def plot_frame(step, parameters, grid, values, coeffs, index=0, view=None, imgsize=(12,9)):
n = parameters["ncomponents"]
k = array(range(parameters["basis_size"]))
# Start new plot
fig = figure(figsize=imgsize)
for s in xrange(n):
y = values[s]
c = squeeze(coeffs[s])
# Plot the probability densities
ax1 = fig.add_subplot(n,2,2*s+1)
ax1.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
plotcf(grid, angle(y), conj(y)*y)
if view is not None:
ax1.set_xlim(view[:2])
ax1.set_ylim(view[2:])
ax1.set_xlabel(r"$x$")
ax1.set_ylabel(r"$\langle\varphi_"+str(s)+r"|\varphi_"+str(s)+r"\rangle$")
# Plot the coefficients of the Hagedorn wavepacket
ax2 = fig.add_subplot(n,2,2*s+2)
ax2.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
stemcf(k, angle(c), abs(c))
# axis formatting:
m = max(abs(c))
ax2.set_xlim(-1,parameters["basis_size"])
ax2.set_ylim(-0.1*m, 1.1*m)
ax2.set_xlabel(r"$k$")
ax2.set_ylabel(r"$|c|$")
fig.suptitle(r"Time $"+str(step*parameters["dt"])+r"$")
fig.savefig("wavepackets_block"+str(index)+"_"+ (7-len(str(step)))*"0"+str(step) +GD.output_format)
close(fig)
from matplotlib.pyplot import * from WaveBlocks.Plot import stemcf x = np.r_[0.0:2.0*np.pi:1j*2**6] u = np.exp(1.0j*x) rvals = np.real(u) ivals = np.imag(u) cvals = np.conjugate(u)*u angles = np.angle(u) figure(figsize=(20,20)) subplot(2,2,1) stemcf(x, angles, rvals) xlim([0,2*np.pi]) ylim([-1.5, 1.5]) xlabel(r"$\Re \psi$") subplot(2,2,2) stemcf(x, angles, ivals, color="k") xlim([0,2*np.pi]) ylim([-1.5, 1.5]) xlabel(r"$\Im \psi$") subplot(2,2,3) stemcf(x, angles, cvals) xlim([0,2*np.pi]) ylim([0, 1.5]) xlabel(r"$|\psi|^2$")
xlabel(r"$x$") ylabel(r"$|\Psi|^2$") # <codecell> c = Psi.get_coefficients(component=0) c = squeeze(c) # <codecell> c.shape # <codecell> figure(figsize=(6,4)) stemcf(arange(c.shape[0]), angle(c), abs(c)**2) xlabel(r"$k$") ylabel(r"$c_k$") # <markdowncell> # Set up the potential $V(x)$ for our simulation. We use a simple harmonic oscillator. # <codecell> V = PotentialFactory().create_potential(params) # <codecell> V.potential
def plot_frames_homogeneous(iom, gid=0, plotphase=False, plotcomponents=False, plotabssqr=True, view=None, imgsize=(12,9)):
"""
:param f: An ``IOManager`` instance providing the simulation data.
"""
parameters = iom.load_parameters()
grid = iom.load_grid(blockid="global")
k = array(range(parameters["basis_size"]))
# Block IDs for mother and child wavepacket
bidm, bidc = iom.get_block_ids(groupid=gid)
# Precompute eigenvectors for efficiency
Potential = PotentialFactory().create_potential(parameters)
timegrid_m = iom.load_wavefunction_timegrid(blockid=bidm)
timegrid_s = iom.load_wavefunction_timegrid(blockid=bidc)
for step in timegrid_m:
print(" Timestep # " + str(step))
# Retrieve spawn data for both packets
try:
wave_m = iom.load_wavefunction(timestep=step, blockid=bidm)
values_m = [ squeeze(wave_m[j,...]) for j in xrange(parameters["ncomponents"]) ]
coeffs_m = squeeze(iom.load_wavepacket_coefficients(timestep=step, blockid=bidm))
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 = [ squeeze(wave_s[j,...]) for j in xrange(parameters["ncomponents"]) ]
coeffs_s = squeeze(iom.load_wavepacket_coefficients(timestep=step, blockid=bidc))
have_spawn_data = True
except ValueError:
have_spawn_data = False
# Start new plot
fig = figure(figsize=imgsize)
ax1 = subplot2grid((2,2), (0,0), colspan=2)
ax1.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
# Plot original Wavefunction
if have_mother_data is True:
for index, component in enumerate(values_m):
if plotcomponents is True:
ax1.plot(grid, real(component))
ax1.plot(grid, imag(component))
ax1.set_ylabel(r"$\Re \varphi_"+str(index)+r", \Im \varphi_"+str(index)+r"$")
if plotabssqr is True:
ax1.plot(grid, component*conj(component))
ax1.set_ylabel(r"$\langle \varphi_"+str(index)+r"| \varphi_"+str(index)+r"\rangle$")
if plotphase is True:
plotcf(grid, angle(component), component*conj(component))
ax1.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):
if plotcomponents is True:
ax1.plot(grid, real(component))
ax1.plot(grid, imag(component))
ax1.set_ylabel(r"$\Re \varphi_"+str(index)+r", \Im \varphi_"+str(index)+r"$")
if plotabssqr is True:
ax1.plot(grid, component*conj(component))
ax1.set_ylabel(r"$\langle \varphi_"+str(index)+r"| \varphi_"+str(index)+r"\rangle$")
if plotphase is True:
plotcf(grid, angle(component), component*conj(component))
ax1.set_ylabel(r"$\langle \varphi_"+str(index)+r"| \varphi_"+str(index)+r"\rangle$")
ax1.set_xlim(view[0:2])
ax1.set_ylim(view[2:4])
ax1.set_xlabel(r"$x$")
ax1.set_title(r"Densities of mother and spawned packets")
# Plot coefficients for mother packet
if have_mother_data is True:
ax2 = subplot2grid((2,2), (1,0))
ax2.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
stemcf(k, angle(coeffs_m), abs(coeffs_m))
ax2.set_xlim((-1, parameters["basis_size"]))
ax2.set_xlabel(r"$k$")
ax2.set_ylabel(r"$|c|$")
ax2.set_title(r"Mother packet $| \Psi^m \rangle$")
# Plot coefficients for spawned packet
if have_spawn_data is True:
ax3 = subplot2grid((2,2), (1,1))
ax3.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
stemcf(k, angle(coeffs_s), abs(coeffs_s))
ax3.set_xlim((-1, parameters["basis_size"]))
ax3.set_xlabel(r"$k$")
ax3.set_ylabel(r"$|c|$")
ax3.set_title(r"Spawned packet $| \Psi^s \rangle$")
fig.suptitle(r"Time $"+str(step*parameters["dt"])+r"$")
fig.savefig("wavepackets_group"+str(gid)+"_"+ (5-len(str(step)))*"0"+str(step) +GD.output_format)
close(fig)
