def compute_energy(iom, blockid=0):
"""
:param iom: An ``IOManager`` instance providing the simulation data.
:param blockid: The data block from which the values are read.
"""
parameters = iom.load_parameters()
# Number of time steps we saved
timesteps = iom.load_wavefunction_timegrid(blockid=blockid)
nrtimesteps = timesteps.shape[0]
# Retrieve simulation data
if iom.has_grid(blockid=blockid):
grid = iom.load_grid(blockid=blockid)
else:
grid = iom.load_grid(blockid="global")
opT, opV = iom.load_fourieroperators(blockid=blockid)
# We want to save norms, thus add a data slot to the data file
iom.add_energy(parameters, timeslots=nrtimesteps, blockid=blockid)
# Precalculate eigenvectors for efficiency
Potential = PotentialFactory().create_potential(parameters)
eigenvectors = Potential.evaluate_eigenvectors_at(grid)
nst = Potential.get_number_components()
WF = WaveFunction(parameters)
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Computing energies of timestep # " + str(step))
values = iom.load_wavefunction(timestep=step, blockid=blockid)
values = [ values[j,...] for j in xrange(parameters["ncomponents"]) ]
# Project wavefunction values to eigenbasis
values = Potential.project_to_eigen(grid, values, eigenvectors)
WF.set_values(values)
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
# Project this vector to the canonical basis
tmp = Potential.project_to_canonical(grid, tmp, eigenvectors)
WF.set_values(tmp)
# And calculate the energies of these components
ekinlist.append(WF.kinetic_energy(opT, summed=True))
epotlist.append(WF.potential_energy(opV, summed=True))
iom.save_energy((ekinlist, epotlist), timestep=step, blockid=blockid)
def compute_evaluate_wavepackets(iom, basis="eigen", blockid=0):
"""Evaluate an in homogeneous Hagdorn wavepacket on a given grid for each timestep.
:param iom: An ``IOManager`` instance providing the simulation data.
:param basis: The basis where the evaluation is done. Can be 'eigen' or 'canonical'.
:param blockid: The data block from which the values are read.
"""
parameters = iom.load_parameters()
# Number of time steps we saved
timesteps = iom.load_inhomogwavepacket_timegrid(blockid=blockid)
nrtimesteps = timesteps.shape[0]
# Prepare the potential for basis transformations
Potential = PotentialFactory().create_potential(parameters)
# Retrieve simulation data
if iom.has_grid(blockid=blockid):
grid = iom.load_grid(blockid=blockid)
else:
grid = iom.load_grid(blockid="global")
params = iom.load_inhomogwavepacket_parameters(blockid=blockid)
coeffs = iom.load_inhomogwavepacket_coefficients(blockid=blockid)
# A data transformation needed by API specification
params = [ [ params[j][i,:] for j in xrange(parameters["ncomponents"]) ] for i in xrange(nrtimesteps) ]
coeffs = [ [ coeffs[i,j,:] for j in xrange(parameters["ncomponents"]) ] for i in xrange(nrtimesteps) ]
# We want to save wavefunctions, thus add a data slot to the data file
iom.add_wavefunction(parameters, timeslots=nrtimesteps, blockid=blockid)
# Hack for allowing data blocks with different basis size than the global one
# todo: remove when we got local parameter sets
parameters.update_parameters({"basis_size": coeffs[0][0].shape[0]})
HAWP = HagedornWavepacketInhomogeneous(parameters)
HAWP.set_quadrature(None)
WF = WaveFunction(parameters)
WF.set_grid(grid)
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Evaluating inhomogeneous wavepacket at timestep "+str(step))
# Configure the wavepacket
HAWP.set_parameters(params[i])
HAWP.set_coefficients(coeffs[i])
# Project to the eigenbasis if desired
if basis == "eigen":
HAWP.project_to_eigen(Potential)
# 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)
def compute_norm(iom, blockid=0):
"""Compute the norm of a wavepacket timeseries.
:param iom: An ``IOManager`` instance providing the simulation data.
:param blockid: The data block from which the values are read.
"""
parameters = iom.load_parameters()
if iom.has_grid(blockid=blockid):
grid = iom.load_grid(blockid=blockid)
else:
grid = iom.load_grid(blockid="global")
# Number of time steps we saved
timesteps = iom.load_wavefunction_timegrid(blockid=blockid)
nrtimesteps = timesteps.shape[0]
# We want to save norms, thus add a data slot to the data file
iom.add_norm(parameters, timeslots=nrtimesteps, blockid=blockid)
# Precalculate eigenvectors for efficiency
Potential = PotentialFactory().create_potential(parameters)
eigenvectors = Potential.evaluate_eigenvectors_at(grid)
WF = WaveFunction(parameters)
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Computing norms of timestep "+str(step))
values = iom.load_wavefunction(timestep=step, blockid=blockid)
values = [ values[j,...] for j in xrange(parameters["ncomponents"]) ]
# Calculate the norm of the wave functions projected into the eigenbasis
values_e = Potential.project_to_eigen(grid, values, eigenvectors)
WF.set_values(values_e)
norms = WF.get_norm()
iom.save_norm(norms, timestep=step, blockid=blockid)
def load_data(resultsdir, evaluation_times, which_norm="wf"):
"""This script assumes filename specification: something_eps=..._dt=..._[h|f]_other_things.
We group the simulations first by eps and then by dt.
"""
iom_f = IOManager()
iom_h = IOManager()
# Group the data from different simulations according to epsilon
ids = get_result_dirs(resultsdir)
eps_groups = group_by(ids, "eps")
# Data structures for results
epsdata = [ None for i in xrange(len(eps_groups)) ]
axisdata = [ [] for i in xrange(len(eps_groups)) ]
normdata = [ [ [] for i in xrange(len(eps_groups)) ] for t in xrange(len(evaluation_times)) ]
# Loop over all simulations, grouped by same eps value
for index, eps_group in enumerate(eps_groups):
# Partition into fourier and hagedorn simulations
dirs_f = gather_all(eps_group, "algorithm=fourier")
dirs_h = gather_all(eps_group, "algorithm=hagedorn")
if len(dirs_f) != len(dirs_h):
raise ValueError("Found different number of fourier and hagedorn simulations!")
# And sort by dt value
dirs_f = sort_by(dirs_f, "dt")
dirs_h = sort_by(dirs_h, "dt")
# Loop over all simulations with same eps values sorted by size of dt
for dir_f, dir_h in zip(dirs_f, dirs_h):
print("Comparing simulation " + dir_h + " with " + dir_f)
resultsfile_f = get_results_file(dir_f)
iom_f.open_file(filename=resultsfile_f)
resultsfile_h = get_results_file(dir_h)
iom_h.open_file(filename=resultsfile_h)
# Read the parameters
parameters_f = iom_f.load_parameters()
parameters_h = iom_h.load_parameters()
# Scalar parameter of the x axis
axisdata[index].append(parameters_f["dt"])
# Get the data
grid = iom_f.load_grid(blockid="global")
WF = WaveFunction(parameters_f)
WF.set_grid(grid)
# Convert times to timesteps using the time manager
tm = parameters_f.get_timemanager()
# Loop over all times
for i, time in enumerate(evaluation_times):
print(" at time T: " + str(time))
step = tm.compute_timestep(time)
data_f = iom_f.load_wavefunction(timestep=step)
data_h = iom_h.load_wavefunction(timestep=step)
# Compute the norm || u_f - u_h || for all timesteps
data_diff = data_f - data_h
if which_norm == "wf":
WF.set_values( [ data_diff[0,...] ] )
no = WF.get_norm(summed=True)
elif which_norm == "2":
no = norm( data_diff[0,...] )
elif which_norm == "max":
no = max( data_diff[0,...] )
# Append norm values to global data structure
normdata[i][index].append(no)
# Scalar parameter of the different curves
# We add this here because the simulation parameters are
# already loaded but not overwritten yet be the next iteration
# Remember: we need only a single epsilon out of each eps_group.
epsdata[index] = parameters_f["eps"]
iom_f.finalize()
iom_h.finalize()
# Convert lists to arrays
epsdata = array(epsdata)
axisdata = [ array(item) for item in axisdata ]
return (times, epsdata, axisdata, normdata)
def read_data(iom_o, iom_s, gid, bid_ref=0):
"""Plot the wave function for a series of timesteps.
:param iom_s: An ``IOManager`` instance providing the spawning simulation data.
:param iom_o: An ``IOManager`` instance providing the reference simulation data.
:param bid_ref: The block ID of the reference data. Default is data block '0'.
"""
parameters_o = iom_o.load_parameters()
parameters_s = iom_s.load_parameters()
# For each mother-child spawn try pair
bidm, bidc = iom_s.get_block_ids(groupid=gid)
# Read original data from first block
grid_o = iom_o.load_grid(blockid="global")
timegrid_o = iom_o.load_wavefunction_timegrid(blockid=bid_ref)
WF = WaveFunction(parameters_o)
WF.set_grid(grid_o)
norms_L2 = []
norms_max = []
for step in timegrid_o:
print(" Timestep # " + str(step))
# Retrieve original reference data
wave_o = iom_o.load_wavefunction(timestep=step, blockid=bid_ref)
values_o = [ wave_o[j,...] for j in xrange(parameters_o["ncomponents"]) ]
# Compute absolute values, assume the data were stored in the eigenbasis
values_o = [ sqrt(conj(item)*item) for item in values_o ]
# Retrieve spawn data for mother and child packets
values_s = []
try:
# Load data of original packet
wave = iom_s.load_wavefunction(timestep=step, blockid=bidm)
values_s.append([ wave[j,...] for j in xrange(parameters_s["ncomponents"]) ])
# Load data of spawned packet
wave = iom_s.load_wavefunction(timestep=step, blockid=bidc)
values_s.append([ wave[j,...] for j in xrange(parameters_s["ncomponents"]) ])
have_spawn_data = True
except ValueError:
have_spawn_data = False
if have_spawn_data is True:
# Sum up the spawned parts
values_sum = []
for i in xrange(parameters_o["ncomponents"]):
values_sum.append(sqrt(reduce(lambda x,y: x+y, [ conj(item[i])*item[i] for item in values_s ])))
# Compute the difference to the original
values_diff = [ item_o - item_s for item_o, item_s in zip(values_o, values_sum) ]
else:
# Return zeros if we did not spawn yet in this timestep
values_diff = [ zeros(values_o[0].shape) for i in xrange(parameters_o["ncomponents"]) ]
# Compute the L^2 norm
WF.set_values(values_diff)
curnorm_L2 = list(WF.get_norm())
curnorm_L2.append(WF.get_norm(summed=True))
# Compute the max norm
curnorm_max = [ max(abs(item)) for item in values_diff ]
curnorm_max.append(max(curnorm_max))
print(" at time " + str(step*parameters_o["dt"]) + " the error in L^2 norm is " + str(curnorm_L2))
norms_L2.append(curnorm_L2)
norms_max.append(curnorm_max)
return (timegrid_o*parameters_o["dt"], array(norms_L2), array(norms_max))
def load_data(resultspath, which_norm="wf"):
# Sort the data from different simulations
ids = FT.get_result_dirs(resultspath)
dirs_f = FT.gather_all(ids, "fourier")
dirs_h = FT.gather_all(ids, "hagedorn")
dirs_f = FT.sort_by(dirs_f, "eps")
dirs_h = FT.sort_by(dirs_h, "eps")
if len(dirs_f) != len(dirs_h):
raise ValueError("Found different number of fourier and hagedorn simulations!")
number_simulations = len(dirs_f)
normdata = []
axisdata = []
iom_f = IOManager()
iom_h = IOManager()
# Loop over all simulations
for dir_f, dir_h in zip(dirs_f, dirs_h):
print("Comparing simulation " + dir_h + " with " + dir_f)
# Load the simulation data files
resultsfile_f = FT.get_results_file(dir_f)
iom_f.open_file(filename=resultsfile_f)
resultsfile_h = FT.get_results_file(dir_h)
iom_h.open_file(filename=resultsfile_h)
# Read the parameters
parameters_f = iom_f.load_parameters()
parameters_h = iom_h.load_parameters()
number_components = parameters_f["ncomponents"]
# Scalar parameter that discriminates the simulations
axisdata.append(parameters_f["eps"])
# Get the data
grid = iom_f.load_grid(blockid="global")
timesteps = iom_f.load_wavefunction_timegrid()
data_f = iom_f.load_wavefunction()
data_h = iom_h.load_wavefunction()
# Compute the norm || u_f - u_h ||_L2 for all timesteps
data_diff = data_f - data_h
WF = WaveFunction(parameters_f)
WF.set_grid(grid)
norms = []
for i, step in enumerate(timesteps):
if which_norm == "wf":
WF.set_values([ data_diff[i,0,:] ])
no = WF.get_norm()
elif which_norm == "2":
no = norm(data_diff[i,0,:])
elif which_norm == "max":
no = max(data_diff[i,0,:])
norms.append(no)
# Append norm values to global data structure
norms = array(norms)
normdata.append(norms)
iom_f.finalize()
iom_h.finalize()
return (axisdata, normdata, number_simulations, number_components)
def load_data(resultspath, which_norm="wf"):
# Group the data from different simulations
ids = FT.get_result_dirs(resultspath)
ids = FT.group_by(ids, "eps")
nsims = FT.get_number_simulations(resultspath)
groupdata = []
axisdata = [ [] for i in xrange(nsims) ]
normdata = [ [] for i in xrange(nsims) ]
iom_f = IOManager()
iom_h = IOManager()
for index, sims in enumerate(ids):
# Sorting based on file names
dirs_f = FT.gather_all(sims, "fourier")
dirs_h = FT.gather_all(sims, "hagedorn")
if len(dirs_f) != len(dirs_h):
raise ValueError("Found different number of fourier and hagedorn simulations!")
dirs_f = FT.sort_by(dirs_f, "eps", as_string=True)
dirs_h = FT.sort_by(dirs_h, "eps", as_string=True)
# Loop over all simulations
for dir_f, dir_h in zip(dirs_f, dirs_h):
print("Comparing simulation " + dir_h + " with " + dir_f)
resultsfile_f = FT.get_results_file(dir_f)
iom_f.open_file(filename=resultsfile_f)
resultsfile_h = FT.get_results_file(dir_h)
iom_h.open_file(filename=resultsfile_h)
# Read the parameters
parameters_f = iom_f.load_parameters()
parameters_h = iom_h.load_parameters()
grid = iom_f.load_grid(blockid="global")
# Precalculate eigenvectors for efficiency
Potential = PotentialFactory().create_potential(parameters_f)
eigenvectors = Potential.evaluate_eigenvectors_at(grid)
# Get the data
# Number of time steps we saved
timesteps = iom_f.load_wavefunction_timegrid()
# Scalar parameter that discriminates the simulations
axisdata[index].append((parameters_f, timesteps))
WF = WaveFunction(parameters_f)
WF.set_grid(grid)
norms = []
for i, step in enumerate(timesteps):
# Load the data that belong to the current timestep
data_f = iom_f.load_wavefunction(timestep=step)
data_h = iom_h.load_wavefunction(timestep=step)
data_f = Potential.project_to_eigen(grid, data_f, eigenvectors)
data_f = array(data_f)
data_diff = data_f - data_h
# Compute the norm || u_f - u_h ||
if which_norm == "wf":
# Rearrange data to fit the input of WF and handle over
WF.set_values([ data_diff[n,:] for n in xrange(parameters_f.ncomponents) ])
curnorm = WF.get_norm()
# More than one component? If yes, compute also the overall norm
if parameters_f.ncomponents > 1:
nosum = WF.get_norm(summed=True)
curnorm = list(curnorm) + [nosum]
elif which_norm == "max":
curnorm = [ max( abs(data_diff[n,:]) ) for n in xrange(parameters_f.ncomponents) ]
# More than one component? If yes, compute also the overall norm
if parameters_f.ncomponents > 1:
nosum = max(curnorm)
curnorm = list(curnorm) + [nosum]
print(" at time " + str(step*parameters_f.dt) + " the error norm is " + str(curnorm))
norms.append(curnorm)
# Append norm values to global data structure
norms = array(norms)
normdata[index].append(norms)
# Scalar parameter of the different curves
# We add this here because the simulation parameters are
# already loaded but not overwritten yet be the next iteration
# Remember: we need only a single epsilon out of each eps_group.
groupdata.append(parameters_f.dt)
iom_f.finalize()
iom_h.finalize()
return (groupdata, axisdata, normdata)