def compute_norm_inhawp(iom, blockid=0, eigentrafo=True):
"""Compute the norm of a wavepacket timeseries.
This function is for inhomogeneous wavepackets.
:param iom: An :py:class:`IOManager` instance providing the simulation data.
:param blockid: The data block from which the values are read.
:type blockid: Integer, Default is ``0``
:param eigentrafo: Whether to make a transformation into the eigenbasis.
:type eigentrafo: Boolean, default is ``True``.
"""
parameters = iom.load_parameters()
# Number of time steps we saved
timesteps = iom.load_inhomogwavepacket_timegrid(blockid=blockid)
nrtimesteps = timesteps.shape[0]
# Basis transformator
if eigentrafo is True:
# The potential used
Potential = BlockFactory().create_potential(parameters)
BT = BasisTransformationHAWP(Potential)
# We want to save norms, thus add a data slot to the data file
iom.add_norm(parameters, timeslots=nrtimesteps, blockid=blockid)
# Initialize a Hagedorn wavepacket with the data
descr = iom.load_inhomogwavepacket_description(blockid=blockid)
HAWP = BlockFactory().create_wavepacket(descr)
if eigentrafo is True:
BT.set_matrix_builder(HAWP.get_quadrature())
# Basis shapes
BS_descr = iom.load_inhomogwavepacket_basisshapes()
BS = {}
for ahash, descr in BS_descr.iteritems():
BS[ahash] = BlockFactory().create_basis_shape(descr)
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Computing norms of timestep "+str(step))
# Retrieve simulation data
params = iom.load_inhomogwavepacket_parameters(timestep=step, blockid=blockid)
hashes, coeffs = iom.load_inhomogwavepacket_coefficients(timestep=step, get_hashes=True, blockid=blockid)
# Configure the wavepacket
HAWP.set_parameters(params)
HAWP.set_basis_shape([ BS[int(ha)] for ha in hashes ])
HAWP.set_coefficients(coeffs)
# Transform to the eigenbasis.
if eigentrafo is True:
BT.transform_to_eigen(HAWP)
# Measure norms in the eigenbasis
norm = HAWP.norm()
# Save the norms
iom.save_norm(norm, timestep=step, blockid=blockid)
def transform_inhawp_to_eigen(iomin, iomout, blockidin=0, blockidout=0):
"""Compute the transformation to the eigenbasis for a wavepacket.
Save the result back to a file.
:param iomin: An :py:class:`IOManager: instance providing the simulation data.
:param iomout: An :py:class:`IOManager: instance for saving the transformed data.
:param blockidin: The data block from which the values are read. Default is `0`.
:param blockidout: The data block to which the values are written. Default is `0`.
"""
parameters = iomin.load_parameters()
# Number of time steps we saved
timesteps = iomin.load_inhomogwavepacket_timegrid(blockid=blockidin)
nrtimesteps = timesteps.shape[0]
# The potential used
Potential = BlockFactory().create_potential(parameters)
# Basis transformator
BT = BasisTransformationHAWP(Potential)
# Initialize a Hagedorn wavepacket with the data
descr = iomin.load_inhomogwavepacket_description(blockid=blockidin)
HAWP = BlockFactory().create_wavepacket(descr)
iomout.add_inhomogwavepacket(descr, timeslots=nrtimesteps, blockid=blockidout)
iomout.save_inhomogwavepacket_description(HAWP.get_description(), blockid=blockidout)
BT.set_matrix_builder(HAWP.get_quadrature())
# Basis shapes
BS_descr = iomin.load_inhomogwavepacket_basisshapes()
BS = {}
for ahash, descr in BS_descr.iteritems():
BS[ahash] = BlockFactory().create_basis_shape(descr)
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Compute eigentransform at timestep # " + str(step))
# Retrieve simulation data
params = iomin.load_inhomogwavepacket_parameters(timestep=step, blockid=blockidin)
hashes, coeffs = iomin.load_inhomogwavepacket_coefficients(timestep=step, get_hashes=True, blockid=blockidin)
# Configure the wavepacket
HAWP.set_parameters(params)
HAWP.set_basis_shape([ BS[int(ha)] for ha in hashes ])
HAWP.set_coefficients(coeffs)
# Transform to the eigenbasis.
BT.transform_to_eigen(HAWP)
# Save the transformed packet
# Pi
iomout.save_inhomogwavepacket_parameters(HAWP.get_parameters(), timestep=step, blockid=blockidout)
# Basis shapes (in case they changed!)
for shape in HAWP.get_basis_shape():
iomout.save_inhomogwavepacket_basisshapes(shape, blockid=blockidout)
# Coefficients
iomout.save_inhomogwavepacket_coefficients(HAWP.get_coefficients(), HAWP.get_basis_shape(), timestep=step, blockid=blockidout)
def read_data_inhomogeneous(iom, blockid=0):
r"""
:param iom: An :py:class:`IOManager` instance providing the simulation data.
:param blockid: The data block from which the values are read.
"""
parameters = iom.load_parameters()
timegrid = iom.load_inhomogwavepacket_timegrid(blockid=blockid)
time = timegrid * parameters["dt"]
# The potential used
Potential = BlockFactory().create_potential(parameters)
# Basis transformator
BT = BasisTransformationHAWP(Potential)
# Basis shapes
BS_descr = iom.load_wavepacket_basisshapes(blockid=blockid)
BS = {}
for ahash, descr in BS_descr.iteritems():
BS[ahash] = BlockFactory().create_basis_shape(descr)
# Initialize a Hagedorn wavepacket with the data
descr = iom.load_inhomogwavepacket_description(blockid=blockid)
HAWP = BlockFactory().create_wavepacket(descr)
BT.set_matrix_builder(HAWP.get_quadrature())
# Store the resulting coefficients here
CI = [ [] for i in xrange(HAWP.get_number_components()) ]
# Iterate over all timesteps, this is an *expensive* transformation
for i, step in enumerate(timegrid):
print(" Computing eigentransformation at timestep "+str(step))
# Retrieve simulation data
params = iom.load_inhomogwavepacket_parameters(timestep=step, blockid=blockid)
hashes, coeffs = iom.load_inhomogwavepacket_coefficients(timestep=step, get_hashes=True, blockid=blockid)
# Configure the wavepacket
HAWP.set_parameters(params)
HAWP.set_basis_shapes([ BS[int(ha)] for ha in hashes ])
HAWP.set_coefficients(coeffs)
# Transform to the eigenbasis.
BT.transform_to_eigen(HAWP)
for index, item in enumerate(HAWP.get_coefficients()):
CI[index].append(item)
CI = [ transpose(hstack(item)) for item in CI ]
return time, CI
def read_data_inhomogeneous(iom, blockid=0):
r"""
:param iom: An :py:class:`IOManager` instance providing the simulation data.
:param blockid: The data block from which the values are read.
"""
parameters = iom.load_parameters()
timegrid = iom.load_inhomogwavepacket_timegrid(blockid=blockid)
dt = parameters["dt"] if "dt" in parameters else 1.0
time = timegrid * dt
# The potential used
Potential = BlockFactory().create_potential(parameters)
# Basis transformator
BT = BasisTransformationHAWP(Potential)
# Initialize a Hagedorn wavepacket with the data
descr = iom.load_inhomogwavepacket_description(blockid=blockid)
HAWP = BlockFactory().create_wavepacket(descr)
BT.set_matrix_builder(HAWP.get_quadrature())
# Store the resulting coefficients here
CI = [[] for i in range(HAWP.get_number_components())]
# Iterate over all timesteps, this is an *expensive* transformation
for i, step in enumerate(timegrid):
print(" Computing eigentransformation at timestep {}".format(step))
# Retrieve simulation data
HAWP = iom.load_inhomogwavepacket(timestep=step, blockid=blockid)
# Transform to the eigenbasis.
BT.transform_to_eigen(HAWP)
for index, item in enumerate(HAWP.get_coefficients()):
CI[index].append(item)
CI = [transpose(hstack(item)) for item in CI]
return time, CI
def read_data_homogeneous(iom, blockid=0):
r"""
:param iom: An :py:class:`IOManager` instance providing the simulation data.
:param blockid: The data block from which the values are read.
"""
parameters = iom.load_parameters()
timegrid = iom.load_wavepacket_timegrid(blockid=blockid)
time = timegrid * parameters["dt"]
# The potential used
Potential = BlockFactory().create_potential(parameters)
# Basis transformator
BT = BasisTransformationHAWP(Potential)
# Basis shapes
BS_descr = iom.load_wavepacket_basisshapes(blockid=blockid)
BS = {}
for ahash, descr in BS_descr.iteritems():
BS[ahash] = BlockFactory().create_basis_shape(descr)
# Initialize a Hagedorn wavepacket with the data
descr = iom.load_wavepacket_description(blockid=blockid)
HAWP = BlockFactory().create_wavepacket(descr)
BT.set_matrix_builder(HAWP.get_quadrature())
# Store the resulting coefficients here
CI = [[] for i in xrange(HAWP.get_number_components())]
# Iterate over all timesteps, this is an *expensive* transformation
for i, step in enumerate(timegrid):
print(" Computing eigentransformation at timestep " + str(step))
# Retrieve simulation data
params = iom.load_wavepacket_parameters(timestep=step, blockid=blockid)
hashes, coeffs = iom.load_wavepacket_coefficients(timestep=step,
get_hashes=True,
blockid=blockid)
# Configure the wavepacket
HAWP.set_parameters(params)
HAWP.set_basis_shape([BS[int(ha)] for ha in hashes])
HAWP.set_coefficients(coeffs)
# Transform to the eigenbasis.
BT.transform_to_eigen(HAWP)
for index, item in enumerate(HAWP.get_coefficients()):
CI[index].append(item)
CI = [transpose(hstack(item)) for item in CI]
return time, CI
def read_data_inhomogeneous(iom, blockid=0):
r"""
:param iom: An :py:class:`IOManager` instance providing the simulation data.
:param blockid: The data block from which the values are read.
"""
parameters = iom.load_parameters()
timegrid = iom.load_inhomogwavepacket_timegrid(blockid=blockid)
dt = parameters["dt"] if "dt" in parameters else 1.0
time = timegrid * dt
# The potential used
Potential = BlockFactory().create_potential(parameters)
# Basis transformator
BT = BasisTransformationHAWP(Potential)
# Initialize a Hagedorn wavepacket with the data
descr = iom.load_inhomogwavepacket_description(blockid=blockid)
HAWP = BlockFactory().create_wavepacket(descr)
BT.set_matrix_builder(HAWP.get_quadrature())
# Store the resulting coefficients here
CI = [[] for i in range(HAWP.get_number_components())]
# Iterate over all timesteps, this is an *expensive* transformation
for i, step in enumerate(timegrid):
print(" Computing eigentransformation at timestep {}".format(step))
# Retrieve simulation data
HAWP = iom.load_inhomogwavepacket(timestep=step, blockid=blockid)
# Transform to the eigenbasis.
BT.transform_to_eigen(HAWP)
for index, item in enumerate(HAWP.get_coefficients()):
CI[index].append(item)
CI = [transpose(hstack(item)) for item in CI]
return time, CI
def compute_energy_inhawp(iom, blockid=0, eigentrafo=True, iseigen=True):
"""Compute the energies of a wavepacket timeseries.
This function is for inhomogeneous wavepackets.
:param iom: An :py:class:`IOManager` instance providing the simulation data.
:param blockid: The data block from which the values are read.
:type blockid: Integer, 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()
BF = BlockFactory()
# Number of time steps we saved
timesteps = iom.load_inhomogwavepacket_timegrid(blockid=blockid)
nrtimesteps = timesteps.shape[0]
# The potential used
Potential = BF.create_potential(parameters)
# Basis transformator
if eigentrafo is True:
BT = BasisTransformationHAWP(Potential)
# We want to save energies, thus add a data slot to the data file
iom.add_energy(parameters, timeslots=nrtimesteps, blockid=blockid)
# Initialize a Hagedorn wavepacket with the data
descr = iom.load_inhomogwavepacket_description(blockid=blockid)
HAWP = BF.create_wavepacket(descr)
# Inner product
if HAWP.get_innerproduct() is None:
IP = BF.create_inner_product(parameters["innerproduct"])
HAWP.set_innerproduct(IP)
if eigentrafo is True:
BT.set_matrix_builder(HAWP.get_innerproduct())
# Basis shapes
BS_descr = iom.load_inhomogwavepacket_basisshapes(blockid=blockid)
BS = {}
for ahash, descr in BS_descr.items():
BS[ahash] = BF.create_basis_shape(descr)
O = ObservablesHAWP()
KEY = ("q", "p", "Q", "P", "S", "adQ")
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Computing energies of timestep %d" % step)
# Retrieve simulation data
params = iom.load_inhomogwavepacket_parameters(timestep=step,
blockid=blockid,
key=KEY)
hashes, coeffs = iom.load_inhomogwavepacket_coefficients(
timestep=step, get_hashes=True, blockid=blockid)
# Configure the wavepacket
HAWP.set_parameters(params, key=KEY)
HAWP.set_basis_shapes([BS[int(ha)] for ha in hashes])
HAWP.set_coefficients(coeffs)
# Transform to the eigenbasis.
if eigentrafo is True:
BT.transform_to_eigen(HAWP)
# Compute the energies
O.set_innerproduct(HAWP.get_innerproduct())
O.set_gradient(HAWP.get_gradient_operator())
ekin = O.kinetic_energy(HAWP)
if iseigen is True:
epot = O.potential_energy(HAWP, Potential.evaluate_eigenvalues_at)
else:
epot = O.potential_energy(HAWP, Potential.evaluate_at)
iom.save_energy((ekin, epot), timestep=step, blockid=blockid)
def compute_autocorrelation_inhawp(iom, obsconfig, blockid=0, eigentrafo=True):
"""Compute the autocorrelation of a wavepacket timeseries.
This function is for inhomogeneous wavepackets.
:param iom: An :py:class:`IOManager` instance providing the simulation data.
:param obsconfig: Configuration parameters describing f.e. the inner product to use.
:type obsconfig: A :py:class:`ParameterProvider` instance.
:param blockid: The data block from which the values are read.
:type blockid: Integer, Default is ``0``
:param eigentrafo: Whether to make a transformation into the eigenbasis.
:type eigentrafo: Boolean, default is ``True``.
"""
parameters = iom.load_parameters()
BF = BlockFactory()
# Number of time steps we saved
timesteps = iom.load_inhomogwavepacket_timegrid(blockid=blockid)
nrtimesteps = timesteps.shape[0]
# Basis transformator
if eigentrafo is True:
# The potential used
Potential = BF.create_potential(parameters)
BT = BasisTransformationHAWP(Potential)
# We want to save autocorrelations, thus add a data slot to the data file
iom.add_autocorrelation(parameters, timeslots=nrtimesteps, blockid=blockid)
# Initialize a Hagedorn wavepacket with the data
descr = iom.load_inhomogwavepacket_description(blockid=blockid)
HAWPo = BF.create_wavepacket(descr)
HAWPt = BF.create_wavepacket(descr)
if eigentrafo is True:
BT.set_matrix_builder(HAWPo.get_innerproduct())
# Basis shapes
BS_descr = iom.load_inhomogwavepacket_basisshapes(blockid=blockid)
BS = {}
for ahash, descr in BS_descr.items():
BS[ahash] = BF.create_basis_shape(descr)
# Comfigure the original wavepacket
# Retrieve simulation data
params = iom.load_inhomogwavepacket_parameters(timestep=0, blockid=blockid)
hashes, coeffs = iom.load_inhomogwavepacket_coefficients(timestep=0, get_hashes=True, blockid=blockid)
# Configure the wavepacket
HAWPo.set_parameters(params)
HAWPo.set_basis_shapes([BS[int(ha)] for ha in hashes])
HAWPo.set_coefficients(coeffs)
# Set up the innerproduct for solving the integrals <phi_0 | phi_t>
IP = BF.create_inner_product(obsconfig["innerproduct"])
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Computing autocorrelations of timestep %d" % step)
# Retrieve simulation data
params = iom.load_inhomogwavepacket_parameters(timestep=step, blockid=blockid)
hashes, coeffs = iom.load_inhomogwavepacket_coefficients(timestep=step, get_hashes=True, blockid=blockid)
# Configure the wavepacket
HAWPt.set_parameters(params)
HAWPt.set_basis_shapes([BS[int(ha)] for ha in hashes])
HAWPt.set_coefficients(coeffs)
# Transform to the eigenbasis.
if eigentrafo is True:
BT.transform_to_eigen(HAWPt)
# Measure autocorrelations in the eigenbasis
acs = IP.quadrature(HAWPo, HAWPt, diagonal=True)
# Save the autocorrelations
iom.save_autocorrelation(acs, timestep=step, blockid=blockid)
def compute_autocorrelation_hawp(iom, obsconfig, blockid=0, eigentrafo=True):
"""Compute the autocorrelation of a wavepacket timeseries.
:param iom: An :py:class:`IOManager` instance providing the simulation data.
:param obsconfig: Configuration parameters describing f.e. the inner product to use.
:type obsconfig: A :py:class:`ParameterProvider` instance.
:param blockid: The data block from which the values are read.
:type blockid: Integer, Default is ``0``
:param eigentrafo: Whether to make a transformation into the eigenbasis.
:type eigentrafo: Boolean, default is ``True``.
"""
parameters = iom.load_parameters()
BF = BlockFactory()
# Number of time steps we saved
timesteps = iom.load_wavepacket_timegrid(blockid=blockid)
nrtimesteps = timesteps.shape[0]
# Basis transformator
if eigentrafo is True:
# The potential used
Potential = BF.create_potential(parameters)
BT = BasisTransformationHAWP(Potential)
# We want to save norms, thus add a data slot to the data file
iom.add_autocorrelation(parameters, timeslots=nrtimesteps, blockid=blockid)
# Initialize a Hagedorn wavepacket with the data
descr = iom.load_wavepacket_description(blockid=blockid)
HAWPo = BF.create_wavepacket(descr)
HAWPt = BF.create_wavepacket(descr)
if eigentrafo is True:
BT.set_matrix_builder(HAWPo.get_innerproduct())
# Basis shapes
BS_descr = iom.load_wavepacket_basisshapes(blockid=blockid)
BS = {}
for ahash, descr in BS_descr.items():
BS[ahash] = BF.create_basis_shape(descr)
# Comfigure the original wavepacket
KEY = ("q", "p", "Q", "P", "S", "adQ")
# Retrieve simulation data
params = iom.load_wavepacket_parameters(timestep=0,
blockid=blockid,
key=KEY)
hashes, coeffs = iom.load_wavepacket_coefficients(timestep=0,
get_hashes=True,
blockid=blockid)
# Configure the wavepacket
HAWPo.set_parameters(params, key=KEY)
HAWPo.set_basis_shapes([BS[int(ha)] for ha in hashes])
HAWPo.set_coefficients(coeffs)
# Set up the innerproduct for solving the integrals <phi_0 | phi_t>
IP = BF.create_inner_product(obsconfig["innerproduct"])
# Transform to the eigenbasis.
if eigentrafo is True:
BT.transform_to_eigen(HAWPo)
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Computing autocorrelation of timestep %d" % step)
# Retrieve simulation data
paramst = iom.load_wavepacket_parameters(timestep=step,
blockid=blockid,
key=KEY)
hashes, coeffs = iom.load_wavepacket_coefficients(timestep=step,
get_hashes=True,
blockid=blockid)
# Configure the wavepacket
HAWPt.set_parameters(paramst, key=KEY)
HAWPt.set_basis_shapes([BS[int(ha)] for ha in hashes])
HAWPt.set_coefficients(coeffs)
# Transform to the eigenbasis.
if eigentrafo is True:
BT.transform_to_eigen(HAWPt)
# Measure autocorrelations in the eigenbasis
acs = IP.quadrature(HAWPo, HAWPt, diagonal=True)
# Save the autocorrelations
iom.save_autocorrelation(acs, timestep=step, blockid=blockid)
def plot_frames(PP,
iom,
blockid=0,
eigentransform=False,
timerange=None,
view=None,
plotphase=True,
plotcomponents=False,
plotabssqr=False,
load=False,
gridblockid=None,
imgsize=(12, 9),
path='.'):
"""Plot the wavepacket for a series of timesteps.
:param iom: An :py:class:`IOManager` instance providing the simulation data.
"""
parameters = iom.load_parameters()
BF = BlockFactory()
if not parameters["dimension"] == 1:
print("No one-dimensional wavepacket, silent return!")
return
if PP is None:
PP = parameters
if load is True:
if gridblockid is None:
gridblockid = blockid
print("Loading grid data from datablock '{}'".format(gridblockid))
G = iom.load_grid(blockid=gridblockid)
grid = real(G.reshape(-1))
else:
print("Creating new grid")
G = BlockFactory().create_grid(PP)
grid = real(G.get_nodes(flat=True).reshape(-1))
if eigentransform:
V = BF.create_potential(parameters)
BT = BasisTransformationHAWP(V)
timegrid = iom.load_wavepacket_timegrid(blockid=blockid)
if timerange is not None:
if len(timerange) == 1:
I = (timegrid == timerange)
else:
I = ((timegrid >= timerange[0]) & (timegrid <= timerange[1]))
if any(I):
timegrid = timegrid[I]
else:
raise ValueError("No valid timestep remains!")
# View
if view is not None:
if view[0] is None:
view[0] = grid.min()
if view[1] is None:
view[1] = grid.max()
for step in timegrid:
print(" Plotting frame of timestep # {}".format(step))
HAWP = iom.load_wavepacket(step, blockid=blockid)
# Transform the values to the eigenbasis
if eigentransform:
BT.transform_to_eigen(HAWP)
values = HAWP.evaluate_at(G.get_nodes(), prefactor=True, component=0)
# Plot
fig = figure(figsize=imgsize)
for index, component in enumerate(values):
ax = fig.add_subplot(parameters["ncomponents"], 1, index + 1)
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
if plotcomponents is True:
ax.plot(grid, real(component))
ax.plot(grid, imag(component))
ax.set_ylabel(r"$\Re \varphi_{%d}, \Im \varphi_{%d}$" %
(index, index))
if plotabssqr is True:
ax.plot(grid, real(component * conj(component)))
ax.set_ylabel(
r"$\langle \varphi_{%d} | \varphi_{%d} \rangle$" %
(index, index))
if plotphase is True:
plotcf(grid, angle(component),
real(component * conj(component)))
ax.set_ylabel(
r"$\langle \varphi_{%d} | \varphi_{%d} \rangle$" %
(index, index))
ax.set_xlabel(r"$x$")
# Set the aspect window
ax.set_xlim(view[:2])
ax.set_ylim(view[2:])
if "dt" in parameters:
fig.suptitle(r"$\Psi$ at time $%f$" % (step * parameters["dt"]))
else:
fig.suptitle(r"$\Psi$")
fig.savefig(
os.path.join(
path,
"wavepacket_block_%s_timestep_%07d.png" % (blockid, step)))
close(fig)
def plot_frames(PP, iom, blockid=0, load=False, eigentransform=False, timerange=None, view=None, path='.'):
"""Plot the wavepacket for a series of timesteps.
:param iom: An :py:class:`IOManager` instance providing the simulation data.
"""
parameters = iom.load_parameters()
BF = BlockFactory()
if not parameters["dimension"] == 2:
print("No two-dimensional wavepacket, silent return!")
return
if PP is None:
PP = parameters
if load is True:
# TODO: Implement reshaping
raise NotImplementedError("Loading of 2D grids is not implemented")
else:
G = BF.create_grid(PP)
if eigentransform:
V = BF.create_potential(parameters)
BT = BasisTransformationHAWP(V)
timegrid = iom.load_wavepacket_timegrid(blockid=blockid)
if timerange is not None:
if len(timerange) == 1:
I = (timegrid == timerange)
else:
I = ((timegrid >= timerange[0]) & (timegrid <= timerange[1]))
if any(I):
timegrid = timegrid[I]
else:
raise ValueError("No valid timestep remains!")
u, v = G.get_axes()
u = real(u.reshape(-1))
v = real(v.reshape(-1))
# View
if view is not None:
if view[0] is None:
view[0] = u.min()
if view[1] is None:
view[1] = u.max()
if view[2] is None:
view[2] = v.min()
if view[3] is None:
view[3] = v.max()
for step in timegrid:
print(" Plotting frame of timestep # {}".format(step))
HAWP = iom.load_wavepacket(step, blockid=blockid)
N = HAWP.get_number_components()
# Transform the values to the eigenbasis
if eigentransform:
BT.transform_to_eigen(HAWP)
psi = HAWP.evaluate_at(G.get_nodes(), prefactor=True, component=0)
# Plot
fig = figure()
for level in range(N):
z = psi[level]
z = z.reshape(G.get_number_nodes())
fig.add_subplot(N, 1, level + 1)
plotcf2d(u, v, z, darken=0.3, limits=view)
fig.savefig(os.path.join(path, "wavepacket_block_%s_level_%d_timestep_%07d.png" % (blockid, level, step)))
close(fig)
def compute_energy_inhawp(iom, blockid=0, eigentrafo=True, iseigen=True):
"""Compute the energies of a wavepacket timeseries.
This function is for inhomogeneous wavepackets.
:param iom: An :py:class:`IOManager` instance providing the simulation data.
:param blockid: The data block from which the values are read.
:type blockid: Integer, 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_inhomogwavepacket_timegrid(blockid=blockid)
nrtimesteps = timesteps.shape[0]
# The potential used
Potential = BlockFactory().create_potential(parameters)
# Basis transformator
if eigentrafo is True:
BT = BasisTransformationHAWP(Potential)
# We want to save energies, thus add a data slot to the data file
iom.add_energy(parameters, timeslots=nrtimesteps, blockid=blockid)
# Initialize a Hagedorn wavepacket with the data
descr = iom.load_inhomogwavepacket_description(blockid=blockid)
HAWP = BlockFactory().create_wavepacket(descr)
if eigentrafo is True:
BT.set_matrix_builder(HAWP.get_innerproduct())
# Basis shapes
BS_descr = iom.load_inhomogwavepacket_basisshapes(blockid=blockid)
BS = {}
for ahash, descr in BS_descr.iteritems():
BS[ahash] = BlockFactory().create_basis_shape(descr)
O = ObservablesHAWP()
KEY = ("q","p","Q","P","S","adQ")
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Computing energies of timestep "+str(step))
# Retrieve simulation data
params = iom.load_inhomogwavepacket_parameters(timestep=step, blockid=blockid, key=KEY)
hashes, coeffs = iom.load_inhomogwavepacket_coefficients(timestep=step, get_hashes=True, blockid=blockid)
# Configure the wavepacket
HAWP.set_parameters(params, key=KEY)
HAWP.set_basis_shapes([ BS[int(ha)] for ha in hashes ])
HAWP.set_coefficients(coeffs)
# Transform to the eigenbasis.
if eigentrafo is True:
BT.transform_to_eigen(HAWP)
# Compute the energies
O.set_innerproduct(HAWP.get_innerproduct())
ekin = O.kinetic_energy(HAWP)
if iseigen is True:
epot = O.potential_energy(HAWP, Potential.evaluate_eigenvalues_at)
else:
epot = O.potential_energy(HAWP, Potential.evaluate_at)
iom.save_energy((ekin, epot), timestep=step, blockid=blockid)
def compute_norm_inhawp(iom, blockid=0, eigentrafo=True):
"""Compute the norm of a wavepacket timeseries.
This function is for inhomogeneous wavepackets.
:param iom: An :py:class:`IOManager` instance providing the simulation data.
:param blockid: The data block from which the values are read.
:type blockid: Integer, Default is ``0``
:param eigentrafo: Whether to make a transformation into the eigenbasis.
:type eigentrafo: Boolean, default is ``True``.
"""
parameters = iom.load_parameters()
# Number of time steps we saved
timesteps = iom.load_inhomogwavepacket_timegrid(blockid=blockid)
nrtimesteps = timesteps.shape[0]
# Basis transformator
if eigentrafo is True:
# The potential used
Potential = BlockFactory().create_potential(parameters)
BT = BasisTransformationHAWP(Potential)
# We want to save norms, thus add a data slot to the data file
iom.add_norm(parameters, timeslots=nrtimesteps, blockid=blockid)
# Initialize a Hagedorn wavepacket with the data
descr = iom.load_inhomogwavepacket_description(blockid=blockid)
HAWP = BlockFactory().create_wavepacket(descr)
if eigentrafo is True:
BT.set_matrix_builder(HAWP.get_quadrature())
# Basis shapes
BS_descr = iom.load_inhomogwavepacket_basisshapes()
BS = {}
for ahash, descr in BS_descr.iteritems():
BS[ahash] = BlockFactory().create_basis_shape(descr)
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Computing norms of timestep " + str(step))
# Retrieve simulation data
params = iom.load_inhomogwavepacket_parameters(timestep=step,
blockid=blockid)
hashes, coeffs = iom.load_inhomogwavepacket_coefficients(
timestep=step, get_hashes=True, blockid=blockid)
# Configure the wavepacket
HAWP.set_parameters(params)
HAWP.set_basis_shape([BS[int(ha)] for ha in hashes])
HAWP.set_coefficients(coeffs)
# Transform to the eigenbasis.
if eigentrafo is True:
BT.transform_to_eigen(HAWP)
# Measure norms in the eigenbasis
norm = HAWP.norm()
# Save the norms
iom.save_norm(norm, timestep=step, blockid=blockid)
def plot_frames(PP, iom, blockid=0, eigentransform=False, timerange=None, view=None,
plotphase=True, plotcomponents=False, plotabssqr=False,
load=False, gridblockid=None, imgsize=(12, 9), path='.'):
"""Plot the wavepacket for a series of timesteps.
:param iom: An :py:class:`IOManager` instance providing the simulation data.
"""
parameters = iom.load_parameters()
BF = BlockFactory()
if not parameters["dimension"] == 1:
print("No one-dimensional wavepacket, silent return!")
return
if PP is None:
PP = parameters
if load is True:
if gridblockid is None:
gridblockid = blockid
print("Loading grid data from datablock '{}'".format(gridblockid))
G = iom.load_grid(blockid=gridblockid)
grid = real(G.reshape(-1))
else:
print("Creating new grid")
G = BlockFactory().create_grid(PP)
grid = real(G.get_nodes(flat=True).reshape(-1))
if eigentransform:
V = BF.create_potential(parameters)
BT = BasisTransformationHAWP(V)
timegrid = iom.load_wavepacket_timegrid(blockid=blockid)
if timerange is not None:
if len(timerange) == 1:
I = (timegrid == timerange)
else:
I = ((timegrid >= timerange[0]) & (timegrid <= timerange[1]))
if any(I):
timegrid = timegrid[I]
else:
raise ValueError("No valid timestep remains!")
# View
if view is not None:
if view[0] is None:
view[0] = grid.min()
if view[1] is None:
view[1] = grid.max()
for step in timegrid:
print(" Plotting frame of timestep # {}".format(step))
HAWP = iom.load_wavepacket(step, blockid=blockid)
# Transform the values to the eigenbasis
if eigentransform:
BT.transform_to_eigen(HAWP)
values = HAWP.evaluate_at(G.get_nodes(), prefactor=True, component=0)
# Plot
fig = figure(figsize=imgsize)
for index, component in enumerate(values):
ax = fig.add_subplot(parameters["ncomponents"], 1, index + 1)
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
if plotcomponents is True:
ax.plot(grid, real(component))
ax.plot(grid, imag(component))
ax.set_ylabel(r"$\Re \varphi_{%d}, \Im \varphi_{%d}$" % (index, index))
if plotabssqr is True:
ax.plot(grid, real(component * conj(component)))
ax.set_ylabel(r"$\langle \varphi_{%d} | \varphi_{%d} \rangle$" % (index, index))
if plotphase is True:
plotcf(grid, angle(component), real(component * conj(component)))
ax.set_ylabel(r"$\langle \varphi_{%d} | \varphi_{%d} \rangle$" % (index, index))
ax.set_xlabel(r"$x$")
# Set the aspect window
ax.set_xlim(view[:2])
ax.set_ylim(view[2:])
if "dt" in parameters:
fig.suptitle(r"$\Psi$ at time $%f$" % (step * parameters["dt"]))
else:
fig.suptitle(r"$\Psi$")
fig.savefig(os.path.join(path, "wavepacket_block_%s_timestep_%07d.png" % (blockid, step)))
close(fig)
def plot_frames(PP,
iom,
blockid=0,
load=False,
eigentransform=False,
timerange=None,
view=None,
path='.'):
"""Plot the wavepacket for a series of timesteps.
:param iom: An :py:class:`IOManager` instance providing the simulation data.
"""
parameters = iom.load_parameters()
BF = BlockFactory()
if not parameters["dimension"] == 2:
print("No two-dimensional wavepacket, silent return!")
return
if PP is None:
PP = parameters
if load is True:
# TODO: Implement reshaping
raise NotImplementedError("Loading of 2D grids is not implemented")
else:
G = BF.create_grid(PP)
if eigentransform:
V = BF.create_potential(parameters)
BT = BasisTransformationHAWP(V)
timegrid = iom.load_wavepacket_timegrid(blockid=blockid)
if timerange is not None:
if len(timerange) == 1:
I = (timegrid == timerange)
else:
I = ((timegrid >= timerange[0]) & (timegrid <= timerange[1]))
if any(I):
timegrid = timegrid[I]
else:
raise ValueError("No valid timestep remains!")
u, v = G.get_axes()
u = real(u.reshape(-1))
v = real(v.reshape(-1))
# View
if view is not None:
if view[0] is None:
view[0] = u.min()
if view[1] is None:
view[1] = u.max()
if view[2] is None:
view[2] = v.min()
if view[3] is None:
view[3] = v.max()
for step in timegrid:
print(" Plotting frame of timestep # {}".format(step))
HAWP = iom.load_wavepacket(step, blockid=blockid)
N = HAWP.get_number_components()
# Transform the values to the eigenbasis
if eigentransform:
BT.transform_to_eigen(HAWP)
psi = HAWP.evaluate_at(G.get_nodes(), prefactor=True, component=0)
# Plot
fig = figure()
for level in range(N):
z = psi[level]
z = z.reshape(G.get_number_nodes())
fig.add_subplot(N, 1, level + 1)
plotcf2d(u, v, z, darken=0.3, limits=view)
fig.savefig(
os.path.join(
path, "wavepacket_block_%s_level_%d_timestep_%07d.png" %
(blockid, level, step)))
close(fig)
def transform_inhawp_to_eigen(iomin, iomout, blockidin=0, blockidout=0):
"""Compute the transformation to the eigenbasis for a wavepacket.
Save the result back to a file.
:param iomin: An :py:class:`IOManager: instance providing the simulation data.
:param iomout: An :py:class:`IOManager: instance for saving the transformed data.
:param blockidin: The data block from which the values are read. Default is `0`.
:param blockidout: The data block to which the values are written. Default is `0`.
"""
parameters = iomin.load_parameters()
# Number of time steps we saved
timesteps = iomin.load_inhomogwavepacket_timegrid(blockid=blockidin)
nrtimesteps = timesteps.shape[0]
# The potential used
Potential = BlockFactory().create_potential(parameters)
# Basis transformator
BT = BasisTransformationHAWP(Potential)
# Initialize a Hagedorn wavepacket with the data
descr = iomin.load_inhomogwavepacket_description(blockid=blockidin)
HAWP = BlockFactory().create_wavepacket(descr)
iomout.add_inhomogwavepacket(descr,
timeslots=nrtimesteps,
blockid=blockidout)
iomout.save_inhomogwavepacket_description(HAWP.get_description(),
blockid=blockidout)
BT.set_matrix_builder(HAWP.get_quadrature())
# Basis shapes
BS_descr = iomin.load_inhomogwavepacket_basisshapes()
BS = {}
for ahash, descr in BS_descr.iteritems():
BS[ahash] = BlockFactory().create_basis_shape(descr)
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Compute eigentransform at timestep # " + str(step))
# Retrieve simulation data
params = iomin.load_inhomogwavepacket_parameters(timestep=step,
blockid=blockidin)
hashes, coeffs = iomin.load_inhomogwavepacket_coefficients(
timestep=step, get_hashes=True, blockid=blockidin)
# Configure the wavepacket
HAWP.set_parameters(params)
HAWP.set_basis_shape([BS[int(ha)] for ha in hashes])
HAWP.set_coefficients(coeffs)
# Transform to the eigenbasis.
BT.transform_to_eigen(HAWP)
# Save the transformed packet
# Pi
iomout.save_inhomogwavepacket_parameters(HAWP.get_parameters(),
timestep=step,
blockid=blockidout)
# Basis shapes (in case they changed!)
for shape in HAWP.get_basis_shape():
iomout.save_inhomogwavepacket_basisshapes(shape,
blockid=blockidout)
# Coefficients
iomout.save_inhomogwavepacket_coefficients(HAWP.get_coefficients(),
HAWP.get_basis_shape(),
timestep=step,
blockid=blockidout)
def compute_evaluate_wavepackets(pp, iom, blockid=0, eigentrafo=True):
"""Evaluate a homogeneous Hagedorn wavepacket on a given grid for each timestep.
:param pp: An :py:class:`ParameterProvider` instance providing the grid data.
:param iom: An :py:class:`IOManager` instance providing the simulation data.
:param blockid: The data block from which the values are read.
:param eigentrafo: Whether or not do an eigentransformation before evaluation is done.
"""
parameters = iom.load_parameters()
if pp is None:
pp = parameters
# Number of time steps we saved
timesteps = iom.load_wavepacket_timegrid(blockid=blockid)
nrtimesteps = timesteps.shape[0]
# Prepare the potential for basis transformations
Potential = BlockFactory().create_potential(parameters)
grid = BlockFactory().create_grid(pp)
# We want to save wavefunctions, thus add a data slot to the data file
d = {"ncomponents": parameters["ncomponents"],
"number_nodes": pp["number_nodes"],
"dimension": parameters["dimension"]}
iom.add_grid(d, blockid=blockid)
iom.add_wavefunction(d, timeslots=nrtimesteps, flat=True, blockid=blockid)
iom.save_grid(grid.get_nodes(), blockid=blockid)
# Initialize a Hagedorn wavepacket with the data
descr = iom.load_wavepacket_description(blockid=blockid)
HAWP = BlockFactory().create_wavepacket(descr)
# Basis transformator
if eigentrafo is True:
BT = BasisTransformationHAWP(Potential)
BT.set_matrix_builder(HAWP.get_innerproduct())
# Basis shapes
BS_descr = iom.load_wavepacket_basisshapes(blockid=blockid)
BS = {}
for ahash, descr in BS_descr.items():
BS[ahash] = BlockFactory().create_basis_shape(descr)
WF = WaveFunction(parameters)
WF.set_grid(grid)
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Evaluating homogeneous wavepacket at timestep %d" % step)
# Retrieve simulation data
params = iom.load_wavepacket_parameters(timestep=step, blockid=blockid, key=("q", "p", "Q", "P", "S", "adQ"))
hashes, coeffs = iom.load_wavepacket_coefficients(timestep=step, get_hashes=True, blockid=blockid)
# Configure the wavepacket
HAWP.set_parameters(params, key=("q", "p", "Q", "P", "S", "adQ"))
HAWP.set_basis_shapes([BS[int(ha)] for ha in hashes])
HAWP.set_coefficients(coeffs)
# Transform to the eigenbasis.
if eigentrafo is True:
BT.transform_to_eigen(HAWP)
# Evaluate the wavepacket
values = HAWP.evaluate_at(grid, prefactor=True)
WF.set_values(values)
# Save the wave function
iom.save_wavefunction(WF.get_values(), timestep=step, blockid=blockid)