def _sesolve_list_td(H_func, psi0, tlist, e_ops, args, opt, progress_bar):
"""!
Evolve the wave function using an ODE solver with time-dependent
Hamiltonian.
"""
if debug:
print(inspect.stack()[0][3])
if not isket(psi0):
raise TypeError("psi0 must be a ket")
#
# configure time-dependent terms and setup ODE solver
#
if len(H_func) != 2:
raise TypeError('Time-dependent Hamiltonian list must have two terms.')
if (not isinstance(H_func[0], (list, np.ndarray))) or \
(len(H_func[0]) <= 1):
raise TypeError('Time-dependent Hamiltonians must be a list with two '
+ 'or more terms')
if (not isinstance(H_func[1], (list, np.ndarray))) or \
(len(H_func[1]) != (len(H_func[0]) - 1)):
raise TypeError('Time-dependent coefficients must be list with ' +
'length N-1 where N is the number of ' +
'Hamiltonian terms.')
tflag = 1
if opt.rhs_reuse and odeconfig.tdfunc is None:
print("No previous time-dependent RHS found.")
print("Generating one for you...")
rhs_generate(H_func, args)
lenh = len(H_func[0])
if opt.tidy:
H_func[0] = [(H_func[0][k]).tidyup() for k in range(lenh)]
# create data arrays for time-dependent RHS function
Hdata = [-1.0j * H_func[0][k].data.data for k in range(lenh)]
Hinds = [H_func[0][k].data.indices for k in range(lenh)]
Hptrs = [H_func[0][k].data.indptr for k in range(lenh)]
# setup ode args string
string = ""
for k in range(lenh):
string += ("Hdata[" + str(k) + "],Hinds[" + str(k) +
"],Hptrs[" + str(k) + "],")
if args:
td_consts = args.items()
for elem in td_consts:
string += str(elem[1])
if elem != td_consts[-1]:
string += (",")
# run code generator
if not opt.rhs_reuse or odeconfig.tdfunc is None:
if opt.rhs_filename is None:
odeconfig.tdname = "rhs" + str(odeconfig.cgen_num)
else:
odeconfig.tdname = opt.rhs_filename
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
#
# setup integrator
#
initial_vector = psi0.full().ravel()
r = scipy.integrate.ode(odeconfig.tdfunc)
r.set_integrator('zvode', method=opt.method, order=opt.order,
atol=opt.atol, rtol=opt.rtol, nsteps=opt.nsteps,
first_step=opt.first_step, min_step=opt.min_step,
max_step=opt.max_step)
r.set_initial_value(initial_vector, tlist[0])
code = compile('r.set_f_params(' + string + ')', '<string>', 'exec')
exec(code)
#
# call generic ODE code
#
return _generic_ode_solve(r, psi0, tlist, e_ops, opt, progress_bar,
norm, dims=psi0.dims)
def rhs_generate(H,
c_ops,
args={},
options=Options(),
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 : Options
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.
"""
config.reset()
config.options = options
if name:
config.tdname = name
else:
config.tdname = "rhs" + str(os.getpid()) + str(config.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,
config=config)
cgen.generate(config.tdname + ".pyx")
code = compile('from ' + config.tdname + ' import cy_td_ode_rhs',
'<string>', 'exec')
exec(code, globals())
config.tdfunc = cy_td_ode_rhs
if cleanup:
try:
os.remove(config.tdname + ".pyx")
except:
pass
def _sesolve_list_str_td(H_list, psi0, tlist, e_ops, args, opt,
progress_bar):
"""
Internal function for solving the master equation. See mesolve for usage.
"""
if debug:
print(inspect.stack()[0][3])
#
# check initial state: must be a density matrix
#
if not isket(psi0):
raise TypeError("The unitary solver requires a ket as initial state")
#
# construct liouvillian
#
Ldata = []
Linds = []
Lptrs = []
Lcoeff = []
# loop over all hamiltonian terms, convert to superoperator form and
# add the data of sparse matrix representation to h_coeff
for h_spec in H_list:
if isinstance(h_spec, Qobj):
h = h_spec
h_coeff = "1.0"
elif isinstance(h_spec, list):
h = h_spec[0]
h_coeff = h_spec[1]
else:
raise TypeError("Incorrect specification of time-dependent " +
"Hamiltonian (expected string format)")
L = -1j * h
Ldata.append(L.data.data)
Linds.append(L.data.indices)
Lptrs.append(L.data.indptr)
Lcoeff.append(h_coeff)
# the total number of liouvillian terms (hamiltonian terms +
# collapse operators)
n_L_terms = len(Ldata)
#
# setup ode args string: we expand the list Ldata, Linds and Lptrs into
# and explicit list of parameters
#
string_list = []
for k in range(n_L_terms):
string_list.append("Ldata[%d], Linds[%d], Lptrs[%d]" % (k, k, k))
for name, value in args.items():
string_list.append(str(value))
parameter_string = ",".join(string_list)
#
# generate and compile new cython code if necessary
#
if not opt.rhs_reuse or odeconfig.tdfunc is None:
if opt.rhs_filename is None:
odeconfig.tdname = "rhs" + str(odeconfig.cgen_num)
else:
odeconfig.tdname = opt.rhs_filename
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
#
# setup integrator
#
initial_vector = psi0.full().ravel()
r = scipy.integrate.ode(odeconfig.tdfunc)
r.set_integrator('zvode', method=opt.method, order=opt.order,
atol=opt.atol, rtol=opt.rtol, nsteps=opt.nsteps,
first_step=opt.first_step, min_step=opt.min_step,
max_step=opt.max_step)
r.set_initial_value(initial_vector, tlist[0])
code = compile('r.set_f_params(' + parameter_string + ')',
'<string>', 'exec')
exec(code)
#
# call generic ODE code
#
return _generic_ode_solve(r, psi0, tlist, e_ops, opt, progress_bar,
norm, dims=psi0.dims)
def _mesolve_list_str_td(H_list, rho0, tlist, c_list, e_ops, args, opt, progress_bar):
"""
Internal function for solving the master equation. See mesolve for usage.
"""
if debug:
print(inspect.stack()[0][3])
#
# check initial state: must be a density matrix
#
if isket(rho0):
rho0 = rho0 * rho0.dag()
#
# construct liouvillian
#
Lconst = 0
Ldata = []
Linds = []
Lptrs = []
Lcoeff = []
# loop over all hamiltonian terms, convert to superoperator form and
# add the data of sparse matrix representation to
for h_spec in H_list:
if isinstance(h_spec, Qobj):
h = h_spec
if isoper(h):
Lconst += -1j * (spre(h) - spost(h))
elif issuper(h):
Lconst += h
else:
raise TypeError(
"Incorrect specification of time-dependent "
+ "Hamiltonian (expected operator or "
+ "superoperator)"
)
elif isinstance(h_spec, list):
h = h_spec[0]
h_coeff = h_spec[1]
if isoper(h):
L = -1j * (spre(h) - spost(h))
elif issuper(h):
L = h
else:
raise TypeError(
"Incorrect specification of time-dependent "
+ "Hamiltonian (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("Incorrect specification of time-dependent " + "Hamiltonian (expected string format)")
# loop over all collapse operators
for c_spec in c_list:
if isinstance(c_spec, Qobj):
c = c_spec
if isoper(c):
cdc = c.dag() * c
Lconst += spre(c) * spost(c.dag()) - 0.5 * spre(cdc) - 0.5 * spost(cdc)
elif issuper(c):
Lconst += c
else:
raise TypeError(
"Incorrect specification of time-dependent "
+ "Liouvillian (expected operator or "
+ "superoperator)"
)
elif isinstance(c_spec, list):
c = c_spec[0]
c_coeff = c_spec[1]
if isoper(c):
cdc = c.dag() * c
L = spre(c) * spost(c.dag()) - 0.5 * spre(cdc) - 0.5 * spost(cdc)
c_coeff = "(" + c_coeff + ")**2"
elif issuper(c):
L = c
else:
raise TypeError(
"Incorrect specification of time-dependent "
+ "Liouvillian (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(
"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)
#
# setup ode args string: we expand the list Ldata, Linds and Lptrs into
# and explicit list of parameters
#
string_list = []
for k in range(n_L_terms):
string_list.append("Ldata[%d], Linds[%d], Lptrs[%d]" % (k, k, k))
for name, value in args.items():
if isinstance(value, np.ndarray):
string_list.append(name)
else:
string_list.append(str(value))
parameter_string = ",".join(string_list)
#
# generate and compile new cython code if necessary
#
if not opt.rhs_reuse or config.tdfunc is None:
if opt.rhs_filename is None:
config.tdname = "rhs" + str(os.getpid()) + str(config.cgen_num)
else:
config.tdname = opt.rhs_filename
cgen = Codegen(h_terms=n_L_terms, h_tdterms=Lcoeff, args=args, config=config)
cgen.generate(config.tdname + ".pyx")
code = compile("from " + config.tdname + " import cy_td_ode_rhs", "<string>", "exec")
exec(code, globals())
config.tdfunc = cy_td_ode_rhs
#
# setup integrator
#
initial_vector = mat2vec(rho0.full()).ravel()
r = scipy.integrate.ode(config.tdfunc)
r.set_integrator(
"zvode",
method=opt.method,
order=opt.order,
atol=opt.atol,
rtol=opt.rtol,
nsteps=opt.nsteps,
first_step=opt.first_step,
min_step=opt.min_step,
max_step=opt.max_step,
)
r.set_initial_value(initial_vector, tlist[0])
code = compile("r.set_f_params(" + parameter_string + ")", "<string>", "exec")
exec(code, locals(), args)
#
# call generic ODE code
#
return _generic_ode_solve(r, rho0, tlist, e_ops, opt, progress_bar)
def _mesolve_list_td(H_func, rho0, tlist, c_op_list, e_ops, args, opt, progress_bar):
"""
Evolve the density matrix using an ODE solver with time dependent
Hamiltonian.
"""
if debug:
print(inspect.stack()[0][3])
#
# check initial state
#
if isket(rho0):
# if initial state is a ket and no collapse operator where given,
# fall back on the unitary schrodinger equation solver
if len(c_op_list) == 0:
return _sesolve_list_td(H_func, rho0, tlist, e_ops, args, opt, progress_bar)
# Got a wave function as initial state: convert to density matrix.
rho0 = ket2dm(rho0)
#
# construct liouvillian
#
if len(H_func) != 2:
raise TypeError("Time-dependent Hamiltonian list must have two terms.")
if not isinstance(H_func[0], (list, np.ndarray)) or len(H_func[0]) <= 1:
raise TypeError("Time-dependent Hamiltonians must be a list " + "with two or more terms")
if (not isinstance(H_func[1], (list, np.ndarray))) or (len(H_func[1]) != (len(H_func[0]) - 1)):
raise TypeError(
"Time-dependent coefficients must be list with "
+ "length N-1 where N is the number of "
+ "Hamiltonian terms."
)
if opt.rhs_reuse and config.tdfunc is None:
rhs_generate(H_func, args)
lenh = len(H_func[0])
if opt.tidy:
H_func[0] = [(H_func[0][k]).tidyup() for k in range(lenh)]
L_func = [[liouvillian(H_func[0][0], c_op_list)], H_func[1]]
for m in range(1, lenh):
L_func[0].append(liouvillian(H_func[0][m], []))
# create data arrays for time-dependent RHS function
Ldata = [L_func[0][k].data.data for k in range(lenh)]
Linds = [L_func[0][k].data.indices for k in range(lenh)]
Lptrs = [L_func[0][k].data.indptr for k in range(lenh)]
# setup ode args string
string = ""
for k in range(lenh):
string += "Ldata[%d], Linds[%d], Lptrs[%d]," % (k, k, k)
if args:
td_consts = args.items()
for elem in td_consts:
string += str(elem[1])
if elem != td_consts[-1]:
string += ","
# run code generator
if not opt.rhs_reuse or config.tdfunc is None:
if opt.rhs_filename is None:
config.tdname = "rhs" + str(os.getpid()) + str(config.cgen_num)
else:
config.tdname = opt.rhs_filename
cgen = Codegen(h_terms=n_L_terms, h_tdterms=Lcoeff, args=args, config=config)
cgen.generate(config.tdname + ".pyx")
code = compile("from " + config.tdname + " import cy_td_ode_rhs", "<string>", "exec")
exec(code, globals())
config.tdfunc = cy_td_ode_rhs
#
# setup integrator
#
initial_vector = mat2vec(rho0.full()).ravel()
r = scipy.integrate.ode(config.tdfunc)
r.set_integrator(
"zvode",
method=opt.method,
order=opt.order,
atol=opt.atol,
rtol=opt.rtol,
nsteps=opt.nsteps,
first_step=opt.first_step,
min_step=opt.min_step,
max_step=opt.max_step,
)
r.set_initial_value(initial_vector, tlist[0])
code = compile("r.set_f_params(" + string + ")", "<string>", "exec")
exec(code)
#
# call generic ODE code
#
return _generic_ode_solve(r, rho0, tlist, e_ops, opt, progress_bar)
def rhs_generate(H, c_ops, args={}, options=Options(), 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 : Options
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.
"""
config.reset()
config.options = options
if name:
config.tdname = name
else:
config.tdname = "rhs" + str(os.getpid()) + str(config.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,
config=config)
cgen.generate(config.tdname + ".pyx")
code = compile('from ' + config.tdname +
' import cy_td_ode_rhs', '<string>', 'exec')
exec(code, globals())
config.tdfunc = cy_td_ode_rhs
if cleanup:
try:
os.remove(config.tdname + ".pyx")
except:
pass
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 _mesolve_list_td(H_func, rho0, tlist, c_op_list, e_ops, args, opt,
progress_bar):
"""
Evolve the density matrix using an ODE solver with time dependent
Hamiltonian.
"""
if debug:
print(inspect.stack()[0][3])
#
# check initial state
#
if isket(rho0):
# if initial state is a ket and no collapse operator where given,
# fall back on the unitary schrodinger equation solver
if len(c_op_list) == 0:
return _sesolve_list_td(H_func, rho0, tlist, e_ops, args, opt,
progress_bar)
# Got a wave function as initial state: convert to density matrix.
rho0 = ket2dm(rho0)
#
# construct liouvillian
#
if len(H_func) != 2:
raise TypeError('Time-dependent Hamiltonian list must have two terms.')
if not isinstance(H_func[0], (list, np.ndarray)) or len(H_func[0]) <= 1:
raise TypeError('Time-dependent Hamiltonians must be a list ' +
'with two or more terms')
if (not isinstance(H_func[1], (list, np.ndarray))) or \
(len(H_func[1]) != (len(H_func[0]) - 1)):
raise TypeError('Time-dependent coefficients must be list with ' +
'length N-1 where N is the number of ' +
'Hamiltonian terms.')
if opt.rhs_reuse and config.tdfunc is None:
rhs_generate(H_func, args)
lenh = len(H_func[0])
if opt.tidy:
H_func[0] = [(H_func[0][k]).tidyup() for k in range(lenh)]
L_func = [[liouvillian(H_func[0][0], c_op_list)], H_func[1]]
for m in range(1, lenh):
L_func[0].append(liouvillian(H_func[0][m], []))
# create data arrays for time-dependent RHS function
Ldata = [L_func[0][k].data.data for k in range(lenh)]
Linds = [L_func[0][k].data.indices for k in range(lenh)]
Lptrs = [L_func[0][k].data.indptr for k in range(lenh)]
# setup ode args string
string = ""
for k in range(lenh):
string += ("Ldata[%d], Linds[%d], Lptrs[%d]," % (k, k, k))
if args:
td_consts = args.items()
for elem in td_consts:
string += str(elem[1])
if elem != td_consts[-1]:
string += (",")
# run code generator
if not opt.rhs_reuse or config.tdfunc is None:
if opt.rhs_filename is None:
config.tdname = "rhs" + str(os.getpid()) + str(config.cgen_num)
else:
config.tdname = opt.rhs_filename
cgen = Codegen(h_terms=n_L_terms,
h_tdterms=Lcoeff,
args=args,
config=config)
cgen.generate(config.tdname + ".pyx")
code = compile('from ' + config.tdname + ' import cy_td_ode_rhs',
'<string>', 'exec')
exec(code, globals())
config.tdfunc = cy_td_ode_rhs
#
# setup integrator
#
initial_vector = mat2vec(rho0.full()).ravel()
r = scipy.integrate.ode(config.tdfunc)
r.set_integrator('zvode',
method=opt.method,
order=opt.order,
atol=opt.atol,
rtol=opt.rtol,
nsteps=opt.nsteps,
first_step=opt.first_step,
min_step=opt.min_step,
max_step=opt.max_step)
r.set_initial_value(initial_vector, tlist[0])
code = compile('r.set_f_params(' + string + ')', '<string>', 'exec')
exec(code)
#
# call generic ODE code
#
return _generic_ode_solve(r, rho0, tlist, e_ops, opt, progress_bar)
def _mesolve_list_str_td(H_list, rho0, tlist, c_list, e_ops, args, opt,
progress_bar):
"""
Internal function for solving the master equation. See mesolve for usage.
"""
if debug:
print(inspect.stack()[0][3])
#
# check initial state: must be a density matrix
#
if isket(rho0):
rho0 = rho0 * rho0.dag()
#
# construct liouvillian
#
Lconst = 0
Ldata = []
Linds = []
Lptrs = []
Lcoeff = []
Lobj = []
# loop over all hamiltonian terms, convert to superoperator form and
# add the data of sparse matrix representation to
for h_spec in H_list:
if isinstance(h_spec, Qobj):
h = h_spec
if isoper(h):
Lconst += -1j * (spre(h) - spost(h))
elif issuper(h):
Lconst += h
else:
raise TypeError("Incorrect specification of time-dependent " +
"Hamiltonian (expected operator or " +
"superoperator)")
elif isinstance(h_spec, list):
h = h_spec[0]
h_coeff = h_spec[1]
if isoper(h):
L = -1j * (spre(h) - spost(h))
elif issuper(h):
L = h
else:
raise TypeError("Incorrect specification of time-dependent " +
"Hamiltonian (expected operator or " +
"superoperator)")
Ldata.append(L.data.data)
Linds.append(L.data.indices)
Lptrs.append(L.data.indptr)
if isinstance(h_coeff, Cubic_Spline):
Lobj.append(h_coeff.coeffs)
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_list:
if isinstance(c_spec, Qobj):
c = c_spec
if isoper(c):
cdc = c.dag() * c
Lconst += spre(c) * spost(c.dag()) - 0.5 * spre(cdc) \
- 0.5 * spost(cdc)
elif issuper(c):
Lconst += c
else:
raise TypeError("Incorrect specification of time-dependent " +
"Liouvillian (expected operator or " +
"superoperator)")
elif isinstance(c_spec, list):
c = c_spec[0]
c_coeff = c_spec[1]
if isoper(c):
cdc = c.dag() * c
L = spre(c) * spost(c.dag()) - 0.5 * spre(cdc) \
- 0.5 * spost(cdc)
c_coeff = "(" + c_coeff + ")**2"
elif issuper(c):
L = c
else:
raise TypeError("Incorrect specification of time-dependent " +
"Liouvillian (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("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)
# Check which components should use OPENMP
omp_components = None
if qset.has_openmp:
if opt.use_openmp:
omp_components = openmp_components(Lptrs)
#
# setup ode args string: we expand the list Ldata, Linds and Lptrs into
# and explicit list of parameters
#
string_list = []
for k in range(n_L_terms):
string_list.append("Ldata[%d], Linds[%d], Lptrs[%d]" % (k, k, k))
# Add object terms to end of ode args string
for k in range(len(Lobj)):
string_list.append("Lobj[%d]" % k)
for name, value in args.items():
if isinstance(value, np.ndarray):
string_list.append(name)
else:
string_list.append(str(value))
parameter_string = ",".join(string_list)
#
# generate and compile new cython code if necessary
#
if not opt.rhs_reuse or config.tdfunc is None:
if opt.rhs_filename is None:
config.tdname = "rhs" + str(os.getpid()) + str(config.cgen_num)
else:
config.tdname = opt.rhs_filename
cgen = Codegen(h_terms=n_L_terms,
h_tdterms=Lcoeff,
args=args,
config=config,
use_openmp=opt.use_openmp,
omp_components=omp_components,
omp_threads=opt.openmp_threads)
cgen.generate(config.tdname + ".pyx")
code = compile('from ' + config.tdname + ' import cy_td_ode_rhs',
'<string>', 'exec')
exec(code, globals())
config.tdfunc = cy_td_ode_rhs
#
# setup integrator
#
initial_vector = mat2vec(rho0.full()).ravel('F')
if issuper(rho0):
r = scipy.integrate.ode(_td_ode_rhs_super)
code = compile('r.set_f_params([' + parameter_string + '])',
'<string>', 'exec')
else:
r = scipy.integrate.ode(config.tdfunc)
code = compile('r.set_f_params(' + parameter_string + ')', '<string>',
'exec')
r.set_integrator('zvode',
method=opt.method,
order=opt.order,
atol=opt.atol,
rtol=opt.rtol,
nsteps=opt.nsteps,
first_step=opt.first_step,
min_step=opt.min_step,
max_step=opt.max_step)
r.set_initial_value(initial_vector, tlist[0])
exec(code, locals(), args)
#
# call generic ODE code
#
return _generic_ode_solve(r, rho0, tlist, e_ops, opt, progress_bar)
def _sesolve_list_str_td(H_list, psi0, tlist, e_ops, args, opt,
progress_bar):
"""
Internal function for solving the master equation. See mesolve for usage.
"""
if debug:
print(inspect.stack()[0][3])
#
# check initial state: must be a density matrix
#
if not isket(psi0):
raise TypeError("The unitary solver requires a ket as initial state")
#
# construct liouvillian
#
Ldata = []
Linds = []
Lptrs = []
Lcoeff = []
# loop over all hamiltonian terms, convert to superoperator form and
# add the data of sparse matrix representation to h_coeff
for h_spec in H_list:
if isinstance(h_spec, Qobj):
h = h_spec
h_coeff = "1.0"
elif isinstance(h_spec, list):
h = h_spec[0]
h_coeff = h_spec[1]
else:
raise TypeError("Incorrect specification of time-dependent " +
"Hamiltonian (expected string format)")
L = -1j * h
Ldata.append(L.data.data)
Linds.append(L.data.indices)
Lptrs.append(L.data.indptr)
Lcoeff.append(h_coeff)
# the total number of liouvillian terms (hamiltonian terms +
# collapse operators)
n_L_terms = len(Ldata)
#
# setup ode args string: we expand the list Ldata, Linds and Lptrs into
# and explicit list of parameters
#
string_list = []
for k in range(n_L_terms):
string_list.append("Ldata[%d], Linds[%d], Lptrs[%d]" % (k, k, k))
for name, value in args.items():
string_list.append(str(value))
parameter_string = ",".join(string_list)
#
# generate and compile new cython code if necessary
#
if not opt.rhs_reuse or odeconfig.tdfunc is None:
if opt.rhs_filename is None:
odeconfig.tdname = "rhs" + str(odeconfig.cgen_num)
else:
odeconfig.tdname = opt.rhs_filename
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
#
# setup integrator
#
initial_vector = psi0.full().ravel()
r = scipy.integrate.ode(odeconfig.tdfunc)
r.set_integrator('zvode', method=opt.method, order=opt.order,
atol=opt.atol, rtol=opt.rtol, nsteps=opt.nsteps,
first_step=opt.first_step, min_step=opt.min_step,
max_step=opt.max_step)
r.set_initial_value(initial_vector, tlist[0])
code = compile('r.set_f_params(' + parameter_string + ')',
'<string>', 'exec')
exec(code)
#
# call generic ODE code
#
return _generic_ode_solve(r, psi0, tlist, e_ops, opt, progress_bar,
norm, dims=psi0.dims)
def _sesolve_list_td(H_func, psi0, tlist, e_ops, args, opt, progress_bar):
"""!
Evolve the wave function using an ODE solver with time-dependent
Hamiltonian.
"""
if debug:
print(inspect.stack()[0][3])
if not isket(psi0):
raise TypeError("psi0 must be a ket")
#
# configure time-dependent terms and setup ODE solver
#
if len(H_func) != 2:
raise TypeError('Time-dependent Hamiltonian list must have two terms.')
if (not isinstance(H_func[0], (list, np.ndarray))) or \
(len(H_func[0]) <= 1):
raise TypeError('Time-dependent Hamiltonians must be a list with two '
+ 'or more terms')
if (not isinstance(H_func[1], (list, np.ndarray))) or \
(len(H_func[1]) != (len(H_func[0]) - 1)):
raise TypeError('Time-dependent coefficients must be list with ' +
'length N-1 where N is the number of ' +
'Hamiltonian terms.')
tflag = 1
if opt.rhs_reuse and odeconfig.tdfunc is None:
print("No previous time-dependent RHS found.")
print("Generating one for you...")
rhs_generate(H_func, args)
lenh = len(H_func[0])
if opt.tidy:
H_func[0] = [(H_func[0][k]).tidyup() for k in range(lenh)]
# create data arrays for time-dependent RHS function
Hdata = [-1.0j * H_func[0][k].data.data for k in range(lenh)]
Hinds = [H_func[0][k].data.indices for k in range(lenh)]
Hptrs = [H_func[0][k].data.indptr for k in range(lenh)]
# setup ode args string
string = ""
for k in range(lenh):
string += ("Hdata[" + str(k) + "],Hinds[" + str(k) +
"],Hptrs[" + str(k) + "],")
if args:
td_consts = args.items()
for elem in td_consts:
string += str(elem[1])
if elem != td_consts[-1]:
string += (",")
# run code generator
if not opt.rhs_reuse or odeconfig.tdfunc is None:
if opt.rhs_filename is None:
odeconfig.tdname = "rhs" + str(odeconfig.cgen_num)
else:
odeconfig.tdname = opt.rhs_filename
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
#
# setup integrator
#
initial_vector = psi0.full().ravel()
r = scipy.integrate.ode(odeconfig.tdfunc)
r.set_integrator('zvode', method=opt.method, order=opt.order,
atol=opt.atol, rtol=opt.rtol, nsteps=opt.nsteps,
first_step=opt.first_step, min_step=opt.min_step,
max_step=opt.max_step)
r.set_initial_value(initial_vector, tlist[0])
code = compile('r.set_f_params(' + string + ')', '<string>', 'exec')
exec(code)
#
# call generic ODE code
#
return _generic_ode_solve(r, psi0, tlist, e_ops, opt, progress_bar,
norm, dims=psi0.dims)
def _sesolve_list_str_td(H_list, psi0, tlist, e_ops, args, opt,
progress_bar):
"""
Internal function for solving the master equation. See mesolve for usage.
"""
if debug:
print(inspect.stack()[0][3])
if psi0.isket:
oper_evo = False
elif psi0.isunitary:
oper_evo = True
else:
raise TypeError("The unitary solver requires psi0 to be"
" a ket as initial state"
" or a unitary as initial operator.")
#
# construct dynamics generator
#
Ldata = []
Linds = []
Lptrs = []
Lcoeff = []
Lobj = []
# loop over all hamiltonian terms, convert to superoperator form and
# add the data of sparse matrix representation to h_coeff
for h_spec in H_list:
if isinstance(h_spec, Qobj):
h = h_spec
h_coeff = "1.0"
elif isinstance(h_spec, list):
h = h_spec[0]
h_coeff = h_spec[1]
else:
raise TypeError("Incorrect specification of time-dependent " +
"Hamiltonian (expected string format)")
L = -1j * h
Ldata.append(L.data.data)
Linds.append(L.data.indices)
Lptrs.append(L.data.indptr)
if isinstance(h_coeff, Cubic_Spline):
Lobj.append(h_coeff.coeffs)
Lcoeff.append(h_coeff)
# the total number of Hamiltonian terms
n_L_terms = len(Ldata)
# Check which components should use OPENMP
omp_components = None
if qset.has_openmp:
if opt.use_openmp:
omp_components = openmp_components(Lptrs)
#
# setup ode args string: we expand the list Ldata, Linds and Lptrs into
# and explicit list of parameters
#
string_list = []
for k in range(n_L_terms):
string_list.append("Ldata[%d], Linds[%d], Lptrs[%d]" % (k, k, k))
# Add object terms to end of ode args string
for k in range(len(Lobj)):
string_list.append("Lobj[%d]" % k)
for name, value in args.items():
if isinstance(value, np.ndarray):
string_list.append(name)
else:
string_list.append(str(value))
parameter_string = ",".join(string_list)
#
# generate and compile new cython code if necessary
#
if not opt.rhs_reuse or config.tdfunc is None:
if opt.rhs_filename is None:
config.tdname = "rhs" + str(os.getpid()) + str(config.cgen_num)
else:
config.tdname = opt.rhs_filename
cgen = Codegen(h_terms=n_L_terms, h_tdterms=Lcoeff, args=args,
config=config, use_openmp=opt.use_openmp,
omp_components=omp_components,
omp_threads=opt.openmp_threads)
cgen.generate(config.tdname + ".pyx")
code = compile('from ' + config.tdname + ' import cy_td_ode_rhs',
'<string>', 'exec')
exec(code, globals())
config.tdfunc = cy_td_ode_rhs
#
# setup integrator
#
if oper_evo:
initial_vector = psi0.full().ravel('F')
r = scipy.integrate.ode(_td_ode_rhs_oper)
code = compile('r.set_f_params([' + parameter_string + '])',
'<string>', 'exec')
else:
initial_vector = psi0.full().ravel()
r = scipy.integrate.ode(config.tdfunc)
code = compile('r.set_f_params(' + parameter_string + ')',
'<string>', 'exec')
r.set_integrator('zvode', method=opt.method, order=opt.order,
atol=opt.atol, rtol=opt.rtol, nsteps=opt.nsteps,
first_step=opt.first_step, min_step=opt.min_step,
max_step=opt.max_step)
r.set_initial_value(initial_vector, tlist[0])
exec(code, locals(), args)
# Remove RHS cython file if necessary
if not opt.rhs_reuse and config.tdname:
_cython_build_cleanup(config.tdname)
#
# call generic ODE code
#
return _generic_ode_solve(r, psi0, tlist, e_ops, opt, progress_bar,
dims=psi0.dims)
def _mesolve_list_str_td(H_list, rho0, tlist, c_list, e_ops, args, opt,
progress_bar):
"""
Internal function for solving the master equation. See mesolve for usage.
"""
if debug:
print(inspect.stack()[0][3])
#
# check initial state: must be a density matrix
#
if isket(rho0):
rho0 = rho0 * rho0.dag()
#
# construct liouvillian
#
Lconst = 0
Ldata = []
Linds = []
Lptrs = []
Lcoeff = []
Lobj = []
me_cops_coeff = []
me_cops_obj = []
me_cops_obj_flags = []
# loop over all hamiltonian terms, convert to superoperator form and
# add the data of sparse matrix representation to
n_not_const_terms = 0
for h_spec in H_list:
if isinstance(h_spec, Qobj):
h = h_spec
if isoper(h):
Lconst += -1j * (spre(h) - spost(h))
elif issuper(h):
Lconst += h
else:
raise TypeError("Incorrect specification of time-dependent " +
"Hamiltonian (expected operator or " +
"superoperator)")
elif isinstance(h_spec, list):
n_not_const_terms +=1
h = h_spec[0]
h_coeff = h_spec[1]
if isoper(h):
L = -1j * (spre(h) - spost(h))
elif issuper(h):
L = h
else:
raise TypeError("Incorrect specification of time-dependent " +
"Hamiltonian (expected operator or " +
"superoperator)")
Ldata.append(L.data.data)
Linds.append(L.data.indices)
Lptrs.append(L.data.indptr)
if isinstance(h_coeff, Cubic_Spline):
Lobj.append(h_coeff.coeffs)
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_list:
if isinstance(c_spec, Qobj):
c = c_spec
if isoper(c):
cdc = c.dag() * c
Lconst += spre(c) * spost(c.dag()) - 0.5 * spre(cdc) \
- 0.5 * spost(cdc)
elif issuper(c):
Lconst += c
else:
raise TypeError("Incorrect specification of time-dependent " +
"Liouvillian (expected operator or " +
"superoperator)")
elif isinstance(c_spec, list):
n_not_const_terms +=1
c = c_spec[0]
c_coeff = c_spec[1]
if isoper(c):
cdc = c.dag() * c
L = spre(c) * spost(c.dag()) - 0.5 * spre(cdc) \
- 0.5 * spost(cdc)
if isinstance(c_coeff, Cubic_Spline):
me_cops_obj.append(c_coeff.coeffs)
me_cops_obj_flags.append(n_not_const_terms)
me_cops_coeff.append(c_coeff)
else:
c_coeff = "(" + c_coeff + ")**2"
Lcoeff.append(c_coeff)
elif issuper(c):
L = c
if isinstance(c_coeff, Cubic_Spline):
me_cops_obj.append(c_coeff.coeffs)
me_cops_obj_flags.append(-n_not_const_terms)
me_cops_coeff.append(c_coeff)
else:
Lcoeff.append(c_coeff)
else:
raise TypeError("Incorrect specification of time-dependent " +
"Liouvillian (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("Incorrect specification of time-dependent " +
"collapse operators (expected string format)")
#prepend the constant part of the liouvillian
if Lconst != 0:
Ldata = [Lconst.data.data]+Ldata
Linds = [Lconst.data.indices]+Linds
Lptrs = [Lconst.data.indptr]+Lptrs
Lcoeff = ["1.0"]+Lcoeff
else:
me_cops_obj_flags = [kk-1 for kk in me_cops_obj_flags]
# the total number of liouvillian terms (hamiltonian terms +
# collapse operators)
n_L_terms = len(Ldata)
n_td_cops = len(me_cops_obj)
# Check which components should use OPENMP
omp_components = None
if qset.has_openmp:
if opt.use_openmp:
omp_components = openmp_components(Lptrs)
#
# setup ode args string: we expand the list Ldata, Linds and Lptrs into
# and explicit list of parameters
#
string_list = []
for k in range(n_L_terms):
string_list.append("Ldata[%d], Linds[%d], Lptrs[%d]" % (k, k, k))
# Add H object terms to ode args string
for k in range(len(Lobj)):
string_list.append("Lobj[%d]" % k)
# Add cop object terms to end of ode args string
for k in range(len(me_cops_obj)):
string_list.append("me_cops_obj[%d]" % k)
for name, value in args.items():
if isinstance(value, np.ndarray):
string_list.append(name)
else:
string_list.append(str(value))
parameter_string = ",".join(string_list)
#
# generate and compile new cython code if necessary
#
if not opt.rhs_reuse or config.tdfunc is None:
if opt.rhs_filename is None:
config.tdname = "rhs" + str(os.getpid()) + str(config.cgen_num)
else:
config.tdname = opt.rhs_filename
cgen = Codegen(h_terms=len(Lcoeff), h_tdterms=Lcoeff,
c_td_splines=me_cops_coeff,
c_td_spline_flags=me_cops_obj_flags, args=args,
config=config, use_openmp=opt.use_openmp,
omp_components=omp_components,
omp_threads=opt.openmp_threads)
cgen.generate(config.tdname + ".pyx")
code = compile('from ' + config.tdname + ' import cy_td_ode_rhs',
'<string>', 'exec')
exec(code, globals())
config.tdfunc = cy_td_ode_rhs
#
# setup integrator
#
initial_vector = mat2vec(rho0.full()).ravel('F')
if issuper(rho0):
r = scipy.integrate.ode(_td_ode_rhs_super)
code = compile('r.set_f_params([' + parameter_string + '])',
'<string>', 'exec')
else:
r = scipy.integrate.ode(config.tdfunc)
code = compile('r.set_f_params(' + parameter_string + ')',
'<string>', 'exec')
r.set_integrator('zvode', method=opt.method, order=opt.order,
atol=opt.atol, rtol=opt.rtol, nsteps=opt.nsteps,
first_step=opt.first_step, min_step=opt.min_step,
max_step=opt.max_step)
r.set_initial_value(initial_vector, tlist[0])
exec(code, locals(), args)
#
# call generic ODE code
#
return _generic_ode_solve(r, rho0, tlist, e_ops, opt, progress_bar)
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 cy_td_ode_rhs", "<string>", "exec")
exec(code, globals())
odeconfig.tdfunc = cy_td_ode_rhs
try:
os.remove(odeconfig.tdname + ".pyx")
except:
pass
def _mesolve_list_td(H_func, rho0, tlist, c_op_list, e_ops, args, opt,
progress_bar):
"""!
Evolve the density matrix using an ODE solver with time dependent
Hamiltonian.
"""
if debug:
print(inspect.stack()[0][3])
#
# check initial state
#
if isket(rho0):
# if initial state is a ket and no collapse operator where given,
# fall back on the unitary schrodinger equation solver
if len(c_op_list) == 0:
return _sesolve_list_td(H_func, rho0, tlist, e_ops, args, opt)
# Got a wave function as initial state: convert to density matrix.
rho0 = ket2dm(rho0)
#
# construct liouvillian
#
if len(H_func) != 2:
raise TypeError('Time-dependent Hamiltonian list must have two terms.')
if not isinstance(H_func[0], (list, np.ndarray)) or len(H_func[0]) <= 1:
raise TypeError('Time-dependent Hamiltonians must be a list ' +
'with two or more terms')
if (not isinstance(H_func[1], (list, np.ndarray))) or \
(len(H_func[1]) != (len(H_func[0]) - 1)):
raise TypeError('Time-dependent coefficients must be list with ' +
'length N-1 where N is the number of ' +
'Hamiltonian terms.')
if opt.rhs_reuse and odeconfig.tdfunc is None:
rhs_generate(H_func, args)
lenh = len(H_func[0])
if opt.tidy:
H_func[0] = [(H_func[0][k]).tidyup() for k in range(lenh)]
L_func = [[liouvillian_fast(H_func[0][0], c_op_list)], H_func[1]]
for m in range(1, lenh):
L_func[0].append(liouvillian_fast(H_func[0][m], []))
# create data arrays for time-dependent RHS function
Ldata = [L_func[0][k].data.data for k in range(lenh)]
Linds = [L_func[0][k].data.indices for k in range(lenh)]
Lptrs = [L_func[0][k].data.indptr for k in range(lenh)]
# setup ode args string
string = ""
for k in range(lenh):
string += ("Ldata[%d], Linds[%d], Lptrs[%d]," % (k, k, k))
if args:
for name, value in args.items():
if isinstance(value, np.ndarray):
globals()['var_%s'%name] = value
string += 'var_%s,'%name
else:
string += str(value) + ','
# run code generator
if not opt.rhs_reuse or odeconfig.tdfunc is None:
if opt.rhs_filename is None:
odeconfig.tdname = "rhs" + str(odeconfig.cgen_num)
else:
odeconfig.tdname = opt.rhs_filename
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
#
# setup integrator
#
initial_vector = mat2vec(rho0.full()).ravel()
r = scipy.integrate.ode(odeconfig.tdfunc)
r.set_integrator('zvode', method=opt.method, order=opt.order,
atol=opt.atol, rtol=opt.rtol, nsteps=opt.nsteps,
first_step=opt.first_step, min_step=opt.min_step,
max_step=opt.max_step)
r.set_initial_value(initial_vector, tlist[0])
code = compile('r.set_f_params(' + string + ')', '<string>', 'exec')
exec(code)
#
# call generic ODE code
#
return _generic_ode_solve(r, rho0, tlist, e_ops, opt, progress_bar)
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