Пример #1
0
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")
Пример #2
0
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")
Пример #4
0
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)
Пример #6
0
    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")