup_dim*self._N_he], dtype=complex)
rho0_he[:sup_dim] = rho0_flat
solver.set_initial_value(rho0_he, tlist[0])
dt = np.diff(tlist)
n_tsteps = len(tlist)
for t_idx, t in enumerate(tlist):
if t_idx < n_tsteps - 1:
solver.integrate(solver.t + dt[t_idx])
rho = Qobj(solver.y[:sup_dim].reshape(rho0.shape,order='F'), dims=rho0.dims)
output.states.append(rho)
return output
def exactsolve(H, psi0, tlist):
"""Calculates exact solution by direct diagonalization."""
dims = psi0.dims
H = H.full()
psi0 = psi0.full()
eigenvalues, eigenvectors = eigh(H)
psi_base_diag = np.matmul(eigenvectors.conj().T, psi0)
U = np.exp(np.outer(-1j * eigenvalues, tlist))
psi_list = np.matmul(
eigenvectors, np.multiply(U, psi_base_diag.reshape([-1, 1]))
)
exact_results = Result()
exact_results.states = [Qobj(state, dims=dims) for state in psi_list.T]
return exact_results
def __init__(self):
self.cpus = config.options.num_cpus
self.nprocs = self.cpus
self.sol = Result()
self.mf = 10
# If returning density matrices, return as sparse or dense?
self.sparse_dms = True
# Run in serial?
self.serial_run = False
self.ntraj = config.ntraj
self.ntrajs = []
self.seed = None
self.psi0_dims = None
self.psi0_shape = None
self.dm_dims = None
self.dm_shape = None
self.unravel_type = 2
self.ptrace_sel = []
self.calc_entropy = False
def solve(self, rho0, tlist, options=None):
"""
Solve the ODE for the evolution of diagonal states and Hamiltonians.
"""
if options is None:
options = Options()
output = Result()
output.solver = "pisolve"
output.times = tlist
output.states = []
output.states.append(Qobj(rho0))
rhs_generate = lambda y, tt, M: M.dot(y)
rho0_flat = np.diag(np.real(rho0.full()))
L = self.coefficient_matrix()
rho_t = odeint(rhs_generate, rho0_flat, tlist, args=(L, ))
for r in rho_t[1:]:
diag = np.diag(r)
output.states.append(Qobj(diag))
return output
def get_result(self, ntraj=[]):
# Store results in the Result object
if not ntraj:
ntraj = [self.num_traj]
elif not isinstance(ntraj, list):
ntraj = [ntraj]
output = Result()
output.solver = 'mcsolve'
output.seeds = self.seeds
options = self.options
output.options = options
if options.steady_state_average:
output.states = self.steady_state
elif options.average_states and options.store_states:
output.states = self.states
elif options.store_states:
output.states = self.runs_states
if options.store_final_state:
if options.average_states:
output.final_state = self.final_state
else:
output.final_state = self.runs_final_states
if options.average_expect:
output.expect = [self.expect_traj_avg(n) for n in ntraj]
if len(output.expect) == 1:
output.expect = output.expect[0]
else:
output.expect = self.runs_expect
# simulation parameters
output.times = self.tlist
output.num_expect = self.e_ops.e_num
output.num_collapse = len(self.ss.td_c_ops)
output.ntraj = self.num_traj
output.col_times = self.collapse_times
output.col_which = self.collapse_which
return output
def _generic_ode_solve(r, psi0, tlist, e_ops, opt, progress_bar, dims=None):
"""
Internal function for solving ODEs.
"""
if opt.normalize_output:
state_norm_func = norm
else:
state_norm_func = None
#
# prepare output array
#
n_tsteps = len(tlist)
output = Result()
output.solver = "sesolve"
output.times = tlist
if opt.store_states:
output.states = []
if isinstance(e_ops, types.FunctionType):
n_expt_op = 0
expt_callback = True
elif isinstance(e_ops, list):
n_expt_op = len(e_ops)
expt_callback = False
if n_expt_op == 0:
# fallback on storing states
output.states = []
opt.store_states = True
else:
output.expect = []
output.num_expect = n_expt_op
for op in e_ops:
if op.isherm:
output.expect.append(np.zeros(n_tsteps))
else:
output.expect.append(np.zeros(n_tsteps, dtype=complex))
else:
raise TypeError("Expectation parameter must be a list or a function")
#
# start evolution
#
progress_bar.start(n_tsteps)
dt = np.diff(tlist)
for t_idx, t in enumerate(tlist):
progress_bar.update(t_idx)
if not r.successful():
raise Exception("ODE integration error: Try to increase "
"the allowed number of substeps by increasing "
"the nsteps parameter in the Options class.")
if state_norm_func:
data = r.y / state_norm_func(r.y)
r.set_initial_value(data, r.t)
if opt.store_states:
output.states.append(Qobj(r.y, dims=dims))
if expt_callback:
# use callback method
e_ops(t, Qobj(r.y, dims=psi0.dims))
for m in range(n_expt_op):
output.expect[m][t_idx] = cy_expect_psi(e_ops[m].data, r.y,
e_ops[m].isherm)
if t_idx < n_tsteps - 1:
r.integrate(r.t + dt[t_idx])
progress_bar.finished()
if not opt.rhs_reuse and config.tdname is not None:
try:
os.remove(config.tdname + ".pyx")
except:
pass
if opt.store_final_state:
output.final_state = Qobj(r.y, dims=dims)
return output
def mcsolve(H, psi0, tlist, c_ops, e_ops, ntraj=None,
args={}, options=None, progress_bar=True,
map_func=None, map_kwargs=None):
"""Monte Carlo evolution of a state vector :math:`|\psi \\rangle` for a
given Hamiltonian and sets of collapse operators, and possibly, operators
for calculating expectation values. Options for the underlying ODE solver
are given by the Options class.
mcsolve supports time-dependent Hamiltonians and collapse operators using
either Python functions of strings to represent time-dependent
coefficients. Note that, the system Hamiltonian MUST have at least one
constant term.
As an example of a time-dependent problem, consider a Hamiltonian with two
terms ``H0`` and ``H1``, where ``H1`` is time-dependent with coefficient
``sin(w*t)``, and collapse operators ``C0`` and ``C1``, where ``C1`` is
time-dependent with coeffcient ``exp(-a*t)``. Here, w and a are constant
arguments with values ``W`` and ``A``.
Using the Python function time-dependent format requires two Python
functions, one for each collapse coefficient. Therefore, this problem could
be expressed as::
def H1_coeff(t,args):
return sin(args['w']*t)
def C1_coeff(t,args):
return exp(-args['a']*t)
H = [H0, [H1, H1_coeff]]
c_ops = [C0, [C1, C1_coeff]]
args={'a': A, 'w': W}
or in String (Cython) format we could write::
H = [H0, [H1, 'sin(w*t)']]
c_ops = [C0, [C1, 'exp(-a*t)']]
args={'a': A, 'w': W}
Constant terms are preferably placed first in the Hamiltonian and collapse
operator lists.
Parameters
----------
H : :class:`qutip.Qobj`
System Hamiltonian.
psi0 : :class:`qutip.Qobj`
Initial state vector
tlist : array_like
Times at which results are recorded.
ntraj : int
Number of trajectories to run.
c_ops : array_like
single collapse operator or ``list`` or ``array`` of collapse
operators.
e_ops : array_like
single operator or ``list`` or ``array`` of operators for calculating
expectation values.
args : dict
Arguments for time-dependent Hamiltonian and collapse operator terms.
options : Options
Instance of ODE solver options.
progress_bar: BaseProgressBar
Optional instance of BaseProgressBar, or a subclass thereof, for
showing the progress of the simulation. Set to None to disable the
progress bar.
map_func: function
A map function for managing the calls to the single-trajactory solver.
map_kwargs: dictionary
Optional keyword arguments to the map_func function.
Returns
-------
results : :class:`qutip.solver.Result`
Object storing all results from the simulation.
.. note::
It is possible to reuse the random number seeds from a previous run
of the mcsolver by passing the output Result object seeds via the
Options class, i.e. Options(seeds=prev_result.seeds).
"""
if debug:
print(inspect.stack()[0][3])
if options is None:
options = Options()
if ntraj is None:
ntraj = options.ntraj
config.map_func = map_func if map_func is not None else parallel_map
config.map_kwargs = map_kwargs if map_kwargs is not None else {}
if not psi0.isket:
raise Exception("Initial state must be a state vector.")
if isinstance(c_ops, Qobj):
c_ops = [c_ops]
if isinstance(e_ops, Qobj):
e_ops = [e_ops]
if isinstance(e_ops, dict):
e_ops_dict = e_ops
e_ops = [e for e in e_ops.values()]
else:
e_ops_dict = None
config.options = options
if progress_bar:
if progress_bar is True:
config.progress_bar = TextProgressBar()
else:
config.progress_bar = progress_bar
else:
config.progress_bar = BaseProgressBar()
# set num_cpus to the value given in qutip.settings if none in Options
if not config.options.num_cpus:
config.options.num_cpus = qutip.settings.num_cpus
if config.options.num_cpus == 1:
# fallback on serial_map if num_cpu == 1, since there is no
# benefit of starting multiprocessing in this case
config.map_func = serial_map
# set initial value data
if options.tidy:
config.psi0 = psi0.tidyup(options.atol).full().ravel()
else:
config.psi0 = psi0.full().ravel()
config.psi0_dims = psi0.dims
config.psi0_shape = psi0.shape
# set options on ouput states
if config.options.steady_state_average:
config.options.average_states = True
# set general items
config.tlist = tlist
if isinstance(ntraj, (list, np.ndarray)):
config.ntraj = np.sort(ntraj)[-1]
else:
config.ntraj = ntraj
# set norm finding constants
config.norm_tol = options.norm_tol
config.norm_steps = options.norm_steps
# convert array based time-dependence to string format
H, c_ops, args = _td_wrap_array_str(H, c_ops, args, tlist)
# SETUP ODE DATA IF NONE EXISTS OR NOT REUSING
# --------------------------------------------
if not options.rhs_reuse or not config.tdfunc:
# reset config collapse and time-dependence flags to default values
config.soft_reset()
# check for type of time-dependence (if any)
time_type, h_stuff, c_stuff = _td_format_check(H, c_ops, 'mc')
c_terms = len(c_stuff[0]) + len(c_stuff[1]) + len(c_stuff[2])
# set time_type for use in multiprocessing
config.tflag = time_type
# check for collapse operators
if c_terms > 0:
config.cflag = 1
else:
config.cflag = 0
# Configure data
_mc_data_config(H, psi0, h_stuff, c_ops, c_stuff, args, e_ops,
options, config)
# compile and load cython functions if necessary
_mc_func_load(config)
else:
# setup args for new parameters when rhs_reuse=True and tdfunc is given
# string based
if config.tflag in [1, 10, 11]:
if any(args):
config.c_args = []
arg_items = list(args.items())
for k in range(len(arg_items)):
config.c_args.append(arg_items[k][1])
# function based
elif config.tflag in [2, 3, 20, 22]:
config.h_func_args = args
# load monte carlo class
mc = _MC(config)
# Run the simulation
mc.run()
# Remove RHS cython file if necessary
if not options.rhs_reuse and config.tdname:
_cython_build_cleanup(config.tdname)
# AFTER MCSOLVER IS DONE
# ----------------------
# Store results in the Result object
output = Result()
output.solver = 'mcsolve'
output.seeds = config.options.seeds
# state vectors
if (mc.psi_out is not None and config.options.average_states
and config.cflag and ntraj != 1):
output.states = parfor(_mc_dm_avg, mc.psi_out.T)
elif mc.psi_out is not None:
output.states = mc.psi_out
# expectation values
if (mc.expect_out is not None and config.cflag
and config.options.average_expect):
# averaging if multiple trajectories
if isinstance(ntraj, int):
output.expect = [np.mean(np.array([mc.expect_out[nt][op]
for nt in range(ntraj)],
dtype=object),
axis=0)
for op in range(config.e_num)]
elif isinstance(ntraj, (list, np.ndarray)):
output.expect = []
for num in ntraj:
expt_data = np.mean(mc.expect_out[:num], axis=0)
data_list = []
if any([not op.isherm for op in e_ops]):
for k in range(len(e_ops)):
if e_ops[k].isherm:
data_list.append(np.real(expt_data[k]))
else:
data_list.append(expt_data[k])
else:
data_list = [data for data in expt_data]
output.expect.append(data_list)
else:
# no averaging for single trajectory or if average_expect flag
# (Options) is off
if mc.expect_out is not None:
output.expect = mc.expect_out
# simulation parameters
output.times = config.tlist
output.num_expect = config.e_num
output.num_collapse = config.c_num
output.ntraj = config.ntraj
output.col_times = mc.collapse_times_out
output.col_which = mc.which_op_out
if e_ops_dict:
output.expect = {e: output.expect[n]
for n, e in enumerate(e_ops_dict.keys())}
return output
def essolve(H, rho0, tlist, c_op_list, e_ops):
"""
Evolution of a state vector or density matrix (`rho0`) for a given
Hamiltonian (`H`) and set of collapse operators (`c_op_list`), by
expressing the ODE as an exponential series. The output is either
the state vector at arbitrary points in time (`tlist`), or the
expectation values of the supplied operators (`e_ops`).
.. deprecated:: 4.6.0
:obj:`~essolev` will be removed in QuTiP 5. Please use :obj:`~sesolve`
or :obj:`~mesolve` for general-purpose integration of the
Schroedinger/Lindblad master equation. This will likely be faster than
:obj:`~essolve` for you.
Parameters
----------
H : qobj/function_type
System Hamiltonian.
rho0 : :class:`qutip.qobj`
Initial state density matrix.
tlist : list/array
``list`` of times for :math:`t`.
c_op_list : list of :class:`qutip.qobj`
``list`` of :class:`qutip.qobj` collapse operators.
e_ops : list of :class:`qutip.qobj`
``list`` of :class:`qutip.qobj` operators for which to evaluate
expectation values.
Returns
-------
expt_array : array
Expectation values of wavefunctions/density matrices for the
times specified in ``tlist``.
.. note:: This solver does not support time-dependent Hamiltonians.
"""
n_expt_op = len(e_ops)
n_tsteps = len(tlist)
# Calculate the Liouvillian
if (c_op_list is None or len(c_op_list) == 0) and isket(rho0):
L = H
else:
L = liouvillian(H, c_op_list)
es = ode2es(L, rho0)
# evaluate the expectation values
if n_expt_op == 0:
results = [Qobj()] * n_tsteps
else:
results = np.zeros([n_expt_op, n_tsteps], dtype=complex)
for n, e in enumerate(e_ops):
results[n, :] = expect(e, esval(es, tlist))
data = Result()
data.solver = "essolve"
data.times = tlist
data.expect = [
np.real(results[n, :]) if e.isherm else results[n, :]
for n, e in enumerate(e_ops)
]
return data
def fsesolve(H, psi0, tlist, e_ops=[], T=None, args={}, Tsteps=100):
"""
Solve the Schrodinger equation using the Floquet formalism.
Parameters
----------
H : :class:`qutip.qobj.Qobj`
System Hamiltonian, time-dependent with period `T`.
psi0 : :class:`qutip.qobj`
Initial state vector (ket).
tlist : *list* / *array*
list of times for :math:`t`.
e_ops : list of :class:`qutip.qobj` / callback function
list of operators for which to evaluate expectation values. If this
list is empty, the state vectors for each time in `tlist` will be
returned instead of expectation values.
T : float
The period of the time-dependence of the hamiltonian.
args : dictionary
Dictionary with variables required to evaluate H.
Tsteps : integer
The number of time steps in one driving period for which to
precalculate the Floquet modes. `Tsteps` should be an even number.
Returns
-------
output : :class:`qutip.solver.Result`
An instance of the class :class:`qutip.solver.Result`, which
contains either an *array* of expectation values or an array of
state vectors, for the times specified by `tlist`.
"""
if not T:
# assume that tlist span exactly one period of the driving
T = tlist[-1]
# find the floquet modes for the time-dependent hamiltonian
f_modes_0, f_energies = floquet_modes(H, T, args)
# calculate the wavefunctions using the from the floquet modes
f_modes_table_t = floquet_modes_table(f_modes_0, f_energies,
np.linspace(0, T, Tsteps + 1), H, T,
args)
# setup Result for storing the results
output = Result()
output.times = tlist
output.solver = "fsesolve"
if isinstance(e_ops, FunctionType):
output.num_expect = 0
expt_callback = True
elif isinstance(e_ops, list):
output.num_expect = len(e_ops)
expt_callback = False
if output.num_expect == 0:
output.states = []
else:
output.expect = []
for op in e_ops:
if op.isherm:
output.expect.append(np.zeros(len(tlist)))
else:
output.expect.append(np.zeros(len(tlist), dtype=complex))
else:
raise TypeError("e_ops must be a list Qobj or a callback function")
psi0_fb = psi0.transform(f_modes_0)
for t_idx, t in enumerate(tlist):
f_modes_t = floquet_modes_t_lookup(f_modes_table_t, t, T)
f_states_t = floquet_states(f_modes_t, f_energies, t)
psi_t = psi0_fb.transform(f_states_t, True)
if expt_callback:
# use callback method
e_ops(t, psi_t)
else:
# calculate all the expectation values, or output psi if
# no expectation value operators where defined
if output.num_expect == 0:
output.states.append(Qobj(psi_t))
else:
for e_idx, e in enumerate(e_ops):
output.expect[e_idx][t_idx] = expect(e, psi_t)
return output
def brmesolve(H,
psi0,
tlist,
a_ops=[],
e_ops=[],
c_ops=[],
args={},
use_secular=True,
tol=qset.atol,
spectra_cb=None,
options=None,
progress_bar=None,
_safe_mode=True):
"""
Solves for the dynamics of a system using the Bloch-Redfield master equation,
given an input Hamiltonian, Hermitian bath-coupling terms and their associated
spectrum functions, as well as possible Lindblad collapse operators.
For time-independent systems, the Hamiltonian must be given as a Qobj,
whereas the bath-coupling terms (a_ops), must be written as a nested list
of operator - spectrum function pairs, where the frequency is specified by
the `w` variable.
*Example*
a_ops = [[a+a.dag(),lambda w: 0.2*(w>=0)]]
For time-dependent systems, the Hamiltonian, a_ops, and Lindblad collapse
operators (c_ops), can be specified in the QuTiP string-based time-dependent
format. For the a_op spectra, the frequency variable must be `w`, and the
string cannot contain any other variables other than the possibility of having
a time-dependence through the time variable `t`:
*Example*
a_ops = [[a+a.dag(), '0.2*exp(-t)*(w>=0)']]
Parameters
----------
H : Qobj / list
System Hamiltonian given as a Qobj or
nested list in string-based format.
psi0: Qobj
Initial density matrix or state vector (ket).
tlist : array_like
List of times for evaluating evolution
a_ops : list
Nested list of Hermitian system operators that couple to
the bath degrees of freedom, along with their associated
spectra.
e_ops : list
List of operators for which to evaluate expectation values.
c_ops : list
List of system collapse operators, or nested list in
string-based format.
args : dict (not implimented)
Placeholder for future implementation, kept for API consistency.
use_secular : bool {True}
Use secular approximation when evaluating bath-coupling terms.
tol : float {qutip.setttings.atol}
Tolerance used for removing small values after
basis transformation.
spectra_cb : list
DEPRECIATED. Do not use.
options : :class:`qutip.solver.Options`
Options for the solver.
progress_bar : BaseProgressBar
Optional instance of BaseProgressBar, or a subclass thereof, for
showing the progress of the simulation.
Returns
-------
result: :class:`qutip.solver.Result`
An instance of the class :class:`qutip.solver.Result`, which contains
either an array of expectation values, for operators given in e_ops,
or a list of states for the times specified by `tlist`.
"""
if isinstance(c_ops, Qobj):
c_ops = [c_ops]
if isinstance(e_ops, Qobj):
e_ops = [e_ops]
if isinstance(e_ops, dict):
e_ops_dict = e_ops
e_ops = [e for e in e_ops.values()]
else:
e_ops_dict = None
if not (spectra_cb is None):
warnings.warn("The use of spectra_cb is depreciated.",
DeprecationWarning)
_a_ops = []
for kk, a in enumerate(a_ops):
_a_ops.append([a, spectra_cb[kk]])
a_ops = _a_ops
if _safe_mode:
_solver_safety_check(H, psi0, a_ops + c_ops, e_ops, args)
# check for type (if any) of time-dependent inputs
_, n_func, n_str = _td_format_check(H, a_ops + c_ops)
if progress_bar is None:
progress_bar = BaseProgressBar()
elif progress_bar is True:
progress_bar = TextProgressBar()
if options is None:
options = Options()
if (not options.rhs_reuse) or (not config.tdfunc):
# reset config collapse and time-dependence flags to default values
config.reset()
#check if should use OPENMP
check_use_openmp(options)
if n_str == 0:
R, ekets = bloch_redfield_tensor(H,
a_ops,
spectra_cb=None,
c_ops=c_ops)
output = Result()
output.solver = "brmesolve"
output.times = tlist
results = bloch_redfield_solve(R,
ekets,
psi0,
tlist,
e_ops,
options,
progress_bar=progress_bar)
if e_ops:
output.expect = results
else:
output.states = results
return output
elif n_str != 0 and n_func == 0:
output = _td_brmesolve(H,
psi0,
tlist,
a_ops=a_ops,
e_ops=e_ops,
c_ops=c_ops,
use_secular=use_secular,
tol=tol,
options=options,
progress_bar=progress_bar,
_safe_mode=_safe_mode)
return output
else:
raise Exception('Cannot mix func and str formats.')
def generic_ode_solve_checkpoint(r, rho0, tlist, e_ops, opt, progress_bar,
save, subdir):
"""
Internal function for solving ME. Solve an ODE which solver parameters
already setup (r). Calculate the required expectation values or invoke
callback function at each time step.
"""
#
# prepare output array
#
n_tsteps = len(tlist)
e_sops_data = []
output = Result()
output.solver = "mesolve"
output.times = tlist
if opt.store_states:
output.states = []
e_ops_dict = e_ops
e_ops = [e for e in e_ops_dict.values()]
headings = [key for key in e_ops_dict.keys()]
if isinstance(e_ops, types.FunctionType):
n_expt_op = 0
expt_callback = True
elif isinstance(e_ops, list):
n_expt_op = len(e_ops)
expt_callback = False
if n_expt_op == 0:
# fall back on storing states
output.states = []
opt.store_states = True
else:
output.expect = []
output.num_expect = n_expt_op
for op in e_ops:
e_sops_data.append(spre(op).data)
if op.isherm and rho0.isherm:
output.expect.append(np.zeros(n_tsteps))
else:
output.expect.append(np.zeros(n_tsteps, dtype=complex))
else:
raise TypeError("Expectation parameter must be a list or a function")
results_row = np.zeros(n_expt_op)
#
# start evolution
#
progress_bar.start(n_tsteps)
rho = Qobj(rho0)
dims = rho.dims
dt = np.diff(tlist)
end_time = tlist[-1]
for t_idx, t in tqdm(enumerate(tlist)):
progress_bar.update(t_idx)
if not r.successful():
raise Exception("ODE integration error: Try to increase "
"the allowed number of substeps by increasing "
"the nsteps parameter in the Options class.")
if opt.store_states or expt_callback:
rho.data = vec2mat(r.y)
if opt.store_states:
output.states.append(Qobj(rho))
if expt_callback:
# use callback method
e_ops(t, rho)
for m in range(n_expt_op):
if output.expect[m].dtype == complex:
output.expect[m][t_idx] = expect_rho_vec(
e_sops_data[m], r.y, 0)
results_row[m] = output.expect[m][t_idx]
else:
output.expect[m][t_idx] = expect_rho_vec(
e_sops_data[m], r.y, 1)
results_row[m] = output.expect[m][t_idx]
results = pd.DataFrame(results_row).T
results.columns = headings
results.index = [t]
results.index.name = 'times'
if t == 0:
first_row = True
else:
first_row = False
if save:
rho_checkpoint = Qobj(vec2mat(r.y))
rho_checkpoint.dims = dims
if t_idx % 200 == 0:
rho_c = rho_checkpoint.ptrace(0)
with open('./cavity_states.pkl', 'ab') as f:
pickle.dump(rho_c, f)
with open('./results.csv', 'a') as file:
results.to_csv(file, header=first_row, float_format='%.15f')
qsave(rho_checkpoint, './state_checkpoint')
save = True
if t_idx < n_tsteps - 1:
r.integrate(r.t + dt[t_idx])
progress_bar.finished()
if not opt.rhs_reuse and config.tdname is not None:
_cython_build_cleanup(config.tdname)
return output
def run(self, rho0, tlist, e_ops=None, ado_init=False, ado_return=False):
"""
Solve for the time evolution of the system.
Parameters
----------
rho0 : Qobj or HierarchyADOsState or numpy.array
Initial state (:obj:`~Qobj` density matrix) of the system
if ``ado_init`` is ``False``.
If ``ado_init`` is ``True``, then ``rho0`` should be an
instance of :obj:`~HierarchyADOsState` or a numpy array
giving the initial state of all ADOs. Usually
the state of the ADOs would be determine from a previous call
to ``.run(..., ado_return=True)``. For example,
``result = solver.run(..., ado_return=True)`` could be followed
by ``solver.run(result.ado_states[-1], tlist, ado_init=True)``.
If a numpy array is passed its shape must be
``(number_of_ados, n, n)`` where ``(n, n)`` is the system shape
(i.e. shape of the system density matrix) and the ADOs must be
in the same order as in ``.ados.labels``.
tlist : list
An ordered list of times at which to return the value of the state.
e_ops : Qobj / callable / list / dict / None, optional
A list or dictionary of operators as `Qobj` and/or callable
functions (they can be mixed) or a single operator or callable
function. For an operator ``op``, the result will be computed
using ``(state * op).tr()`` and the state at each time ``t``. For
callable functions, ``f``, the result is computed using
``f(t, ado_state)``. The values are stored in ``expect`` on
(see the return section below).
ado_init: bool, default False
Indicates if initial condition is just the system state, or a
numpy array including all ADOs.
ado_return: bool, default True
Whether to also return as output the full state of all ADOs.
Returns
-------
:class:`qutip.solver.Result`
The results of the simulation run, with the following attributes:
* ``times``: the times ``t`` (i.e. the ``tlist``).
* ``states``: the system state at each time ``t`` (only available
if ``e_ops`` was ``None`` or if the solver option
``store_states`` was set to ``True``).
* ``ado_states``: the full ADO state at each time (only available
if ``ado_return`` was set to ``True``). Each element is an
instance of :class:`HierarchyADOsState`. .
The state of a particular ADO may be extracted from
``result.ado_states[i]`` by calling :meth:`.extract`.
* ``expect``: the value of each ``e_ops`` at time ``t`` (only
available if ``e_ops`` were given). If ``e_ops`` was passed
as a dictionary, then ``expect`` will be a dictionary with
the same keys as ``e_ops`` and values giving the list of
outcomes for the corresponding key.
"""
e_ops, expected = self._convert_e_ops(e_ops)
e_ops_callables = any(not isinstance(op, Qobj)
for op in e_ops.values())
n = self._sys_shape
rho_shape = (n, n)
rho_dims = self._sys_dims
hierarchy_shape = (self._n_ados, n, n)
output = Result()
output.solver = "HEOMSolver"
output.times = tlist
if e_ops:
output.expect = expected
if not e_ops or self.options.store_states:
output.states = []
if ado_init:
if isinstance(rho0, HierarchyADOsState):
rho0_he = rho0._ado_state
else:
rho0_he = rho0
if rho0_he.shape != hierarchy_shape:
raise ValueError(
f"ADOs passed with ado_init have shape {rho0_he.shape}"
f"but the solver hierarchy shape is {hierarchy_shape}")
rho0_he = rho0_he.reshape(n**2 * self._n_ados)
else:
rho0_he = np.zeros([n**2 * self._n_ados], dtype=complex)
rho0_he[:n**2] = rho0.full().ravel('F')
if ado_return:
output.ado_states = []
solver = self._ode
solver.set_initial_value(rho0_he, tlist[0])
self.progress_bar.start(len(tlist))
for t_idx, t in enumerate(tlist):
self.progress_bar.update(t_idx)
if t_idx != 0:
solver.integrate(t)
if not solver.successful():
raise RuntimeError(
"HEOMSolver ODE integration error. Try increasing"
" the nsteps given in the HEOMSolver options"
" (which increases the allowed substeps in each"
" step between times given in tlist).")
rho = Qobj(
solver.y[:n**2].reshape(rho_shape, order='F'),
dims=rho_dims,
)
if self.options.store_states:
output.states.append(rho)
if ado_return or e_ops_callables:
ado_state = HierarchyADOsState(
rho, self.ados, solver.y.reshape(hierarchy_shape))
if ado_return:
output.ado_states.append(ado_state)
for e_key, e_op in e_ops.items():
if isinstance(e_op, Qobj):
e_result = (rho * e_op).tr()
else:
e_result = e_op(t, ado_state)
output.expect[e_key].append(e_result)
self.progress_bar.finished()
return output
def mcsolve_f90(H,
psi0,
tlist,
c_ops,
e_ops,
ntraj=None,
options=Options(),
sparse_dms=True,
serial=False,
ptrace_sel=[],
calc_entropy=False):
"""
Monte-Carlo wave function solver with fortran 90 backend.
Usage is identical to qutip.mcsolve, for problems without explicit
time-dependence, and with some optional input:
Parameters
----------
H : qobj
System Hamiltonian.
psi0 : qobj
Initial state vector
tlist : array_like
Times at which results are recorded.
ntraj : int
Number of trajectories to run.
c_ops : array_like
``list`` or ``array`` of collapse operators.
e_ops : array_like
``list`` or ``array`` of operators for calculating expectation values.
options : Options
Instance of solver options.
sparse_dms : boolean
If averaged density matrices are returned, they will be stored as
sparse (Compressed Row Format) matrices during computation if
sparse_dms = True (default), and dense matrices otherwise. Dense
matrices might be preferable for smaller systems.
serial : boolean
If True (default is False) the solver will not make use of the
multiprocessing module, and simply run in serial.
ptrace_sel: list
This optional argument specifies a list of components to keep when
returning a partially traced density matrix. This can be convenient for
large systems where memory becomes a problem, but you are only
interested in parts of the density matrix.
calc_entropy : boolean
If ptrace_sel is specified, calc_entropy=True will have the solver
return the averaged entropy over trajectories in results.entropy. This
can be interpreted as a measure of entanglement. See Phys. Rev. Lett.
93, 120408 (2004), Phys. Rev. A 86, 022310 (2012).
Returns
-------
results : Result
Object storing all results from simulation.
"""
if ntraj is None:
ntraj = options.ntraj
if psi0.type != 'ket':
raise Exception("Initial state must be a state vector.")
config.options = options
# set num_cpus to the value given in qutip.settings
# if none in Options
if not config.options.num_cpus:
config.options.num_cpus = qutip.settings.num_cpus
# set initial value data
if options.tidy:
config.psi0 = psi0.tidyup(options.atol).full()
else:
config.psi0 = psi0.full()
config.psi0_dims = psi0.dims
config.psi0_shape = psi0.shape
# set general items
config.tlist = tlist
if isinstance(ntraj, (list, np.ndarray)):
raise Exception("ntraj as list argument is not supported.")
else:
config.ntraj = ntraj
# ntraj_list = [ntraj]
# set norm finding constants
config.norm_tol = options.norm_tol
config.norm_steps = options.norm_steps
if not options.rhs_reuse:
config.soft_reset()
# no time dependence
config.tflag = 0
# check for collapse operators
if len(c_ops) > 0:
config.cflag = 1
else:
config.cflag = 0
# Configure data
_mc_data_config(H, psi0, [], c_ops, [], [], e_ops, options, config)
# Load Monte Carlo class
mc = _MC_class()
# Set solver type
if (options.method == 'adams'):
mc.mf = 10
elif (options.method == 'bdf'):
mc.mf = 22
else:
if debug:
print('Unrecognized method for ode solver, using "adams".')
mc.mf = 10
# store ket and density matrix dims and shape for convenience
mc.psi0_dims = psi0.dims
mc.psi0_shape = psi0.shape
mc.dm_dims = (psi0 * psi0.dag()).dims
mc.dm_shape = (psi0 * psi0.dag()).shape
# use sparse density matrices during computation?
mc.sparse_dms = sparse_dms
# run in serial?
mc.serial_run = serial or (ntraj == 1)
# are we doing a partial trace for returned states?
mc.ptrace_sel = ptrace_sel
if (ptrace_sel != []):
if debug:
print("ptrace_sel set to " + str(ptrace_sel))
print("We are using dense density matrices during computation " +
"when performing partial trace. Setting sparse_dms = False")
print("This feature is experimental.")
mc.sparse_dms = False
mc.dm_dims = psi0.ptrace(ptrace_sel).dims
mc.dm_shape = psi0.ptrace(ptrace_sel).shape
if (calc_entropy):
if (ptrace_sel == []):
if debug:
print("calc_entropy = True, but ptrace_sel = []. Please set " +
"a list of components to keep when calculating average" +
" entropy of reduced density matrix in ptrace_sel. " +
"Setting calc_entropy = False.")
calc_entropy = False
mc.calc_entropy = calc_entropy
# construct output Result object
output = Result()
# Run
mc.run()
output.states = mc.sol.states
output.expect = mc.sol.expect
output.col_times = mc.sol.col_times
output.col_which = mc.sol.col_which
if (hasattr(mc.sol, 'entropy')):
output.entropy = mc.sol.entropy
output.solver = 'Fortran 90 Monte Carlo solver'
# simulation parameters
output.times = config.tlist
output.num_expect = config.e_num
output.num_collapse = config.c_num
output.ntraj = config.ntraj
return output
def _gather(sols):
# gather list of Result objects, sols, into one.
sol = Result()
# sol = sols[0]
ntraj = sum([a.ntraj for a in sols])
sol.col_times = np.zeros((ntraj), dtype=np.ndarray)
sol.col_which = np.zeros((ntraj), dtype=np.ndarray)
sol.col_times[0:sols[0].ntraj] = sols[0].col_times
sol.col_which[0:sols[0].ntraj] = sols[0].col_which
sol.states = np.array(sols[0].states, dtype=object)
sol.expect = np.array(sols[0].expect)
if (hasattr(sols[0], 'entropy')):
sol.entropy = np.array(sols[0].entropy)
sofar = 0
for j in range(1, len(sols)):
sofar = sofar + sols[j - 1].ntraj
sol.col_times[sofar:sofar + sols[j].ntraj] = (sols[j].col_times)
sol.col_which[sofar:sofar + sols[j].ntraj] = (sols[j].col_which)
if (config.e_num == 0):
if (config.options.average_states):
# collect states, averaged over trajectories
sol.states += np.array(sols[j].states)
else:
# collect states, all trajectories
sol.states = np.vstack((sol.states, np.array(sols[j].states)))
else:
if (config.options.average_expect):
# collect expectation values, averaged
for i in range(config.e_num):
sol.expect[i] += np.array(sols[j].expect[i])
else:
# collect expectation values, all trajectories
sol.expect = np.vstack((sol.expect, np.array(sols[j].expect)))
if (hasattr(sols[j], 'entropy')):
if (config.options.average_states
or config.options.average_expect):
# collect entropy values, averaged
sol.entropy += np.array(sols[j].entropy)
else:
# collect entropy values, all trajectories
sol.entropy = np.vstack(
(sol.entropy, np.array(sols[j].entropy)))
if (config.options.average_states or config.options.average_expect):
if (config.e_num == 0):
sol.states = sol.states / len(sols)
else:
sol.expect = list(sol.expect / len(sols))
inds = np.where(config.e_ops_isherm)[0]
for jj in inds:
sol.expect[jj] = np.real(sol.expect[jj])
if (hasattr(sols[0], 'entropy')):
sol.entropy = sol.entropy / len(sols)
# convert sol.expect array to list and fix dtypes of arrays
if (not config.options.average_expect) and config.e_num != 0:
temp = [list(sol.expect[ii]) for ii in range(ntraj)]
for ii in range(ntraj):
for jj in np.where(config.e_ops_isherm)[0]:
temp[ii][jj] = np.real(temp[ii][jj])
sol.expect = temp
# convert to list/array to be consistent with qutip mcsolve
sol.states = list(sol.states)
return sol
def evolve_serial(self, args):
if debug:
print(inspect.stack()[0][3] + ":" + str(os.getpid()))
# run ntraj trajectories for one process via fortran
# get args
queue, ntraj, instanceno, rngseed = args
# initialize the problem in fortran
_init_tlist()
_init_psi0()
if (self.ptrace_sel != []):
_init_ptrace_stuff(self.ptrace_sel)
_init_hamilt()
if (config.c_num != 0):
_init_c_ops()
if (config.e_num != 0):
_init_e_ops()
# set options
qtf90.qutraj_run.n_c_ops = config.c_num
qtf90.qutraj_run.n_e_ops = config.e_num
qtf90.qutraj_run.ntraj = ntraj
qtf90.qutraj_run.unravel_type = self.unravel_type
qtf90.qutraj_run.average_states = config.options.average_states
qtf90.qutraj_run.average_expect = config.options.average_expect
qtf90.qutraj_run.init_result(config.psi0_shape[0],
config.options.atol,
config.options.rtol,
mf=self.mf,
norm_steps=config.norm_steps,
norm_tol=config.norm_tol)
# set optional arguments
qtf90.qutraj_run.order = config.options.order
qtf90.qutraj_run.nsteps = config.options.nsteps
qtf90.qutraj_run.first_step = config.options.first_step
qtf90.qutraj_run.min_step = config.options.min_step
qtf90.qutraj_run.max_step = config.options.max_step
qtf90.qutraj_run.norm_steps = config.options.norm_steps
qtf90.qutraj_run.norm_tol = config.options.norm_tol
# use sparse density matrices during computation?
qtf90.qutraj_run.rho_return_sparse = self.sparse_dms
# calculate entropy of reduced density matrice?
qtf90.qutraj_run.calc_entropy = self.calc_entropy
# run
show_progress = 1 if debug else 0
qtf90.qutraj_run.evolve(instanceno, rngseed, show_progress)
# construct Result instance
sol = Result()
sol.ntraj = ntraj
# sol.col_times = qtf90.qutraj_run.col_times
# sol.col_which = qtf90.qutraj_run.col_which-1
sol.col_times, sol.col_which = self.get_collapses(ntraj)
if (config.e_num == 0):
sol.states = self.get_states(len(config.tlist), ntraj)
else:
sol.expect = self.get_expect(len(config.tlist), ntraj)
if (self.calc_entropy):
sol.entropy = self.get_entropy(len(config.tlist))
if (not self.serial_run):
# put to queue
queue.put(sol)
queue.join()
# deallocate stuff
# finalize()
return sol
def run(self, rho0, tlist):
"""
Function to solve for an open quantum system using the
HEOM model.
Parameters
----------
rho0 : Qobj
Initial state (density matrix) of the system.
tlist : list
Time over which system evolves.
Returns
-------
results : :class:`qutip.solver.Result`
Object storing all results from the simulation.
"""
start_run = timeit.default_timer()
sup_dim = self._sup_dim
stats = self.stats
r = self._ode
if not self._configured:
raise RuntimeError("Solver must be configured before it is run")
if stats:
ss_conf = stats.sections.get('config')
if ss_conf is None:
raise RuntimeError("No config section for solver stats")
ss_run = stats.sections.get('run')
if ss_run is None:
ss_run = stats.add_section('run')
# Set up terms of the matsubara and tanimura boundaries
output = Result()
output.solver = "hsolve"
output.times = tlist
output.states = []
if stats: start_init = timeit.default_timer()
output.states.append(Qobj(rho0))
rho0_flat = rho0.full().ravel('F') # Using 'F' effectively transposes
rho0_he = np.zeros([sup_dim * self._N_he], dtype=complex)
rho0_he[:sup_dim] = rho0_flat
r.set_initial_value(rho0_he, tlist[0])
if stats:
stats.add_timing('initialize',
timeit.default_timer() - start_init, ss_run)
start_integ = timeit.default_timer()
dt = np.diff(tlist)
n_tsteps = len(tlist)
for t_idx, t in enumerate(tlist):
if t_idx < n_tsteps - 1:
r.integrate(r.t + dt[t_idx])
rho = Qobj(r.y[:sup_dim].reshape(rho0.shape), dims=rho0.dims)
output.states.append(rho)
if stats:
time_now = timeit.default_timer()
stats.add_timing('integrate', time_now - start_integ, ss_run)
if ss_run.total_time is None:
ss_run.total_time = time_now - start_run
else:
ss_run.total_time += time_now - start_run
stats.total_time = ss_conf.total_time + ss_run.total_time
return output
def _generic_ode_solve(r, rho0, tlist, e_ops, opt, progress_bar):
"""
Internal function for solving ME. Solve an ODE which solver parameters
already setup (r). Calculate the required expectation values or invoke
callback function at each time step.
"""
#
# prepare output array
#
n_tsteps = len(tlist)
e_sops_data = []
output = Result()
output.solver = "mesolve"
output.times = tlist
if opt.store_states:
output.states = []
if isinstance(e_ops, types.FunctionType):
n_expt_op = 0
expt_callback = True
elif isinstance(e_ops, list):
n_expt_op = len(e_ops)
expt_callback = False
if n_expt_op == 0:
# fall back on storing states
output.states = []
opt.store_states = True
else:
output.expect = []
output.num_expect = n_expt_op
for op in e_ops:
e_sops_data.append(spre(op).data)
if op.isherm and rho0.isherm:
output.expect.append(np.zeros(n_tsteps))
else:
output.expect.append(np.zeros(n_tsteps, dtype=complex))
else:
raise TypeError("Expectation parameter must be a list or a function")
#
# start evolution
#
progress_bar.start(n_tsteps)
rho = Qobj(rho0)
dt = np.diff(tlist)
for t_idx, t in enumerate(tlist):
progress_bar.update(t_idx)
if not r.successful():
raise Exception("ODE integration error: Try to increase "
"the allowed number of substeps by increasing "
"the nsteps parameter in the Options class.")
if opt.store_states or expt_callback:
rho.data = dense2D_to_fastcsr_fmode(vec2mat(r.y), rho.shape[0],
rho.shape[1])
if opt.store_states:
output.states.append(Qobj(rho, isherm=True))
if expt_callback:
# use callback method
e_ops(t, rho)
for m in range(n_expt_op):
if output.expect[m].dtype == complex:
output.expect[m][t_idx] = expect_rho_vec(
e_sops_data[m], r.y, 0)
else:
output.expect[m][t_idx] = expect_rho_vec(
e_sops_data[m], r.y, 1)
if t_idx < n_tsteps - 1:
r.integrate(r.t + dt[t_idx])
progress_bar.finished()
if (not opt.rhs_reuse) and (config.tdname is not None):
_cython_build_cleanup(config.tdname)
if opt.store_final_state:
rho.data = dense2D_to_fastcsr_fmode(vec2mat(r.y), rho.shape[0],
rho.shape[1])
output.final_state = Qobj(rho, dims=rho0.dims, isherm=True)
return output
def krylovsolve(
H: Qobj,
psi0: Qobj,
tlist: np.array,
krylov_dim: int,
e_ops=None,
options=None,
progress_bar: bool = None,
sparse: bool = False,
):
"""
Time evolution of state vectors for time independent Hamiltonians.
Evolve the state vector ("psi0") finding an approximation for the time
evolution operator of Hamiltonian ("H") by obtaining the projection of
the time evolution operator on a set of small dimensional Krylov
subspaces (m << dim(H)).
The output is either the state vector or the expectation values of
supplied operators ("e_ops") at arbitrary points at ("tlist").
**Additional options**
Additional options to krylovsolve can be set with the following:
* "store_states": stores states even though expectation values are
requested via the "e_ops" argument.
* "store_final_state": store final state even though expectation values are
requested via the "e_ops" argument.
Parameters
----------
H : :class:`qutip.Qobj`
System Hamiltonian.
psi0 : :class: `qutip.Qobj`
Initial state vector (ket).
tlist : None / *list* / *array*
List of times on which to evolve the initial state. If None, nothing
happens but the code won't break.
krylov_dim: int
Dimension of Krylov approximation subspaces used for the time
evolution approximation.
e_ops : None / list of :class:`qutip.Qobj`
Single operator or list of operators for which to evaluate
expectation values.
options : Options
Instance of ODE solver options, as well as krylov parameters.
atol: controls (approximately) the error desired for the final
solution. (Defaults to 1e-8)
nsteps: maximum number of krylov's internal number of Lanczos
iterations. (Defaults to 10000)
progress_bar : None / BaseProgressBar
Optional instance of BaseProgressBar, or a subclass thereof, for
showing the progress of the simulation.
sparse : bool (default False)
Use np.array to represent system Hamiltonians. If True, scipy sparse
arrays are used instead.
Returns
-------
result: :class:`qutip.solver.Result`
An instance of the class :class:`qutip.solver.Result`, which contains
either an *array* `result.expect` of expectation values for the times
`tlist`, or an *array* `result.states` of state vectors corresponding
to the times `tlist` [if `e_ops` is an empty list].
"""
# check the physics
_check_inputs(H, psi0, krylov_dim)
# check extra inputs
e_ops, e_ops_dict = _check_e_ops(e_ops)
pbar = _check_progress_bar(progress_bar)
# transform inputs type from Qobj to np.ndarray/csr_matrix
if sparse:
_H = H.get_data() # (fast_) csr_matrix
else:
_H = H.full().copy() # np.ndarray
_psi = psi0.full().copy()
_psi = _psi / np.linalg.norm(_psi)
# create internal variable and output containers
if options is None:
options = Options(nsteps=10000)
krylov_results = Result()
krylov_results.solver = "krylovsolve"
# handle particular cases of an empty tlist or single element
n_tlist_steps = len(tlist)
if n_tlist_steps < 1:
return krylov_results
if n_tlist_steps == 1: # if tlist has only one element, return it
krylov_results = particular_tlist_or_happy_breakdown(
tlist, n_tlist_steps, options, psi0, e_ops, krylov_results,
pbar) # this will also raise a warning
return krylov_results
tf = tlist[-1]
t0 = tlist[0]
# optimization step using Lanczos, then reuse it for the first partition
dim_m = krylov_dim
krylov_basis, T_m = lanczos_algorithm(_H,
_psi,
krylov_dim=dim_m,
sparse=sparse)
# check if a happy breakdown occurred
if T_m.shape[0] < krylov_dim + 1:
if T_m.shape[0] == 1:
# this means that the state does not evolve in time, it lies in a
# symmetry of H subspace. Thus, theres no work to be done.
krylov_results = particular_tlist_or_happy_breakdown(
tlist,
n_tlist_steps,
options,
psi0,
e_ops,
krylov_results,
pbar,
happy_breakdown=True,
)
return krylov_results
else:
# no optimization is required, convergence is guaranteed.
delta_t = tf - t0
n_timesteps = 1
else:
# calculate optimal number of internal timesteps.
delta_t = _optimize_lanczos_timestep_size(T_m,
krylov_basis=krylov_basis,
tlist=tlist,
options=options)
n_timesteps = int(ceil((tf - t0) / delta_t))
if n_timesteps >= options.nsteps:
raise Exception(
f"Optimization requires a number {n_timesteps} of lanczos iterations, "
f"which exceeds the defined allowed number {options.nsteps}. This can "
"be increased via the 'Options.nsteps' property.")
partitions = _make_partitions(tlist=tlist, n_timesteps=n_timesteps)
if progress_bar:
pbar.start(len(partitions))
# update parameters regarding e_ops
krylov_results, expt_callback, options, n_expt_op = _e_ops_outputs(
krylov_results, e_ops, n_tlist_steps, options)
# parameters for the lazy iteration evolve tlist
psi_norm = np.linalg.norm(_psi)
last_t = t0
for idx, partition in enumerate(partitions):
evolved_states = _evolve_krylov_tlist(
H=_H,
psi0=_psi,
krylov_dim=dim_m,
tlist=partition,
t0=last_t,
psi_norm=psi_norm,
krylov_basis=krylov_basis,
T_m=T_m,
sparse=sparse,
)
if idx == 0:
krylov_basis = None
T_m = None
t_idx = 0
_psi = evolved_states[-1]
psi_norm = np.linalg.norm(_psi)
last_t = partition[-1]
# apply qobj to each evolved state, remove repeated tail elements
qobj_evolved_states = [
Qobj(state, dims=psi0.dims) for state in evolved_states[1:-1]
]
krylov_results = _expectation_values(
e_ops,
n_expt_op,
expt_callback,
krylov_results,
qobj_evolved_states,
partitions,
idx,
t_idx,
options,
)
t_idx += len(partition[1:-1])
pbar.update(idx)
pbar.finished()
if e_ops_dict:
krylov_results.expect = {
e: krylov_results.expect[n]
for n, e in enumerate(e_ops_dict.keys())
}
return krylov_results
def ttmsolve(dynmaps, rho0, times, e_ops=[], learningtimes=None, tensors=None,
**kwargs):
"""
Solve time-evolution using the Transfer Tensor Method, based on a set of
precomputed dynamical maps.
Parameters
----------
dynmaps : list of :class:`qutip.Qobj`
List of precomputed dynamical maps (superoperators),
or a callback function that returns the
superoperator at a given time.
rho0 : :class:`qutip.Qobj`
Initial density matrix or state vector (ket).
times : array_like
list of times :math:`t_n` at which to compute :math:`\\rho(t_n)`.
Must be uniformily spaced.
e_ops : list of :class:`qutip.Qobj` / callback function
single operator or list of operators for which to evaluate
expectation values.
learningtimes : array_like
list of times :math:`t_k` for which we have knowledge of the dynamical
maps :math:`E(t_k)`.
tensors : array_like
optional list of precomputed tensors :math:`T_k`
kwargs : dictionary
Optional keyword arguments. See
:class:`qutip.nonmarkov.ttm.TTMSolverOptions`.
Returns
-------
output: :class:`qutip.solver.Result`
An instance of the class :class:`qutip.solver.Result`.
"""
opt = TTMSolverOptions(dynmaps=dynmaps, times=times,
learningtimes=learningtimes, **kwargs)
diff = None
if isket(rho0):
rho0 = ket2dm(rho0)
output = Result()
e_sops_data = []
if callable(e_ops):
n_expt_op = 0
expt_callback = True
else:
try:
tmp = e_ops[:]
del tmp
n_expt_op = len(e_ops)
expt_callback = False
if n_expt_op == 0:
# fall back on storing states
opt.store_states = True
for op in e_ops:
e_sops_data.append(spre(op).data)
if op.isherm and rho0.isherm:
output.expect.append(np.zeros(len(times)))
else:
output.expect.append(np.zeros(len(times), dtype=complex))
except TypeError:
raise TypeError("Argument 'e_ops' should be a callable or" +
"list-like.")
if tensors is None:
tensors, diff = _generatetensors(dynmaps, learningtimes, opt=opt)
if rho0.isoper:
# vectorize density matrix
rho0vec = operator_to_vector(rho0)
else:
# rho0 might be a super in which case we should not vectorize
rho0vec = rho0
K = len(tensors)
states = [rho0vec]
for n in range(1, len(times)):
states.append(None)
for k in range(n):
if n-k < K:
states[-1] += tensors[n-k]*states[k]
for i, r in enumerate(states):
if opt.store_states or expt_callback:
if r.type == 'operator-ket':
states[i] = vector_to_operator(r)
else:
states[i] = r
if expt_callback:
# use callback method
e_ops(times[i], states[i])
for m in range(n_expt_op):
if output.expect[m].dtype == complex:
output.expect[m][i] = expect_rho_vec(e_sops_data[m], r, 0)
else:
output.expect[m][i] = expect_rho_vec(e_sops_data[m], r, 1)
output.solver = "ttmsolve"
output.times = times
output.ttmconvergence = diff
if opt.store_states:
output.states = states
return output
def _generic_ode_solve(func, ode_args, psi0, tlist, e_ops, opt,
progress_bar, dims=None):
"""
Internal function for solving ODEs.
"""
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# This function is made similar to mesolve's one for futur merging in a
# solver class
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# prepare output array
n_tsteps = len(tlist)
output = Result()
output.solver = "sesolve"
output.times = tlist
if psi0.isunitary:
initial_vector = psi0.full().ravel('F')
oper_evo = True
size = psi0.shape[0]
# oper_n = dims[0][0]
# norm_dim_factor = np.sqrt(oper_n)
elif psi0.isket:
initial_vector = psi0.full().ravel()
oper_evo = False
# norm_dim_factor = 1.0
r = scipy.integrate.ode(func)
r.set_integrator('zvode', method=opt.method, order=opt.order,
atol=opt.atol, rtol=opt.rtol, nsteps=opt.nsteps,
first_step=opt.first_step, min_step=opt.min_step,
max_step=opt.max_step)
if ode_args:
r.set_f_params(*ode_args)
r.set_initial_value(initial_vector, tlist[0])
e_ops_data = []
output.expect = []
if callable(e_ops):
n_expt_op = 0
expt_callback = True
output.num_expect = 1
elif isinstance(e_ops, list):
n_expt_op = len(e_ops)
expt_callback = False
output.num_expect = n_expt_op
if n_expt_op == 0:
# fallback on storing states
opt.store_states = True
else:
for op in e_ops:
if not isinstance(op, Qobj) and callable(op):
output.expect.append(np.zeros(n_tsteps, dtype=complex))
continue
if op.isherm:
output.expect.append(np.zeros(n_tsteps))
else:
output.expect.append(np.zeros(n_tsteps, dtype=complex))
if oper_evo:
for e in e_ops:
if isinstance(e, Qobj):
e_ops_data.append(e.dag().data)
continue
e_ops_data.append(e)
else:
for e in e_ops:
if isinstance(e, Qobj):
e_ops_data.append(e.data)
continue
e_ops_data.append(e)
else:
raise TypeError("Expectation parameter must be a list or a function")
if opt.store_states:
output.states = []
if oper_evo:
def get_curr_state_data(r):
return vec2mat(r.y)
else:
def get_curr_state_data(r):
return r.y
#
# start evolution
#
dt = np.diff(tlist)
cdata = None
progress_bar.start(n_tsteps)
for t_idx, t in enumerate(tlist):
progress_bar.update(t_idx)
if not r.successful():
raise Exception("ODE integration error: Try to increase "
"the allowed number of substeps by increasing "
"the nsteps parameter in the Options class.")
# get the current state / oper data if needed
if opt.store_states or opt.normalize_output \
or n_expt_op > 0 or expt_callback:
cdata = get_curr_state_data(r)
if opt.normalize_output:
# normalize per column
if oper_evo:
cdata /= la_norm(cdata, axis=0)
#cdata *= norm_dim_factor / la_norm(cdata)
r.set_initial_value(cdata.ravel('F'), r.t)
else:
#cdata /= la_norm(cdata)
norm = normalize_inplace(cdata)
if norm > 1e-12:
# only reset the solver if state changed
r.set_initial_value(cdata, r.t)
else:
r._y = cdata
if opt.store_states:
if oper_evo:
fdata = dense2D_to_fastcsr_fmode(cdata, size, size)
output.states.append(Qobj(fdata, dims=dims))
else:
fdata = dense1D_to_fastcsr_ket(cdata)
output.states.append(Qobj(fdata, dims=dims, fast='mc'))
if expt_callback:
# use callback method
output.expect.append(e_ops(t, Qobj(cdata, dims=dims)))
if oper_evo:
for m in range(n_expt_op):
if callable(e_ops_data[m]):
func = e_ops_data[m]
output.expect[m][t_idx] = func(t, Qobj(cdata, dims=dims))
continue
output.expect[m][t_idx] = (e_ops_data[m] * cdata).trace()
else:
for m in range(n_expt_op):
if callable(e_ops_data[m]):
func = e_ops_data[m]
output.expect[m][t_idx] = func(t, Qobj(cdata, dims=dims))
continue
output.expect[m][t_idx] = cy_expect_psi(e_ops_data[m], cdata,
e_ops[m].isherm)
if t_idx < n_tsteps - 1:
r.integrate(r.t + dt[t_idx])
progress_bar.finished()
if opt.store_final_state:
cdata = get_curr_state_data(r)
if opt.normalize_output:
cdata /= la_norm(cdata, axis=0)
# cdata *= norm_dim_factor / la_norm(cdata)
output.final_state = Qobj(cdata, dims=dims)
return output
def _td_brmesolve(H,
psi0,
tlist,
a_ops=[],
e_ops=[],
c_ops=[],
use_secular=True,
tol=qset.atol,
options=None,
progress_bar=None,
_safe_mode=True):
if isket(psi0):
rho0 = ket2dm(psi0)
else:
rho0 = psi0
nrows = rho0.shape[0]
H_terms = []
H_td_terms = []
H_obj = []
A_terms = []
A_td_terms = []
C_terms = []
C_td_terms = []
C_obj = []
spline_count = [0, 0]
if isinstance(H, Qobj):
H_terms.append(H.full('f'))
H_td_terms.append('1')
else:
for kk, h in enumerate(H):
if isinstance(h, Qobj):
H_terms.append(h.full('f'))
H_td_terms.append('1')
elif isinstance(h, list):
H_terms.append(h[0].full('f'))
if isinstance(h[1], Cubic_Spline):
H_obj.append(h[1].coeffs)
spline_count[0] += 1
H_td_terms.append(h[1])
else:
raise Exception('Invalid Hamiltonian specifiction.')
for kk, c in enumerate(c_ops):
if isinstance(c, Qobj):
C_terms.append(c.full('f'))
C_td_terms.append('1')
elif isinstance(c, list):
C_terms.append(c[0].full('f'))
if isinstance(c[1], Cubic_Spline):
C_obj.append(c[1].coeffs)
spline_count[0] += 1
C_td_terms.append(c[1])
else:
raise Exception('Invalid collape operator specifiction.')
for kk, a in enumerate(a_ops):
if isinstance(a, list):
A_terms.append(a[0].full('f'))
A_td_terms.append(a[1])
if isinstance(a[1], tuple):
if not len(a[1]) == 2:
raise Exception('Tuple must be len=2.')
if isinstance(a[1][0], Cubic_Spline):
spline_count[1] += 1
if isinstance(a[1][1], Cubic_Spline):
spline_count[1] += 1
else:
raise Exception('Invalid bath-coupling specifiction.')
string_list = []
for kk, _ in enumerate(H_td_terms):
string_list.append("H_terms[{0}]".format(kk))
for kk, _ in enumerate(H_obj):
string_list.append("H_obj[{0}]".format(kk))
for kk, _ in enumerate(C_td_terms):
string_list.append("C_terms[{0}]".format(kk))
for kk, _ in enumerate(C_obj):
string_list.append("C_obj[{0}]".format(kk))
for kk, _ in enumerate(A_td_terms):
string_list.append("A_terms[{0}]".format(kk))
#Add nrows to parameters
string_list.append('nrows')
parameter_string = ",".join(string_list)
#
# generate and compile new cython code if necessary
#
if not options.rhs_reuse or config.tdfunc is None:
if options.rhs_filename is None:
config.tdname = "rhs" + str(os.getpid()) + str(config.cgen_num)
else:
config.tdname = opt.rhs_filename
cgen = BR_Codegen(
h_terms=len(H_terms),
h_td_terms=H_td_terms,
h_obj=H_obj,
c_terms=len(C_terms),
c_td_terms=C_td_terms,
c_obj=C_obj,
a_terms=len(A_terms),
a_td_terms=A_td_terms,
spline_count=spline_count,
config=config,
sparse=False,
use_secular=use_secular,
use_openmp=options.use_openmp,
omp_thresh=qset.openmp_thresh if qset.has_openmp else None,
omp_threads=options.num_cpus,
atol=tol)
cgen.generate(config.tdname + ".pyx")
code = compile('from ' + config.tdname + ' import cy_td_ode_rhs',
'<string>', 'exec')
exec(code, globals())
config.tdfunc = cy_td_ode_rhs
initial_vector = mat2vec(rho0.full()).ravel()
_ode = scipy.integrate.ode(config.tdfunc)
code = compile('_ode.set_f_params(' + parameter_string + ')', '<string>',
'exec')
_ode.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)
_ode.set_initial_value(initial_vector, tlist[0])
exec(code, locals())
#
# prepare output array
#
n_tsteps = len(tlist)
e_sops_data = []
output = Result()
output.solver = "brmesolve"
output.times = tlist
if options.store_states:
output.states = []
if isinstance(e_ops, types.FunctionType):
n_expt_op = 0
expt_callback = True
elif isinstance(e_ops, list):
n_expt_op = len(e_ops)
expt_callback = False
if n_expt_op == 0:
# fall back on storing states
output.states = []
options.store_states = True
else:
output.expect = []
output.num_expect = n_expt_op
for op in e_ops:
e_sops_data.append(spre(op).data)
if op.isherm:
output.expect.append(np.zeros(n_tsteps))
else:
output.expect.append(np.zeros(n_tsteps, dtype=complex))
else:
raise TypeError("Expectation parameter must be a list or a function")
#
# start evolution
#
progress_bar.start(n_tsteps)
rho = Qobj(rho0)
dt = np.diff(tlist)
for t_idx, t in enumerate(tlist):
progress_bar.update(t_idx)
if not _ode.successful():
raise Exception("ODE integration error: Try to increase "
"the allowed number of substeps by increasing "
"the nsteps parameter in the Options class.")
if options.store_states or expt_callback:
rho.data = dense2D_to_fastcsr_fmode(vec2mat(_ode.y), rho.shape[0],
rho.shape[1])
if options.store_states:
output.states.append(Qobj(rho, isherm=True))
if expt_callback:
# use callback method
e_ops(t, rho)
for m in range(n_expt_op):
if output.expect[m].dtype == complex:
output.expect[m][t_idx] = expect_rho_vec(
e_sops_data[m], _ode.y, 0)
else:
output.expect[m][t_idx] = expect_rho_vec(
e_sops_data[m], _ode.y, 1)
if t_idx < n_tsteps - 1:
_ode.integrate(_ode.t + dt[t_idx])
progress_bar.finished()
if (not options.rhs_reuse) and (config.tdname is not None):
_cython_build_cleanup(config.tdname)
if options.store_final_state:
rho.data = dense2D_to_fastcsr_fmode(vec2mat(_ode.y), rho.shape[0],
rho.shape[1])
output.final_state = Qobj(rho, dims=rho0.dims, isherm=True)
return output
def _generic_ode_solve(r, psi0, tlist, e_ops, opt, progress_bar, dims=None):
"""
Internal function for solving ODEs.
"""
#
# prepare output array
#
n_tsteps = len(tlist)
output = Result()
output.solver = "sesolve"
output.times = tlist
if psi0.isunitary:
oper_evo = True
oper_n = dims[0][0]
norm_dim_factor = np.sqrt(oper_n)
else:
oper_evo = False
norm_dim_factor = 1.0
if opt.store_states:
output.states = []
if isinstance(e_ops, types.FunctionType):
n_expt_op = 0
expt_callback = True
elif isinstance(e_ops, list):
n_expt_op = len(e_ops)
expt_callback = False
if n_expt_op == 0:
# fallback on storing states
output.states = []
opt.store_states = True
else:
output.expect = []
output.num_expect = n_expt_op
for op in e_ops:
if op.isherm:
output.expect.append(np.zeros(n_tsteps))
else:
output.expect.append(np.zeros(n_tsteps, dtype=complex))
else:
raise TypeError("Expectation parameter must be a list or a function")
def get_curr_state_data():
if oper_evo:
return vec2mat(r.y)
else:
return r.y
#
# start evolution
#
progress_bar.start(n_tsteps)
dt = np.diff(tlist)
for t_idx, t in enumerate(tlist):
progress_bar.update(t_idx)
if not r.successful():
raise Exception("ODE integration error: Try to increase "
"the allowed number of substeps by increasing "
"the nsteps parameter in the Options class.")
# get the current state / oper data if needed
cdata = None
if opt.store_states or opt.normalize_output or n_expt_op > 0:
cdata = get_curr_state_data()
if opt.normalize_output:
# cdata *= _get_norm_factor(cdata, oper_evo)
cdata *= norm_dim_factor / la_norm(cdata)
if oper_evo:
r.set_initial_value(cdata.ravel('F'), r.t)
else:
r.set_initial_value(cdata, r.t)
if opt.store_states:
output.states.append(Qobj(cdata, dims=dims))
if expt_callback:
# use callback method
e_ops(t, Qobj(cdata, dims=dims))
for m in range(n_expt_op):
output.expect[m][t_idx] = cy_expect_psi(e_ops[m].data,
cdata, e_ops[m].isherm)
if t_idx < n_tsteps - 1:
r.integrate(r.t + dt[t_idx])
progress_bar.finished()
if not opt.rhs_reuse and config.tdname is not None:
try:
os.remove(config.tdname + ".pyx")
except:
pass
if opt.store_final_state:
cdata = get_curr_state_data()
if opt.normalize_output:
cdata *= norm_dim_factor / la_norm(cdata)
output.final_state = Qobj(cdata, dims=dims)
return output
def _generic_ode_solve(func,
ode_args,
rho0,
tlist,
e_ops,
opt,
progress_bar,
dims=None):
"""
Internal function for solving ME.
Calculate the required expectation values or invoke
callback function at each time step.
"""
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# This function is made similar to sesolve's one for futur merging in a
# solver class
# %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# prepare output array
n_tsteps = len(tlist)
output = Result()
output.solver = "mesolve"
output.times = tlist
size = rho0.shape[0]
initial_vector = rho0.full().ravel('F')
r = scipy.integrate.ode(func)
r.set_integrator('zvode',
method=opt.method,
order=opt.order,
atol=opt.atol,
rtol=opt.rtol,
nsteps=opt.nsteps,
first_step=opt.first_step,
min_step=opt.min_step,
max_step=opt.max_step)
if ode_args:
r.set_f_params(*ode_args)
r.set_initial_value(initial_vector, tlist[0])
e_ops_data = []
output.expect = []
if callable(e_ops):
n_expt_op = 0
expt_callback = True
output.num_expect = 1
elif isinstance(e_ops, list):
n_expt_op = len(e_ops)
expt_callback = False
output.num_expect = n_expt_op
if n_expt_op == 0:
# fall back on storing states
opt.store_states = True
else:
for op in e_ops:
if not isinstance(op, Qobj) and callable(op):
output.expect.append(np.zeros(n_tsteps, dtype=complex))
continue
if op.dims != rho0.dims:
raise TypeError(f"e_ops dims ({op.dims}) are not "
f"compatible with the state's "
f"({rho0.dims})")
e_ops_data.append(spre(op).data)
if op.isherm and rho0.isherm:
output.expect.append(np.zeros(n_tsteps))
else:
output.expect.append(np.zeros(n_tsteps, dtype=complex))
else:
raise TypeError("Expectation parameter must be a list or a function")
if opt.store_states:
output.states = []
def get_curr_state_data(r):
return vec2mat(r.y)
#
# start evolution
#
dt = np.diff(tlist)
cdata = None
progress_bar.start(n_tsteps)
for t_idx, t in enumerate(tlist):
progress_bar.update(t_idx)
if not r.successful():
raise Exception("ODE integration error: Try to increase "
"the allowed number of substeps by increasing "
"the nsteps parameter in the Options class.")
if opt.store_states or expt_callback:
cdata = get_curr_state_data(r)
fdata = dense2D_to_fastcsr_fmode(cdata, size, size)
# Try to guess if there is a fast path for rho_t
if issuper(rho0) or not rho0.isherm:
rho_t = Qobj(fdata, dims=dims)
else:
rho_t = Qobj(fdata, dims=dims, fast="mc-dm")
if opt.store_states:
output.states.append(rho_t)
if expt_callback:
# use callback method
output.expect.append(e_ops(t, rho_t))
for m in range(n_expt_op):
if not isinstance(e_ops[m], Qobj) and callable(e_ops[m]):
output.expect[m][t_idx] = e_ops[m](t, rho_t)
continue
output.expect[m][t_idx] = expect_rho_vec(
e_ops_data[m], r.y, e_ops[m].isherm and rho0.isherm)
if t_idx < n_tsteps - 1:
r.integrate(r.t + dt[t_idx])
progress_bar.finished()
if opt.store_final_state:
cdata = get_curr_state_data(r)
output.final_state = Qobj(cdata, dims=dims, isherm=rho0.isherm or None)
return output
def _ssepdpsolve_generic(sso, options, progress_bar):
"""
For internal use. See ssepdpsolve.
"""
if debug:
logger.debug(inspect.stack()[0][3])
N_store = len(sso.times)
N_substeps = sso.nsubsteps
dt = (sso.times[1] - sso.times[0]) / N_substeps
nt = sso.ntraj
data = Result()
data.solver = "sepdpsolve"
data.times = sso.tlist
data.expect = np.zeros((len(sso.e_ops), N_store), dtype=complex)
data.ss = np.zeros((len(sso.e_ops), N_store), dtype=complex)
data.jump_times = []
data.jump_op_idx = []
# effective hamiltonian for deterministic part
Heff = sso.H
for c in sso.c_ops:
Heff += -0.5j * c.dag() * c
progress_bar.start(sso.ntraj)
for n in range(sso.ntraj):
progress_bar.update(n)
psi_t = sso.state0.full().ravel()
states_list, jump_times, jump_op_idx = \
_ssepdpsolve_single_trajectory(data, Heff, dt, sso.times,
N_store, N_substeps,
psi_t, sso.state0.dims,
sso.c_ops, sso.e_ops)
data.states.append(states_list)
data.jump_times.append(jump_times)
data.jump_op_idx.append(jump_op_idx)
progress_bar.finished()
# average density matrices
if options.average_states and np.any(data.states):
data.states = [
sum([data.states[m][n] for m in range(nt)]).unit()
for n in range(len(data.times))
]
# average
data.expect = data.expect / nt
# standard error
if nt > 1:
data.se = (data.ss - nt * (data.expect**2)) / (nt * (nt - 1))
else:
data.se = None
# convert complex data to real if hermitian
data.expect = [
np.real(data.expect[n, :]) if e.isherm else data.expect[n, :]
for n, e in enumerate(sso.e_ops)
]
return data
def floquet_markov_mesolve(R,
ekets,
rho0,
tlist,
e_ops,
f_modes_table=None,
options=None,
floquet_basis=True):
"""
Solve the dynamics for the system using the Floquet-Markov master equation.
"""
if options is None:
opt = Options()
else:
opt = options
if opt.tidy:
R.tidyup()
#
# check initial state
#
if isket(rho0):
# Got a wave function as initial state: convert to density matrix.
rho0 = ket2dm(rho0)
#
# prepare output array
#
n_tsteps = len(tlist)
dt = tlist[1] - tlist[0]
output = Result()
output.solver = "fmmesolve"
output.times = tlist
if isinstance(e_ops, FunctionType):
n_expt_op = 0
expt_callback = True
elif isinstance(e_ops, list):
n_expt_op = len(e_ops)
expt_callback = False
if n_expt_op == 0:
output.states = []
else:
if not f_modes_table:
raise TypeError("The Floquet mode table has to be provided " +
"when requesting expectation values.")
output.expect = []
output.num_expect = n_expt_op
for op in e_ops:
if op.isherm:
output.expect.append(np.zeros(n_tsteps))
else:
output.expect.append(np.zeros(n_tsteps, dtype=complex))
else:
raise TypeError("Expectation parameter must be a list or a function")
#
# transform the initial density matrix to the eigenbasis: from
# computational basis to the floquet basis
#
if ekets is not None:
rho0 = rho0.transform(ekets)
#
# setup integrator
#
initial_vector = mat2vec(rho0.full())
r = scipy.integrate.ode(cy_ode_rhs)
r.set_f_params(R.data.data, R.data.indices, R.data.indptr)
r.set_integrator('zvode',
method=opt.method,
order=opt.order,
atol=opt.atol,
rtol=opt.rtol,
max_step=opt.max_step)
r.set_initial_value(initial_vector, tlist[0])
#
# start evolution
#
rho = Qobj(rho0)
t_idx = 0
for t in tlist:
if not r.successful():
break
rho = Qobj(vec2mat(r.y), rho0.dims, rho0.shape)
if expt_callback:
# use callback method
if floquet_basis:
e_ops(t, Qobj(rho))
else:
f_modes_table_t, T = f_modes_table
f_modes_t = floquet_modes_t_lookup(f_modes_table_t, t, T)
e_ops(t, Qobj(rho).transform(f_modes_t, True))
else:
# calculate all the expectation values, or output rho if
# no operators
if n_expt_op == 0:
if floquet_basis:
output.states.append(Qobj(rho))
else:
f_modes_table_t, T = f_modes_table
f_modes_t = floquet_modes_t_lookup(f_modes_table_t, t, T)
output.states.append(Qobj(rho).transform(f_modes_t, True))
else:
f_modes_table_t, T = f_modes_table
f_modes_t = floquet_modes_t_lookup(f_modes_table_t, t, T)
for m in range(0, n_expt_op):
output.expect[m][t_idx] = \
expect(e_ops[m], rho.transform(f_modes_t, False))
r.integrate(r.t + dt)
t_idx += 1
return output
def floquet_markov_mesolve(
R,
rho0,
tlist,
e_ops,
options=None,
floquet_basis=True,
f_modes_0=None,
f_modes_table_t=None,
f_energies=None,
T=None,
):
"""
Solve the dynamics for the system using the Floquet-Markov master equation.
.. note::
It is important to understand in which frame and basis the results
are returned here.
Parameters
----------
R : array
The Floquet-Markov master equation tensor `R`.
rho0 : :class:`qutip.qobj`
Initial density matrix. If ``f_modes_0`` is not passed, this density
matrix is assumed to be in the Floquet picture.
tlist : *list* / *array*
list of times for :math:`t`.
e_ops : list of :class:`qutip.qobj` / callback function
list of operators for which to evaluate expectation values.
options : :class:`qutip.solver.Options`
options for the ODE solver.
floquet_basis: bool, True
If ``True``, states and expectation values will be returned in the
Floquet basis. If ``False``, a transformation will be made to the
computational basis; this will be in the lab frame if
``f_modes_table``, ``T` and ``f_energies`` are all supplied, or the
interaction picture (defined purely be f_modes_0) if they are not.
f_modes_0 : list of :class:`qutip.qobj` (kets), optional
A list of initial Floquet modes, used to transform the given starting
density matrix into the Floquet basis. If this is not passed, it is
assumed that ``rho`` is already in the Floquet basis.
f_modes_table_t : nested list of :class:`qutip.qobj` (kets), optional
A lookup-table of Floquet modes at times precalculated by
:func:`qutip.floquet.floquet_modes_table`. Necessary if
``floquet_basis`` is ``False`` and the transformation should be made
back to the lab frame.
f_energies : array_like of float, optional
The precalculated Floquet quasienergies. Necessary if
``floquet_basis`` is ``False`` and the transformation should be made
back to the lab frame.
T : float, optional
The time period of driving. Necessary if ``floquet_basis`` is
``False`` and the transformation should be made back to the lab frame.
Returns
-------
output : :class:`qutip.solver.Result`
An instance of the class :class:`qutip.solver.Result`, which
contains either an *array* of expectation values or an array of
state vectors, for the times specified by `tlist`.
"""
opt = options or Options()
if opt.tidy:
R.tidyup()
rho0 = rho0.proj() if rho0.isket else rho0
# Prepare output object.
dt = tlist[1] - tlist[0]
output = Result()
output.solver = "fmmesolve"
output.times = tlist
if isinstance(e_ops, FunctionType):
expt_callback = True
store_states = opt.store_states or False
else:
expt_callback = False
try:
e_ops = list(e_ops)
except TypeError:
raise TypeError("`e_ops` must be iterable or a function") from None
n_expt_op = len(e_ops)
if n_expt_op == 0:
store_states = True
else:
output.expect = []
output.num_expect = n_expt_op
for op in e_ops:
dtype = np.float64 if op.isherm else np.complex128
output.expect.append(np.zeros(len(tlist), dtype=dtype))
store_states = opt.store_states or (n_expt_op == 0)
if store_states:
output.states = []
# Choose which frame transformations should be done on the initial and
# evolved states.
lab_lookup = [f_modes_table_t, f_energies, T]
if (any(x is None for x in lab_lookup)
and not all(x is None for x in lab_lookup)):
warnings.warn(
"if transformation back to the computational basis in the lab"
"frame is desired, all of `f_modes_t`, `f_energies` and `T` must"
"be supplied.")
f_modes_table_t = f_energies = T = None
# Initial state.
if f_modes_0 is not None:
rho0 = rho0.transform(f_modes_0)
# Evolved states.
if floquet_basis:
def transform(rho, t):
return rho
elif f_modes_table_t is not None:
# Lab frame, computational basis.
def transform(rho, t):
f_modes_t = floquet_modes_t_lookup(f_modes_table_t, t, T)
f_states_t = floquet_states(f_modes_t, f_energies, t)
return rho.transform(f_states_t, True)
elif f_modes_0 is not None:
# Interaction picture, computational basis.
def transform(rho, t):
return rho.transform(f_modes_0, False)
else:
raise ValueError(
"cannot transform out of the Floquet basis without some knowledge "
"of the Floquet modes. Pass `f_modes_0`, or all of `f_modes_t`, "
"`f_energies` and `T`.")
# Setup integrator.
initial_vector = mat2vec(rho0.full())
r = scipy.integrate.ode(cy_ode_rhs)
r.set_f_params(R.data.data, R.data.indices, R.data.indptr)
r.set_integrator('zvode',
method=opt.method,
order=opt.order,
atol=opt.atol,
rtol=opt.rtol,
max_step=opt.max_step)
r.set_initial_value(initial_vector, tlist[0])
# Main evolution loop.
for t_idx, t in enumerate(tlist):
if not r.successful():
break
rho = transform(Qobj(vec2mat(r.y), rho0.dims, rho0.shape), t)
if expt_callback:
e_ops(t, rho)
else:
for m, e_op in enumerate(e_ops):
output.expect[m][t_idx] = expect(e_op, rho)
if store_states:
output.states.append(rho)
r.integrate(r.t + dt)
return output
def brmesolve(H,
psi0,
tlist,
a_ops,
e_ops=[],
spectra_cb=[],
c_ops=[],
args={},
options=Options()):
"""
Solve the dynamics for a system using the Bloch-Redfield master equation.
.. note::
This solver does not currently support time-dependent Hamiltonians.
Parameters
----------
H : :class:`qutip.Qobj`
System Hamiltonian.
rho0 / psi0: :class:`qutip.Qobj`
Initial density matrix or state vector (ket).
tlist : *list* / *array*
List of times for :math:`t`.
a_ops : list of :class:`qutip.qobj`
List of system operators that couple to bath degrees of freedom.
e_ops : list of :class:`qutip.qobj` / callback function
List of operators for which to evaluate expectation values.
c_ops : list of :class:`qutip.qobj`
List of system collapse operators.
args : *dictionary*
Placeholder for future implementation, kept for API consistency.
options : :class:`qutip.solver.Options`
Options for the solver.
Returns
-------
result: :class:`qutip.solver.Result`
An instance of the class :class:`qutip.solver.Result`, which contains
either an array of expectation values, for operators given in e_ops,
or a list of states for the times specified by `tlist`.
"""
if not spectra_cb:
# default to infinite temperature white noise
spectra_cb = [lambda w: 1.0 for _ in a_ops]
R, ekets = bloch_redfield_tensor(H, a_ops, spectra_cb, c_ops)
output = Result()
output.solver = "brmesolve"
output.times = tlist
results = bloch_redfield_solve(R, ekets, psi0, tlist, e_ops, options)
if e_ops:
output.expect = results
else:
output.states = results
return output
def _generic_ode_solve(r, rho0, tlist, e_ops, opt, progress_bar):
"""
Internal function for solving ME. Solve an ODE which solver parameters
already setup (r). Calculate the required expectation values or invoke
callback function at each time step.
"""
#
# prepare output array
#
n_tsteps = len(tlist)
e_sops_data = []
output = Result()
output.solver = "mesolve"
output.times = tlist
if opt.store_states:
output.states = []
if isinstance(e_ops, types.FunctionType):
n_expt_op = 0
expt_callback = True
elif isinstance(e_ops, list):
n_expt_op = len(e_ops)
expt_callback = False
if n_expt_op == 0:
# fall back on storing states
output.states = []
opt.store_states = True
else:
output.expect = []
output.num_expect = n_expt_op
for op in e_ops:
e_sops_data.append(spre(op).data)
if op.isherm and rho0.isherm:
output.expect.append(np.zeros(n_tsteps))
else:
output.expect.append(np.zeros(n_tsteps, dtype=complex))
else:
raise TypeError("Expectation parameter must be a list or a function")
#
# start evolution
#
progress_bar.start(n_tsteps)
rho = Qobj(rho0)
dt = np.diff(tlist)
for t_idx, t in enumerate(tlist):
progress_bar.update(t_idx)
if not r.successful():
break
if opt.store_states or expt_callback:
rho.data = vec2mat(r.y)
if opt.store_states:
output.states.append(Qobj(rho))
if expt_callback:
# use callback method
e_ops(t, rho)
for m in range(n_expt_op):
if output.expect[m].dtype == complex:
output.expect[m][t_idx] = expect_rho_vec(
e_sops_data[m], r.y, 0)
else:
output.expect[m][t_idx] = expect_rho_vec(
e_sops_data[m], r.y, 1)
if t_idx < n_tsteps - 1:
r.integrate(r.t + dt[t_idx])
progress_bar.finished()
if not opt.rhs_reuse and config.tdname is not None:
try:
os.remove(config.tdname + ".pyx")
except:
pass
if opt.store_final_state:
rho.data = vec2mat(r.y)
output.final_state = Qobj(rho)
return output
