def compute_evaluate_wavepackets(iom, basis="eigen", blockid=0):
"""Evaluate a 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_wavepacket_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_wavepacket_parameters(blockid=blockid)
coeffs = iom.load_wavepacket_coefficients(blockid=blockid)
# A data transformation needed by API specification
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 = HagedornWavepacket(parameters)
HAWP.set_quadrature(None)
WF = WaveFunction(parameters)
WF.set_grid(grid)
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Evaluating homogeneous 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 aposteriori_spawning(fin, fout, pin, pout, bid1, bid2):
"""
:param f: An ``IOManager`` instance providing the simulation data.
:param datablock: The data block where the results are.
"""
# Number of time steps we saved
timesteps = fin.load_wavepacket_timegrid()
nrtimesteps = timesteps.shape[0]
params = fin.load_wavepacket_parameters()
coeffs = fin.load_wavepacket_coefficients()
# A data transformation needed by API specification
coeffs = [ [ coeffs[i,j,:] for j in xrange(pin["ncomponents"]) ] for i in xrange(nrtimesteps) ]
# Initialize a mother Hagedorn wavepacket with the data from another simulation
HAWP = HagedornWavepacket(pin)
HAWP.set_quadrature(None)
# Initialize an empty wavepacket for spawning
SWP = HagedornWavepacket(pout)
SWP.set_quadrature(None)
# Initialize a Spawner
AS = AdiabaticSpawner(pout)
# Iterate over all timesteps and spawn
for i, step in enumerate(timesteps):
print(" Try spawning at timestep "+str(step))
# Configure the wave packet and project to the eigenbasis.
HAWP.set_parameters(params[i])
HAWP.set_coefficients(coeffs[i])
#HAWP.project_to_eigen(Potential)
# Try spawning a new packet
ps = AS.estimate_parameters(HAWP, 0)
if ps is not None:
SWP.set_parameters(ps)
AS.project_coefficients(HAWP, SWP)
# Save the spawned packet
fout.save_wavepacket_parameters(HAWP.get_parameters(), timestep=step, blockid=bid1)
fout.save_wavepacket_coefficients(HAWP.get_coefficients(), timestep=step, blockid=bid1)
fout.save_wavepacket_parameters(SWP.get_parameters(), timestep=step, blockid=bid2)
fout.save_wavepacket_coefficients(SWP.get_coefficients(), timestep=step, blockid=bid2)
def compute_energy(iom, blockid=0):
p = iom.load_parameters()
# Number of time steps we saved
timesteps = iom.load_wavepacket_timegrid(blockid=blockid)
nrtimesteps = timesteps.shape[0]
# We want to save energies, thus add a data slot to the data file
iom.add_energy(p, timeslots=nrtimesteps, blockid=blockid, total=True)
Potential = PotentialFactory().create_potential(p)
params = iom.load_wavepacket_parameters(blockid=blockid)
coeffs = iom.load_wavepacket_coefficients(blockid=blockid)
# A data transformation needed by API specification
coeffs = [ [ coeffs[i,j,:] for j in xrange(p.ncomponents) ] for i in xrange(nrtimesteps) ]
# Initialize a hagedorn wave packet with the data
HAWP = HagedornWavepacket(p)
HAWP.set_quadrature(None)
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Computing energies of timestep "+str(step))
# Configure the wave packet
HAWP.set_parameters(params[i])
HAWP.set_coefficients(coeffs[i])
# Compute overall energy in canonical basis
ekin = HAWP.kinetic_energy(summed=True)
epot = HAWP.potential_energy(Potential.evaluate_at, summed=True)
etot = ekin + epot
iom.save_energy_total(etot, timestep=step, blockid=blockid)
# Transform to eigenbasis
HAWP.project_to_eigen(Potential)
# Compute the components' energies in the eigenbasis
ekin = HAWP.kinetic_energy()
epot = HAWP.potential_energy(Potential.evaluate_eigenvalues_at)
iom.save_energy((ekin, epot), timestep=step, blockid=blockid)
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_wavepacket_timegrid(blockid=blockid)
nrtimesteps = timesteps.shape[0]
Potential = PotentialFactory().create_potential(parameters)
# Retrieve simulation data
params = iom.load_wavepacket_parameters(blockid=blockid)
coeffs = iom.load_wavepacket_coefficients(blockid=blockid)
# A data transformation needed by API specification
coeffs = [ [ coeffs[i,j,:] for j in xrange(parameters["ncomponents"]) ] for i in xrange(nrtimesteps) ]
# We want to save energies, thus add a data slot to the data file
iom.add_energy(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]})
# Initialize a Hagedorn wave packet with the data
HAWP = HagedornWavepacket(parameters)
HAWP.set_quadrature(None)
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Computing energies of timestep "+str(step))
# Configure the wave packet and project to the eigenbasis.
HAWP.set_parameters(params[i])
HAWP.set_coefficients(coeffs[i])
HAWP.project_to_eigen(Potential)
# Compute the energies
ekin = HAWP.kinetic_energy()
epot = HAWP.potential_energy(Potential.evaluate_eigenvalues_at)
iom.save_energy((ekin, epot), timestep=step, blockid=blockid)
def plot_frames_homogeneous(iom, blockid=0, view=None):
"""
:param iom: An ``IOManager`` instance providing the simulation data.
"""
parameters = iom.load_parameters()
# Number of time steps we saved
timesteps = iom.load_wavepacket_timegrid(blockid=blockid)
nrtimesteps = timesteps.shape[0]
# Initialize a Hagedorn wavepacket with the data
Potential = PotentialFactory().create_potential(parameters)
# Retrieve simulation data
grid = iom.load_grid(blockid="global")
params = iom.load_wavepacket_parameters(blockid=blockid)
coeffs = iom.load_wavepacket_coefficients(blockid=blockid)
# A data transformation needed by API specification
coeffs = [ [ coeffs[i,j,:] for j in xrange(parameters["ncomponents"]) ] for i in xrange(nrtimesteps)]
# 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 = HagedornWavepacket(parameters)
HAWP.set_quadrature(None)
# Iterate over all timesteps
for i, step in enumerate(timesteps):
print(" Plotting frame of timestep "+str(step))
# Configure the wavepacket and project to the eigenbasis.
HAWP.set_parameters(params[i])
HAWP.set_coefficients(coeffs[i])
HAWP.project_to_eigen(Potential)
values = HAWP.evaluate_at(grid, prefactor=True)
coeffi = HAWP.get_coefficients()
plot_frame(step, parameters, grid, values, coeffi, index=blockid, view=view)
print(" Plotting frames finished")
def aposteriori_spawning(fin, fout, pin, pout, save_canonical=False):
"""
:param f: An ``IOManager`` instance providing the simulation data.
:param datablock: The data block where the results are.
"""
# Number of time steps we saved
timesteps = fin.load_wavepacket_timegrid()
nrtimesteps = timesteps.shape[0]
params = fin.load_wavepacket_parameters()
coeffs = fin.load_wavepacket_coefficients()
# A data transformation needed by API specification
coeffs = [ [ coeffs[i,j,:] for j in xrange(pin["ncomponents"]) ] for i in xrange(nrtimesteps) ]
# The potential
Potential = PotentialFactory().create_potential(pin)
# Initialize a mother Hagedorn wavepacket with the data from another simulation
HAWP = HagedornWavepacket(pin)
HAWP.set_quadrature(None)
# Initialize an empty wavepacket for spawning
SWP = HagedornWavepacket(pout)
SWP.set_quadrature(None)
# Initialize a Spawner
NAS = NonAdiabaticSpawnerKF(pout)
# Try spawning for these components, if none is given, try it for all.
if not "spawn_components" in parametersout:
components = range(pin["ncomponents"])
else:
components = parametersout["spawn_components"]
# Iterate over all timesteps and spawn
for i, step in enumerate(timesteps):
print(" Try spawning at timestep "+str(step))
# Configure the wave packet and project to the eigenbasis.
HAWP.set_parameters(params[i])
HAWP.set_coefficients(coeffs[i])
# Project to the eigenbasis as the parameter estimation
# has to happen there because of coupling.
T = HAWP.clone()
T.project_to_eigen(Potential)
# Try spawning a new packet for each component
estps = [ NAS.estimate_parameters(T, component=acomp) for acomp in components ]
# The quadrature
quadrature = InhomogeneousQuadrature()
# Quadrature, assume same quadrature order for both packets
# Assure the "right" quadrature is choosen if mother and child have
# different basis sizes
if max(HAWP.get_basis_size()) > max(SWP.get_basis_size()):
quadrature.set_qr(HAWP.get_quadrature().get_qr())
else:
quadrature.set_qr(SWP.get_quadrature().get_qr())
for index, ps in enumerate(estps):
if ps is not None:
# One choice of the sign
U = SWP.clone()
U.set_parameters(ps)
# Project the coefficients to the spawned packet
tmp = T.clone()
NAS.project_coefficients(tmp, U, component=components[index])
# Other choice of the sign
V = SWP.clone()
# Transform parameters
psm = list(ps)
B = ps[0]
Bm = -np.real(B)+1.0j*np.imag(B)
psm[0] = Bm
V.set_parameters(psm)
# Project the coefficients to the spawned packet
tmp = T.clone()
NAS.project_coefficients(tmp, V, component=components[index])
# Compute some inner products to finally determine which parameter set we use
ou = abs(quadrature.quadrature(T,U, component=components[index]))
ov = abs(quadrature.quadrature(T,V, component=components[index]))
# Choose the packet which maximizes the inner product. This is the main point!
if ou >= ov:
U = U
else:
U = V
# Finally do the spawning, this is essentially to get the remainder T right
# The packet U is already ok by now.
NAS.project_coefficients(T, U, component=components[index])
# Transform back
if save_canonical is True:
T.project_to_canonical(Potential)
U.project_to_canonical(Potential)
# Save the mother packet rest
fout.save_wavepacket_parameters(T.get_parameters(), timestep=step, blockid=2*index)
fout.save_wavepacket_coefficients(T.get_coefficients(), timestep=step, blockid=2*index)
# Save the spawned packet
fout.save_wavepacket_parameters(U.get_parameters(), timestep=step, blockid=2*index+1)
fout.save_wavepacket_coefficients(U.get_coefficients(), timestep=step, blockid=2*index+1)
from matplotlib.pyplot import *
from WaveBlocks import HagedornWavepacket
from WaveBlocks import HomogeneousQuadrature
from WaveBlocks import InhomogeneousQuadrature
nmax = 6
params = {}
params["eps"] = 0.2
params["basis_size"] = 4
params["ncomponents"] = 1
WP1 = HagedornWavepacket(params)
WP1.set_parameters((1.0j, 1.0, 0.0, 0.0, 0.85))
WP1.set_coefficient(0, 0, 1)
WP1.set_quadrature(None)
params["basis_size"] = 6
WP2 = HagedornWavepacket(params)
WP2.set_coefficient(0, 0, 1)
WP2.set_quadrature(None)
HQ1 = HomogeneousQuadrature()
HQ1.build_qr(max(WP1.get_basis_size()))
HQ2 = HomogeneousQuadrature()
HQ2.build_qr(max(WP2.get_basis_size()))
x = params["f"] * pi * arange(-1, 1, 2.0/params["ngn"], dtype=np.complexfloating) # Fourierspace grid omega_1 = arange(-params["ngn"]/2.0, 0, 1) omega_2 = arange(0, params["ngn"]/2.0) omega = hstack([omega_1, omega_2]) k = omega / (2*params["f"] * pi) #k = omega / params["ngn"] # A HAWP HAWP = HagedornWavepacket(params) HAWP.set_quadrature(None) HAWP.set_parameters((1j, 1, 0, 3, -2)) HAWP.set_coefficient(0,2,1) # Evaluate in real space y = HAWP.evaluate_at(x)[0] # Transform to Fourier space HAWP.to_fourier_space() # Evaluate in Fourier space w = HAWP.evaluate_at(k)[0] HAWP.to_real_space() # Evaluate in real space again z = HAWP.evaluate_at(x)[0]
@copyright: Copyright (C) 2010, 2011 R. Bourquin
@license: Modified BSD License
"""
from numpy import *
from matplotlib.pyplot import *
from WaveBlocks import HagedornWavepacket
from WaveBlocks.Plot import plotcf
nmax = 10
amp0 = 0.5
params = {}
params["eps"] = 0.2
params["basis_size"] = nmax
params["ncomponents"] = 1
HAWP = HagedornWavepacket(params)
HAWP.set_parameters((1.0j, 1.0, 0.0, -1.0, 0.0))
for i in range(0,nmax):
HAWP.set_coefficient(0, i, amp0/ 2**i)
x = linspace(-4,4,4000)
y = HAWP.evaluate_at(x, prefactor=True, component=0)
figure()
plotcf(x, angle(y), conj(y)*y)
show()