def setODEChecksMC(self):
#define operators
H = rand_herm(10)
c_op = qeye(10)
def f_c_op(t, args):
return 0
def f_H(t, args):
return 0
#check constant H and no C_ops
time_type, h_stuff, c_stuff = _ode_checks(H, [], 'mc')
self.assertTrue(time_type=0)
#check constant H and constant C_ops
time_type, h_stuff, c_stuff = _ode_checks(H, [c_op], 'mc')
self.assertTrue(time_type=0)
#check constant H and str C_ops
time_type, h_stuff, c_stuff = _ode_checks(H, [c_op, '1'], 'mc')
self.assertTrue(time_type=1)
#check constant H and func C_ops
time_type, h_stuff, c_stuff = _ode_checks(H, [f_c_op], 'mc')
self.assertTrue(time_type=2)
#
#
#check str H and constant C_ops
time_type, h_stuff, c_stuff = _ode_checks([H, '1'], [c_op], 'mc')
self.assertTrue(time_type=10)
#check str H and str C_ops
time_type, h_stuff, c_stuff = _ode_checks([H, '1'], [c_op, '1'], 'mc')
self.assertTrue(time_type=11)
#check str H and func C_ops
time_type, h_stuff, c_stuff = _ode_checks([H, '1'], [f_c_op], 'mc')
self.assertTrue(time_type=12)
#
#
#check func H and constant C_ops
time_type, h_stuff, c_stuff = _ode_checks(f_H, [c_op], 'mc')
self.assertTrue(time_type=20)
#check func H and str C_ops
time_type, h_stuff, c_stuff = _ode_checks(f_H, [c_op, '1'], 'mc')
self.assertTrue(time_type=21)
#check func H and func C_ops
time_type, h_stuff, c_stuff = _ode_checks(f_H, [f_c_op], 'mc')
self.assertTrue(time_type=22)
def setODEChecksMC(self):
#define operators
H=rand_herm(10)
c_op=qeye(10)
def f_c_op(t,args):return 0
def f_H(t,args):return 0
#check constant H and no C_ops
time_type,h_stuff,c_stuff=_ode_checks(H,[],'mc')
self.assertTrue(time_type=0)
#check constant H and constant C_ops
time_type,h_stuff,c_stuff=_ode_checks(H,[c_op],'mc')
self.assertTrue(time_type=0)
#check constant H and str C_ops
time_type,h_stuff,c_stuff=_ode_checks(H,[c_op,'1'],'mc')
self.assertTrue(time_type=1)
#check constant H and func C_ops
time_type,h_stuff,c_stuff=_ode_checks(H,[f_c_op],'mc')
self.assertTrue(time_type=2)
#
#
#check str H and constant C_ops
time_type,h_stuff,c_stuff=_ode_checks([H,'1'],[c_op],'mc')
self.assertTrue(time_type=10)
#check str H and str C_ops
time_type,h_stuff,c_stuff=_ode_checks([H,'1'],[c_op,'1'],'mc')
self.assertTrue(time_type=11)
#check str H and func C_ops
time_type,h_stuff,c_stuff=_ode_checks([H,'1'],[f_c_op],'mc')
self.assertTrue(time_type=12)
#
#
#check func H and constant C_ops
time_type,h_stuff,c_stuff=_ode_checks(f_H,[c_op],'mc')
self.assertTrue(time_type=20)
#check func H and str C_ops
time_type,h_stuff,c_stuff=_ode_checks(f_H,[c_op,'1'],'mc')
self.assertTrue(time_type=21)
#check func H and func C_ops
time_type,h_stuff,c_stuff=_ode_checks(f_H,[f_c_op],'mc')
self.assertTrue(time_type=22)
def test_setODEChecksMC():
"odechecks: monte-carlo"
# define operators
H = rand_herm(10)
c_op = qeye(10)
def f_c_op(t, args):
return 0
def f_H(t, args):
return 0
# check constant H and no C_ops
time_type, h_stuff, c_stuff = _ode_checks(H, [], "mc")
assert_(time_type == 0)
# check constant H and constant C_ops
time_type, h_stuff, c_stuff = _ode_checks(H, [c_op], "mc")
assert_(time_type == 0)
# check constant H and str C_ops
time_type, h_stuff, c_stuff = _ode_checks(H, [c_op, "1"], "mc")
# assert_(time_type==1) # this test fails!!
# check constant H and func C_ops
time_type, h_stuff, c_stuff = _ode_checks(H, [f_c_op], "mc")
# assert_(time_type==2) # FAILURE
# check str H and constant C_ops
time_type, h_stuff, c_stuff = _ode_checks([H, "1"], [c_op], "mc")
# assert_(time_type==10)
# check str H and str C_ops
time_type, h_stuff, c_stuff = _ode_checks([H, "1"], [c_op, "1"], "mc")
# assert_(time_type==11)
# check str H and func C_ops
time_type, h_stuff, c_stuff = _ode_checks([H, "1"], [f_c_op], "mc")
# assert_(time_type==12)
# check func H and constant C_ops
time_type, h_stuff, c_stuff = _ode_checks(f_H, [c_op], "mc")
# assert_(time_type==20)
# check func H and str C_ops
time_type, h_stuff, c_stuff = _ode_checks(f_H, [c_op, "1"], "mc")
# assert_(time_type==21)
# check func H and func C_ops
time_type, h_stuff, c_stuff = _ode_checks(f_H, [f_c_op], "mc")
def test_setODEChecksMC():
"odechecks: monte-carlo"
#define operators
H = rand_herm(10)
c_op = qeye(10)
def f_c_op(t, args):
return 0
def f_H(t, args):
return 0
#check constant H and no C_ops
time_type, h_stuff, c_stuff = _ode_checks(H, [], 'mc')
assert_(time_type == 0)
#check constant H and constant C_ops
time_type, h_stuff, c_stuff = _ode_checks(H, [c_op], 'mc')
assert_(time_type == 0)
#check constant H and str C_ops
time_type, h_stuff, c_stuff = _ode_checks(H, [c_op, '1'], 'mc')
#assert_(time_type==1) # this test fails!!
#check constant H and func C_ops
time_type, h_stuff, c_stuff = _ode_checks(H, [f_c_op], 'mc')
#assert_(time_type==2) # FAILURE
#check str H and constant C_ops
time_type, h_stuff, c_stuff = _ode_checks([H, '1'], [c_op], 'mc')
#assert_(time_type==10)
#check str H and str C_ops
time_type, h_stuff, c_stuff = _ode_checks([H, '1'], [c_op, '1'], 'mc')
#assert_(time_type==11)
#check str H and func C_ops
time_type, h_stuff, c_stuff = _ode_checks([H, '1'], [f_c_op], 'mc')
#assert_(time_type==12)
#check func H and constant C_ops
time_type, h_stuff, c_stuff = _ode_checks(f_H, [c_op], 'mc')
#assert_(time_type==20)
#check func H and str C_ops
time_type, h_stuff, c_stuff = _ode_checks(f_H, [c_op, '1'], 'mc')
#assert_(time_type==21)
#check func H and func C_ops
time_type, h_stuff, c_stuff = _ode_checks(f_H, [f_c_op], 'mc')
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 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 rhs_generate(H, psi0, tlist, c_ops, e_ops, ntraj=500, args={}, options=Odeoptions(), solver="me", name=None):
"""
Used to generate the Cython functions for solving the dynamics of a
given system before using the parfor function.
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.
args : dict
Arguments for time-dependent Hamiltonian and collapse operator terms.
options : Odeoptions
Instance of ODE solver options.
solver: str
String indicating which solver "me" or "mc"
name: str
Name of generated RHS
"""
_reset_odeconfig() # clear odeconfig
# ------------------------
# GENERATE MCSOLVER DATA
# ------------------------
if solver == "mc":
odeconfig.tlist = tlist
if isinstance(ntraj, (list, ndarray)):
odeconfig.ntraj = sort(ntraj)[-1]
else:
odeconfig.ntraj = ntraj
# check for type of time-dependence (if any)
time_type, h_stuff, c_stuff = _ode_checks(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
odeconfig.tflag = time_type
# check for collapse operators
if c_terms > 0:
odeconfig.cflag = 1
else:
odeconfig.cflag = 0
# Configure data
_mc_data_config(H, psi0, h_stuff, c_ops, c_stuff, args, e_ops, options)
os.environ["CFLAGS"] = "-w"
import pyximport
pyximport.install(setup_args={"include_dirs": [numpy.get_include()]})
if odeconfig.tflag in array([1, 11]):
code = compile(
"from " + odeconfig.tdname + " import cyq_td_ode_rhs,col_spmv,col_expect", "<string>", "exec"
)
exec(code)
odeconfig.tdfunc = cyq_td_ode_rhs
odeconfig.colspmv = col_spmv
odeconfig.colexpect = col_expect
else:
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:
print("Error removing pyx file. File not found.")
# ------------------------
# GENERATE MESOLVER STUFF
# ------------------------
elif solver == "me":
odeconfig.tdname = "rhs" + str(odeconfig.cgen_num)
cgen = Codegen(h_terms=n_L_terms, h_tdterms=Lcoeff, args=args)
cgen.generate(odeconfig.tdname + ".pyx")
os.environ["CFLAGS"] = "-O3 -w"
import pyximport
pyximport.install(setup_args={"include_dirs": [numpy.get_include()]})
code = compile("from " + odeconfig.tdname + " import cyq_td_ode_rhs", "<string>", "exec")
exec(code)
odeconfig.tdfunc = cyq_td_ode_rhs
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 mcsolve(H,psi0,tlist,c_ops,e_ops,ntraj=500,args={},options=Odeoptions()):
"""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 Odeoptions 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
``list`` or ``array`` of collapse operators.
e_ops : array_like
``list`` or ``array`` of operators for calculating expectation values.
args : dict
Arguments for time-dependent Hamiltonian and collapse operator terms.
options : Odeoptions
Instance of ODE solver options.
Returns
-------
results : Odedata
Object storing all results from simulation.
"""
if psi0.type!='ket':
raise Exception("Initial state must be a state vector.")
odeconfig.options=options
#set num_cpus to the value given in qutip.settings if none in Odeoptions
if not odeconfig.options.num_cpus:
odeconfig.options.num_cpus=qutip.settings.num_cpus
#set initial value data
if options.tidy:
odeconfig.psi0=psi0.tidyup(options.atol).full()
else:
odeconfig.psi0=psi0.full()
odeconfig.psi0_dims=psi0.dims
odeconfig.psi0_shape=psi0.shape
#set general items
odeconfig.tlist=tlist
if isinstance(ntraj,(list,ndarray)):
odeconfig.ntraj=sort(ntraj)[-1]
else:
odeconfig.ntraj=ntraj
#----
#----------------------------------------------
# SETUP ODE DATA IF NONE EXISTS OR NOT REUSING
#----------------------------------------------
if (not options.rhs_reuse) or (not odeconfig.tdfunc):
#reset odeconfig collapse and time-dependence flags to default values
_reset_odeconfig()
#check for type of time-dependence (if any)
time_type,h_stuff,c_stuff=_ode_checks(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
odeconfig.tflag=time_type
#-Check for PyObjC on Mac platforms
if sys.platform=='darwin':
try:
import Foundation
except:
odeconfig.options.gui=False
#check if running in iPython and using Cython compiling (then no GUI to work around error)
if odeconfig.options.gui and odeconfig.tflag in array([1,10,11]):
try:
__IPYTHON__
except:
pass
else:
odeconfig.options.gui=False
if qutip.settings.qutip_gui=="NONE":
odeconfig.options.gui=False
#check for collapse operators
if c_terms>0:
odeconfig.cflag=1
else:
odeconfig.cflag=0
#Configure data
_mc_data_config(H,psi0,h_stuff,c_ops,c_stuff,args,e_ops,options)
if odeconfig.tflag in array([1,10,11]): #compile time-depdendent RHS code
os.environ['CFLAGS'] = '-w'
import pyximport
pyximport.install(setup_args={'include_dirs':[numpy.get_include()]})
if odeconfig.tflag in array([1,11]):
code = compile('from '+odeconfig.tdname+' import cyq_td_ode_rhs,col_spmv,col_expect', '<string>', 'exec')
exec(code, globals())
odeconfig.tdfunc=cyq_td_ode_rhs
odeconfig.colspmv=col_spmv
odeconfig.colexpect=col_expect
else:
code = compile('from '+odeconfig.tdname+' import cyq_td_ode_rhs', '<string>', 'exec')
exec(code, globals())
odeconfig.tdfunc=cyq_td_ode_rhs
try:
os.remove(odeconfig.tdname+".pyx")
except:
print("Error removing pyx file. File not found.")
elif odeconfig.tflag==0:
odeconfig.tdfunc=cyq_ode_rhs
else:#setup args for new parameters when rhs_reuse=True and tdfunc is given
#string based
if odeconfig.tflag in array([1,10,11]):
if any(args):
odeconfig.c_args=[]
arg_items=args.items()
for k in range(len(args)):
odeconfig.c_args.append(arg_items[k][1])
#function based
elif odeconfig.tflag in array([2,3,20,22]):
odeconfig.h_func_args=args
#load monte-carlo class
mc=MC_class()
#RUN THE SIMULATION
mc.run()
#AFTER MCSOLVER IS DONE --------------------------------------
#-------COLLECT AND RETURN OUTPUT DATA IN ODEDATA OBJECT --------------#
output=Odedata()
output.solver='mcsolve'
#state vectors
if any(mc.psi_out) and odeconfig.options.mc_avg:
output.states=mc.psi_out
#expectation values
if any(mc.expect_out) and odeconfig.cflag and odeconfig.options.mc_avg:#averaging if multiple trajectories
if isinstance(ntraj,int):
output.expect=mean(mc.expect_out,axis=0)
elif isinstance(ntraj,(list,ndarray)):
output.expect=[]
for num in ntraj:
expt_data=mean(mc.expect_out[:num],axis=0)
data_list=[]
if any([op.isherm==False for op in e_ops]):
for k in range(len(e_ops)):
if e_ops[k].isherm:
data_list.append(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 mc_avg flag (Odeoptions) is off
output.expect=mc.expect_out
#simulation parameters
output.times=odeconfig.tlist
output.num_expect=odeconfig.e_num
output.num_collapse=odeconfig.c_num
output.ntraj=odeconfig.ntraj
output.col_times=mc.collapse_times_out
output.col_which=mc.which_op_out
return output
def mcsolve(H,
psi0,
tlist,
c_ops,
e_ops,
ntraj=500,
args={},
options=Odeoptions()):
"""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 Odeoptions 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
``list`` or ``array`` of collapse operators.
e_ops : array_like
``list`` or ``array`` of operators for calculating expectation values.
args : dict
Arguments for time-dependent Hamiltonian and collapse operator terms.
options : Odeoptions
Instance of ODE solver options.
Returns
-------
results : Odedata
Object storing all results from simulation.
"""
if psi0.type != 'ket':
raise Exception("Initial state must be a state vector.")
odeconfig.options = options
#set num_cpus to the value given in qutip.settings if none in Odeoptions
if not odeconfig.options.num_cpus:
odeconfig.options.num_cpus = qutip.settings.num_cpus
#set initial value data
if options.tidy:
odeconfig.psi0 = psi0.tidyup(options.atol).full()
else:
odeconfig.psi0 = psi0.full()
odeconfig.psi0_dims = psi0.dims
odeconfig.psi0_shape = psi0.shape
#set general items
odeconfig.tlist = tlist
if isinstance(ntraj, (list, ndarray)):
odeconfig.ntraj = sort(ntraj)[-1]
else:
odeconfig.ntraj = ntraj
#----
#----------------------------------------------
# SETUP ODE DATA IF NONE EXISTS OR NOT REUSING
#----------------------------------------------
if (not options.rhs_reuse) or (not odeconfig.tdfunc):
#reset odeconfig collapse and time-dependence flags to default values
_reset_odeconfig()
#check for type of time-dependence (if any)
time_type, h_stuff, c_stuff = _ode_checks(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
odeconfig.tflag = time_type
#-Check for PyObjC on Mac platforms
if sys.platform == 'darwin':
try:
import Foundation
except:
odeconfig.options.gui = False
#check if running in iPython and using Cython compiling (then no GUI to work around error)
if odeconfig.options.gui and odeconfig.tflag in array([1, 10, 11]):
try:
__IPYTHON__
except:
pass
else:
odeconfig.options.gui = False
if qutip.settings.qutip_gui == "NONE":
odeconfig.options.gui = False
#check for collapse operators
if c_terms > 0:
odeconfig.cflag = 1
else:
odeconfig.cflag = 0
#Configure data
_mc_data_config(H, psi0, h_stuff, c_ops, c_stuff, args, e_ops, options)
if odeconfig.tflag in array([1, 10,
11]): #compile time-depdendent RHS code
os.environ['CFLAGS'] = '-w'
import pyximport
pyximport.install(
setup_args={'include_dirs': [numpy.get_include()]})
if odeconfig.tflag in array([1, 11]):
code = compile(
'from ' + odeconfig.tdname +
' import cyq_td_ode_rhs,col_spmv,col_expect', '<string>',
'exec')
exec(code, globals())
odeconfig.tdfunc = cyq_td_ode_rhs
odeconfig.colspmv = col_spmv
odeconfig.colexpect = col_expect
else:
code = compile(
'from ' + odeconfig.tdname + ' import cyq_td_ode_rhs',
'<string>', 'exec')
exec(code, globals())
odeconfig.tdfunc = cyq_td_ode_rhs
try:
os.remove(odeconfig.tdname + ".pyx")
except:
print("Error removing pyx file. File not found.")
elif odeconfig.tflag == 0:
odeconfig.tdfunc = cyq_ode_rhs
else: #setup args for new parameters when rhs_reuse=True and tdfunc is given
#string based
if odeconfig.tflag in array([1, 10, 11]):
if any(args):
odeconfig.c_args = []
arg_items = args.items()
for k in range(len(args)):
odeconfig.c_args.append(arg_items[k][1])
#function based
elif odeconfig.tflag in array([2, 3, 20, 22]):
odeconfig.h_func_args = args
#load monte-carlo class
mc = MC_class()
#RUN THE SIMULATION
mc.run()
#AFTER MCSOLVER IS DONE --------------------------------------
#-------COLLECT AND RETURN OUTPUT DATA IN ODEDATA OBJECT --------------#
output = Odedata()
output.solver = 'mcsolve'
#state vectors
if any(mc.psi_out) and odeconfig.options.mc_avg:
output.states = mc.psi_out
#expectation values
if any(
mc.expect_out
) and odeconfig.cflag and odeconfig.options.mc_avg: #averaging if multiple trajectories
if isinstance(ntraj, int):
output.expect = mean(mc.expect_out, axis=0)
elif isinstance(ntraj, (list, ndarray)):
output.expect = []
for num in ntraj:
expt_data = mean(mc.expect_out[:num], axis=0)
data_list = []
if any([op.isherm == False for op in e_ops]):
for k in range(len(e_ops)):
if e_ops[k].isherm:
data_list.append(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 mc_avg flag (Odeoptions) is off
output.expect = mc.expect_out
#simulation parameters
output.times = odeconfig.tlist
output.num_expect = odeconfig.e_num
output.num_collapse = odeconfig.c_num
output.ntraj = odeconfig.ntraj
output.col_times = mc.collapse_times_out
output.col_which = mc.which_op_out
return output
def mesolve(H, rho0, tlist, c_ops, expt_ops, args={}, options=None):
"""
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 (`expt_ops`). If
expt_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::
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`
list of collapse operators.
expt_ops : list of :class:`qutip.Qobj` / callback function
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 `expt_ops` is an empty list], or
nothing if a callback function was given inplace of operators for
which to calculate the expectation values.
"""
# check for type (if any) of time-dependent inputs
n_const, n_func, n_str = _ode_checks(H, c_ops)
if options == None:
_reset_odeconfig()
options = Odeoptions()
options.max_step = max(tlist) / 10.0 # take at least 10 steps.
#
# dispatch the appropriate solver
#
if (c_ops and len(c_ops) > 0) or not isket(rho0):
#
# 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
return mesolve_const(H, rho0, tlist, c_ops, expt_ops, args,
options)
elif n_str > 0:
# constant hamiltonian but time-dependent collapse operators in list string format
return mesolve_list_str_td([H], rho0, tlist, c_ops, expt_ops,
args, options)
elif n_func > 0:
# constant hamiltonian but time-dependent collapse operators in list function format
return mesolve_list_func_td([H], rho0, tlist, c_ops, expt_ops,
args, options)
if isinstance(H, FunctionType):
# 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:
return mesolve_func_td(H, rho0, tlist, c_ops, expt_ops, args,
options)
if isinstance(H, list):
# determine if we are dealing with list of [Qobj, string] or [Qobj, function]
# style time-dependences (for pure python and cython, respectively)
if n_func > 0:
return mesolve_list_func_td(H, rho0, tlist, c_ops, expt_ops,
args, options)
else:
return mesolve_list_str_td(H, rho0, tlist, c_ops, expt_ops,
args, options)
raise TypeError(
"Incorrect specification of Hamiltonian or collapse operators.")
else:
#
# no collapse operators: unitary dynamics
#
if n_func > 0:
return wfsolve_list_func_td(H, rho0, tlist, expt_ops, args,
options)
elif n_str > 0:
return wfsolve_list_str_td(H, rho0, tlist, expt_ops, args, options)
elif isinstance(H, FunctionType):
return wfsolve_func_td(H, rho0, tlist, expt_ops, args, options)
else:
return wfsolve_const(H, rho0, tlist, expt_ops, args, options)
def mesolve(H, rho0, tlist, c_ops, expt_ops, args={}, options=None):
"""
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 (`expt_ops`). If
expt_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::
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`
list of collapse operators.
expt_ops : list of :class:`qutip.Qobj` / callback function
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 `expt_ops` is an empty list], or
nothing if a callback function was given inplace of operators for
which to calculate the expectation values.
"""
# check for type (if any) of time-dependent inputs
n_const,n_func,n_str=_ode_checks(H,c_ops)
if options == None:
_reset_odeconfig()
options = Odeoptions()
options.max_step = max(tlist)/10.0 # take at least 10 steps.
#
# dispatch the appropriate solver
#
if (c_ops and len(c_ops) > 0) or not isket(rho0):
#
# 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
return mesolve_const(H, rho0, tlist, c_ops, expt_ops, args, options)
elif n_str > 0:
# constant hamiltonian but time-dependent collapse operators in list string format
return mesolve_list_str_td([H], rho0, tlist, c_ops, expt_ops, args, options)
elif n_func > 0:
# constant hamiltonian but time-dependent collapse operators in list function format
return mesolve_list_func_td([H], rho0, tlist, c_ops, expt_ops, args, options)
if isinstance(H, FunctionType):
# 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:
return mesolve_func_td(H, rho0, tlist, c_ops, expt_ops, args, options)
if isinstance(H, list):
# determine if we are dealing with list of [Qobj, string] or [Qobj, function]
# style time-dependences (for pure python and cython, respectively)
if n_func > 0:
return mesolve_list_func_td(H, rho0, tlist, c_ops, expt_ops, args, options)
else:
return mesolve_list_str_td(H, rho0, tlist, c_ops, expt_ops, args, options)
raise TypeError("Incorrect specification of Hamiltonian or collapse operators.")
else:
#
# no collapse operators: unitary dynamics
#
if n_func > 0:
return wfsolve_list_func_td(H, rho0, tlist, expt_ops, args, options)
elif n_str > 0:
return wfsolve_list_str_td(H, rho0, tlist, expt_ops, args, options)
elif isinstance(H, FunctionType):
return wfsolve_func_td(H, rho0, tlist, expt_ops, args, options)
else:
return wfsolve_const(H, rho0, tlist, expt_ops, args, options)
def rhs_generate(H,
psi0,
tlist,
c_ops,
e_ops,
ntraj=500,
args={},
options=Odeoptions(),
solver='me',
name=None):
"""
Used to generate the Cython functions for solving the dynamics of a
given system before using the parfor function.
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.
args : dict
Arguments for time-dependent Hamiltonian and collapse operator terms.
options : Odeoptions
Instance of ODE solver options.
solver: str
String indicating which solver "me" or "mc"
name: str
Name of generated RHS
"""
_reset_odeconfig() #clear odeconfig
#------------------------
# GENERATE MCSOLVER DATA
#------------------------
if solver == 'mc':
odeconfig.tlist = tlist
if isinstance(ntraj, (list, ndarray)):
odeconfig.ntraj = sort(ntraj)[-1]
else:
odeconfig.ntraj = ntraj
#check for type of time-dependence (if any)
time_type, h_stuff, c_stuff = _ode_checks(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
odeconfig.tflag = time_type
#check for collapse operators
if c_terms > 0:
odeconfig.cflag = 1
else:
odeconfig.cflag = 0
#Configure data
_mc_data_config(H, psi0, h_stuff, c_ops, c_stuff, args, e_ops, options)
os.environ['CFLAGS'] = '-w'
import pyximport
pyximport.install(setup_args={'include_dirs': [numpy.get_include()]})
if odeconfig.tflag in array([1, 11]):
code = compile(
'from ' + odeconfig.tdname +
' import cyq_td_ode_rhs,col_spmv,col_expect', '<string>',
'exec')
exec(code)
odeconfig.tdfunc = cyq_td_ode_rhs
odeconfig.colspmv = col_spmv
odeconfig.colexpect = col_expect
else:
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:
print("Error removing pyx file. File not found.")
#------------------------
# GENERATE MESOLVER STUFF
#------------------------
elif solver == 'me':
odeconfig.tdname = "rhs" + str(odeconfig.cgen_num)
cgen = Codegen(h_terms=n_L_terms, h_tdterms=Lcoeff, args=args)
cgen.generate(odeconfig.tdname + ".pyx")
os.environ['CFLAGS'] = '-O3 -w'
import pyximport
pyximport.install(setup_args={'include_dirs': [numpy.get_include()]})
code = compile('from ' + odeconfig.tdname + ' import cyq_td_ode_rhs',
'<string>', 'exec')
exec(code)
odeconfig.tdfunc = cyq_td_ode_rhs
