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.
"""
BF = BlockFactory()
parameters = iom.load_parameters()
timegrid = iom.load_inhomogwavepacket_timegrid(blockid=blockid)
# Basis shapes
bsdescr = iom.load_inhomogwavepacket_basisshapes(blockid=blockid)
BS = {}
for ahash, descr in bsdescr.iteritems():
BS[ahash] = BF.create_basis_shape(descr)
# Plot the coefficients for all timesteps
for j, step in enumerate(timegrid):
hashes, coeffs = iom.load_inhomogwavepacket_coefficients(timestep=step, blockid=blockid, get_hashes=True)
k = []
for i in xrange(parameters["ncomponents"]):
bs = BS[int(hashes[i])]
ki = array([bs[node] for node in bs.get_node_iterator()])
k.append(ki)
plot_coefficients(k, coeffs, step, parameters["dt"], index=blockid)
def plot_frames(
iom,
blockid=0
): #, view=None, plotphase=True, plotcomponents=False, plotabssqr=False, imgsize=(12,9)):
parameters = iom.load_parameters()
if not parameters["dimension"] == 2:
print("No wavefunction of two space dimensions, silent return!")
return
G = BlockFactory().create_grid(parameters)
V = BlockFactory().create_potential(parameters)
print(G.get_extensions())
WF = WaveFunction(parameters)
WF.set_grid(G)
BT = BasisTransformationWF(V)
BT.set_grid(G)
timegrid = iom.load_wavefunction_timegrid(blockid=blockid)
u, v = G.get_nodes(split=True, flat=False)
u = real(u)
v = real(v)
N = WF.get_number_components()
for step in timegrid:
print(" Plotting frame of timestep # " + str(step))
wave = iom.load_wavefunction(blockid=blockid, timestep=step)
values = [wave[j, ...] for j in xrange(parameters["ncomponents"])]
WF.set_values(values)
# Transform the values to the eigenbasis
# TODO: improve this:
if parameters["algorithm"] == "fourier":
BT.transform_to_eigen(WF)
else:
pass
Psi = WF.get_values()
fig = figure()
for level in xrange(N):
z = Psi[level]
subplot(N, 1, level + 1)
plotcm(z, darken=0.3)
savefig("wavefunction_level_" + str(level) + "_timestep_" +
(5 - len(str(step))) * "0" + str(step) + ".png")
close(fig)
print(" Plotting frames finished")
def plot_frames(iom, blockid=0):
parameters = iom.load_parameters()
if not parameters["dimension"] == 2:
print("No wavefunction of two space dimensions, silent return!")
return
G = BlockFactory().create_grid(parameters)
V = BlockFactory().create_potential(parameters)
WF = WaveFunction(parameters)
WF.set_grid(G)
BT = BasisTransformationWF(V)
BT.set_grid(G)
timegrid = iom.load_wavefunction_timegrid(blockid=blockid)
u, v = G.get_nodes(split=True, flat=False)
u = real(u)
v = real(v)
N = WF.get_number_components()
for step in timegrid:
print(" Plotting frame of timestep # " + str(step))
wave = iom.load_wavefunction(blockid=blockid, timestep=step)
values = [ wave[j,...] for j in xrange(parameters["ncomponents"]) ]
WF.set_values(values)
# Transform the values to the eigenbasis
# TODO: improve this:
if parameters["algorithm"] == "fourier":
BT.transform_to_eigen(WF)
else:
pass
Psi = WF.get_values()
for level in xrange(N):
z = Psi[level]
# Plot the probability densities projected to the eigenbasis
fig = mlab.figure(size=(800,700))
surfcf(u, v, angle(z), abs(z))
#mlab.contour_surf(u, v, abs(z))
#mlab.outline()
#mlab.axes()
mlab.savefig("wavefunction_level_"+str(level)+"_timestep_"+(5-len(str(step)))*"0"+str(step)+".png")
mlab.close(fig)
print(" Plotting frames finished")
def plot_frames(iom, blockid=0):#, view=None, plotphase=True, plotcomponents=False, plotabssqr=False, imgsize=(12,9)):
parameters = iom.load_parameters()
if not parameters["dimension"] == 2:
print("No wavefunction of two space dimensions, silent return!")
return
G = BlockFactory().create_grid(parameters)
V = BlockFactory().create_potential(parameters)
print(G.get_extensions())
WF = WaveFunction(parameters)
WF.set_grid(G)
BT = BasisTransformationWF(V)
BT.set_grid(G)
timegrid = iom.load_wavefunction_timegrid(blockid=blockid)
u, v = G.get_nodes(split=True, flat=False)
u = real(u)
v = real(v)
N = WF.get_number_components()
for step in timegrid:
print(" Plotting frame of timestep # " + str(step))
wave = iom.load_wavefunction(blockid=blockid, timestep=step)
values = [ wave[j,...] for j in xrange(parameters["ncomponents"]) ]
WF.set_values(values)
# Transform the values to the eigenbasis
# TODO: improve this:
if parameters["algorithm"] == "fourier":
BT.transform_to_eigen(WF)
else:
pass
Psi = WF.get_values()
fig = figure()
for level in xrange(N):
z = Psi[level]
subplot(N,1,level+1)
plotcm(z, darken=0.3)
savefig("wavefunction_level_"+str(level)+"_timestep_"+(5-len(str(step)))*"0"+str(step)+".png")
close(fig)
print(" Plotting frames finished")
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 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 transform_wavefunction_to_eigen(iomin, iomout, blockidin=0, blockidout=0):
"""Compute the transformation to the eigenbasis for a wavefunction.
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_wavefunction_timegrid(blockid=blockidin)
nrtimesteps = timesteps.shape[0]
iomout.add_wavefunction(parameters,
timeslots=nrtimesteps,
blockid=blockidout)
# The grid on the domain
grid = BlockFactory().create_grid(parameters)
# The potential used
Potential = BlockFactory().create_potential(parameters)
# Basis transformator
BT = BasisTransformationWF(Potential)
BT.set_grid(grid)
# And two empty wavefunctions
WF = WaveFunction(parameters)
WF.set_grid(grid)
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Compute eigentransform at timestep # " + str(step))
# Retrieve simulation data
values = iomin.load_wavefunction(timestep=step, blockid=blockidin)
values = [values[j, ...] for j in xrange(parameters["ncomponents"])]
WF.set_values(values)
# Project wavefunction values to eigenbasis
BT.transform_to_eigen(WF)
# Save the transformed values
iomout.save_wavefunction(WF.get_values(),
timestep=step,
blockid=blockidout)
def compute_norm(iom, blockid=0, eigentrafo=True):
"""Compute the norm of a wavefunction timeseries.
: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``.
"""
parameters = iom.load_parameters()
# Number of time steps we saved
timesteps = iom.load_wavefunction_timegrid(blockid=blockid)
nrtimesteps = timesteps.shape[0]
# Construct the grid from the parameters
grid = BlockFactory().create_grid(parameters)
# Basis transformator
if eigentrafo is True:
# The potential used
Potential = BlockFactory().create_potential(parameters)
BT = BasisTransformationWF(Potential)
BT.set_grid(grid)
# And two empty wavefunctions
WF = WaveFunction(parameters)
WF.set_grid(grid)
# We want to save norms, thus add a data slot to the data file
iom.add_norm(parameters, timeslots=nrtimesteps, blockid=blockid)
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Computing norms 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
if eigentrafo is True:
BT.transform_to_eigen(WF)
# Calculate the norm of the wave functions projected into the eigenbasis
norms = WF.norm()
iom.save_norm(norms, timestep=step, blockid=blockid)
def read_data_inhomogeneous(iom, blockid=0, timerange=None, path='.'):
r"""
:param iom: An :py:class:`IOManager` instance providing the simulation data.
:param blockid: The data block from which the values are read.
"""
BF = BlockFactory()
if iom.has_parameters():
parameters = iom.load_parameters()
if "dt" in parameters:
dt = parameters["dt"]
else:
dt = None
timegrid = iom.load_inhomogwavepacket_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!")
# Basis shapes
bsdescr = iom.load_inhomogwavepacket_basisshapes(blockid=blockid)
BS = {}
for ahash, descr in bsdescr.items():
BS[ahash] = BF.create_basis_shape(descr)
# Plot the coefficients for all timesteps
for j, step in enumerate(timegrid):
allhashes, allcoeffs = iom.load_inhomogwavepacket_coefficients(
timestep=step, blockid=blockid, get_hashes=True)
k = []
ck = []
for ahash, coeffs in zip(allhashes, allcoeffs):
bs = BS[int(ahash)]
ki = array([bs[node] for node in bs.get_node_iterator(mode="mag")])
ck.append(coeffs[ki])
ki.sort()
k.append(ki)
plot_coefficients(k, ck, step, dt, blockid=blockid, path=path)
def read_data_inhomogeneous(iom, blockid=0, timerange=None, path='.'):
r"""
:param iom: An :py:class:`IOManager` instance providing the simulation data.
:param blockid: The data block from which the values are read.
"""
BF = BlockFactory()
parameters = iom.load_parameters()
timegrid = iom.load_inhomogwavepacket_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!")
# Basis shapes
bsdescr = iom.load_inhomogwavepacket_basisshapes(blockid=blockid)
BS = {}
for ahash, descr in bsdescr.items():
BS[ahash] = BF.create_basis_shape(descr)
# Plot the coefficients for all timesteps
for j, step in enumerate(timegrid):
allhashes, allcoeffs = iom.load_inhomogwavepacket_coefficients(timestep=step, blockid=blockid, get_hashes=True)
k = []
ck = []
for ahash, coeffs in zip(allhashes, allcoeffs):
bs = BS[int(ahash)]
ki = array([bs[node] for node in bs.get_node_iterator(mode="mag")])
ck.append(coeffs[ki])
ki.sort()
k.append(ki)
dt = parameters["dt"] if "dt" in parameters else None
plot_coefficients(k, ck, step, dt, blockid=blockid, path=path)
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 plot_coefficients(parameters, data, index=0, imgsize=(10, 20)):
"""
:param parameters: A :py:class:`ParameterProvider` instance.
:param timegrid: The timegrid that belongs to the coefficient values.
:param coeffs: The coefficient values.
:param imgsize: The size of the plot. For a large number of plotted
coefficients, we might have to increase this value.
"""
print("Plotting the coefficients of data block '" + str(index) + "'")
# Check if we have enough coefficients to plot
timegrid, coeffs, hashes = data
N = len(coeffs)
# Reconstruct basis shapes
BS = []
for i in xrange(N):
d = iom.load_wavepacket_basisshapes(the_hash=hashes[i][0])
bs = BlockFactory().create_basis_shape(d)
BS.append(bs)
# Compute all multi indices available (union of all shapes)
allvects = set([])
for bs in BS:
allvects.update(set([i for i in bs]))
# And plot
for vect in allvects:
print(" Plotting coefficient " + str(vect) + " out of " +
str(len(allvects)))
fig = figure()
for level in xrange(N):
j = BS[level][vect]
if j is not None:
ax = fig.add_subplot(N, 1, level + 1)
ax.plot(timegrid, real(coeffs[level][:, j]))
ax.plot(timegrid, imag(coeffs[level][:, j]))
ax.plot(timegrid, abs(coeffs[level][:, j]))
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.set_xlabel(r"$t$")
ax.set_ylabel(r"$c^" + str(level) + r"$")
fig.suptitle(r"$\underline{k} = " + str(vect) + r"$")
fig.savefig("coefficient_k" + str(vect) + "_block" + str(index) +
GD.output_format)
close(fig)
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 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 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(iom, obsconfig=None, blockid=0, eigentrafo=True):
"""Compute the autocorrelation of a wavefunction 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.
Value has no effect in this class.
: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_wavefunction_timegrid(blockid=blockid)
nrtimesteps = timesteps.shape[0]
# Construct the grid from the parameters
grid = BlockFactory().create_grid(parameters)
# Basis transformator
if eigentrafo is True:
# The potential used
Potential = BlockFactory().create_potential(parameters)
BT = BasisTransformationWF(Potential)
BT.set_grid(grid)
# And two empty wavefunctions
WFo = WaveFunction(parameters)
WFo.set_grid(grid)
WFt = WaveFunction(parameters)
WFt.set_grid(grid)
# We want to save norms, thus add a data slot to the data file
iom.add_autocorrelation(parameters, timeslots=nrtimesteps, blockid=blockid)
# Preconfigure the
values = iom.load_wavefunction(timestep=0, blockid=blockid)
values = [values[j, ...] for j in range(parameters["ncomponents"])]
WFo.set_values(values)
# Project wavefunction values to eigenbasis
if eigentrafo is True:
BT.transform_to_eigen(WFo)
# Fourier transform the values
WFo.set_values([fftn(value) for value in WFo.get_values()])
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Computing autocorrelations of timestep %d" % step)
# Retrieve simulation data
values = iom.load_wavefunction(timestep=step, blockid=blockid)
values = [values[j, ...] for j in range(parameters["ncomponents"])]
WFt.set_values(values)
# Project wavefunction values to eigenbasis
if eigentrafo is True:
BT.transform_to_eigen(WFt)
# Fourier transform the values
WFt.set_values([fftn(value) for value in WFt.get_values()])
# Compute the prefactor
T = grid.get_extensions()
N = grid.get_number_nodes()
prefactor = product(array(T) / array(N).astype(floating)**2)
# Compute the autocorrelation
# TODO: Consider splitting into cases `fft` versus `fftn`
valueso = WFo.get_values()
valuest = WFt.get_values()
acs = [prefactor * ifftn(sum(conjugate(valueso[n]) * valuest[n])) for n in range(parameters["ncomponents"])]
iom.save_autocorrelation(acs, timestep=step, blockid=blockid)
iom = IOManager()
iom.open_file(filename=datafile)
# Read file with parameter data for grid
parameters = iom.load_parameters()
if args.parametersfile:
PL = ParameterLoader()
gridparams = PL.load_from_file(parametersfile)
else:
gridparams = parameters
# The axes rectangle that is plotted
view = args.xrange + args.yrange + args.zrange
# Plot
if parameters["dimension"] == 2:
Potential = BlockFactory().create_potential(parameters)
Grid = TensorProductGrid(gridparams["limits"],
gridparams["number_nodes"])
plot_potential(Grid,
Potential,
sparsify=args.sparsify,
view=view,
interactive=args.interactive,
path=resultspath)
else:
print("Not a potential in two space dimensions, silent return!")
iom.finalize()
potvars = map(lambda x: ":math:`"+str(x)+"`", potvars)
potvars = reduce(lambda a,b: a+", "+b, potvars)
if type(potdef["potential"]) == str:
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:
def compute_eigenstate(parameters, filename="eigenstates.hdf5", computepq=True, computePQ=True):
r"""
Special variables necessary in configuration:
* eigenstate_of_level (default: 0)
* eigenstates_indices (default: [0])
* starting_point (default: (2, ..., 2))
* hawp_template
* innerproduct
"""
D = parameters["dimension"]
if "eigenstate_of_level" in parameters:
N = parameters["eigenstate_of_level"]
else:
# Upper-most potential surface
N = 0
# Create output file now, in case this fails we did not waste computation time
IOM = IOManager()
IOM.create_file(filename)
# Save the simulation parameters
IOM.add_parameters()
IOM.save_parameters(parameters)
gid = IOM.create_group()
BF = BlockFactory()
# Create the potential
V = BF.create_potential(parameters)
V.calculate_local_quadratic()
# Compute position and momentum
if computepq:
# Minimize the potential to find q0
f = lambda x: real((squeeze(V.evaluate_at(x)[N])))
# Start with an offset because exact 0.0 values can give
# issues, especially with the Hessian evaluation. This way
# the minimizer will always stay away from zero a tiny bit.
# The current starting point can give issues if the potential
# is stationary at the point (2, ..., 2) but that is less likely.
if "starting_point" in parameters:
x0 = atleast_1d(parameters["starting_point"])
else:
x0 = 0.5 * ones(D)
q0 = fmin(f, x0, xtol=1e-12)
q0 = q0.reshape((D, 1))
# We are at the minimum with no momentum
p0 = zeros_like(q0)
else:
if "q0" in parameters:
q0 = atleast_2d(parameters["q0"])
else:
q0 = zeros((D, 1))
if "p0" in parameters:
p0 = atleast_2d(parameters["p0"])
else:
p0 = zeros((D, 1))
# Compute spreads
if computePQ:
# Q_0 = H^(-1/4)
H = V.evaluate_hessian_at(q0)
Q0 = inv(sqrtm(sqrtm(H)))
# P_0 = i Q_0^(-1)
P0 = 1.0j * inv(Q0)
else:
if "Q0" in parameters:
Q0 = atleast_2d(parameters["Q0"])
else:
Q0 = identity(D)
if "P0" in parameters:
P0 = atleast_2d(parameters["P0"])
else:
P0 = 1.0j * inv(Q0)
# The parameter set Pi
print(70 * "-")
print("Parameter values are:")
print("---------------------")
print(" q0:")
print(str(q0))
print(" p0:")
print(str(p0))
print(" Q0:")
print(str(Q0))
print(" P0:")
print(str(P0))
# Consistency check
print(" Consistency check:")
print(" P^T Q - Q^T P =?= 0")
print(dot(P0.T, Q0) - dot(Q0.T, P0))
print(" Q^H P - P^H Q =?= 2i")
print(dot(transpose(conjugate(Q0)), P0) - dot(transpose(conjugate(P0)), Q0))
# Next find the new coefficients c'
HAWP = BF.create_wavepacket(parameters["hawp_template"])
# Set the parameter values
Pi = HAWP.get_parameters()
Pi[0] = q0
Pi[1] = p0
Pi[2] = Q0
Pi[3] = P0
HAWP.set_parameters(Pi)
# Next compute the matrix M_ij = <phi_i | T + V | phi_j>
# The potential part
HQ = BF.create_inner_product(parameters["innerproduct"])
opV = lambda x, q, entry: V.evaluate_at(x, entry=entry)
MV = HQ.build_matrix(HAWP, operator=opV)
# The kinetic part
MT = zeros_like(MV, dtype=complexfloating)
GR = GradientHAWP()
BS = HAWP.get_basis_shapes(component=N)
vects = {}
for i in BS:
z = zeros_like(HAWP.get_coefficient_vector(), dtype=complexfloating)
HAWP.set_coefficient_vector(z)
HAWP.set_coefficient(N, i, 1.0)
Kn, cnew = GR.apply_gradient(HAWP, component=N, as_packet=False)
vects[i] = cnew
for j in BS:
for k in BS:
cj = vects[j]
ck = vects[k]
entry = 0.5 * squeeze(sum(conjugate(cj) * ck))
MT[BS[j], BS[k]] = entry
# Find eigenvalues and eigenvectors of the whole matrix
M = MT + MV
ew, ev = eigh(M)
ind = argsort(ew)
# Build the requested energy levels and states
if "eigenstates_indices" in parameters:
states = parameters["eigenstates_indices"]
else:
# Groundstate only
states = [0]
BS = HAWP.get_basis_shapes(component=0)
KEY = ("q", "p", "Q", "P", "S", "adQ")
print(70 * "-")
for state in states:
if state > BS.get_basis_size():
print("Warning: can not compute energy level {} with basis size of {}".format((state, BS)))
continue
index = ind[state]
coeffs = ev[:, index]
energy = ew[index]
# Try to resolve ambiguities in sign
imax = argmax(abs(coeffs))
a = abs(angle(coeffs[imax]))
if a > pi / 2.0:
coeffs *= -1
print("State: {}".format(state))
print("Energy: {}".format(energy))
print("Coefficients: \n")
print(str(coeffs))
print(70 * "-")
HAWP.set_coefficient_vector(coeffs.reshape((-1, 1)))
# Save all the wavepacket data
bid = IOM.create_block(groupid=gid)
IOM.add_wavepacket(parameters, blockid=bid, key=KEY)
IOM.save_wavepacket(HAWP, 0, blockid=bid, key=KEY)
IOM.finalize()
# TODO: Find better criterion
if norm(q0) > 1000:
print("+----------------------------------+")
print("| Run-away minimum? |")
print("| Maybe try different: |")
print("| starting_point = [x0, y0, ...] |")
print("+----------------------------------+")
def load_from_file(filepath, blockid=0, timestep=0, sizeK=None):
r"""Utility script to load wavepacket parameters and coefficients
from another simulation result in a form suitable for the input
configuration of a new simulation. This is (mainly) used
to start simulations with previously computed eigenstates.
:param filepath: The path to the `.hdf5` file from which data will be read.
:param blockid: The `datablock` from which to read the data.
Default is the block with `blockid=0`.
:param timestep: Load the data corresponding to the given `timestep`.
The default timestep is `0`.
:param sizeK: Load at most 'sizeK' many coefficients. Note that the order
is defined by the linearization mapping :math:`\mu` of the
packet's current basis shape. We then pick the first `sizeK`
ones.
"""
IOM = IOManager()
IOM.open_file(filepath)
# Check if we have data
tg = IOM.load_wavepacket_timegrid(blockid=blockid)
if timestep not in tg:
raise ValueError("No data for timestep {}".format(timestep))
# Load data and assemble packet
BF = BlockFactory()
# 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)
# Create a packet
wpd = IOM.load_wavepacket_description(blockid=blockid)
HAWP = BF.create_wavepacket(wpd)
# Data
ha, ci = IOM.load_wavepacket_coefficients(blockid=blockid, timestep=timestep, get_hashes=True)
Pi = IOM.load_wavepacket_parameters(blockid=blockid, timestep=timestep)
HAWP.set_parameters(Pi)
HAWP.set_basis_shapes([BS[int(h)] for h in ha])
HAWP.set_coefficients(ci)
# Reformat data
C = []
for n in range(HAWP.get_number_components()):
B = HAWP.get_basis_shapes(component=n)
cn = HAWP.get_coefficients(component=n)
l = []
for i in range(B.get_basis_size()):
l.append((B[i], cn[i, 0]))
C.append(l)
if sizeK is not None:
# We load at most 'sizeK' coefficients.
# Note that this does NOT specify which
# ones in terms of multi-indices.
C = [c[:sizeK] for c in C]
return Pi, C
def plot_frames(PP, iom, blockid=0, load=False):
r"""
"""
parameters = iom.load_parameters()
if not parameters["dimension"] == 2:
print("No wavefunction of two space dimensions, 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")
#G = iom.load_grid(blockid=blockid)
#G = grid.reshape((1, -1))
else:
G = BlockFactory().create_grid(PP)
V = BlockFactory().create_potential(parameters)
WF = WaveFunction(parameters)
WF.set_grid(G)
BT = BasisTransformationWF(V)
BT.set_grid(G)
timegrid = iom.load_wavefunction_timegrid(blockid=blockid)
u, v = G.get_nodes(split=True, flat=False)
u = real(u)
v = real(v)
N = WF.get_number_components()
for step in timegrid:
print(" Plotting frame of timestep # " + str(step))
wave = iom.load_wavefunction(blockid=blockid, timestep=step)
values = [ wave[j,...] for j in xrange(parameters["ncomponents"]) ]
WF.set_values(values)
# Transform the values to the eigenbasis
# TODO: improve this:
if parameters["algorithm"] == "fourier":
BT.transform_to_eigen(WF)
else:
pass
Psi = WF.get_values()
for level in xrange(N):
z = Psi[level]
z = z.reshape(G.get_number_nodes())
# Plot the probability densities projected to the eigenbasis
fig = mlab.figure(size=(800,700))
surfcf(u, v, angle(z), abs(z))
#mlab.contour_surf(u, v, abs(z))
#mlab.outline()
#mlab.axes()
mlab.savefig("wavefunction_level_"+str(level)+"_timestep_"+(5-len(str(step)))*"0"+str(step)+".png")
mlab.close(fig)
print(" Plotting frames finished")
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 plot_frames(PP,
iom,
blockid=0,
load=False,
eigentransform=False,
timerange=None,
sparsify=10,
view=None,
interactive=False,
path='.'):
"""Plot the wave function for a series of timesteps.
:param iom: An :py:class:`IOManager` instance providing the simulation data.
"""
parameters = iom.load_parameters()
if not parameters["dimension"] == 2:
print("No wavefunction of two space dimensions, 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 = BlockFactory().create_grid(PP)
if eigentransform:
V = BlockFactory().create_potential(parameters)
BT = BasisTransformationWF(V)
BT.set_grid(G)
WF = WaveFunction(parameters)
WF.set_grid(G)
N = WF.get_number_components()
timegrid = iom.load_wavefunction_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_nodes(split=True, flat=False)
u = real(u[::sparsify, ::sparsify])
v = real(v[::sparsify, ::sparsify])
# 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))
# Load the data
wave = iom.load_wavefunction(blockid=blockid, timestep=step)
values = [wave[j, ...] for j in range(parameters["ncomponents"])]
WF.set_values(values)
# Transform the values to the eigenbasis
if eigentransform:
BT.transform_to_eigen(WF)
Psi = WF.get_values()
for level in range(N):
# Wavefunction data
z = Psi[level]
z = z.reshape(G.get_number_nodes())[::sparsify, ::sparsify]
# View
if view is not None:
if view[4] is None:
view[4] = 0.0
if view[5] is None:
view[5] = 1.1 * abs(z).max()
# Plot
# if not interactive:
# mlab.options.offscreen = True
fig = mlab.figure(size=(800, 700))
surfcf(u, v, angle(z), abs(z), view=view)
mlab.draw()
if interactive:
mlab.show()
else:
mlab.savefig(
os.path.join(
"wavefunction_surface_block_%s_level_%d_timestep_%07d.png"
% (blockid, level, step)))
mlab.close(fig)
def plot_frames(PP, iom, blockid=0, view=None, plotphase=True, plotcomponents=False, plotabssqr=False, load=True, gridblockid=None, imgsize=(12,9)):
"""Plot the wave function for a series of timesteps.
:param iom: An :py:class:`IOManager` instance providing the simulation data.
:param view: The aspect ratio.
:param plotphase: Whether to plot the complex phase. (slow)
:param plotcomponents: Whether to plot the real/imaginary parts..
:param plotabssqr: Whether to plot the absolute value squared.
"""
parameters = iom.load_parameters()
if not parameters["dimension"] == 1:
print("No wavefunction of one space dimensions, silent return!")
return
if PP is None:
PP = parameters
if load is True:
print("Loading grid data from datablock 'global'")
if gridblockid is None:
gridblockid = blockid
G = iom.load_grid(blockid=gridblockid)
G = G.reshape((1, -1))
grid = G
else:
print("Creating new grid")
G = BlockFactory().create_grid(PP)
grid = G.get_nodes(flat=True)
timegrid = iom.load_wavefunction_timegrid(blockid=blockid)
for step in timegrid:
print(" Plotting frame of timestep # " + str(step))
wave = iom.load_wavefunction(blockid=blockid, timestep=step)
values = [ wave[j,...] for j in xrange(parameters["ncomponents"]) ]
# Plot the probability densities projected to the eigenbasis
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(squeeze(grid), real(component))
ax.plot(squeeze(grid), imag(component))
ax.set_ylabel(r"$\Re \varphi_"+str(index)+r", \Im \varphi_"+str(index)+r"$")
if plotabssqr is True:
ax.plot(squeeze(grid), component*conj(component))
ax.set_ylabel(r"$\langle \varphi_"+str(index)+r"| \varphi_"+str(index)+r"\rangle$")
if plotphase is True:
plotcf(squeeze(grid), angle(component), component*conj(component))
ax.set_ylabel(r"$\langle \varphi_"+str(index)+r"| \varphi_"+str(index)+r"\rangle$")
ax.set_xlabel(r"$x$")
# Set the aspect window
if view is not None:
ax.set_xlim(view[:2])
ax.set_ylim(view[2:])
if parameters.has_key("dt"):
fig.suptitle(r"$\Psi$ at time $"+str(step*parameters["dt"])+r"$")
else:
fig.suptitle(r"$\Psi$")
fig.savefig("wavefunction_block"+str(blockid)+"_"+ (7-len(str(step)))*"0"+str(step) +GD.output_format)
close(fig)
print(" Plotting frames finished")
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,
timerange=None,
view=None,
plotphase=True,
plotcomponents=False,
plotabssqr=False,
load=True,
gridblockid=None,
imgsize=(12, 9),
path='.'):
"""Plot the wave function for a series of timesteps.
:param iom: An :py:class:`IOManager` instance providing the simulation data.
:param view: The aspect ratio.
:param plotphase: Whether to plot the complex phase. (slow)
:param plotcomponents: Whether to plot the real/imaginary parts..
:param plotabssqr: Whether to plot the absolute value squared.
"""
parameters = iom.load_parameters()
if not parameters["dimension"] == 1:
print("No two-dimensional wavefunction, 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 '%s'" % 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))
# View
if view[0] is None:
view[0] = grid.min()
if view[1] is None:
view[1] = grid.max()
timegrid = iom.load_wavefunction_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!")
for step in timegrid:
print(" Plotting frame of timestep # {}".format(step))
wave = iom.load_wavefunction(blockid=blockid, timestep=step)
values = [wave[j, ...] for j in range(parameters["ncomponents"])]
# 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,
"wavefunction_block_%s_timestep_%07d.png" % (blockid, step)))
close(fig)
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)
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)
def plot_frames(PP, iom, blockid=0, load=False, eigentransform=False, timerange=None, sparsify=10, view=None, interactive=False, path='.'):
"""Plot the wave function for a series of timesteps.
:param iom: An :py:class:`IOManager` instance providing the simulation data.
"""
parameters = iom.load_parameters()
if not parameters["dimension"] == 2:
print("No wavefunction of two space dimensions, 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 = BlockFactory().create_grid(PP)
if eigentransform:
V = BlockFactory().create_potential(parameters)
BT = BasisTransformationWF(V)
BT.set_grid(G)
WF = WaveFunction(parameters)
WF.set_grid(G)
N = WF.get_number_components()
timegrid = iom.load_wavefunction_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_nodes(split=True, flat=False)
u = real(u[::sparsify, ::sparsify])
v = real(v[::sparsify, ::sparsify])
# 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))
# Load the data
wave = iom.load_wavefunction(blockid=blockid, timestep=step)
values = [wave[j, ...] for j in range(parameters["ncomponents"])]
WF.set_values(values)
# Transform the values to the eigenbasis
if eigentransform:
BT.transform_to_eigen(WF)
Psi = WF.get_values()
for level in range(N):
# Wavefunction data
z = Psi[level]
z = z.reshape(G.get_number_nodes())[::sparsify, ::sparsify]
# View
if view is not None:
if view[4] is None:
view[4] = 0.0
if view[5] is None:
view[5] = 1.1 * abs(z).max()
# Plot
# if not interactive:
# mlab.options.offscreen = True
fig = mlab.figure(size=(800, 700))
surfcf(u, v, angle(z), abs(z), view=view)
mlab.draw()
if interactive:
mlab.show()
else:
mlab.savefig(os.path.join("wavefunction_surface_block_%s_level_%d_timestep_%07d.png" % (blockid, level, step)))
mlab.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 load_from_file(filepath, blockid=0, timestep=0, sizeK=None):
r"""Utility script to load wavepacket parameters and coefficients
from another simulation result in a form suitable for the input
configuration of a new simulation. This is (mainly) used
to start simulations with previously computed eigenstates.
:param filepath: The path to the `.hdf5` file from which data will be read.
:param blockid: The `datablock` from which to read the data.
Default is the block with `blockid=0`.
:param timestep: Load the data corresponding to the given `timestep`.
The default timestep is `0`.
:param sizeK: Load at most 'sizeK' many coefficients. Note that the order
is defined by the linearization mapping :math:`\mu` of the
packet's current basis shape. We then pick the first `sizeK`
ones.
"""
IOM = IOManager()
IOM.open_file(filepath)
# Check if we have data
tg = IOM.load_wavepacket_timegrid(blockid=blockid)
if timestep not in tg:
raise ValueError("No data for timestep {}".format(timestep))
# Load data and assemble packet
BF = BlockFactory()
# 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)
# Create a packet
wpd = IOM.load_wavepacket_description(blockid=blockid)
HAWP = BF.create_wavepacket(wpd)
# Data
ha, ci = IOM.load_wavepacket_coefficients(blockid=blockid,
timestep=timestep,
get_hashes=True)
Pi = IOM.load_wavepacket_parameters(blockid=blockid, timestep=timestep)
HAWP.set_parameters(Pi)
HAWP.set_basis_shapes([BS[int(h)] for h in ha])
HAWP.set_coefficients(ci)
# Reformat data
C = []
for n in range(HAWP.get_number_components()):
B = HAWP.get_basis_shapes(component=n)
cn = HAWP.get_coefficients(component=n)
l = []
for i in range(B.get_basis_size()):
l.append((B[i], cn[i, 0]))
C.append(l)
if sizeK is not None:
# We load at most 'sizeK' coefficients.
# Note that this does NOT specify which
# ones in terms of multi-indices.
C = [c[:sizeK] for c in C]
return Pi, C
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()
KEY = ("q","p","Q","P","S","adQ")
# 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, key=KEY)
iomout.save_inhomogwavepacket_description(HAWP.get_description(), blockid=blockidout)
BT.set_matrix_builder(HAWP.get_innerproduct())
# Basis shapes
BS_descr = iomin.load_inhomogwavepacket_basisshapes(blockid=blockidin)
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, key=KEY)
hashes, coeffs = iomin.load_inhomogwavepacket_coefficients(timestep=step, get_hashes=True, blockid=blockidin)
# 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.
BT.transform_to_eigen(HAWP)
# Save the transformed packet
# Pi
iomout.save_inhomogwavepacket_parameters(HAWP.get_parameters(key=KEY), timestep=step, blockid=blockidout, key=KEY)
# Basis shapes (in case they changed!)
for shape in HAWP.get_basis_shapes():
iomout.save_inhomogwavepacket_basisshapes(shape, blockid=blockidout)
# Coefficients
iomout.save_inhomogwavepacket_coefficients(HAWP.get_coefficients(), HAWP.get_basis_shapes(), timestep=step, blockid=blockidout)
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,
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()
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 plot_coefficients(parameters,
data,
absang=False,
index=0,
reim=False,
imgsize=(10, 20),
view=[None, None],
path='.'):
"""
:param parameters: A :py:class:`ParameterProvider` instance.
"""
print("Plotting the coefficients of data block '%s'" % index)
# Check if we have enough coefficients to plot
time, coeffs, hashes = data
# View
if view[0] is None:
view[0] = nanmin(time)
if view[1] is None:
view[1] = nanmax(time)
N = len(coeffs)
# Reconstruct basis shapes
BS = []
for i in range(N):
d = iom.load_wavepacket_basisshapes(the_hash=hashes[i][0])
bs = BlockFactory().create_basis_shape(d)
BS.append(bs)
# Compute all multi indices available (union of all shapes)
allvects = set([])
for bs in BS:
allvects.update(set([i for i in bs]))
# Plot
for vect in allvects:
print(" Plotting coefficient {} out of {}".format(vect, len(allvects)))
fig = figure()
for level in range(N):
j = BS[level][vect]
if j is not None:
ax = fig.add_subplot(N, 1, level + 1)
if not reim:
ax.plot(time,
angle(coeffs[level][:, j]),
label=r"$\arg c$")
else:
ax.plot(time, real(coeffs[level][:, j]), label=r"$\Re c$")
ax.plot(time, imag(coeffs[level][:, j]), label=r"$\Im c$")
ax.plot(time, abs(coeffs[level][:, j]), "r", label=r"$|c|$")
ax.grid(True)
ax.set_xlim(view[0], view[1])
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.legend(loc='upper right')
ax.set_xlabel(r"$t$")
ax.set_ylabel(r"$c^{%d}$" % level)
fig.suptitle(r"$\underline{k} = " + str(vect) + r"$")
fig.savefig(
os.path.join(
path, "coefficient_k" + str(vect) + "_block" + str(index) +
GD.output_format))
close(fig)
def plot_frames(PP,
iom,
blockid=0,
load=False,
eigentransform=False,
timerange=None,
view=None,
path='.'):
"""Plot the wave function for a series of timesteps.
:param iom: An :py:class:`IOManager` instance providing the simulation data.
"""
parameters = iom.load_parameters()
if not parameters["dimension"] == 2:
print("No wavefunction of two space dimensions, 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 = BlockFactory().create_grid(PP)
if eigentransform:
V = BlockFactory().create_potential(parameters)
BT = BasisTransformationWF(V)
BT.set_grid(G)
WF = WaveFunction(parameters)
WF.set_grid(G)
N = WF.get_number_components()
timegrid = iom.load_wavefunction_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))
# Load the data
wave = iom.load_wavefunction(blockid=blockid, timestep=step)
values = [wave[j, ...] for j in range(parameters["ncomponents"])]
WF.set_values(values)
# Transform the values to the eigenbasis
if eigentransform:
BT.transform_to_eigen(WF)
Psi = WF.get_values()
# Plot
fig = figure()
for level in range(N):
# Wavefunction data
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,
"wavefunction_contour_block_%s_level_%d_timestep_%07d.png" %
(blockid, level, step)))
close(fig)
def plot_frames(PP, iom, blockid=0, load=False, limits=None):
r"""
"""
parameters = iom.load_parameters()
BF = BlockFactory()
if not parameters["dimension"] == 2:
print("No wavepacket of two space dimensions, 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")
#G = iom.load_grid(blockid=blockid)
#G = grid.reshape((1, -1))
else:
G = BF.create_grid(PP)
u, v = map(squeeze, G.get_axes())
V = BF.create_potential(parameters)
BT = BasisTransformationHAWP(V)
wpd = iom.load_wavepacket_description(blockid=blockid)
HAWP = BF.create_wavepacket(wpd)
# Basis shapes
BS_descr = iom.load_wavepacket_basisshapes(blockid=blockid)
BS = {}
for ahash, descr in BS_descr.iteritems():
BS[ahash] = BF.create_basis_shape(descr)
timegrid = iom.load_wavepacket_timegrid(blockid=blockid)
N = HAWP.get_number_components()
for step in timegrid:
print(" Plotting frame of timestep # " + str(step))
hi, ci = iom.load_wavepacket_coefficients(timestep=step, get_hashes=True, blockid=blockid)
Pi = iom.load_wavepacket_parameters(timestep=step, blockid=blockid)
HAWP.set_parameters(Pi)
HAWP.set_basis_shapes([ BS[int(ha)] for ha in hi ])
HAWP.set_coefficients(ci)
psi = HAWP.evaluate_at(G, prefactor=True, component=0)
fig = figure()
for level in xrange(N):
z = psi[level]
z = z.reshape(G.get_number_nodes())
subplot(N,1,level+1)
#plotcm(z.reshape(G.get_number_nodes()), darken=0.3)
plotcf2d(u, v, z, darken=0.3, limits=limits)
savefig("wavepacket_block_"+str(blockid)+"_level_"+str(level)+"_timestep_"+(5-len(str(step)))*"0"+str(step)+".png")
close(fig)
print(" Plotting frames finished")
def compute_eigenstate(parameters):
r"""
Special variables necessary in configuration:
* eigenstate_of_level (default: 0)
* states_indices (default: [0])
"""
D = parameters["dimension"]
if parameters.has_key("eigenstate_of_level"):
N = parameters["eigenstate_of_level"]
else:
# Upper-most potential surface
N = 0
# Create output file now, in case this fails we did not waste computations
IOM = IOManager()
IOM.create_file("eigenstates.hdf5")
# Save the simulation parameters
IOM.add_parameters()
IOM.save_parameters(parameters)
gid = IOM.create_group()
BF = BlockFactory()
# Create the potential
V = BF.create_potential(parameters)
V.calculate_local_quadratic()
# Minimize the potential to find q0
f = lambda x: real((squeeze(V.evaluate_at(x)[N])))
# Start with an offset because exact 0.0 values can give
# issues, especially with the Hessian evaluation. This way
# the minimizer will always stay away from zero a tiny bit.
# The current starting point can give issues if the potential
# is stationary at the point (2, ..., 2) but that is less likely.
x0 = 2.0*ones(D)
q0 = fmin(f, x0, xtol=1e-12)
q0 = q0.reshape((D,1))
# We are at the minimum with no momentum
p0 = zeros_like(q0)
# Compute spreads now
# Q_0 = H^(-1/4)
H = V.evaluate_hessian_at(q0)
Q0 = inv(sqrtm(sqrtm(H)))
# Take P_00 = i Q_0^(-1)
P0 = 1.0j * inv(Q0)
#
print(70*"-")
print("Parameter values are:")
print("---------------------")
print(" q0:")
print(str(q0))
print(" p0:")
print(str(p0))
print(" Q0:")
print(str(Q0))
print(" P0:")
print(str(P0))
# Consistency check
print(" consistency:")
print(str(conj(Q0)*P0 - conj(P0)*Q0))
print(70*"-")
# Next find the new coefficients c'
HAWP = BF.create_wavepacket(parameters["hawp_template"])
# Set the parameter values
Pi = HAWP.get_parameters()
Pi[0] = q0
Pi[1] = p0
Pi[2] = Q0
Pi[3] = P0
HAWP.set_parameters(Pi)
# Next compute the matrix M_ij = <phi_i | T + V | phi_j>
# The potential part
HQ = BF.create_inner_product(parameters["innerproduct"])
opV = lambda x, q, entry: V.evaluate_at(x, entry=entry)
MV = HQ.build_matrix(HAWP, operator=opV)
# The kinetic part
MT = zeros_like(MV, dtype=complexfloating)
GR = GradientHAWP()
BS = HAWP.get_basis_shapes(N)
vects = {}
for i in BS:
z = zeros_like(HAWP.get_coefficient_vector(), dtype=complexfloating)
HAWP.set_coefficient_vector(z)
HAWP.set_coefficient(N, i, 1.0)
Kn, cnew = GR.apply_gradient(HAWP, N)
vects[i] = cnew
for j in BS:
for k in BS:
cj = vects[j]
ck = vects[k]
entry = 0.5 * squeeze(sum(conj(cj) * ck))
MT[BS[j], BS[k]] = entry
# Find eigenvalues and eigenvectors of the whole matrix
M = MT + MV
ew, ev = eigh(M)
ind = argsort(ew)
# Build the requested energy levels and states
if parameters.has_key("eigenstates_indices"):
states = parameters["eigenstates_indices"]
else:
# Groundstate only
states = [0]
BS = HAWP.get_basis_shapes(component=0)
KEY = ("q","p","Q","P","S","adQ")
print(70*"-")
for state in states:
if state > BS.get_basis_size():
print("Warning: can not compute energy level "+state+" with basis size of "+str(BS))
continue
index = ind[state]
coeffs = ev[:,index]
energy = ew[index]
print("Level: "+str(state))
print("Energy: "+str(energy))
print("Coefficients: \n")
print(str(coeffs))
print(70*"-")
HAWP.set_coefficient_vector(coeffs.reshape((-1, 1)))
# Save all the wavepacket data
bid = IOM.create_block(groupid=gid)
IOM.add_wavepacket(parameters, blockid=bid, key=KEY)
IOM.save_wavepacket_description(HAWP.get_description(), blockid=bid)
for shape in HAWP.get_basis_shapes():
IOM.save_wavepacket_basisshapes(shape, blockid=bid)
IOM.save_wavepacket_parameters(HAWP.get_parameters(key=KEY), timestep=0, blockid=bid, key=KEY)
IOM.save_wavepacket_coefficients(HAWP.get_coefficients(), HAWP.get_basis_shapes(), timestep=0, blockid=bid)
IOM.finalize()
def plot_frames(PP, iom, blockid=0, load=False, eigentransform=False, timerange=None, view=None, path='.'):
"""Plot the wave function for a series of timesteps.
:param iom: An :py:class:`IOManager` instance providing the simulation data.
"""
parameters = iom.load_parameters()
if not parameters["dimension"] == 2:
print("No wavefunction of two space dimensions, 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 = BlockFactory().create_grid(PP)
if eigentransform:
V = BlockFactory().create_potential(parameters)
BT = BasisTransformationWF(V)
BT.set_grid(G)
WF = WaveFunction(parameters)
WF.set_grid(G)
N = WF.get_number_components()
timegrid = iom.load_wavefunction_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))
# Load the data
wave = iom.load_wavefunction(blockid=blockid, timestep=step)
values = [wave[j, ...] for j in range(parameters["ncomponents"])]
WF.set_values(values)
# Transform the values to the eigenbasis
if eigentransform:
BT.transform_to_eigen(WF)
Psi = WF.get_values()
# Plot
fig = figure()
for level in range(N):
# Wavefunction data
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, "wavefunction_contour_block_%s_level_%d_timestep_%07d.png" % (blockid, level, step)))
close(fig)
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 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 compute_eigenstate(parameters,
filename="eigenstates.hdf5",
computepq=True,
computePQ=True):
r"""
Special variables necessary in configuration:
* eigenstate_of_level (default: 0)
* eigenstates_indices (default: [0])
* starting_point (default: (2, ..., 2))
* hawp_template
* innerproduct
"""
D = parameters["dimension"]
if "eigenstate_of_level" in parameters:
N = parameters["eigenstate_of_level"]
else:
# Upper-most potential surface
N = 0
# Create output file now, in case this fails we did not waste computation time
IOM = IOManager()
IOM.create_file(filename)
# Save the simulation parameters
IOM.add_parameters()
IOM.save_parameters(parameters)
gid = IOM.create_group()
BF = BlockFactory()
# Create the potential
V = BF.create_potential(parameters)
V.calculate_local_quadratic()
# Compute position and momentum
if computepq:
# Minimize the potential to find q0
f = lambda x: real((squeeze(V.evaluate_at(x)[N])))
# Start with an offset because exact 0.0 values can give
# issues, especially with the Hessian evaluation. This way
# the minimizer will always stay away from zero a tiny bit.
# The current starting point can give issues if the potential
# is stationary at the point (2, ..., 2) but that is less likely.
if "starting_point" in parameters:
x0 = atleast_1d(parameters["starting_point"])
else:
x0 = 0.5 * ones(D)
q0 = fmin(f, x0, xtol=1e-12)
q0 = q0.reshape((D, 1))
# We are at the minimum with no momentum
p0 = zeros_like(q0)
else:
if "q0" in parameters:
q0 = atleast_2d(parameters["q0"])
else:
q0 = zeros((D, 1))
if "p0" in parameters:
p0 = atleast_2d(parameters["p0"])
else:
p0 = zeros((D, 1))
# Compute spreads
if computePQ:
# Q_0 = H^(-1/4)
H = V.evaluate_hessian_at(q0)
Q0 = inv(sqrtm(sqrtm(H)))
# P_0 = i Q_0^(-1)
P0 = 1.0j * inv(Q0)
else:
if "Q0" in parameters:
Q0 = atleast_2d(parameters["Q0"])
else:
Q0 = identity(D)
if "P0" in parameters:
P0 = atleast_2d(parameters["P0"])
else:
P0 = 1.0j * inv(Q0)
# The parameter set Pi
print(70 * "-")
print("Parameter values are:")
print("---------------------")
print(" q0:")
print(str(q0))
print(" p0:")
print(str(p0))
print(" Q0:")
print(str(Q0))
print(" P0:")
print(str(P0))
# Consistency check
print(" Consistency check:")
print(" P^T Q - Q^T P =?= 0")
print(dot(P0.T, Q0) - dot(Q0.T, P0))
print(" Q^H P - P^H Q =?= 2i")
print(
dot(transpose(conjugate(Q0)), P0) - dot(transpose(conjugate(P0)), Q0))
# Next find the new coefficients c'
HAWP = BF.create_wavepacket(parameters["hawp_template"])
# Set the parameter values
Pi = HAWP.get_parameters()
Pi[0] = q0
Pi[1] = p0
Pi[2] = Q0
Pi[3] = P0
HAWP.set_parameters(Pi)
# Next compute the matrix M_ij = <phi_i | T + V | phi_j>
# The potential part
HQ = BF.create_inner_product(parameters["innerproduct"])
opV = lambda x, q, entry: V.evaluate_at(x, entry=entry)
MV = HQ.build_matrix(HAWP, operator=opV)
# The kinetic part
MT = zeros_like(MV, dtype=complexfloating)
GR = GradientHAWP()
BS = HAWP.get_basis_shapes(component=N)
vects = {}
for i in BS:
z = zeros_like(HAWP.get_coefficient_vector(), dtype=complexfloating)
HAWP.set_coefficient_vector(z)
HAWP.set_coefficient(N, i, 1.0)
Kn, cnew = GR.apply_gradient(HAWP, component=N, as_packet=False)
vects[i] = cnew
for j in BS:
for k in BS:
cj = vects[j]
ck = vects[k]
entry = 0.5 * squeeze(sum(conjugate(cj) * ck))
MT[BS[j], BS[k]] = entry
# Find eigenvalues and eigenvectors of the whole matrix
M = MT + MV
ew, ev = eigh(M)
ind = argsort(ew)
# Build the requested energy levels and states
if "eigenstates_indices" in parameters:
states = parameters["eigenstates_indices"]
else:
# Groundstate only
states = [0]
BS = HAWP.get_basis_shapes(component=0)
KEY = ("q", "p", "Q", "P", "S", "adQ")
print(70 * "-")
for state in states:
if state > BS.get_basis_size():
print(
"Warning: can not compute energy level {} with basis size of {}"
.format((state, BS)))
continue
index = ind[state]
coeffs = ev[:, index]
energy = ew[index]
# Try to resolve ambiguities in sign
imax = argmax(abs(coeffs))
a = abs(angle(coeffs[imax]))
if a > pi / 2.0:
coeffs *= -1
print("State: {}".format(state))
print("Energy: {}".format(energy))
print("Coefficients: \n")
print(str(coeffs))
print(70 * "-")
HAWP.set_coefficient_vector(coeffs.reshape((-1, 1)))
# Save all the wavepacket data
bid = IOM.create_block(groupid=gid)
IOM.add_wavepacket(parameters, blockid=bid, key=KEY)
IOM.save_wavepacket(HAWP, 0, blockid=bid, key=KEY)
IOM.finalize()
# TODO: Find better criterion
if norm(q0) > 1000:
print("+----------------------------------+")
print("| Run-away minimum? |")
print("| Maybe try different: |")
print("| starting_point = [x0, y0, ...] |")
print("+----------------------------------+")
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)
potvars = map(lambda x: ":math:`" + str(x) + "`", potvars)
potvars = reduce(lambda a, b: a + ", " + b, potvars)
if type(potdef["potential"]) == str:
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:
def compute_autocorrelation(iom, obsconfig=None, blockid=0, eigentrafo=True):
"""Compute the autocorrelation of a wavefunction 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.
Value has no effect in this class.
: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_wavefunction_timegrid(blockid=blockid)
nrtimesteps = timesteps.shape[0]
# Construct the grid from the parameters
grid = BlockFactory().create_grid(parameters)
# Basis transformator
if eigentrafo is True:
# The potential used
Potential = BlockFactory().create_potential(parameters)
BT = BasisTransformationWF(Potential)
BT.set_grid(grid)
# And two empty wavefunctions
WFo = WaveFunction(parameters)
WFo.set_grid(grid)
WFt = WaveFunction(parameters)
WFt.set_grid(grid)
# We want to save norms, thus add a data slot to the data file
iom.add_autocorrelation(parameters, timeslots=nrtimesteps, blockid=blockid)
# Preconfigure the
values = iom.load_wavefunction(timestep=0, blockid=blockid)
values = [values[j, ...] for j in range(parameters["ncomponents"])]
WFo.set_values(values)
# Project wavefunction values to eigenbasis
if eigentrafo is True:
BT.transform_to_eigen(WFo)
# Fourier transform the values
WFo.set_values([fftn(value) for value in WFo.get_values()])
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Computing autocorrelations of timestep %d" % step)
# Retrieve simulation data
values = iom.load_wavefunction(timestep=step, blockid=blockid)
values = [values[j, ...] for j in range(parameters["ncomponents"])]
WFt.set_values(values)
# Project wavefunction values to eigenbasis
if eigentrafo is True:
BT.transform_to_eigen(WFt)
# Fourier transform the values
WFt.set_values([fftn(value) for value in WFt.get_values()])
# Compute the prefactor
T = grid.get_extensions()
N = grid.get_number_nodes()
prefactor = product(array(T) / array(N).astype(floating)**2)
# Compute the autocorrelation
# TODO: Consider splitting into cases `fft` versus `fftn`
valueso = WFo.get_values()
valuest = WFt.get_values()
acs = [
prefactor * ifftn(sum(conjugate(valueso[n]) * valuest[n]))
for n in range(parameters["ncomponents"])
]
iom.save_autocorrelation(acs, timestep=step, blockid=blockid)