potformula = latex(sympify(potdef["potential"]))
else:
potformula = latex(Matrix(sympify(potdef["potential"])))
if potdef.has_key("defaults"):
potdefaults = potdef["defaults"]
else:
potdefaults = {}
# Create the potential "the right way"
params["potential"] = potdef
P = BlockFactory().create_potential(params)
if len(potdef["variables"]) == 1:
# Plot the potential
values = P.evaluate_eigenvalues_at(x)
figure(figsize=(4, 3))
for value in values:
plot(squeeze(x), squeeze(value))
grid(True)
xlabel(r"$x$")
ylabel(r"$\lambda_i\left(x\right)$")
xlim(min(x), max(x))
savefig(potdef["name"] + ".png")
elif len(potdef["variables"]) == 2:
values = P.evaluate_eigenvalues_at(G)
f = mlab.figure()
for value in values:
def compute_energy(iom, blockid=0, eigentrafo=True, iseigen=True):
"""
:param iom: An :py:class:`IOManager: instance providing the simulation data.
:param blockid: The data block from which the values are read. Default is `0`.
:param eigentrafo: Whether to make a transformation into the eigenbasis.
:type eigentrafo: Boolean, default is ``True``.
:param iseigen: Whether the data is assumed to be in the eigenbasis.
:type iseigen: Boolean, default is ``True``
"""
parameters = iom.load_parameters()
# Number of time steps we saved
timesteps = iom.load_wavefunction_timegrid(blockid=blockid)
nrtimesteps = timesteps.shape[0]
# Construct grid from the parameters
grid = BlockFactory().create_grid(parameters)
# The potential used
Potential = BlockFactory().create_potential(parameters)
# The operators
KO = KineticOperator(grid)
KO.calculate_operator(parameters["eps"])
opT = KO
if eigentrafo is True:
opV = Potential.evaluate_at(grid)
else:
if iseigen is True:
opV = Potential.evaluate_eigenvalues_at(grid, as_matrix=True)
else:
opV = Potential.evaluate_at(grid, as_matrix=True)
# Basis transformator
if eigentrafo is True:
BT = BasisTransformationWF(Potential)
BT.set_grid(grid)
# And two empty wavefunctions
WF = WaveFunction(parameters)
WF.set_grid(grid)
WF2 = WaveFunction(parameters)
WF2.set_grid(grid)
# We want to save norms, thus add a data slot to the data file
iom.add_energy(parameters, timeslots=nrtimesteps, blockid=blockid)
nst = Potential.get_number_components()
if eigentrafo is True:
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Computing energies of timestep # " + str(step))
# Retrieve simulation data
values = iom.load_wavefunction(timestep=step, blockid=blockid)
values = [ values[j,...] for j in xrange(parameters["ncomponents"]) ]
WF.set_values(values)
# Project wavefunction values to eigenbasis
BT.transform_to_eigen(WF)
ekinlist = []
epotlist = []
# For each component of |Psi>
values = WF.get_values()
for index, item in enumerate(values):
# tmp is the Vector (0, 0, 0, \psi_i, 0, 0, ...)
tmp = [ zeros(item.shape) for z in xrange(nst) ]
tmp[index] = item
WF2.set_values(tmp)
# Project this vector to the canonical basis
BT.transform_to_canonical(WF2)
# And calculate the energies of these components
ekinlist.append(WF2.kinetic_energy(opT, summed=True))
epotlist.append(WF2.potential_energy(opV, summed=True))
iom.save_energy((ekinlist, epotlist), timestep=step, blockid=blockid)
else:
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Computing energies of timestep # " + str(step))
# Retrieve simulation data
values = iom.load_wavefunction(timestep=step, blockid=blockid)
values = [ values[j,...] for j in xrange(parameters["ncomponents"]) ]
WF.set_values(values)
# And calculate the energies of these components
ekinlist = WF.kinetic_energy(opT, summed=False)
epotlist = WF.potential_energy(opV, summed=False)
iom.save_energy((ekinlist, epotlist), timestep=step, blockid=blockid)
potformula = latex(sympify(potdef["potential"]))
else:
potformula = latex(Matrix(sympify(potdef["potential"])))
if potdef.has_key("defaults"):
potdefaults = potdef["defaults"]
else:
potdefaults = {}
# Create the potential "the right way"
params["potential"] = potdef
P = BlockFactory().create_potential(params)
if len(potdef["variables"]) == 1:
# Plot the potential
values = P.evaluate_eigenvalues_at(x)
figure(figsize=(4,3))
for value in values:
plot(squeeze(x), squeeze(value))
grid(True)
xlabel(r"$x$")
ylabel(r"$\lambda_i\left(x\right)$")
xlim(min(x), max(x))
savefig(potdef["name"] + ".png")
elif len(potdef["variables"]) == 2:
values = P.evaluate_eigenvalues_at(G)
f = mlab.figure()
for value in values:
def compute_energy(iom, blockid=0, eigentrafo=True, iseigen=True):
"""
:param iom: An :py:class:`IOManager: instance providing the simulation data.
:param blockid: The data block from which the values are read. Default is `0`.
:param eigentrafo: Whether to make a transformation into the eigenbasis.
:type eigentrafo: Boolean, default is ``True``.
:param iseigen: Whether the data is assumed to be in the eigenbasis.
:type iseigen: Boolean, default is ``True``
"""
parameters = iom.load_parameters()
# Number of time steps we saved
timesteps = iom.load_wavefunction_timegrid(blockid=blockid)
nrtimesteps = timesteps.shape[0]
# Construct grid from the parameters
grid = BlockFactory().create_grid(parameters)
# The potential used
Potential = BlockFactory().create_potential(parameters)
# The operators
KO = KineticOperator(grid)
KO.calculate_operator(parameters["eps"])
opT = KO
if eigentrafo is True:
opV = Potential.evaluate_at(grid)
else:
if iseigen is True:
opV = Potential.evaluate_eigenvalues_at(grid, as_matrix=True)
else:
opV = Potential.evaluate_at(grid, as_matrix=True)
# Basis transformator
if eigentrafo is True:
BT = BasisTransformationWF(Potential)
BT.set_grid(grid)
# And two empty wavefunctions
WF = WaveFunction(parameters)
WF.set_grid(grid)
WF2 = WaveFunction(parameters)
WF2.set_grid(grid)
# We want to save norms, thus add a data slot to the data file
iom.add_energy(parameters, timeslots=nrtimesteps, blockid=blockid)
nst = Potential.get_number_components()
if eigentrafo is True:
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Computing energies of timestep # " + str(step))
# Retrieve simulation data
values = iom.load_wavefunction(timestep=step, blockid=blockid)
values = [
values[j, ...] for j in xrange(parameters["ncomponents"])
]
WF.set_values(values)
# Project wavefunction values to eigenbasis
BT.transform_to_eigen(WF)
ekinlist = []
epotlist = []
# For each component of |Psi>
values = WF.get_values()
for index, item in enumerate(values):
# tmp is the Vector (0, 0, 0, \psi_i, 0, 0, ...)
tmp = [zeros(item.shape) for z in xrange(nst)]
tmp[index] = item
WF2.set_values(tmp)
# Project this vector to the canonical basis
BT.transform_to_canonical(WF2)
# And calculate the energies of these components
ekinlist.append(WF2.kinetic_energy(opT, summed=True))
epotlist.append(WF2.potential_energy(opV, summed=True))
iom.save_energy((ekinlist, epotlist),
timestep=step,
blockid=blockid)
else:
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Computing energies of timestep # " + str(step))
# Retrieve simulation data
values = iom.load_wavefunction(timestep=step, blockid=blockid)
values = [
values[j, ...] for j in xrange(parameters["ncomponents"])
]
WF.set_values(values)
# And calculate the energies of these components
ekinlist = WF.kinetic_energy(opT, summed=False)
epotlist = WF.potential_energy(opV, summed=False)
iom.save_energy((ekinlist, epotlist),
timestep=step,
blockid=blockid)
