def mesolve(H, rho0, tlist, c_ops, e_ops, args={}, options=None,
progress_bar=BaseProgressBar()):
"""
Master equation evolution of a density matrix for a given Hamiltonian.
Evolve the state vector or density matrix (`rho0`) using a given
Hamiltonian (`H`) and an [optional] set of collapse operators
(`c_op_list`), by integrating the set of ordinary differential equations
that define the system. In the absense of collase operators the system is
evolved according to the unitary evolution of the Hamiltonian.
The output is either the state vector at arbitrary points in time
(`tlist`), or the expectation values of the supplied operators
(`e_ops`). If e_ops is a callback function, it is invoked for each
time in `tlist` with time and the state as arguments, and the function
does not use any return values.
**Time-dependent operators**
For problems with time-dependent problems `H` and `c_ops` can be callback
functions that takes two arguments, time and `args`, and returns the
Hamiltonian or Liuovillian for the system at that point in time
(*callback format*).
Alternatively, `H` and `c_ops` can be a specified in a nested-list format
where each element in the list is a list of length 2, containing an
operator (:class:`qutip.qobj`) at the first element and where the
second element is either a string (*list string format*) or a callback
function (*list callback format*) that evaluates to the time-dependent
coefficient for the corresponding operator.
*Examples*
H = [[H0, 'sin(w*t)'], [H1, 'sin(2*w*t)']]
H = [[H0, f0_t], [H1, f1_t]]
where f0_t and f1_t are python functions with signature f_t(t, args).
In the *list string format* and *list callback format*, the string
expression and the callback function must evaluate to a real or complex
number (coefficient for the corresponding operator).
In all cases of time-dependent operators, `args` is a dictionary of
parameters that is used when evaluating operators. It is passed to the
callback functions as second argument
.. note::
If an element in the list-specification of the Hamiltonian or
the list of collapse operators are in super-operator for it will be
added to the total Liouvillian of the problem with out further
transformation. This allows for using mesolve for solving master
equations that are not on standard Lindblad form.
.. note::
On using callback function: mesolve transforms all :class:`qutip.qobj`
objects to sparse matrices before handing the problem to the integrator
function. In order for your callback function to work correctly, pass
all :class:`qutip.qobj` objects that are used in constructing the
Hamiltonian via args. odesolve will check for :class:`qutip.qobj` in
`args` and handle the conversion to sparse matrices. All other
:class:`qutip.qobj` objects that are not passed via `args` will be
passed on to the integrator to scipy who will raise an NotImplemented
exception.
Parameters
----------
H : :class:`qutip.qobj`
system Hamiltonian, or a callback function for time-dependent
Hamiltonians.
rho0 : :class:`qutip.qobj`
initial density matrix or state vector (ket).
tlist : *list* / *array*
list of times for :math:`t`.
c_ops : list of :class:`qutip.qobj`
single collapse operator, or list of collapse operators.
e_ops : list of :class:`qutip.qobj` / callback function single
single operator or list of operators for which to evaluate
expectation values.
args : *dictionary*
dictionary of parameters for time-dependent Hamiltonians and
collapse operators.
options : :class:`qutip.Odeoptions`
with options for the ODE solver.
Returns
-------
output: :class:`qutip.odedata`
An instance of the class :class:`qutip.odedata`, which contains either
an *array* of expectation values for the times specified by `tlist`, or
an *array* or state vectors or density matrices corresponding to the
times in `tlist` [if `e_ops` is an empty list], or
nothing if a callback function was given inplace of operators for
which to calculate the expectation values.
"""
# check whether c_ops or e_ops is is a single operator
# if so convert it to a list containing only that operator
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
# check for type (if any) of time-dependent inputs
n_const, n_func, n_str = _ode_checks(H, c_ops)
if options is None:
options = Odeoptions()
if (not options.rhs_reuse) or (not odeconfig.tdfunc):
# reset odeconfig collapse and time-dependence flags to default values
odeconfig.reset()
res = None
#
# dispatch the appropriate solver
#
if ((c_ops and len(c_ops) > 0)
or (not isket(rho0))
or (isinstance(H, Qobj) and issuper(H))
or (isinstance(H, list) and
isinstance(H[0], Qobj) and issuper(H[0]))):
#
# we have collapse operators
#
#
# find out if we are dealing with all-constant hamiltonian and
# collapse operators or if we have at least one time-dependent
# operator. Then delegate to appropriate solver...
#
if isinstance(H, Qobj):
# constant hamiltonian
if n_func == 0 and n_str == 0:
# constant collapse operators
res = _mesolve_const(H, rho0, tlist, c_ops,
e_ops, args, options,
progress_bar)
elif n_str > 0:
# constant hamiltonian but time-dependent collapse
# operators in list string format
res = _mesolve_list_str_td([H], rho0, tlist, c_ops,
e_ops, args, options,
progress_bar)
elif n_func > 0:
# constant hamiltonian but time-dependent collapse
# operators in list function format
res = _mesolve_list_func_td([H], rho0, tlist, c_ops,
e_ops, args, options,
progress_bar)
elif isinstance(H, (types.FunctionType,
types.BuiltinFunctionType, partial)):
# old style time-dependence: must have constant collapse operators
if n_str > 0: # or n_func > 0:
raise TypeError("Incorrect format: function-format " +
"Hamiltonian cannot be mixed with " +
"time-dependent collapse operators.")
else:
res = _mesolve_func_td(H, rho0, tlist, c_ops,
e_ops, args, options,
progress_bar)
elif isinstance(H, list):
# determine if we are dealing with list of [Qobj, string] or
# [Qobj, function] style time-dependencies (for pure python and
# cython, respectively)
if n_func > 0:
res = _mesolve_list_func_td(H, rho0, tlist, c_ops,
e_ops, args, options,
progress_bar)
else:
res = _mesolve_list_str_td(H, rho0, tlist, c_ops,
e_ops, args, options,
progress_bar)
else:
raise TypeError("Incorrect specification of Hamiltonian " +
"or collapse operators.")
else:
#
# no collapse operators: unitary dynamics
#
if n_func > 0:
res = _sesolve_list_func_td(H, rho0, tlist,
e_ops, args, options, progress_bar)
elif n_str > 0:
res = _sesolve_list_str_td(H, rho0, tlist,
e_ops, args, options, progress_bar)
elif isinstance(H, (types.FunctionType,
types.BuiltinFunctionType, partial)):
res = _sesolve_func_td(H, rho0, tlist,
e_ops, args, options, progress_bar)
else:
res = _sesolve_const(H, rho0, tlist,
e_ops, args, options, progress_bar)
if e_ops_dict:
res.expect = {e: res.expect[n] for n, e in enumerate(e_ops_dict.keys())}
return res
def sesolve(H, rho0, tlist, e_ops, args={}, options=None,
progress_bar=BaseProgressBar()):
"""
Schrodinger equation evolution of a state vector for a given Hamiltonian.
Evolve the state vector or density matrix (`rho0`) using a given
Hamiltonian (`H`), by integrating the set of ordinary differential
equations that define the system.
The output is either the state vector at arbitrary points in time
(`tlist`), or the expectation values of the supplied operators
(`e_ops`). If e_ops is a callback function, it is invoked for each
time in `tlist` with time and the state as arguments, and the function
does not use any return values.
Parameters
----------
H : :class:`qutip.qobj`
system Hamiltonian, or a callback function for time-dependent
Hamiltonians.
rho0 : :class:`qutip.qobj`
initial density matrix or state vector (ket).
tlist : *list* / *array*
list of times for :math:`t`.
e_ops : list of :class:`qutip.qobj` / callback function single
single operator or list of operators for which to evaluate
expectation values.
args : *dictionary*
dictionary of parameters for time-dependent Hamiltonians and
collapse operators.
options : :class:`qutip.Qdeoptions`
with options for the ODE solver.
Returns
-------
output: :class:`qutip.odedata`
An instance of the class :class:`qutip.odedata`, which contains either
an *array* of expectation values for the times specified by `tlist`, or
an *array* or state vectors or density matrices corresponding to the
times in `tlist` [if `e_ops` is an empty list], or
nothing if a callback function was given inplace of operators for
which to calculate the expectation values.
"""
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
# check for type (if any) of time-dependent inputs
n_const, n_func, n_str = _ode_checks(H, [])
if options is None:
options = Odeoptions()
if (not options.rhs_reuse) or (not odeconfig.tdfunc):
# reset odeconfig time-dependence flags to default values
odeconfig.reset()
if n_func > 0:
res = _sesolve_list_func_td(H, rho0, tlist, e_ops, args, options,
progress_bar)
elif n_str > 0:
res = _sesolve_list_str_td(H, rho0, tlist, e_ops, args, options,
progress_bar)
elif isinstance(H, (types.FunctionType,
types.BuiltinFunctionType,
partial)):
res = _sesolve_func_td(H, rho0, tlist, e_ops, args, options,
progress_bar)
else:
res = _sesolve_const(H, rho0, tlist, e_ops, args, options,
progress_bar)
if e_ops_dict:
res.expect = {e: res.expect[n] for n, e in enumerate(e_ops_dict.keys())}
return res
def mesolve(H,
rho0,
tlist,
c_ops,
e_ops,
args={},
options=None,
progress_bar=BaseProgressBar()):
"""
Master equation evolution of a density matrix for a given Hamiltonian.
Evolve the state vector or density matrix (`rho0`) using a given
Hamiltonian (`H`) and an [optional] set of collapse operators
(`c_op_list`), by integrating the set of ordinary differential equations
that define the system. In the absense of collase operators the system is
evolved according to the unitary evolution of the Hamiltonian.
The output is either the state vector at arbitrary points in time
(`tlist`), or the expectation values of the supplied operators
(`e_ops`). If e_ops is a callback function, it is invoked for each
time in `tlist` with time and the state as arguments, and the function
does not use any return values.
**Time-dependent operators**
For problems with time-dependent problems `H` and `c_ops` can be callback
functions that takes two arguments, time and `args`, and returns the
Hamiltonian or Liuovillian for the system at that point in time
(*callback format*).
Alternatively, `H` and `c_ops` can be a specified in a nested-list format
where each element in the list is a list of length 2, containing an
operator (:class:`qutip.qobj`) at the first element and where the
second element is either a string (*list string format*) or a callback
function (*list callback format*) that evaluates to the time-dependent
coefficient for the corresponding operator.
*Examples*
H = [[H0, 'sin(w*t)'], [H1, 'sin(2*w*t)']]
H = [[H0, f0_t], [H1, f1_t]]
where f0_t and f1_t are python functions with signature f_t(t, args).
In the *list string format* and *list callback format*, the string
expression and the callback function must evaluate to a real or complex
number (coefficient for the corresponding operator).
In all cases of time-dependent operators, `args` is a dictionary of
parameters that is used when evaluating operators. It is passed to the
callback functions as second argument
.. note::
If an element in the list-specification of the Hamiltonian or
the list of collapse operators are in super-operator for it will be
added to the total Liouvillian of the problem with out further
transformation. This allows for using mesolve for solving master
equations that are not on standard Lindblad form.
.. note::
On using callback function: mesolve transforms all :class:`qutip.qobj`
objects to sparse matrices before handing the problem to the integrator
function. In order for your callback function to work correctly, pass
all :class:`qutip.qobj` objects that are used in constructing the
Hamiltonian via args. odesolve will check for :class:`qutip.qobj` in
`args` and handle the conversion to sparse matrices. All other
:class:`qutip.qobj` objects that are not passed via `args` will be
passed on to the integrator to scipy who will raise an NotImplemented
exception.
Parameters
----------
H : :class:`qutip.qobj`
system Hamiltonian, or a callback function for time-dependent
Hamiltonians.
rho0 : :class:`qutip.qobj`
initial density matrix or state vector (ket).
tlist : *list* / *array*
list of times for :math:`t`.
c_ops : list of :class:`qutip.qobj`
single collapse operator, or list of collapse operators.
e_ops : list of :class:`qutip.qobj` / callback function single
single operator or list of operators for which to evaluate
expectation values.
args : *dictionary*
dictionary of parameters for time-dependent Hamiltonians and
collapse operators.
options : :class:`qutip.Odeoptions`
with options for the ODE solver.
Returns
-------
output: :class:`qutip.odedata`
An instance of the class :class:`qutip.odedata`, which contains either
an *array* of expectation values for the times specified by `tlist`, or
an *array* or state vectors or density matrices corresponding to the
times in `tlist` [if `e_ops` is an empty list], or
nothing if a callback function was given inplace of operators for
which to calculate the expectation values.
"""
# check whether c_ops or e_ops is is a single operator
# if so convert it to a list containing only that operator
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
# check for type (if any) of time-dependent inputs
n_const, n_func, n_str = _ode_checks(H, c_ops)
if options is None:
options = Odeoptions()
if (not options.rhs_reuse) or (not odeconfig.tdfunc):
# reset odeconfig collapse and time-dependence flags to default values
odeconfig.reset()
res = None
#
# dispatch the appropriate solver
#
if ((c_ops and len(c_ops) > 0) or (not isket(rho0))
or (isinstance(H, Qobj) and issuper(H)) or
(isinstance(H, list) and isinstance(H[0], Qobj) and issuper(H[0]))):
#
# we have collapse operators
#
#
# find out if we are dealing with all-constant hamiltonian and
# collapse operators or if we have at least one time-dependent
# operator. Then delegate to appropriate solver...
#
if isinstance(H, Qobj):
# constant hamiltonian
if n_func == 0 and n_str == 0:
# constant collapse operators
res = _mesolve_const(H, rho0, tlist, c_ops, e_ops, args,
options, progress_bar)
elif n_str > 0:
# constant hamiltonian but time-dependent collapse
# operators in list string format
res = _mesolve_list_str_td([H], rho0, tlist, c_ops, e_ops,
args, options, progress_bar)
elif n_func > 0:
# constant hamiltonian but time-dependent collapse
# operators in list function format
res = _mesolve_list_func_td([H], rho0, tlist, c_ops, e_ops,
args, options, progress_bar)
elif isinstance(
H, (types.FunctionType, types.BuiltinFunctionType, partial)):
# old style time-dependence: must have constant collapse operators
if n_str > 0: # or n_func > 0:
raise TypeError("Incorrect format: function-format " +
"Hamiltonian cannot be mixed with " +
"time-dependent collapse operators.")
else:
res = _mesolve_func_td(H, rho0, tlist, c_ops, e_ops, args,
options, progress_bar)
elif isinstance(H, list):
# determine if we are dealing with list of [Qobj, string] or
# [Qobj, function] style time-dependencies (for pure python and
# cython, respectively)
if n_func > 0:
res = _mesolve_list_func_td(H, rho0, tlist, c_ops, e_ops, args,
options, progress_bar)
else:
res = _mesolve_list_str_td(H, rho0, tlist, c_ops, e_ops, args,
options, progress_bar)
else:
raise TypeError("Incorrect specification of Hamiltonian " +
"or collapse operators.")
else:
#
# no collapse operators: unitary dynamics
#
if n_func > 0:
res = _sesolve_list_func_td(H, rho0, tlist, e_ops, args, options,
progress_bar)
elif n_str > 0:
res = _sesolve_list_str_td(H, rho0, tlist, e_ops, args, options,
progress_bar)
elif isinstance(
H, (types.FunctionType, types.BuiltinFunctionType, partial)):
res = _sesolve_func_td(H, rho0, tlist, e_ops, args, options,
progress_bar)
else:
res = _sesolve_const(H, rho0, tlist, e_ops, args, options,
progress_bar)
if e_ops_dict:
res.expect = {
e: res.expect[n]
for n, e in enumerate(e_ops_dict.keys())
}
return res
def sesolve(H, rho0, tlist, e_ops, args={}, options=None,
progress_bar=BaseProgressBar()):
"""
Schrodinger equation evolution of a state vector for a given Hamiltonian.
Evolve the state vector or density matrix (`rho0`) using a given
Hamiltonian (`H`), by integrating the set of ordinary differential
equations that define the system.
The output is either the state vector at arbitrary points in time
(`tlist`), or the expectation values of the supplied operators
(`e_ops`). If e_ops is a callback function, it is invoked for each
time in `tlist` with time and the state as arguments, and the function
does not use any return values.
Parameters
----------
H : :class:`qutip.qobj`
system Hamiltonian, or a callback function for time-dependent
Hamiltonians.
rho0 : :class:`qutip.qobj`
initial density matrix or state vector (ket).
tlist : *list* / *array*
list of times for :math:`t`.
e_ops : list of :class:`qutip.qobj` / callback function single
single operator or list of operators for which to evaluate
expectation values.
args : *dictionary*
dictionary of parameters for time-dependent Hamiltonians and
collapse operators.
options : :class:`qutip.Qdeoptions`
with options for the ODE solver.
Returns
-------
output: :class:`qutip.odedata`
An instance of the class :class:`qutip.odedata`, which contains either
an *array* of expectation values for the times specified by `tlist`, or
an *array* or state vectors or density matrices corresponding to the
times in `tlist` [if `e_ops` is an empty list], or
nothing if a callback function was given inplace of operators for
which to calculate the expectation values.
"""
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
# check for type (if any) of time-dependent inputs
n_const, n_func, n_str = _ode_checks(H, [])
if options is None:
options = Odeoptions()
if (not options.rhs_reuse) or (not odeconfig.tdfunc):
# reset odeconfig time-dependence flags to default values
odeconfig.reset()
if n_func > 0:
res = _sesolve_list_func_td(H, rho0, tlist, e_ops, args, options,
progress_bar)
elif n_str > 0:
res = _sesolve_list_str_td(H, rho0, tlist, e_ops, args, options,
progress_bar)
elif isinstance(H, (types.FunctionType,
types.BuiltinFunctionType,
partial)):
res = _sesolve_func_td(H, rho0, tlist, e_ops, args, options,
progress_bar)
else:
res = _sesolve_const(H, rho0, tlist, e_ops, args, options,
progress_bar)
if e_ops_dict:
res.expect = {e: res.expect[n] for n, e in enumerate(e_ops_dict.keys())}
return res
def rhs_generate(H, c_ops, args={}, options=Odeoptions(), name=None):
"""
Generates the Cython functions needed for solving the dynamics of a
given system using the mesolve function inside a parfor loop.
Parameters
----------
H : qobj
System Hamiltonian.
c_ops : list
``list`` of collapse operators.
args : dict
Arguments for time-dependent Hamiltonian and collapse operator terms.
options : Odeoptions
Instance of ODE solver options.
name: str
Name of generated RHS
Notes
-----
Using this function with any solver other than the mesolve function
will result in an error.
"""
odeconfig.reset()
odeconfig.options = options
if name:
odeconfig.tdname = name
else:
odeconfig.tdname = "rhs" + str(odeconfig.cgen_num)
Lconst = 0
Ldata = []
Linds = []
Lptrs = []
Lcoeff = []
# loop over all hamiltonian terms, convert to superoperator form and
# add the data of sparse matrix represenation to
for h_spec in H:
if isinstance(h_spec, Qobj):
h = h_spec
Lconst += -1j * (spre(h) - spost(h))
elif isinstance(h_spec, list):
h = h_spec[0]
h_coeff = h_spec[1]
L = -1j * (spre(h) - spost(h))
Ldata.append(L.data.data)
Linds.append(L.data.indices)
Lptrs.append(L.data.indptr)
Lcoeff.append(h_coeff)
else:
raise TypeError("Incorrect specification of time-dependent " +
"Hamiltonian (expected string format)")
# loop over all collapse operators
for c_spec in c_ops:
if isinstance(c_spec, Qobj):
c = c_spec
cdc = c.dag() * c
Lconst += spre(
c) * spost(c.dag()) - 0.5 * spre(cdc) - 0.5 * spost(cdc)
elif isinstance(c_spec, list):
c = c_spec[0]
c_coeff = c_spec[1]
cdc = c.dag() * c
L = spre(c) * spost(c.dag()) - 0.5 * spre(cdc) - 0.5 * spost(cdc)
Ldata.append(L.data.data)
Linds.append(L.data.indices)
Lptrs.append(L.data.indptr)
Lcoeff.append("(" + c_coeff + ")**2")
else:
raise TypeError("Incorrect specification of time-dependent " +
"collapse operators (expected string format)")
# add the constant part of the lagrangian
if Lconst != 0:
Ldata.append(Lconst.data.data)
Linds.append(Lconst.data.indices)
Lptrs.append(Lconst.data.indptr)
Lcoeff.append("1.0")
# the total number of liouvillian terms (hamiltonian terms + collapse
# operators)
n_L_terms = len(Ldata)
cgen = Codegen(h_terms=n_L_terms, h_tdterms=Lcoeff, args=args,
odeconfig=odeconfig)
cgen.generate(odeconfig.tdname + ".pyx")
code = compile('from ' + odeconfig.tdname +
' import cyq_td_ode_rhs', '<string>', 'exec')
exec(code)
odeconfig.tdfunc = cyq_td_ode_rhs
try:
os.remove(odeconfig.tdname + ".pyx")
except:
pass
def rhs_generate(H, c_ops, args={}, options=Odeoptions(), name=None):
"""
Generates the Cython functions needed for solving the dynamics of a
given system using the mesolve function inside a parfor loop.
Parameters
----------
H : qobj
System Hamiltonian.
c_ops : list
``list`` of collapse operators.
args : dict
Arguments for time-dependent Hamiltonian and collapse operator terms.
options : Odeoptions
Instance of ODE solver options.
name: str
Name of generated RHS
Notes
-----
Using this function with any solver other than the mesolve function
will result in an error.
"""
odeconfig.reset()
odeconfig.options = options
if name:
odeconfig.tdname = name
else:
odeconfig.tdname = "rhs" + str(odeconfig.cgen_num)
Lconst = 0
Ldata = []
Linds = []
Lptrs = []
Lcoeff = []
# loop over all hamiltonian terms, convert to superoperator form and
# add the data of sparse matrix represenation to
for h_spec in H:
if isinstance(h_spec, Qobj):
h = h_spec
Lconst += -1j * (spre(h) - spost(h))
elif isinstance(h_spec, list):
h = h_spec[0]
h_coeff = h_spec[1]
L = -1j * (spre(h) - spost(h))
Ldata.append(L.data.data)
Linds.append(L.data.indices)
Lptrs.append(L.data.indptr)
Lcoeff.append(h_coeff)
else:
raise TypeError("Incorrect specification of time-dependent " +
"Hamiltonian (expected string format)")
# loop over all collapse operators
for c_spec in c_ops:
if isinstance(c_spec, Qobj):
c = c_spec
cdc = c.dag() * c
Lconst += spre(c) * spost(
c.dag()) - 0.5 * spre(cdc) - 0.5 * spost(cdc)
elif isinstance(c_spec, list):
c = c_spec[0]
c_coeff = c_spec[1]
cdc = c.dag() * c
L = spre(c) * spost(c.dag()) - 0.5 * spre(cdc) - 0.5 * spost(cdc)
Ldata.append(L.data.data)
Linds.append(L.data.indices)
Lptrs.append(L.data.indptr)
Lcoeff.append("(" + c_coeff + ")**2")
else:
raise TypeError("Incorrect specification of time-dependent " +
"collapse operators (expected string format)")
# add the constant part of the lagrangian
if Lconst != 0:
Ldata.append(Lconst.data.data)
Linds.append(Lconst.data.indices)
Lptrs.append(Lconst.data.indptr)
Lcoeff.append("1.0")
# the total number of liouvillian terms (hamiltonian terms + collapse
# operators)
n_L_terms = len(Ldata)
cgen = Codegen(h_terms=n_L_terms,
h_tdterms=Lcoeff,
args=args,
odeconfig=odeconfig)
cgen.generate(odeconfig.tdname + ".pyx")
code = compile('from ' + odeconfig.tdname + ' import cyq_td_ode_rhs',
'<string>', 'exec')
exec(code)
odeconfig.tdfunc = cyq_td_ode_rhs
try:
os.remove(odeconfig.tdname + ".pyx")
except:
pass
def rhs_generate(H, c_ops, args={}, options=Odeoptions(), name=None, cleanup=True):
"""
Generates the Cython functions needed for solving the dynamics of a
given system using the mesolve function inside a parfor loop.
Parameters
----------
H : qobj
System Hamiltonian.
c_ops : list
``list`` of collapse operators.
args : dict
Arguments for time-dependent Hamiltonian and collapse operator terms.
options : Odeoptions
Instance of ODE solver options.
name: str
Name of generated RHS
cleanup: bool
Whether the generated cython file should be automatically removed or
not.
Notes
-----
Using this function with any solver other than the mesolve function
will result in an error.
"""
odeconfig.reset()
odeconfig.options = options
if name:
odeconfig.tdname = name
else:
odeconfig.tdname = "rhs" + str(odeconfig.cgen_num)
Lconst = 0
Ldata = []
Linds = []
Lptrs = []
Lcoeff = []
# loop over all hamiltonian terms, convert to superoperator form and
# add the data of sparse matrix represenation to
msg = "Incorrect specification of time-dependence: "
for h_spec in H:
if isinstance(h_spec, Qobj):
h = h_spec
if not isinstance(h, Qobj):
raise TypeError(msg + "expected Qobj")
if h.isoper:
Lconst += -1j * (spre(h) - spost(h))
elif h.issuper:
Lconst += h
else:
raise TypeError(msg + "expected operator or superoperator")
elif isinstance(h_spec, list):
h = h_spec[0]
h_coeff = h_spec[1]
if not isinstance(h, Qobj):
raise TypeError(msg + "expected Qobj")
if h.isoper:
L = -1j * (spre(h) - spost(h))
elif h.issuper:
L = h
else:
raise TypeError(msg + "expected operator or superoperator")
Ldata.append(L.data.data)
Linds.append(L.data.indices)
Lptrs.append(L.data.indptr)
Lcoeff.append(h_coeff)
else:
raise TypeError(msg + "expected string format")
# loop over all collapse operators
for c_spec in c_ops:
if isinstance(c_spec, Qobj):
c = c_spec
if not isinstance(c, Qobj):
raise TypeError(msg + "expected Qobj")
if c.isoper:
cdc = c.dag() * c
Lconst += spre(c) * spost(c.dag()) - 0.5 * spre(cdc) - 0.5 * spost(cdc)
elif c.issuper:
Lconst += c
else:
raise TypeError(msg + "expected operator or superoperator")
elif isinstance(c_spec, list):
c = c_spec[0]
c_coeff = c_spec[1]
if not isinstance(c, Qobj):
raise TypeError(msg + "expected Qobj")
if c.isoper:
cdc = c.dag() * c
L = spre(c) * spost(c.dag()) - 0.5 * spre(cdc) - 0.5 * spost(cdc)
c_coeff = "(" + c_coeff + ")**2"
elif c.issuper:
L = c
else:
raise TypeError(msg + "expected operator or superoperator")
Ldata.append(L.data.data)
Linds.append(L.data.indices)
Lptrs.append(L.data.indptr)
Lcoeff.append(c_coeff)
else:
raise TypeError(msg + "expected string format")
# add the constant part of the lagrangian
if Lconst != 0:
Ldata.append(Lconst.data.data)
Linds.append(Lconst.data.indices)
Lptrs.append(Lconst.data.indptr)
Lcoeff.append("1.0")
# the total number of liouvillian terms (hamiltonian terms + collapse
# operators)
n_L_terms = len(Ldata)
cgen = Codegen(h_terms=n_L_terms, h_tdterms=Lcoeff, args=args, odeconfig=odeconfig)
cgen.generate(odeconfig.tdname + ".pyx")
code = compile("from " + odeconfig.tdname + " import cy_td_ode_rhs", "<string>", "exec")
exec(code, globals())
odeconfig.tdfunc = cy_td_ode_rhs
if cleanup:
try:
os.remove(odeconfig.tdname + ".pyx")
except:
pass
