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_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 _mc_data_config(H, psi0, h_stuff, c_ops, c_stuff, args, e_ops,
options, config):
"""Creates the appropriate data structures for the monte carlo solver
based on the given time-dependent, or indepdendent, format.
"""
if debug:
print(inspect.stack()[0][3])
config.soft_reset()
# take care of expectation values, if any
if any(e_ops):
config.e_num = len(e_ops)
for op in e_ops:
if isinstance(op, list):
op = op[0]
config.e_ops_data.append(op.data.data)
config.e_ops_ind.append(op.data.indices)
config.e_ops_ptr.append(op.data.indptr)
config.e_ops_isherm.append(op.isherm)
config.e_ops_data = np.array(config.e_ops_data)
config.e_ops_ind = np.array(config.e_ops_ind)
config.e_ops_ptr = np.array(config.e_ops_ptr)
config.e_ops_isherm = np.array(config.e_ops_isherm)
# take care of collapse operators, if any
if any(c_ops):
config.c_num = len(c_ops)
for c_op in c_ops:
if isinstance(c_op, list):
c_op = c_op[0]
n_op = c_op.dag() * c_op
config.c_ops_data.append(c_op.data.data)
config.c_ops_ind.append(c_op.data.indices)
config.c_ops_ptr.append(c_op.data.indptr)
# norm ops
config.n_ops_data.append(n_op.data.data)
config.n_ops_ind.append(n_op.data.indices)
config.n_ops_ptr.append(n_op.data.indptr)
# to array
config.c_ops_data = np.array(config.c_ops_data)
config.c_ops_ind = np.array(config.c_ops_ind)
config.c_ops_ptr = np.array(config.c_ops_ptr)
config.n_ops_data = np.array(config.n_ops_data)
config.n_ops_ind = np.array(config.n_ops_ind)
config.n_ops_ptr = np.array(config.n_ops_ptr)
if config.tflag == 0:
# CONSTANT H & C_OPS CODE
# -----------------------
if config.cflag:
config.c_const_inds = np.arange(len(c_ops))
for c_op in c_ops:
n_op = c_op.dag() * c_op
H -= 0.5j * \
n_op # combine Hamiltonian and collapse terms into one
# construct Hamiltonian data structures
if options.tidy:
H = H.tidyup(options.atol)
config.h_data = -1.0j * H.data.data
config.h_ind = H.data.indices
config.h_ptr = H.data.indptr
elif config.tflag in [1, 10, 11]:
# STRING BASED TIME-DEPENDENCE
# ----------------------------
# take care of arguments for collapse operators, if any
if any(args):
for item in args.items():
config.c_args.append(item[1])
# constant Hamiltonian / string-type collapse operators
if config.tflag == 1:
H_inds = np.arange(1)
H_tdterms = 0
len_h = 1
C_inds = np.arange(config.c_num)
# find inds of time-dependent terms
C_td_inds = np.array(c_stuff[2])
# find inds of constant terms
C_const_inds = np.setdiff1d(C_inds, C_td_inds)
# extract time-dependent coefficients (strings)
C_tdterms = [c_ops[k][1] for k in C_td_inds]
# store indicies of constant collapse terms
config.c_const_inds = C_const_inds
# store indicies of time-dependent collapse terms
config.c_td_inds = C_td_inds
for k in config.c_const_inds:
H -= 0.5j * (c_ops[k].dag() * c_ops[k])
if options.tidy:
H = H.tidyup(options.atol)
config.h_data = [H.data.data]
config.h_ind = [H.data.indices]
config.h_ptr = [H.data.indptr]
for k in config.c_td_inds:
op = c_ops[k][0].dag() * c_ops[k][0]
config.h_data.append(-0.5j * op.data.data)
config.h_ind.append(op.data.indices)
config.h_ptr.append(op.data.indptr)
config.h_data = -1.0j * np.array(config.h_data)
config.h_ind = np.array(config.h_ind)
config.h_ptr = np.array(config.h_ptr)
else:
# string-type Hamiltonian & at least one string-type
# collapse operator
# -----------------
H_inds = np.arange(len(H))
# find inds of time-dependent terms
H_td_inds = np.array(h_stuff[2])
# find inds of constant terms
H_const_inds = np.setdiff1d(H_inds, H_td_inds)
# extract time-dependent coefficients (strings or functions)
H_tdterms = [H[k][1] for k in H_td_inds]
# combine time-INDEPENDENT terms into one.
H = np.array([np.sum(H[k] for k in H_const_inds)] +
[H[k][0] for k in H_td_inds], dtype=object)
len_h = len(H)
H_inds = np.arange(len_h)
# store indicies of time-dependent Hamiltonian terms
config.h_td_inds = np.arange(1, len_h)
# if there are any collapse operators
if config.c_num > 0:
if config.tflag == 10:
# constant collapse operators
config.c_const_inds = np.arange(config.c_num)
for k in config.c_const_inds:
H[0] -= 0.5j * (c_ops[k].dag() * c_ops[k])
C_inds = np.arange(config.c_num)
C_tdterms = np.array([])
else:
# some time-dependent collapse terms
C_inds = np.arange(config.c_num)
# find inds of time-dependent terms
C_td_inds = np.array(c_stuff[2])
# find inds of constant terms
C_const_inds = np.setdiff1d(C_inds, C_td_inds)
C_tdterms = [c_ops[k][1] for k in C_td_inds]
# extract time-dependent coefficients (strings)
# store indicies of constant collapse terms
config.c_const_inds = C_const_inds
# store indicies of time-dependent collapse terms
config.c_td_inds = C_td_inds
for k in config.c_const_inds:
H[0] -= 0.5j * (c_ops[k].dag() * c_ops[k])
else:
# set empty objects if no collapse operators
C_const_inds = np.arange(config.c_num)
config.c_const_inds = np.arange(config.c_num)
config.c_td_inds = np.array([])
C_tdterms = np.array([])
C_inds = np.array([])
# tidyup
if options.tidy:
H = np.array([H[k].tidyup(options.atol)
for k in range(len_h)], dtype=object)
# construct data sets
config.h_data = [H[k].data.data for k in range(len_h)]
config.h_ind = [H[k].data.indices for k in range(len_h)]
config.h_ptr = [H[k].data.indptr for k in range(len_h)]
for k in config.c_td_inds:
config.h_data.append(-0.5j * config.n_ops_data[k])
config.h_ind.append(config.n_ops_ind[k])
config.h_ptr.append(config.n_ops_ptr[k])
config.h_data = -1.0j * np.array(config.h_data)
config.h_ind = np.array(config.h_ind)
config.h_ptr = np.array(config.h_ptr)
# set execuatble code for collapse expectation values and spmv
col_spmv_code = ("state = _cy_col_spmv_func(j, ODE.t, " +
"config.c_ops_data[j], config.c_ops_ind[j], " +
"config.c_ops_ptr[j], ODE.y")
col_expect_code = ("for i in config.c_td_inds: " +
"n_dp.append(_cy_col_expect_func(i, ODE.t, " +
"config.n_ops_data[i], " +
"config.n_ops_ind[i], " +
"config.n_ops_ptr[i], ODE.y")
for kk in range(len(config.c_args)):
col_spmv_code += ",config.c_args[" + str(kk) + "]"
col_expect_code += ",config.c_args[" + str(kk) + "]"
col_spmv_code += ")"
col_expect_code += "))"
config.col_spmv_code = col_spmv_code
config.col_expect_code = col_expect_code
# setup ode args string
config.string = ""
data_range = range(len(config.h_data))
for k in data_range:
config.string += ("config.h_data[" + str(k) +
"], config.h_ind[" + str(k) +
"], config.h_ptr[" + str(k) + "]")
if k != data_range[-1]:
config.string += ","
# attach args to ode args string
if len(config.c_args) > 0:
for kk in range(len(config.c_args)):
config.string += "," + "config.c_args[" + str(kk) + "]"
name = "rhs" + str(os.getpid()) + str(config.cgen_num)
config.tdname = name
cgen = Codegen(H_inds, H_tdterms, config.h_td_inds, args,
C_inds, C_tdterms, config.c_td_inds, type='mc',
config=config)
cgen.generate(name + ".pyx")
elif config.tflag in [2, 20, 22]:
# PYTHON LIST-FUNCTION BASED TIME-DEPENDENCE
# ------------------------------------------
# take care of Hamiltonian
if config.tflag == 2:
# constant Hamiltonian, at least one function based collapse
# operators
H_inds = np.array([0])
H_tdterms = 0
len_h = 1
else:
# function based Hamiltonian
H_inds = np.arange(len(H))
H_td_inds = np.array(h_stuff[1])
H_const_inds = np.setdiff1d(H_inds, H_td_inds)
config.h_funcs = np.array([H[k][1] for k in H_td_inds])
config.h_func_args = args
Htd = np.array([H[k][0] for k in H_td_inds], dtype=object)
config.h_td_inds = np.arange(len(Htd))
H = np.sum(H[k] for k in H_const_inds)
# take care of collapse operators
C_inds = np.arange(config.c_num)
# find inds of time-dependent terms
C_td_inds = np.array(c_stuff[1])
# find inds of constant terms
C_const_inds = np.setdiff1d(C_inds, C_td_inds)
# store indicies of constant collapse terms
config.c_const_inds = C_const_inds
# store indicies of time-dependent collapse terms
config.c_td_inds = C_td_inds
config.c_funcs = np.zeros(config.c_num, dtype=FunctionType)
for k in config.c_td_inds:
config.c_funcs[k] = c_ops[k][1]
config.c_func_args = args
# combine constant collapse terms with constant H and construct data
for k in config.c_const_inds:
H -= 0.5j * (c_ops[k].dag() * c_ops[k])
if options.tidy:
H = H.tidyup(options.atol)
Htd = np.array([Htd[j].tidyup(options.atol)
for j in config.h_td_inds], dtype=object)
# setup constant H terms data
config.h_data = -1.0j * H.data.data
config.h_ind = H.data.indices
config.h_ptr = H.data.indptr
# setup td H terms data
config.h_td_data = np.array(
[-1.0j * Htd[k].data.data for k in config.h_td_inds])
config.h_td_ind = np.array(
[Htd[k].data.indices for k in config.h_td_inds])
config.h_td_ptr = np.array(
[Htd[k].data.indptr for k in config.h_td_inds])
elif config.tflag == 3:
# PYTHON FUNCTION BASED HAMILTONIAN
# ---------------------------------
# take care of Hamiltonian
config.h_funcs = H
config.h_func_args = args
# take care of collapse operators
config.c_const_inds = np.arange(config.c_num)
config.c_td_inds = np.array([])
if len(config.c_const_inds) > 0:
H = 0
for k in config.c_const_inds:
H -= 0.5j * (c_ops[k].dag() * c_ops[k])
if options.tidy:
H = H.tidyup(options.atol)
config.h_data = -1.0j * H.data.data
config.h_ind = H.data.indices
config.h_ptr = H.data.indptr
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 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 _mc_data_config(H, psi0, h_stuff, c_ops, c_stuff, args, e_ops,
options, config):
"""Creates the appropriate data structures for the monte carlo solver
based on the given time-dependent, or indepdendent, format.
"""
if debug:
print(inspect.stack()[0][3])
config.soft_reset()
# take care of expectation values, if any
if any(e_ops):
config.e_num = len(e_ops)
for op in e_ops:
if isinstance(op, list):
op = op[0]
config.e_ops_data.append(op.data.data)
config.e_ops_ind.append(op.data.indices)
config.e_ops_ptr.append(op.data.indptr)
config.e_ops_isherm.append(op.isherm)
config.e_ops_data = np.array(config.e_ops_data)
config.e_ops_ind = np.array(config.e_ops_ind)
config.e_ops_ptr = np.array(config.e_ops_ptr)
config.e_ops_isherm = np.array(config.e_ops_isherm)
# take care of collapse operators, if any
if any(c_ops):
config.c_num = len(c_ops)
for c_op in c_ops:
if isinstance(c_op, list):
c_op = c_op[0]
n_op = c_op.dag() * c_op
config.c_ops_data.append(c_op.data.data)
config.c_ops_ind.append(c_op.data.indices)
config.c_ops_ptr.append(c_op.data.indptr)
# norm ops
config.n_ops_data.append(n_op.data.data)
config.n_ops_ind.append(n_op.data.indices)
config.n_ops_ptr.append(n_op.data.indptr)
# to array
config.c_ops_data = np.array(config.c_ops_data)
config.c_ops_ind = np.array(config.c_ops_ind)
config.c_ops_ptr = np.array(config.c_ops_ptr)
config.n_ops_data = np.array(config.n_ops_data)
config.n_ops_ind = np.array(config.n_ops_ind)
config.n_ops_ptr = np.array(config.n_ops_ptr)
if config.tflag == 0:
# CONSTANT H & C_OPS CODE
# -----------------------
if config.cflag:
config.c_const_inds = np.arange(len(c_ops))
for c_op in c_ops:
n_op = c_op.dag() * c_op
H -= 0.5j * \
n_op # combine Hamiltonian and collapse terms into one
# construct Hamiltonian data structures
if options.tidy:
H = H.tidyup(options.atol)
config.h_data = -1.0j * H.data.data
config.h_ind = H.data.indices
config.h_ptr = H.data.indptr
elif config.tflag in [1, 10, 11]:
# STRING BASED TIME-DEPENDENCE
# ----------------------------
# take care of arguments for collapse operators, if any
if any(args):
for item in args.items():
config.c_args.append(item[1])
# constant Hamiltonian / string-type collapse operators
if config.tflag == 1:
H_inds = np.arange(1)
H_tdterms = 0
len_h = 1
C_inds = np.arange(config.c_num)
# find inds of time-dependent terms
C_td_inds = np.array(c_stuff[2])
# find inds of constant terms
C_const_inds = np.setdiff1d(C_inds, C_td_inds)
# extract time-dependent coefficients (strings)
C_tdterms = [c_ops[k][1] for k in C_td_inds]
# store indicies of constant collapse terms
config.c_const_inds = C_const_inds
# store indicies of time-dependent collapse terms
config.c_td_inds = C_td_inds
for k in config.c_const_inds:
H -= 0.5j * (c_ops[k].dag() * c_ops[k])
if options.tidy:
H = H.tidyup(options.atol)
config.h_data = [H.data.data]
config.h_ind = [H.data.indices]
config.h_ptr = [H.data.indptr]
for k in config.c_td_inds:
op = c_ops[k][0].dag() * c_ops[k][0]
config.h_data.append(-0.5j * op.data.data)
config.h_ind.append(op.data.indices)
config.h_ptr.append(op.data.indptr)
config.h_data = -1.0j * np.array(config.h_data)
config.h_ind = np.array(config.h_ind)
config.h_ptr = np.array(config.h_ptr)
else:
# string-type Hamiltonian & at least one string-type
# collapse operator
# -----------------
H_inds = np.arange(len(H))
# find inds of time-dependent terms
H_td_inds = np.array(h_stuff[2])
# find inds of constant terms
H_const_inds = np.setdiff1d(H_inds, H_td_inds)
# extract time-dependent coefficients (strings or functions)
H_tdterms = [H[k][1] for k in H_td_inds]
# combine time-INDEPENDENT terms into one.
H = np.array([np.sum(H[k] for k in H_const_inds)] +
[H[k][0] for k in H_td_inds], dtype=object)
len_h = len(H)
H_inds = np.arange(len_h)
# store indicies of time-dependent Hamiltonian terms
config.h_td_inds = np.arange(1, len_h)
# if there are any collapse operators
if config.c_num > 0:
if config.tflag == 10:
# constant collapse operators
config.c_const_inds = np.arange(config.c_num)
for k in config.c_const_inds:
H[0] -= 0.5j * (c_ops[k].dag() * c_ops[k])
C_inds = np.arange(config.c_num)
C_tdterms = np.array([])
else:
# some time-dependent collapse terms
C_inds = np.arange(config.c_num)
# find inds of time-dependent terms
C_td_inds = np.array(c_stuff[2])
# find inds of constant terms
C_const_inds = np.setdiff1d(C_inds, C_td_inds)
C_tdterms = [c_ops[k][1] for k in C_td_inds]
# extract time-dependent coefficients (strings)
# store indicies of constant collapse terms
config.c_const_inds = C_const_inds
# store indicies of time-dependent collapse terms
config.c_td_inds = C_td_inds
for k in config.c_const_inds:
H[0] -= 0.5j * (c_ops[k].dag() * c_ops[k])
else:
# set empty objects if no collapse operators
C_const_inds = np.arange(config.c_num)
config.c_const_inds = np.arange(config.c_num)
config.c_td_inds = np.array([])
C_tdterms = np.array([])
C_inds = np.array([])
# tidyup
if options.tidy:
H = np.array([H[k].tidyup(options.atol)
for k in range(len_h)], dtype=object)
# construct data sets
config.h_data = [H[k].data.data for k in range(len_h)]
config.h_ind = [H[k].data.indices for k in range(len_h)]
config.h_ptr = [H[k].data.indptr for k in range(len_h)]
for k in config.c_td_inds:
config.h_data.append(-0.5j * config.n_ops_data[k])
config.h_ind.append(config.n_ops_ind[k])
config.h_ptr.append(config.n_ops_ptr[k])
config.h_data = -1.0j * np.array(config.h_data)
config.h_ind = np.array(config.h_ind)
config.h_ptr = np.array(config.h_ptr)
# set execuatble code for collapse expectation values and spmv
col_spmv_code = ("state = _cy_col_spmv_func(j, ODE.t, " +
"config.c_ops_data[j], config.c_ops_ind[j], " +
"config.c_ops_ptr[j], ODE.y")
col_expect_code = ("for i in config.c_td_inds: " +
"n_dp.append(_cy_col_expect_func(i, ODE.t, " +
"config.n_ops_data[i], " +
"config.n_ops_ind[i], " +
"config.n_ops_ptr[i], ODE.y")
for kk in range(len(config.c_args)):
col_spmv_code += ",config.c_args[" + str(kk) + "]"
col_expect_code += ",config.c_args[" + str(kk) + "]"
col_spmv_code += ")"
col_expect_code += "))"
config.col_spmv_code = col_spmv_code
config.col_expect_code = col_expect_code
# setup ode args string
config.string = ""
data_range = range(len(config.h_data))
for k in data_range:
config.string += ("config.h_data[" + str(k) +
"], config.h_ind[" + str(k) +
"], config.h_ptr[" + str(k) + "]")
if k != data_range[-1]:
config.string += ","
# attach args to ode args string
if len(config.c_args) > 0:
for kk in range(len(config.c_args)):
config.string += "," + "config.c_args[" + str(kk) + "]"
name = "rhs" + str(os.getpid()) + str(config.cgen_num)
config.tdname = name
cgen = Codegen(H_inds, H_tdterms, config.h_td_inds, args,
C_inds, C_tdterms, config.c_td_inds, type='mc',
config=config)
cgen.generate(name + ".pyx")
elif config.tflag in [2, 20, 22]:
# PYTHON LIST-FUNCTION BASED TIME-DEPENDENCE
# ------------------------------------------
# take care of Hamiltonian
if config.tflag == 2:
# constant Hamiltonian, at least one function based collapse
# operators
H_inds = np.array([0])
H_tdterms = 0
len_h = 1
else:
# function based Hamiltonian
H_inds = np.arange(len(H))
H_td_inds = np.array(h_stuff[1])
H_const_inds = np.setdiff1d(H_inds, H_td_inds)
config.h_funcs = np.array([H[k][1] for k in H_td_inds])
config.h_func_args = args
Htd = np.array([H[k][0] for k in H_td_inds], dtype=object)
config.h_td_inds = np.arange(len(Htd))
H = np.sum(H[k] for k in H_const_inds)
# take care of collapse operators
C_inds = np.arange(config.c_num)
# find inds of time-dependent terms
C_td_inds = np.array(c_stuff[1])
# find inds of constant terms
C_const_inds = np.setdiff1d(C_inds, C_td_inds)
# store indicies of constant collapse terms
config.c_const_inds = C_const_inds
# store indicies of time-dependent collapse terms
config.c_td_inds = C_td_inds
config.c_funcs = np.zeros(config.c_num, dtype=FunctionType)
for k in config.c_td_inds:
config.c_funcs[k] = c_ops[k][1]
config.c_func_args = args
# combine constant collapse terms with constant H and construct data
for k in config.c_const_inds:
H -= 0.5j * (c_ops[k].dag() * c_ops[k])
if options.tidy:
H = H.tidyup(options.atol)
Htd = np.array([Htd[j].tidyup(options.atol)
for j in config.h_td_inds], dtype=object)
# setup constant H terms data
config.h_data = -1.0j * H.data.data
config.h_ind = H.data.indices
config.h_ptr = H.data.indptr
# setup td H terms data
config.h_td_data = np.array(
[-1.0j * Htd[k].data.data for k in config.h_td_inds])
config.h_td_ind = np.array(
[Htd[k].data.indices for k in config.h_td_inds])
config.h_td_ptr = np.array(
[Htd[k].data.indptr for k in config.h_td_inds])
elif config.tflag == 3:
# PYTHON FUNCTION BASED HAMILTONIAN
# ---------------------------------
# take care of Hamiltonian
config.h_funcs = H
config.h_func_args = args
# take care of collapse operators
config.c_const_inds = np.arange(config.c_num)
config.c_td_inds = np.array([])
if len(config.c_const_inds) > 0:
H = 0
for k in config.c_const_inds:
H -= 0.5j * (c_ops[k].dag() * c_ops[k])
if options.tidy:
H = H.tidyup(options.atol)
config.h_data = -1.0j * H.data.data
config.h_ind = H.data.indices
config.h_ptr = H.data.indptr
