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_energy_inhawp(iom, blockid=0, eigentrafo=True, iseigen=True): """Compute the energies of a wavepacket timeseries. This function is for inhomogeneous wavepackets. :param iom: An :py:class:`IOManager` instance providing the simulation data. :param blockid: The data block from which the values are read. :type blockid: Integer, Default is ``0`` :param eigentrafo: Whether to make a transformation into the eigenbasis. :type eigentrafo: Boolean, default is ``True``. :param iseigen: Whether the data is assumed to be in the eigenbasis. :type iseigen: Boolean, default is ``True`` """ parameters = iom.load_parameters() BF = BlockFactory() # Number of time steps we saved timesteps = iom.load_inhomogwavepacket_timegrid(blockid=blockid) nrtimesteps = timesteps.shape[0] # The potential used Potential = BF.create_potential(parameters) # Basis transformator if eigentrafo is True: BT = BasisTransformationHAWP(Potential) # We want to save energies, thus add a data slot to the data file iom.add_energy(parameters, timeslots=nrtimesteps, blockid=blockid) # Initialize a Hagedorn wavepacket with the data descr = iom.load_inhomogwavepacket_description(blockid=blockid) HAWP = BF.create_wavepacket(descr) # Inner product if HAWP.get_innerproduct() is None: IP = BF.create_inner_product(parameters["innerproduct"]) HAWP.set_innerproduct(IP) if eigentrafo is True: BT.set_matrix_builder(HAWP.get_innerproduct()) # Basis shapes BS_descr = iom.load_inhomogwavepacket_basisshapes(blockid=blockid) BS = {} for ahash, descr in BS_descr.items(): BS[ahash] = BF.create_basis_shape(descr) O = ObservablesHAWP() KEY = ("q", "p", "Q", "P", "S", "adQ") # Iterate over all timesteps for i, step in enumerate(timesteps): print(" Computing energies of timestep %d" % step) # Retrieve simulation data params = iom.load_inhomogwavepacket_parameters(timestep=step, blockid=blockid, key=KEY) hashes, coeffs = iom.load_inhomogwavepacket_coefficients( timestep=step, get_hashes=True, blockid=blockid) # Configure the wavepacket HAWP.set_parameters(params, key=KEY) HAWP.set_basis_shapes([BS[int(ha)] for ha in hashes]) HAWP.set_coefficients(coeffs) # Transform to the eigenbasis. if eigentrafo is True: BT.transform_to_eigen(HAWP) # Compute the energies O.set_innerproduct(HAWP.get_innerproduct()) O.set_gradient(HAWP.get_gradient_operator()) ekin = O.kinetic_energy(HAWP) if iseigen is True: epot = O.potential_energy(HAWP, Potential.evaluate_eigenvalues_at) else: epot = O.potential_energy(HAWP, Potential.evaluate_at) iom.save_energy((ekin, epot), timestep=step, blockid=blockid)
def compute_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 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 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 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, 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, 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_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()) 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)