class PathToField(Solver):
"""PathToField is a solver that solves the control fields for a
given path of dipole moment projection.
Class PathToField is used to solve a set of control fields that
drive the dipole moment projection of the system of interest to
follow a given path. The system of interest by default is a rotor
(molecule.Rotor.)
Parameters
----------
path_desired: numpy.array, shape=(n,2)
A desired path of molecule dipole moment projection.
dt: float, optional (default=1000)
Difference of time between two adjacent time points. This is
path-specific and is currently calculated when a
dataContainer.DataContainer object is instantiated with a
desired path.
molecule: Molecule object, optional (default=Rotor)
System of interest. Default to a Rotor molecule with a system
dimension of m=8 specified in constants.py.
Attributes
----------
molecule: Molecule object
System of interest.
path: numpy.array, shape=(n,2)
Path specified.
n: int
Number of time points.
dt: float
Delta t between two adjacent time points.
time: numpy.array, shape=(n,)
Time vector in atomic units.
"""
def __init__(self, path_desired, dt=1000, molecule=None):
# Create a Rotor object as the system of interest if not
# provided by the user
if molecule is None:
## System of interest.
## Default value is a rotor (solver.molecule.Rotor)
self.molecule = Rotor(const.m)
else:
self.molecule = rotor
## Path specified
self.path = path_desired
self._path_predicted = np.zeros_like(path_desired)
## Number of time points
self.n = path_desired.shape[0]
## Delta t between two adjacent time points.
self.dt = dt
self._t_final = self.n * self.dt
## Time vector in unit of ?
self.time = np.arange(self._t_final, step=self.dt, dtype=float)
self._ddpath = np.stack((f.d2dt2(
self.path[:, 0], self.dt), f.d2dt2(self.path[:, 1], self.dt)),
axis=1)
# operators used only by private methods within class instance
m = self.molecule.m
self._op1 = (f.cosphi(m) + 4 * f.sinphi(m) @ f.ddphi(m) -
4 * f.cosphi(m) @ f.d2dphi2(m))
self._op2 = (f.sinphi(m) - 4 * f.cosphi(m) @ f.ddphi(m) -
4 * f.sinphi(m) @ f.d2dphi2(m))
self._cosphi2 = f.cosphi(m) @ f.cosphi(m)
self._sinphi2 = f.sinphi(m) @ f.sinphi(m)
self._cosphi_sinphi = f.cosphi(m) @ f.sinphi(m)
self._sinphi_cosphi = f.sinphi(m) @ f.cosphi(m)
#calc and set initial field, but not using molecule.update_field()
field = self._get_field(0, real=True)
self.molecule.set_field(field)
def solve(self):
"""Calculate the control field required for each time step.
"""
for j in tqdm.tqdm(range(1, self.n)):
self.molecule.evolve(self.dt)
field = self._get_field(j, real=True)
self.molecule.update_field(field)
# self._velidate()
def export(self):
"""Export calculated time vector, fields, path, and states
as np.ndarray.
Returns
-------
time: numpy.array, shape=(n,)
Time vector based on dt. In unit of picoseconds.
fields: numpy.array, shape=(n,2)
Control fields required for the path of interest. In
unit of V/angstrom.
path: numpy.array, shape=(n,2)
Resulting path based on the calculated fields.
states: numpy.array, shape=(2m+1,n)
State amplitudes of the system at every time point.
"""
time = self.molecule.get_time_asarray()
time = time * 2.418 * 10**(-17) * 10**12 #time in picoseconds
states = self.molecule.get_states_asarray()
fields = self.molecule.get_fields_asarray()
field_const = 5.142 * 10**11 * 10**(-10) #amplitude in V/angstrom
fields = fields * field_const
path = np.zeros((self.n, 2))
oper_x = self.molecule.dipole_x
oper_y = self.molecule.dipole_y
states_list = self.molecule.history['state']
for i in range(self.n):
path[i, 0] = states_list[i].get_expt(oper_x).real
path[i, 1] = states_list[i].get_expt(oper_y).real
return time, fields, path, states
def _get_field(self, j, real=False):
"""Calculate the required field for the next step.
Parameters
----------
j: int
System is at the j-th time point.
real: bool, optional (default=False)
If True, force the returned value to be only the real
part of a complex number.
Returns
-------
field: numpy.array, shape=(2,)
An array of size 2 containing x- and y-component of the
control field for the next step.
"""
field = self._get_Ainv() @ self._get_b(j)
if real:
field = field.real
return field.flatten()
def _get_det(self):
"""Calculate determinant of matrix A"""
state = self.molecule.state
c = 4 * const.B**2 * const.mu**2 / const.hbar**4
det = (c *
(state.get_expt(self._sinphi2) * state.get_expt(self._cosphi2) -
state.get_expt(self._sinphi_cosphi)**2))
return det
def _get_Ainv(self):
"""Calculate inverse of matrix A"""
state = self.molecule.state
c = 2 * const.B * const.mu / const.hbar**2
a11 = c * state.get_expt(self._sinphi2)
a12 = -c * state.get_expt(self._cosphi_sinphi)
a21 = -c * state.get_expt(self._sinphi_cosphi)
a22 = c * state.get_expt(self._cosphi2)
det = self._get_det()
A_inv = 1 / det * np.array([[a22, -a12], [-a21, a11]])
return A_inv
def _get_b(self, i):
"""Calculate b vector"""
state = self.molecule.state
c = const.B**2 / const.hbar**2
b1 = self._ddpath[i, 0] + np.real(c * state.get_expt(self._op1))
b2 = self._ddpath[i, 1] + np.real(c * state.get_expt(self._op2))
return np.array([b1, b2])
class FieldToPath(Solver):
"""Calculate the resulting path from a given set of control fields.
Class FieldToPath is used to solve the trajectory of molecule's
dipole moment projection for a given set of control fields in
time. The system of interest by default is a rotor
(molecule.Rotor.)
Parameters
----------
fields: numpy.array, shape=(n,2)
A prescribed set of control fields to apply to the molecule.
dt: float, optional (default=1000)
Difference of time between two adjacent time points. This is
path-specific and is currently calculated when a
dataContainer.DataContainer object is instantiated with a
desired path.
molecule: Molecule object, optional (default=Rotor)
System of interest. Default to a Rotor molecule with a system
dimension of m=8 specified in constants.py.
Attributes
----------
molecule: Molecule object
System of interest.
n: int
Number of time points.
fields: numpy.array, shape=(n,2)
Time-series of control field prescribed.
dt: float
Delta t between two adjacent time points.
time: numpy.array, shape=(n,)
Time vector in atomic units.
path: numpy.array, shape=(n,2)
Resulting path of molecule's dipole moment projection.
"""
def __init__(self, fields, dt=1000, molecule=None):
# Create a Rotor object as the system of interest if not
# provided by the user
if molecule is None:
## System of interest
## Default: a Rotor object with quantum number = const.m
self.molecule = Rotor(const.m)
else:
self.molecule = rotor
## Number of time points
self.n = fields.shape[0]
## An nx2 np.ndarray containing the given field.
## Each row is the x- and y-component of such field at a time point.
self.fields = fields
field_const = 5.142 * 10**11 * 10**(-10) #amplitude in V/angstrom
self.fields = self.fields / field_const #back to atomic units
self._fields_list = [
self.fields[i, :].flatten() for i in range(self.n)
]
## The resulting path from the given fields.
self.path = np.zeros((self.n, 2))
## Time difference between two adjacent time points.
self.dt = dt
self._t_final = self.dt * self.n
## Time vector containing all time points.
self.time = np.arange(self._t_final, step=self.dt, dtype=float)
self.time_in_ps = self.time * 2.418e-5 #time in picoseconds
#get and set initial field, but not using molecule.update_field()
field = self._fields_list[0]
self.molecule.set_field(field)
def solve(self):
"""Calculate path of rotor dipole moment projection from
given fields.
"""
for i in tqdm.tqdm(range(1, self.n)):
self.molecule.evolve(self.dt)
self.molecule.set_field(self._fields_list[i])
def export(self):
"""Export calculated time vector, fields, and states as
np.ndarray.
Returns
-------
time: numpy.array, shape=(n,)
Time vector based on dt. In unit of picoseconds.
path: numpy.array, shape=(n,2)
Resulting path of molecule's dipole moment projection.
states: numpy.array, shape=(2m+1,n)
State amplitudes of the system at every time point.
"""
time = self.molecule.get_time_asarray()
# time = self.time
states = self.molecule.get_states_asarray()
states_list = self.molecule.history['state']
path = np.zeros((self.n, 2))
oper_x = self.molecule.dipole_x
oper_y = self.molecule.dipole_y
for i in range(self.n):
path[i, 0] = states_list[i].get_expt(oper_x).real
path[i, 1] = states_list[i].get_expt(oper_y).real
return time, path, states