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 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)
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 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 mcsolve(H, psi0, tlist, c_ops, e_ops, ntraj=None, args={}, options=Options()):
"""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_op_list=[C0,[C1,C1_coeff]]
args={'a':A,'w':W}
or in String (Cython) format we could write::
H=[H0,[H1,'sin(w*t)']]
c_op_list=[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 : 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
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.
Returns
-------
results : Result
Object storing all results from simulation.
"""
if debug:
print(inspect.stack()[0][3])
if ntraj is None:
ntraj = options.ntraj
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 isinstance(ntraj, list):
config.progress_bar = TextProgressBar(max(ntraj))
else:
config.progress_bar = TextProgressBar(ntraj)
# 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().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, ndarray)):
config.ntraj = 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")
h_terms = len(h_stuff[0]) + len(h_stuff[1]) + len(h_stuff[2])
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 array([1, 10, 11]):
if any(args):
config.c_args = []
arg_items = args.items()
for k in range(len(args)):
config.c_args.append(arg_items[k][1])
# function based
elif config.tflag in array([2, 3, 20, 22]):
config.h_func_args = args
# load monte-carlo class
mc = _MC_class(config)
# RUN THE SIMULATION
mc.run()
# remove RHS cython file if necessary
if not options.rhs_reuse and config.tdname:
try:
os.remove(config.tdname + ".pyx")
except:
pass
# AFTER MCSOLVER IS DONE --------------------------------------
# ------- COLLECT AND RETURN OUTPUT DATA IN ODEDATA OBJECT --------------
output = Result()
output.solver = "mcsolve"
# 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
elif mc.expect_out is not None and config.cflag and config.options.average_expect:
# averaging if multiple trajectories
if isinstance(ntraj, int):
output.expect = [mean([mc.expect_out[nt][op] for nt in range(ntraj)], axis=0) for op in range(config.e_num)]
elif isinstance(ntraj, (list, ndarray)):
output.expect = []
for num in ntraj:
expt_data = 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_states 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 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 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