def d1_psi_heterodyne(A, psi):
"""
Todo: cythonize
.. math::
D_1(\psi, t) = -\\frac{1}{2}(C^\\dagger C - \\langle C^\\dagger \\rangle C +
\\frac{1}{2}\\langle C \\rangle\\langle C^\\dagger \\rangle))\psi
"""
e_C = cy_expect_psi_csr(A[0].data, A[0].indices, A[0].indptr, psi) # e_C
B = A[0].T.conj()
e_Cd = cy_expect_psi_csr(B.data, B.indices, B.indptr, psi) # e_Cd
return (-0.5 * spmv(A[3], psi) +
0.5 * e_Cd * spmv(A[0], psi) -
0.25 * e_C * e_Cd * psi)
def d2_psi_heterodyne(A, psi):
"""
Todo: cythonize
X = \\frac{1}{2}(C + C^\\dagger)
Y = \\frac{1}{2}(C - C^\\dagger)
D_{2,1}(\psi, t) = \\sqrt(1/2) * (C - \\langle X \\rangle) \\psi
D_{2,2}(\psi, t) = -i\\sqrt(1/2) * (C - \\langle Y \\rangle) \\psi
"""
X = 0.5 * cy_expect_psi_csr(A[1].data, A[1].indices, A[1].indptr, psi)
Y = 0.5 * cy_expect_psi_csr(A[2].data, A[2].indices, A[2].indptr, psi)
d2_1 = np.sqrt(0.5) * (spmv(A[0], psi) - X * psi)
d2_2 = -1.0j * np.sqrt(0.5) * (spmv(A[0], psi) - Y * psi)
return [d2_1, d2_2]
def d2_psi_homodyne(A, psi):
"""
OK
Todo: cythonize
.. math::
D_2(\psi, t) = (C - \\frac{1}{2}\\langle C + C^\\dagger\\rangle)\\psi
"""
e1 = cy_expect_psi_csr(A[1].data, A[1].indices, A[1].indptr, psi)
return [spmv(A[0], psi) - 0.5 * e1 * psi]
def d1_psi_homodyne(A, psi):
"""
OK
Todo: cythonize
.. math::
D_1(\psi, t) = \\frac{1}{2}(\\langle C + C^\\dagger\\rangle\\psi -
C^\\dagger C\\psi - \\frac{1}{4}\\langle C + C^\\dagger\\rangle^2\\psi)
"""
e1 = cy_expect_psi_csr(A[1].data, A[1].indices, A[1].indptr, psi)
return 0.5 * (e1 * spmv(A[0], psi) -
spmv(A[3], psi) -
0.25 * e1 ** 2 * psi)
def _mc_alg_evolve(nt, config, opt, seeds):
"""
Monte Carlo algorithm returning state-vector or expectation values
at times tlist for a single trajectory.
"""
global _cy_rhs_func
global _cy_col_spmv_func, _cy_col_expect_func
global _cy_col_spmv_call_func, _cy_col_expect_call_func
tlist = config.tlist
num_times = len(tlist)
if not _cy_rhs_func:
_mc_func_load(config)
if config.options.steady_state_average:
states_out = np.zeros((1), dtype=object)
else:
states_out = np.zeros((num_times), dtype=object)
temp = sp.csr_matrix(
np.reshape(config.psi0, (config.psi0.shape[0], 1)),
dtype=complex)
if (config.options.average_states and
not config.options.steady_state_average):
# output is averaged states, so use dm
states_out[0] = Qobj(temp*temp.conj().transpose(),
[config.psi0_dims[0],
config.psi0_dims[0]],
[config.psi0_shape[0],
config.psi0_shape[0]],
fast='mc-dm')
elif (not config.options.average_states and
not config.options.steady_state_average):
# output is not averaged, so write state vectors
states_out[0] = Qobj(temp, config.psi0_dims,
config.psi0_shape, fast='mc')
elif config.options.steady_state_average:
states_out[0] = temp * temp.conj().transpose()
# PRE-GENERATE LIST FOR EXPECTATION VALUES
expect_out = []
for i in range(config.e_num):
if config.e_ops_isherm[i]:
# preallocate real array of zeros
expect_out.append(np.zeros(num_times, dtype=float))
else:
# preallocate complex array of zeros
expect_out.append(np.zeros(num_times, dtype=complex))
expect_out[i][0] = \
cy_expect_psi_csr(config.e_ops_data[i],
config.e_ops_ind[i],
config.e_ops_ptr[i],
config.psi0,
config.e_ops_isherm[i])
collapse_times = []
which_oper = []
# SEED AND RNG AND GENERATE
prng = RandomState(seeds[nt])
# first rand is collapse norm, second is which operator
rand_vals = prng.rand(2)
# CREATE ODE OBJECT CORRESPONDING TO DESIRED TIME-DEPENDENCE
if config.tflag in [1, 10, 11]:
ODE = ode(_cy_rhs_func)
code = compile('ODE.set_f_params(' + config.string + ')',
'<string>', 'exec')
exec(code)
elif config.tflag == 2:
ODE = ode(_cRHStd)
ODE.set_f_params(config)
elif config.tflag in [20, 22]:
if config.options.rhs_with_state:
ODE = ode(_tdRHStd_with_state)
else:
ODE = ode(_tdRHStd)
ODE.set_f_params(config)
elif config.tflag == 3:
if config.options.rhs_with_state:
ODE = ode(_pyRHSc_with_state)
else:
ODE = ode(_pyRHSc)
ODE.set_f_params(config)
else:
ODE = ode(_cy_rhs_func)
ODE.set_f_params(config.h_data, config.h_ind,
config.h_ptr)
# initialize ODE solver for RHS
ODE._integrator = qutip_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)
if not len(ODE._y):
ODE.t = 0.0
ODE._y = np.array([0.0], complex)
ODE._integrator.reset(len(ODE._y), ODE.jac is not None)
# set initial conditions
ODE.set_initial_value(config.psi0, tlist[0])
# make array for collapse operator inds
cinds = np.arange(config.c_num)
# RUN ODE UNTIL EACH TIME IN TLIST
for k in range(1, num_times):
# ODE WHILE LOOP FOR INTEGRATE UP TO TIME TLIST[k]
while ODE.t < tlist[k]:
t_prev = ODE.t
y_prev = ODE.y
norm2_prev = dznrm2(ODE._y) ** 2
# integrate up to tlist[k], one step at a time.
ODE.integrate(tlist[k], step=1)
if not ODE.successful():
raise Exception("ZVODE failed!")
norm2_psi = dznrm2(ODE._y) ** 2
if norm2_psi <= rand_vals[0]:
# collapse has occured:
# find collapse time to within specified tolerance
# ------------------------------------------------
ii = 0
t_final = ODE.t
while ii < config.norm_steps:
ii += 1
t_guess = t_prev + \
np.log(norm2_prev / rand_vals[0]) / \
np.log(norm2_prev / norm2_psi) * (t_final - t_prev)
ODE._y = y_prev
ODE.t = t_prev
ODE._integrator.call_args[3] = 1
ODE.integrate(t_guess, step=0)
if not ODE.successful():
raise Exception(
"ZVODE failed after adjusting step size!")
norm2_guess = dznrm2(ODE._y)**2
if (np.abs(rand_vals[0] - norm2_guess) <
config.norm_tol * rand_vals[0]):
break
elif (norm2_guess < rand_vals[0]):
# t_guess is still > t_jump
t_final = t_guess
norm2_psi = norm2_guess
else:
# t_guess < t_jump
t_prev = t_guess
y_prev = ODE.y
norm2_prev = norm2_guess
if ii > config.norm_steps:
raise Exception("Norm tolerance not reached. " +
"Increase accuracy of ODE solver or " +
"Options.norm_steps.")
collapse_times.append(ODE.t)
# some string based collapse operators
if config.tflag in [1, 11]:
n_dp = [cy_expect_psi_csr(config.n_ops_data[i],
config.n_ops_ind[i],
config.n_ops_ptr[i],
ODE._y, 1)
for i in config.c_const_inds]
_locals = locals()
# calculates the expectation values for time-dependent
# norm collapse operators
exec(_cy_col_expect_call_func, globals(), _locals)
n_dp = np.array(_locals['n_dp'])
elif config.tflag in [2, 20, 22]:
# some Python function based collapse operators
n_dp = [cy_expect_psi_csr(config.n_ops_data[i],
config.n_ops_ind[i],
config.n_ops_ptr[i],
ODE._y, 1)
for i in config.c_const_inds]
n_dp += [abs(config.c_funcs[i](
ODE.t, config.c_func_args)) ** 2 *
cy_expect_psi_csr(config.n_ops_data[i],
config.n_ops_ind[i],
config.n_ops_ptr[i],
ODE._y, 1)
for i in config.c_td_inds]
n_dp = np.array(n_dp)
else:
# all constant collapse operators.
n_dp = np.array(
[cy_expect_psi_csr(config.n_ops_data[i],
config.n_ops_ind[i],
config.n_ops_ptr[i],
ODE._y, 1)
for i in range(config.c_num)])
# determine which operator does collapse and store it
kk = np.cumsum(n_dp / np.sum(n_dp))
j = cinds[kk >= rand_vals[1]][0]
which_oper.append(j)
if j in config.c_const_inds:
state = spmv_csr(config.c_ops_data[j],
config.c_ops_ind[j],
config.c_ops_ptr[j], ODE._y)
else:
if config.tflag in [1, 11]:
_locals = locals()
# calculates the state vector for collapse by a
# time-dependent collapse operator
exec(_cy_col_spmv_call_func, globals(), _locals)
state = _locals['state']
else:
state = \
config.c_funcs[j](ODE.t,
config.c_func_args) * \
spmv_csr(config.c_ops_data[j],
config.c_ops_ind[j],
config.c_ops_ptr[j], ODE._y)
state = state / dznrm2(state)
ODE._y = state
ODE._integrator.call_args[3] = 1
rand_vals = prng.rand(2)
# after while loop
# ----------------
out_psi = ODE._y / dznrm2(ODE._y)
if config.e_num == 0 or config.options.store_states:
out_psi_csr = sp.csr_matrix(np.reshape(out_psi,
(out_psi.shape[0], 1)),
dtype=complex)
if (config.options.average_states and
not config.options.steady_state_average):
states_out[k] = Qobj(
out_psi_csr * out_psi_csr.conj().transpose(),
[config.psi0_dims[0], config.psi0_dims[0]],
[config.psi0_shape[0], config.psi0_shape[0]],
fast='mc-dm')
elif config.options.steady_state_average:
states_out[0] = (
states_out[0] +
(out_psi_csr * out_psi_csr.conj().transpose()))
else:
states_out[k] = Qobj(out_psi_csr, config.psi0_dims,
config.psi0_shape, fast='mc')
for jj in range(config.e_num):
expect_out[jj][k] = cy_expect_psi_csr(
config.e_ops_data[jj], config.e_ops_ind[jj],
config.e_ops_ptr[jj], out_psi,
config.e_ops_isherm[jj])
# Run at end of mc_alg function
# -----------------------------
if config.options.steady_state_average:
states_out = np.array([Qobj(states_out[0] / float(len(tlist)),
[config.psi0_dims[0],
config.psi0_dims[0]],
[config.psi0_shape[0],
config.psi0_shape[0]],
fast='mc-dm')])
return (states_out, expect_out,
np.array(collapse_times, dtype=float),
np.array(which_oper, dtype=int))
def _evolve_no_collapse_expect_out(config):
"""
Calculates expect.values at times tlist if no collapse ops. given
"""
global _cy_rhs_func
global _cy_col_spmv_func, _cy_col_expect_func
global _cy_col_spmv_call_func, _cy_col_expect_call_func
if debug:
print(inspect.stack()[0][3])
num_times = len(config.tlist)
expect_out = []
for i in range(config.e_num):
if config.e_ops_isherm[i]:
# preallocate real array of zeros
expect_out.append(np.zeros(num_times, dtype=float))
else:
# preallocate complex array of zeros
expect_out.append(np.zeros(num_times, dtype=complex))
expect_out[i][0] = \
cy_expect_psi_csr(config.e_ops_data[i],
config.e_ops_ind[i],
config.e_ops_ptr[i],
config.psi0,
config.e_ops_isherm[i])
if not _cy_rhs_func:
_mc_func_load(config)
opt = config.options
if config.tflag in [1, 10, 11]:
ODE = ode(_cy_rhs_func)
code = compile('ODE.set_f_params(' + config.string + ')',
'<string>', 'exec')
exec(code)
elif config.tflag == 2:
ODE = ode(_cRHStd)
ODE.set_f_params(config)
elif config.tflag in [20, 22]:
if config.options.rhs_with_state:
ODE = ode(_tdRHStd_with_state)
else:
ODE = ode(_tdRHStd)
ODE.set_f_params(config)
elif config.tflag == 3:
if config.options.rhs_with_state:
ODE = ode(_pyRHSc_with_state)
else:
ODE = ode(_pyRHSc)
ODE.set_f_params(config)
else:
ODE = ode(cy_ode_rhs)
ODE.set_f_params(config.h_data, config.h_ind, config.h_ptr)
ODE.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)
ODE.set_initial_value(config.psi0, config.tlist[0])
for jj in range(config.e_num):
expect_out[jj][0] = cy_expect_psi_csr(
config.e_ops_data[jj], config.e_ops_ind[jj],
config.e_ops_ptr[jj], config.psi0,
config.e_ops_isherm[jj])
for k in range(1, num_times):
ODE.integrate(config.tlist[k], step=0) # integrate up to tlist[k]
if ODE.successful():
state = ODE.y / dznrm2(ODE.y)
for jj in range(config.e_num):
expect_out[jj][k] = cy_expect_psi_csr(
config.e_ops_data[jj], config.e_ops_ind[jj],
config.e_ops_ptr[jj], state,
config.e_ops_isherm[jj])
else:
raise ValueError('Error in ODE solver')
return expect_out
def _ssepdpsolve_single_trajectory(data, Heff, dt, times, N_store, N_substeps,
psi_t, dims, c_ops, e_ops):
"""
Internal function. See ssepdpsolve.
"""
states_list = []
phi_t = np.copy(psi_t)
prng = RandomState() # todo: seed it
r_jump, r_op = prng.rand(2)
jump_times = []
jump_op_idx = []
for t_idx, t in enumerate(times):
if e_ops:
for e_idx, e in enumerate(e_ops):
s = cy_expect_psi_csr(e.data.data, e.data.indices,
e.data.indptr, psi_t, 0)
data.expect[e_idx, t_idx] += s
data.ss[e_idx, t_idx] += s**2
else:
states_list.append(Qobj(psi_t, dims=dims))
for j in range(N_substeps):
if norm(phi_t)**2 < r_jump:
# jump occurs
p = np.array([norm(c.data * psi_t)**2 for c in c_ops])
p = np.cumsum(p / np.sum(p))
n = np.where(p >= r_op)[0][0]
# apply jump
psi_t = c_ops[n].data * psi_t
psi_t /= norm(psi_t)
phi_t = np.copy(psi_t)
# store info about jump
jump_times.append(times[t_idx] + dt * j)
jump_op_idx.append(n)
# get new random numbers for next jump
r_jump, r_op = prng.rand(2)
# deterministic evolution wihtout correction for norm decay
dphi_t = (-1.0j * dt) * (Heff.data * phi_t)
# deterministic evolution with correction for norm decay
dpsi_t = (-1.0j * dt) * (Heff.data * psi_t)
A = 0.5 * np.sum([norm(c.data * psi_t)**2 for c in c_ops])
dpsi_t += dt * A * psi_t
# increment wavefunctions
phi_t += dphi_t
psi_t += dpsi_t
# ensure that normalized wavefunction remains normalized
# this allows larger time step than otherwise would be possible
psi_t /= norm(psi_t)
return states_list, jump_times, jump_op_idx
def _mc_alg_evolve(nt, args, config):
"""
Monte-Carlo algorithm returning state-vector or expectation values
at times tlist for a single trajectory.
"""
global _cy_rhs_func
global _cy_col_spmv_func, _cy_col_expect_func
global _cy_col_spmv_call_func, _cy_col_expect_call_func
if not _cy_rhs_func:
_mc_func_load(config)
try:
# get input data
mc_alg_out, opt, tlist, num_times, seeds = args
collapse_times = [] # times of collapses
which_oper = [] # which operator did the collapse
# SEED AND RNG AND GENERATE
prng = RandomState(seeds[nt])
# first rand is collapse norm, second is which operator
rand_vals = prng.rand(2)
# CREATE ODE OBJECT CORRESPONDING TO DESIRED TIME-DEPENDENCE
if config.tflag in array([1, 10, 11]):
ODE = ode(_cy_rhs_func)
code = compile("ODE.set_f_params(" + config.string + ")", "<string>", "exec")
exec(code)
elif config.tflag == 2:
ODE = ode(_cRHStd)
ODE.set_f_params(config)
elif config.tflag in array([20, 22]):
if config.options.rhs_with_state:
ODE = ode(_tdRHStd_with_state)
else:
ODE = ode(_tdRHStd)
ODE.set_f_params(config)
elif config.tflag == 3:
if config.options.rhs_with_state:
ODE = ode(_pyRHSc_with_state)
else:
ODE = ode(_pyRHSc)
ODE.set_f_params(config)
else:
ODE = ode(_cy_rhs_func)
ODE.set_f_params(config.h_data, config.h_ind, config.h_ptr)
# initialize ODE solver for RHS
ODE.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,
)
# set initial conditions
ODE.set_initial_value(config.psi0, tlist[0])
# make array for collapse operator inds
cinds = np.arange(config.c_num)
# RUN ODE UNTIL EACH TIME IN TLIST
for k in range(1, num_times):
# ODE WHILE LOOP FOR INTEGRATE UP TO TIME TLIST[k]
while ODE.t < tlist[k]:
t_prev = ODE.t
y_prev = ODE.y
norm2_prev = dznrm2(ODE.y) ** 2
# integrate up to tlist[k], one step at a time.
ODE.integrate(tlist[k], step=1)
if not ODE.successful():
raise Exception("ZVODE failed!")
# check if ODE jumped over tlist[k], if so,
# integrate until tlist exactly
if ODE.t > tlist[k]:
ODE.set_initial_value(y_prev, t_prev)
ODE.integrate(tlist[k], step=0)
if not ODE.successful():
raise Exception("ZVODE failed!")
norm2_psi = dznrm2(ODE.y) ** 2
if norm2_psi <= rand_vals[0]: # <== collapse has occured
# find collapse time to within specified tolerance
# ---------------------------------------------------
ii = 0
t_final = ODE.t
while ii < config.norm_steps:
ii += 1
t_guess = t_prev + np.log(norm2_prev / rand_vals[0]) / np.log(norm2_prev / norm2_psi) * (
t_final - t_prev
)
ODE.set_initial_value(y_prev, t_prev)
ODE.integrate(t_guess, step=0)
if not ODE.successful():
raise Exception("ZVODE failed after adjusting step size!")
norm2_guess = dznrm2(ODE.y) ** 2
if np.abs(rand_vals[0] - norm2_guess) < config.norm_tol * rand_vals[0]:
break
elif norm2_guess < rand_vals[0]:
# t_guess is still > t_jump
t_final = t_guess
norm2_psi = norm2_guess
else:
# t_guess < t_jump
t_prev = t_guess
y_prev = ODE.y
norm2_prev = norm2_guess
if ii > config.norm_steps:
raise Exception(
"Norm tolerance not reached. "
+ "Increase accuracy of ODE solver or "
+ "Options.norm_steps."
)
# ---------------------------------------------------
collapse_times.append(ODE.t)
# some string based collapse operators
if config.tflag in array([1, 11]):
n_dp = [
cy_expect_psi_csr(config.n_ops_data[i], config.n_ops_ind[i], config.n_ops_ptr[i], ODE.y, 1)
for i in config.c_const_inds
]
_locals = locals()
# calculates the expectation values for time-dependent
# norm collapse operators
exec(_cy_col_expect_call_func, globals(), _locals)
n_dp = array(_locals["n_dp"])
# some Python function based collapse operators
elif config.tflag in array([2, 20, 22]):
n_dp = [
cy_expect_psi_csr(config.n_ops_data[i], config.n_ops_ind[i], config.n_ops_ptr[i], ODE.y, 1)
for i in config.c_const_inds
]
n_dp += [
abs(config.c_funcs[i](ODE.t, config.c_func_args)) ** 2
* cy_expect_psi_csr(
config.n_ops_data[i], config.n_ops_ind[i], config.n_ops_ptr[i], ODE.y, 1
)
for i in config.c_td_inds
]
n_dp = array(n_dp)
# all constant collapse operators.
else:
n_dp = array(
[
cy_expect_psi_csr(
config.n_ops_data[i], config.n_ops_ind[i], config.n_ops_ptr[i], ODE.y, 1
)
for i in range(config.c_num)
]
)
# determine which operator does collapse and store it
kk = cumsum(n_dp / sum(n_dp))
j = cinds[kk >= rand_vals[1]][0]
which_oper.append(j)
if j in config.c_const_inds:
state = spmv_csr(config.c_ops_data[j], config.c_ops_ind[j], config.c_ops_ptr[j], ODE.y)
else:
if config.tflag in array([1, 11]):
_locals = locals()
# calculates the state vector for collapse by a
# time-dependent collapse operator
exec(_cy_col_spmv_call_func, globals(), _locals)
state = _locals["state"]
else:
state = config.c_funcs[j](ODE.t, config.c_func_args) * spmv_csr(
config.c_ops_data[j], config.c_ops_ind[j], config.c_ops_ptr[j], ODE.y
)
state = state / dznrm2(state)
ODE.set_initial_value(state, ODE.t)
rand_vals = prng.rand(2)
# -------------------------------------------------------
# -- after while loop --
out_psi = ODE.y / dznrm2(ODE.y)
if config.e_num == 0:
out_psi = sp.csr_matrix(np.reshape(out_psi, (out_psi.shape[0], 1)), dtype=complex)
if config.options.average_states and not config.options.steady_state_average:
mc_alg_out[k] = Qobj(
out_psi * out_psi.conj().transpose(),
[config.psi0_dims[0], config.psi0_dims[0]],
[config.psi0_shape[0], config.psi0_shape[0]],
fast="mc-dm",
)
elif config.options.steady_state_average:
mc_alg_out[0] = mc_alg_out[0] + (out_psi * out_psi.conj().transpose())
else:
mc_alg_out[k] = Qobj(out_psi, config.psi0_dims, config.psi0_shape, fast="mc")
else:
for jj in range(config.e_num):
mc_alg_out[jj][k] = cy_expect_psi_csr(
config.e_ops_data[jj],
config.e_ops_ind[jj],
config.e_ops_ptr[jj],
out_psi,
config.e_ops_isherm[jj],
)
# Run at end of mc_alg function
# ------------------------------
if config.options.steady_state_average:
mc_alg_out = array(
[
Qobj(
mc_alg_out[0] / float(len(tlist)),
[config.psi0_dims[0], config.psi0_dims[0]],
[config.psi0_shape[0], config.psi0_shape[0]],
fast="mc-dm",
)
]
)
return (nt, mc_alg_out, np.array(collapse_times, dtype=float), np.array(which_oper, dtype=int))
except Exception as e:
print("failed to run _mc_alg_evolve: " + str(e))
def _no_collapse_expect_out(num_times, expect_out, config):
"""
Calculates expect.values at times tlist if no collapse ops. given
"""
global _cy_rhs_func
global _cy_col_spmv_func, _cy_col_expect_func
global _cy_col_spmv_call_func, _cy_col_expect_call_func
if debug:
print(inspect.stack()[0][3])
if not _cy_rhs_func:
_mc_func_load(config)
opt = config.options
if config.tflag in array([1, 10, 11]):
ODE = ode(_cy_rhs_func)
code = compile("ODE.set_f_params(" + config.string + ")", "<string>", "exec")
exec(code)
elif config.tflag == 2:
ODE = ode(_cRHStd)
ODE.set_f_params(config)
elif config.tflag in array([20, 22]):
if config.options.rhs_with_state:
ODE = ode(_tdRHStd_with_state)
else:
ODE = ode(_tdRHStd)
ODE.set_f_params(config)
elif config.tflag == 3:
if config.options.rhs_with_state:
ODE = ode(_pyRHSc_with_state)
else:
ODE = ode(_pyRHSc)
ODE.set_f_params(config)
else:
ODE = ode(cy_ode_rhs)
ODE.set_f_params(config.h_data, config.h_ind, config.h_ptr)
ODE.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,
)
ODE.set_initial_value(config.psi0, config.tlist[0])
for jj in range(config.e_num):
expect_out[jj][0] = cy_expect_psi_csr(
config.e_ops_data[jj], config.e_ops_ind[jj], config.e_ops_ptr[jj], config.psi0, config.e_ops_isherm[jj]
)
for k in range(1, num_times):
ODE.integrate(config.tlist[k], step=0) # integrate up to tlist[k]
if ODE.successful():
state = ODE.y / dznrm2(ODE.y)
for jj in range(config.e_num):
expect_out[jj][k] = cy_expect_psi_csr(
config.e_ops_data[jj], config.e_ops_ind[jj], config.e_ops_ptr[jj], state, config.e_ops_isherm[jj]
)
else:
raise ValueError("Error in ODE solver")
return expect_out
def run(self):
if debug:
print(inspect.stack()[0][3])
if self.config.c_num == 0:
if self.config.ntraj != 1:
# ntraj != 1 is pointless for no collapse operators
self.config.ntraj = 1
if self.config.e_num == 0: # return psi at each requested time
self.psi_out = _no_collapse_psi_out(self.num_times, self.psi_out, self.config)
else: # return expectation values of requested operators
self.expect_out = _no_collapse_expect_out(self.num_times, self.expect_out, self.config)
elif self.config.c_num != 0:
if self.seeds is None:
self.seeds = random_integers(1e8, size=self.config.ntraj)
# else:
# if len(self.seeds) != self.config.ntraj:
# raise "Incompatible size of seeds vector in config."
if self.config.e_num == 0:
if config.options.steady_state_average:
mc_alg_out = zeros((1), dtype=object)
else:
mc_alg_out = zeros((self.num_times), dtype=object)
temp = sp.csr_matrix(np.reshape(self.config.psi0, (self.config.psi0.shape[0], 1)), dtype=complex)
if self.config.options.average_states and not config.options.steady_state_average:
# output is averaged states, so use dm
mc_alg_out[0] = Qobj(
temp * temp.conj().transpose(),
[config.psi0_dims[0], config.psi0_dims[0]],
[config.psi0_shape[0], config.psi0_shape[0]],
fast="mc-dm",
)
elif not self.config.options.average_states and not config.options.steady_state_average:
# output is not averaged, so write state vectors
mc_alg_out[0] = Qobj(temp, config.psi0_dims, config.psi0_shape, fast="mc")
elif config.options.steady_state_average:
mc_alg_out[0] = temp * temp.conj().transpose()
else:
# PRE-GENERATE LIST OF EXPECTATION VALUES
mc_alg_out = []
for i in range(self.config.e_num):
if self.config.e_ops_isherm[i]:
# preallocate real array of zeros
mc_alg_out.append(zeros(self.num_times, dtype=float))
else:
# preallocate complex array of zeros
mc_alg_out.append(zeros(self.num_times, dtype=complex))
mc_alg_out[i][0] = cy_expect_psi_csr(
self.config.e_ops_data[i],
self.config.e_ops_ind[i],
self.config.e_ops_ptr[i],
self.config.psi0,
self.config.e_ops_isherm[i],
)
# set arguments for input to monte-carlo
args = (mc_alg_out, self.config.options, self.config.tlist, self.num_times, self.seeds)
self.config.progress_bar.start(self.config.ntraj)
self.parallel(args, self)
self.config.progress_bar.finished()
def __init__(self, config):
# -----------------------------------
# INIT MC CLASS
# -----------------------------------
self.config = config
# ----MAIN OBJECT PROPERTIES--------------------
# holds instance of the ProgressBar class
self.bar = None
# holds instance of the Pthread class
self.thread = None
# Number of completed trajectories
self.count = 0
# step-size for count attribute
self.step = 1
# Percent of trajectories completed
self.percent = 0.0
# used in implimenting the command line progress ouput
self.level = 0.1
# times at which to output state vectors or expectation values
# number of time steps in tlist
self.num_times = len(self.config.tlist)
# holds seed for random number generator
self.seeds = self.config.options.seeds
# number of cpus to be used
self.cpus = self.config.options.num_cpus
# set output variables, even if they are not used to simplify output
# code.
self.psi_out = None
self.expect_out = []
self.collapse_times_out = None
self.which_op_out = None
# FOR EVOLUTION FOR NO COLLAPSE OPERATORS
if config.c_num == 0:
if config.e_num == 0:
# Output array of state vectors calculated at times in tlist
self.psi_out = array([Qobj()] * self.num_times)
elif config.e_num != 0: # no collapse expectation values
# List of output expectation values calculated at times in
# tlist
self.expect_out = []
for i in range(config.e_num):
if config.e_ops_isherm[i]:
# preallocate real array of zeros
self.expect_out.append(zeros(self.num_times, dtype=float))
else: # preallocate complex array of zeros
self.expect_out.append(zeros(self.num_times, dtype=complex))
self.expect_out[i][0] = cy_expect_psi_csr(
config.e_ops_data[i],
config.e_ops_ind[i],
config.e_ops_ptr[i],
config.psi0,
config.e_ops_isherm[i],
)
# FOR EVOLUTION WITH COLLAPSE OPERATORS
elif config.c_num != 0:
# preallocate #ntraj arrays for state vectors, collapse times, and
# which operator
self.collapse_times_out = zeros((config.ntraj), dtype=ndarray)
self.which_op_out = zeros((config.ntraj), dtype=ndarray)
if config.e_num == 0:
# if no expectation operators, preallocate #ntraj arrays
# for state vectors
if self.config.options.steady_state_average:
self.psi_out = array([zeros((1), dtype=object) for q in range(config.ntraj)])
else:
self.psi_out = array([zeros((self.num_times), dtype=object) for q in range(config.ntraj)])
else: # preallocate array of lists for expectation values
self.expect_out = [[] for x in range(config.ntraj)]
def _sepdpsolve_single_trajectory(data, Heff, dt, tlist, N_store, N_substeps,
psi_t, c_ops, e_ops):
"""
Internal function.
"""
states_list = []
phi_t = np.copy(psi_t)
prng = RandomState() # todo: seed it
r_jump, r_op = prng.rand(2)
jump_times = []
jump_op_idx = []
for t_idx, t in enumerate(tlist):
if e_ops:
for e_idx, e in enumerate(e_ops):
s = cy_expect_psi_csr(
e.data.data, e.data.indices, e.data.indptr, psi_t)
data.expect[e_idx, t_idx] += s
data.ss[e_idx, t_idx] += s ** 2
else:
states_list.append(Qobj(psi_t))
for j in range(N_substeps):
if norm(phi_t) ** 2 < r_jump:
# jump occurs
p = np.array([norm(c.data * psi_t) ** 2 for c in c_ops])
p = np.cumsum(p / np.sum(p))
n = np.where(p >= r_op)[0][0]
# apply jump
psi_t = c_ops[n].data * psi_t
psi_t /= norm(psi_t)
phi_t = np.copy(psi_t)
# store info about jump
jump_times.append(tlist[t_idx] + dt * j)
jump_op_idx.append(n)
# get new random numbers for next jump
r_jump, r_op = prng.rand(2)
# deterministic evolution wihtout correction for norm decay
dphi_t = (-1.0j * dt) * (Heff.data * phi_t)
# deterministic evolution with correction for norm decay
dpsi_t = (-1.0j * dt) * (Heff.data * psi_t)
A = 0.5 * np.sum([norm(c.data * psi_t) ** 2 for c in c_ops])
dpsi_t += dt * A * psi_t
# increment wavefunctions
phi_t += dphi_t
psi_t += dpsi_t
# ensure that normalized wavefunction remains normalized
# this allows larger time step than otherwise would be possible
psi_t /= norm(psi_t)
return states_list, jump_times, jump_op_idx
def _ssesolve_single_trajectory(data, H, dt, tlist, N_store, N_substeps, psi_t,
A_ops, e_ops, m_ops, rhs, d1, d2, d2_len,
dW_factors, homogeneous, distribution, args,
store_measurement=False, noise=None,
normalize=True):
"""
Internal function. See ssesolve.
"""
if noise is None:
if homogeneous:
if distribution == 'normal':
dW = np.sqrt(
dt) * scipy.randn(len(A_ops), N_store, N_substeps, d2_len)
else:
raise TypeError('Unsupported increment distribution for homogeneous process.')
else:
if distribution != 'poisson':
raise TypeError('Unsupported increment distribution for inhomogeneous process.')
dW = np.zeros((len(A_ops), N_store, N_substeps, d2_len))
else:
dW = noise
states_list = []
measurements = np.zeros((len(tlist), len(m_ops), d2_len), dtype=complex)
for t_idx, t in enumerate(tlist):
if e_ops:
for e_idx, e in enumerate(e_ops):
s = cy_expect_psi_csr(e.data.data, e.data.indices, e.data.indptr, psi_t, 0)
data.expect[e_idx, t_idx] += s
data.ss[e_idx, t_idx] += s ** 2
else:
states_list.append(Qobj(psi_t))
psi_prev = np.copy(psi_t)
for j in range(N_substeps):
if noise is None and not homogeneous:
for a_idx, A in enumerate(A_ops):
dw_expect = norm(spmv(A[0], psi_t)) ** 2 * dt
dW[a_idx, t_idx, j, :] = np.random.poisson(dw_expect, d2_len)
psi_t = rhs(H.data, psi_t, t + dt * j,
A_ops, dt, dW[:, t_idx, j, :], d1, d2, args)
# optionally renormalize the wave function
if normalize:
psi_t /= norm(psi_t)
if store_measurement:
for m_idx, m in enumerate(m_ops):
for dW_idx, dW_factor in enumerate(dW_factors):
if m[dW_idx]:
m_expt = norm(spmv(m[dW_idx].data, psi_prev)) ** 2
else:
m_expt = 0
measurements[t_idx, m_idx, dW_idx] = (m_expt +
dW_factor * dW[m_idx, t_idx, :, dW_idx].sum() / (dt * N_substeps))
if d2_len == 1:
measurements = measurements.squeeze(axis=(2))
return states_list, dW, measurements
def _mc_alg_evolve(nt, config, opt, seeds):
"""
Monte Carlo algorithm returning state-vector or expectation values
at times tlist for a single trajectory.
"""
global _cy_rhs_func
global _cy_col_spmv_func, _cy_col_expect_func
global _cy_col_spmv_call_func, _cy_col_expect_call_func
tlist = config.tlist
num_times = len(tlist)
if not _cy_rhs_func:
_mc_func_load(config)
if config.options.steady_state_average:
states_out = np.zeros((1), dtype=object)
else:
states_out = np.zeros((num_times), dtype=object)
temp = sp.csr_matrix(
np.reshape(config.psi0, (config.psi0.shape[0], 1)),
dtype=complex)
if (config.options.average_states and
not config.options.steady_state_average):
# output is averaged states, so use dm
states_out[0] = Qobj(temp*temp.conj().transpose(),
[config.psi0_dims[0],
config.psi0_dims[0]],
[config.psi0_shape[0],
config.psi0_shape[0]],
fast='mc-dm')
elif (not config.options.average_states and
not config.options.steady_state_average):
# output is not averaged, so write state vectors
states_out[0] = Qobj(temp, config.psi0_dims,
config.psi0_shape, fast='mc')
elif config.options.steady_state_average:
states_out[0] = temp * temp.conj().transpose()
# PRE-GENERATE LIST FOR EXPECTATION VALUES
expect_out = []
for i in range(config.e_num):
if config.e_ops_isherm[i]:
# preallocate real array of zeros
expect_out.append(np.zeros(num_times, dtype=float))
else:
# preallocate complex array of zeros
expect_out.append(np.zeros(num_times, dtype=complex))
expect_out[i][0] = \
cy_expect_psi_csr(config.e_ops_data[i],
config.e_ops_ind[i],
config.e_ops_ptr[i],
config.psi0,
config.e_ops_isherm[i])
collapse_times = []
which_oper = []
# SEED AND RNG AND GENERATE
prng = RandomState(seeds[nt])
# first rand is collapse norm, second is which operator
rand_vals = prng.rand(2)
# CREATE ODE OBJECT CORRESPONDING TO DESIRED TIME-DEPENDENCE
if config.tflag in [1, 10, 11]:
ODE = ode(_cy_rhs_func)
code = compile('ODE.set_f_params(' + config.string + ')',
'<string>', 'exec')
exec(code)
elif config.tflag == 2:
ODE = ode(_cRHStd)
ODE.set_f_params(config)
elif config.tflag in [20, 22]:
if config.options.rhs_with_state:
ODE = ode(_tdRHStd_with_state)
else:
ODE = ode(_tdRHStd)
ODE.set_f_params(config)
elif config.tflag == 3:
if config.options.rhs_with_state:
ODE = ode(_pyRHSc_with_state)
else:
ODE = ode(_pyRHSc)
ODE.set_f_params(config)
else:
ODE = ode(_cy_rhs_func)
ODE.set_f_params(config.h_data, config.h_ind,
config.h_ptr)
# initialize ODE solver for RHS
ODE._integrator = qutip_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)
if not len(ODE._y):
ODE.t = 0.0
ODE._y = np.array([0.0], complex)
ODE._integrator.reset(len(ODE._y), ODE.jac is not None)
# set initial conditions
ODE.set_initial_value(config.psi0, tlist[0])
# make array for collapse operator inds
cinds = np.arange(config.c_num)
# RUN ODE UNTIL EACH TIME IN TLIST
for k in range(1, num_times):
# ODE WHILE LOOP FOR INTEGRATE UP TO TIME TLIST[k]
while ODE.t < tlist[k]:
t_prev = ODE.t
y_prev = ODE.y
norm2_prev = dznrm2(ODE._y) ** 2
# integrate up to tlist[k], one step at a time.
ODE.integrate(tlist[k], step=1)
if not ODE.successful():
raise Exception("ZVODE failed!")
norm2_psi = dznrm2(ODE._y) ** 2
if norm2_psi <= rand_vals[0]:
# collapse has occured:
# find collapse time to within specified tolerance
# ------------------------------------------------
ii = 0
t_final = ODE.t
while ii < config.norm_steps:
ii += 1
t_guess = t_prev + \
np.log(norm2_prev / rand_vals[0]) / \
np.log(norm2_prev / norm2_psi) * (t_final - t_prev)
ODE._y = y_prev
ODE.t = t_prev
ODE._integrator.call_args[3] = 1
ODE.integrate(t_guess, step=0)
if not ODE.successful():
raise Exception(
"ZVODE failed after adjusting step size!")
norm2_guess = dznrm2(ODE._y)**2
if (np.abs(rand_vals[0] - norm2_guess) <
config.norm_tol * rand_vals[0]):
break
elif (norm2_guess < rand_vals[0]):
# t_guess is still > t_jump
t_final = t_guess
norm2_psi = norm2_guess
else:
# t_guess < t_jump
t_prev = t_guess
y_prev = ODE.y
norm2_prev = norm2_guess
if ii > config.norm_steps:
raise Exception("Norm tolerance not reached. " +
"Increase accuracy of ODE solver or " +
"Options.norm_steps.")
collapse_times.append(ODE.t)
# some string based collapse operators
if config.tflag in [1, 11]:
n_dp = [cy_expect_psi_csr(config.n_ops_data[i],
config.n_ops_ind[i],
config.n_ops_ptr[i],
ODE._y, 1)
for i in config.c_const_inds]
_locals = locals()
# calculates the expectation values for time-dependent
# norm collapse operators
exec(_cy_col_expect_call_func, globals(), _locals)
n_dp = np.array(_locals['n_dp'])
elif config.tflag in [2, 20, 22]:
# some Python function based collapse operators
n_dp = [cy_expect_psi_csr(config.n_ops_data[i],
config.n_ops_ind[i],
config.n_ops_ptr[i],
ODE._y, 1)
for i in config.c_const_inds]
n_dp += [abs(config.c_funcs[i](
ODE.t, config.c_func_args)) ** 2 *
cy_expect_psi_csr(config.n_ops_data[i],
config.n_ops_ind[i],
config.n_ops_ptr[i],
ODE._y, 1)
for i in config.c_td_inds]
n_dp = np.array(n_dp)
else:
# all constant collapse operators.
n_dp = np.array(
[cy_expect_psi_csr(config.n_ops_data[i],
config.n_ops_ind[i],
config.n_ops_ptr[i],
ODE._y, 1)
for i in range(config.c_num)])
# determine which operator does collapse and store it
kk = np.cumsum(n_dp / np.sum(n_dp))
j = cinds[kk >= rand_vals[1]][0]
which_oper.append(j)
if j in config.c_const_inds:
state = spmv_csr(config.c_ops_data[j],
config.c_ops_ind[j],
config.c_ops_ptr[j], ODE._y)
else:
if config.tflag in [1, 11]:
_locals = locals()
# calculates the state vector for collapse by a
# time-dependent collapse operator
exec(_cy_col_spmv_call_func, globals(), _locals)
state = _locals['state']
else:
state = \
config.c_funcs[j](ODE.t,
config.c_func_args) * \
spmv_csr(config.c_ops_data[j],
config.c_ops_ind[j],
config.c_ops_ptr[j], ODE._y)
state = state / dznrm2(state)
ODE._y = state
ODE._integrator.call_args[3] = 1
rand_vals = prng.rand(2)
# after while loop
# ----------------
out_psi = ODE._y / dznrm2(ODE._y)
if config.e_num == 0 or config.options.store_states:
out_psi_csr = sp.csr_matrix(np.reshape(out_psi,
(out_psi.shape[0], 1)),
dtype=complex)
if (config.options.average_states and
not config.options.steady_state_average):
states_out[k] = Qobj(
out_psi_csr * out_psi_csr.conj().transpose(),
[config.psi0_dims[0], config.psi0_dims[0]],
[config.psi0_shape[0], config.psi0_shape[0]],
fast='mc-dm')
elif config.options.steady_state_average:
states_out[0] = (
states_out[0] +
(out_psi_csr * out_psi_csr.conj().transpose()))
else:
states_out[k] = Qobj(out_psi_csr, config.psi0_dims,
config.psi0_shape, fast='mc')
for jj in range(config.e_num):
expect_out[jj][k] = cy_expect_psi_csr(
config.e_ops_data[jj], config.e_ops_ind[jj],
config.e_ops_ptr[jj], out_psi,
config.e_ops_isherm[jj])
# Run at end of mc_alg function
# -----------------------------
if config.options.steady_state_average:
states_out = np.array([Qobj(states_out[0] / float(len(tlist)),
[config.psi0_dims[0],
config.psi0_dims[0]],
[config.psi0_shape[0],
config.psi0_shape[0]],
fast='mc-dm')])
return (states_out, expect_out,
np.array(collapse_times, dtype=float),
np.array(which_oper, dtype=int))
def _evolve_no_collapse_expect_out(config):
"""
Calculates expect.values at times tlist if no collapse ops. given
"""
global _cy_rhs_func
global _cy_col_spmv_func, _cy_col_expect_func
global _cy_col_spmv_call_func, _cy_col_expect_call_func
if debug:
print(inspect.stack()[0][3])
num_times = len(config.tlist)
expect_out = []
for i in range(config.e_num):
if config.e_ops_isherm[i]:
# preallocate real array of zeros
expect_out.append(np.zeros(num_times, dtype=float))
else:
# preallocate complex array of zeros
expect_out.append(np.zeros(num_times, dtype=complex))
expect_out[i][0] = \
cy_expect_psi_csr(config.e_ops_data[i],
config.e_ops_ind[i],
config.e_ops_ptr[i],
config.psi0,
config.e_ops_isherm[i])
if not _cy_rhs_func:
_mc_func_load(config)
opt = config.options
if config.tflag in [1, 10, 11]:
ODE = ode(_cy_rhs_func)
code = compile('ODE.set_f_params(' + config.string + ')',
'<string>', 'exec')
exec(code)
elif config.tflag == 2:
ODE = ode(_cRHStd)
ODE.set_f_params(config)
elif config.tflag in [20, 22]:
if config.options.rhs_with_state:
ODE = ode(_tdRHStd_with_state)
else:
ODE = ode(_tdRHStd)
ODE.set_f_params(config)
elif config.tflag == 3:
if config.options.rhs_with_state:
ODE = ode(_pyRHSc_with_state)
else:
ODE = ode(_pyRHSc)
ODE.set_f_params(config)
else:
ODE = ode(cy_ode_rhs)
ODE.set_f_params(config.h_data, config.h_ind, config.h_ptr)
ODE.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)
ODE.set_initial_value(config.psi0, config.tlist[0])
for jj in range(config.e_num):
expect_out[jj][0] = cy_expect_psi_csr(
config.e_ops_data[jj], config.e_ops_ind[jj],
config.e_ops_ptr[jj], config.psi0,
config.e_ops_isherm[jj])
for k in range(1, num_times):
ODE.integrate(config.tlist[k], step=0) # integrate up to tlist[k]
if ODE.successful():
state = ODE.y / dznrm2(ODE.y)
for jj in range(config.e_num):
expect_out[jj][k] = cy_expect_psi_csr(
config.e_ops_data[jj], config.e_ops_ind[jj],
config.e_ops_ptr[jj], state,
config.e_ops_isherm[jj])
else:
raise ValueError('Error in ODE solver')
return expect_out
