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