def plot_frames(iom, blockid=0, view=None, plotphase=True, plotcomponents=False, plotabssqr=False, imgsize=(12,9)): """Plot the wave function for a series of timesteps. :param iom: An ``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() grid = iom.load_grid(blockid="global") timegrid = iom.load_wavefunction_timegrid(blockid=blockid) # Precompute eigenvectors for efficiency Potential = PotentialFactory().create_potential(parameters) eigenvectors = Potential.evaluate_eigenvectors_at(grid) 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"]) ] # Transform the values to the eigenbasis # TODO: improve this: if parameters["algorithm"] == "fourier": ve = Potential.project_to_eigen(grid, values, eigenvectors) else: ve = values # Plot the probability densities projected to the eigenbasis fig = figure(figsize=imgsize) for index, component in enumerate(ve): 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"$\Re \varphi_"+str(index)+r", \Im \varphi_"+str(index)+r"$") if plotabssqr is True: ax.plot(grid, component*conj(component)) ax.set_ylabel(r"$\langle \varphi_"+str(index)+r"| \varphi_"+str(index)+r"\rangle$") if plotphase is True: plotcf(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:]) fig.suptitle(r"$\Psi$ at time $"+str(step*parameters["dt"])+r"$") fig.savefig("wavefunction_block"+str(blockid)+"_"+ (7-len(str(step)))*"0"+str(step) +GD.output_format) close(fig) print(" Plotting frames finished")
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 plot_frames(iom, blockid=0, view=None, imgsize=(12,9)): """Plot the phase of a wavefunction for a series of timesteps. :param iom: An ``IOManager`` instance providing the simulation data. :param view: The aspect ratio. """ parameters = iom.load_parameters() grid = iom.load_grid(blockid="global") timegrid = iom.load_wavefunction_timegrid(blockid=blockid) # Precompute eigenvectors for efficiency Potential = PotentialFactory().create_potential(parameters) eigenvectors = Potential.evaluate_eigenvectors_at(grid) 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"]) ] # Transform the values to the eigenbasis # TODO: improve this: if parameters["algorithm"] == "fourier": ve = Potential.project_to_eigen(grid, values, eigenvectors) else: ve = values fig = figure(figsize=imgsize) for index, component in enumerate(ve): ax = fig.add_subplot(parameters["ncomponents"],1,index+1) ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y") # Plot the wavefunction ax.plot(grid, component*conj(component), color="gray") ax.set_ylabel(r"$\langle \varphi_"+str(index)+r"| \varphi_"+str(index)+r"\rangle$") ax.set_xlabel(r"$x$") # Compute the phase from the wavefunction restricted to "important" regions restr_grid = grid[component*conj(component) > 10e-8] restr_comp = component[component*conj(component) > 10e-8] # Plot the phase ax.plot(restr_grid, angle(restr_comp), "-", color="green") ax.plot(restr_grid, ComplexMath.continuate(angle(restr_comp)), ".", color="green") # Set the aspect window if view is not None: ax.set_xlim(view[:2]) #ax.set_ylim(view[2:]) fig.suptitle(r"$\arg \Psi$ at time $"+str(step*parameters["dt"])+r"$") fig.savefig("wavefunction_phase_block"+str(blockid)+"_"+ (7-len(str(step)))*"0"+str(step) +GD.output_format) close(fig) print(" Plotting frames finished")
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(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)
potname = pot.replace("_","\_") 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"] = pot P = PotentialFactory().create_potential(params) y = P.evaluate_eigenvalues_at(x) # Plot the potential figure() for yvals in y: plot(x, yvals) xlabel(r"$x$") ylabel(r"$\lambda_i\left(x\right)$") xlim(min(x), max(x)) savefig(pot + ".pdf") # The latex code ls = """ \\begin{minipage}{0.5\\linewidth} Name: \\texttt{""" + potname + """}
def plot_frames(iom, gid=0, view=None, plotphase=True, plotcomponents=False, plotabssqr=False, imgsize=(12,9)): """Plot the wave function for a series of timesteps. :param iom: An ``IOManager`` instance providing the simulation data. :param gid: The group ID of the group where the two packets are stored. :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() # Block IDs for mother and child wavepacket bidm, bidc = iom.get_block_ids(groupid=gid) grid = iom.load_grid(blockid="global") # Precompute eigenvectors for efficiency Potential = PotentialFactory().create_potential(parameters) eigenvectors = Potential.evaluate_eigenvectors_at(grid) timegrid = iom.load_wavefunction_timegrid(blockid=bidm) for step in timegrid: print(" Timestep # " + str(step)) # Retrieve spawn data for both packets try: wave_m = iom.load_wavefunction(timestep=step, blockid=bidm) values_m = [ wave_m[j,...] for j in xrange(parameters["ncomponents"]) ] have_mother_data = True except ValueError: have_mother_data = False # Retrieve spawn data try: wave_s = iom.load_wavefunction(timestep=step, blockid=bidc) values_s = [ wave_s[j,...] for j in xrange(parameters["ncomponents"]) ] have_spawn_data = True except ValueError: have_spawn_data = False # Plot the probability densities projected to the eigenbasis fig = figure(figsize=imgsize) # Create a bunch of subplots axes = [] for index, component in enumerate(values_m): ax = fig.add_subplot(parameters["ncomponents"],1,index+1) ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y") axes.append(ax) # Plot original Wavefunction if have_mother_data is True: for index, component in enumerate(values_m): if plotcomponents is True: axes[index].plot(grid, real(component)) axes[index].plot(grid, imag(component)) axes[index].set_ylabel(r"$\Re \varphi_"+str(index)+r", \Im \varphi_"+str(index)+r"$") if plotabssqr is True: axes[index].plot(grid, component*conj(component)) axes[index].set_ylabel(r"$\langle \varphi_"+str(index)+r"| \varphi_"+str(index)+r"\rangle$") if plotphase is True: plotcf(grid, angle(component), component*conj(component)) axes[index].set_ylabel(r"$\langle \varphi_"+str(index)+r"| \varphi_"+str(index)+r"\rangle$") # Overlay spawned parts if have_spawn_data is True: for index, component in enumerate(values_s): axes[index].plot(grid, component*conj(component), "-r") axes[index].set_ylabel(r"$\langle \varphi_"+str(index)+r"| \varphi_"+str(index)+r"\rangle$") # Set the axis properties for index in xrange(len(values_m)): axes[index].set_xlabel(r"$x$") # Set the aspect window if view is not None: axes[index].set_xlim(view[:2]) axes[index].set_ylim(view[2:]) fig.suptitle(r"$\Psi$ at time $"+str(step*parameters["dt"])+r"$") fig.savefig("wavefunction_"+ (5-len(str(step)))*"0"+str(step) +GD.output_format) close(fig) print(" Plotting frames finished")
def plot_frames_split(iom, gid=0, view=None, plotphase=True, plotcomponents=False, plotabssqr=False, imgsize=(12,9)): """Plot the wave function for a series of timesteps. :param iom: An ``IOManager`` instance providing the simulation data. :param gid: The group ID of the group where the two packets are stored. :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() n = parameters["ncomponents"] # Block IDs for mother and child wavepacket bidm, bidc = iom.get_block_ids(groupid=gid) grid = iom.load_grid(blockid="global") # Precompute eigenvectors for efficiency Potential = PotentialFactory().create_potential(parameters) eigenvectors = Potential.evaluate_eigenvectors_at(grid) timegrid = iom.load_wavefunction_timegrid(blockid=bidm) for step in timegrid: print(" Timestep # " + str(step)) # Split grid gl = grid[grid<=X0] gr = grid[grid>X0] # Retrieve spawn data for both packets and split the data as necessary try: wave_m = iom.load_wavefunction(timestep=step, blockid=bidm) values_m = [ wave_m[j,...] for j in xrange(parameters["ncomponents"]) ] yl = values_m[0][grid<=X0] yr = values_m[0][grid>X0] have_mother_data = True except ValueError: have_mother_data = False # Retrieve spawn data try: wave_s = iom.load_wavefunction(timestep=step, blockid=bidc) values_s = [ wave_s[j,...] for j in xrange(parameters["ncomponents"]) ] ysl = values_s[0][grid<=X0] ysr = values_s[0][grid>X0] have_spawn_data = True except ValueError: have_spawn_data = False # Plot the probability densities projected to the eigenbasis fig = figure(figsize=imgsize) # Plot the probability density, left to X0 ax1 = fig.add_subplot(1,2,1) ax1.ticklabel_format(style="sci", scilimits=(0,0), axis="y") # mother if have_mother_data is True: plotcf(gl, angle(yl), conj(yl)*yl) # spawned if have_spawn_data is True: plot(gl, conj(ysl)*ysl, "-r") if view is not None: ax1.set_xlim(view[0],0) ax1.set_ylim(view[2:4]) ax1.set_xlabel(r"$x \le 0$") ax1.set_ylabel(r"$\langle\varphi |\varphi \rangle$") # Plot the probability density, right to X0 ax2 = fig.add_subplot(1,2,2) ax2.ticklabel_format(style="sci", scilimits=(0,0), axis="y") # mother if have_mother_data is True: plotcf(gr, angle(yr), conj(yr)*yr) # spawned if have_spawn_data is True: plot(gr, conj(ysr)*ysr, "-r") if view is not None: ax2.set_xlim(0, view[1]) ax2.set_ylim(view[4:]) ax2.set_xlabel(r"$x > 0$") ax2.set_ylabel(r"$\langle\varphi |\varphi \rangle$") fig.suptitle(r"Time $"+str(step*parameters["dt"])+r"$") fig.savefig("wavepackets_"+ (5-len(str(step)))*"0"+str(step) +GD.output_format) close(fig) print(" Plotting frames finished")