def plot_potential(grid, potential, view=None, size=(12,9), fill=False):
# The Grid
u = grid.get_nodes(split=True, flat=False)
u = real(u[0])
# Create potential and evaluate eigenvalues
potew = potential.evaluate_eigenvalues_at(grid)
potew = [ level.reshape(grid.get_number_nodes(overall=False)) for level in potew ]
# Plot the energy surfaces of the potential
fig = figure(figsize=size)
ax = fig.gca()
for index, ew in enumerate(potew):
if fill:
ax.fill(u, ew, facecolor="blue", alpha=0.25)
ax.plot(u, ew, label=r"$\lambda_"+str(index)+r"$")
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.grid(True)
# Set the aspect window
if view is not None:
ax.set_xlim(view[:2])
ax.set_ylim(view[2:])
ax.set_xlabel(r"$x$")
ax.set_ylabel(r"$\lambda_i\left(x\right)$")
legend(loc="outer right")
ax.set_title(r"The eigenvalues $\lambda_i$ of the potential $V\left(x\right)$")
fig.savefig("potential"+GD.output_format)
close(fig)
def plot_potential(grid, potential, view=None, size=(12, 9), path="."):
# The Grid
u = grid.get_nodes(split=True)
u = real(u[0])
# Create potential and evaluate eigenvalues
potew = potential.evaluate_eigenvalues_at(grid)
potew = [real(level).reshape(-1) for level in potew]
# View
if view[0] is None:
view[0] = u.min()
if view[1] is None:
view[1] = u.max()
# Plot the energy surfaces of the potential
fig = figure(figsize=size)
ax = fig.gca()
for index, ew in enumerate(potew):
ax.plot(u, ew, label=r"$\lambda_{%d}$" % index)
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.grid(True)
ax.set_xlim(view[:2])
ax.set_ylim(view[2:])
ax.set_xlabel(r"$x$")
ax.set_ylabel(r"$\lambda_i\left(x\right)$")
legend(loc="outer right")
ax.set_title(r"The eigenvalues $\lambda_i$ of the potential $V\left(x\right)$")
fig.savefig(os.path.join(path, "potential" + GD.output_format))
close(fig)
def plot_autocorrelations(data, index=0):
print("Plotting the autocorrelations of data block '"+str(index)+"'")
timegrid, autocorrelations = data
# Plot the autocorrelations
fig = figure()
ax = fig.gca()
# Plot the autocorrelations of the individual wavepackets
for i, datum in enumerate(autocorrelations[:-1]):
label_i = r"$|\langle \Phi_"+str(i)+r"(0) | \Phi_"+str(i)+r"(t) \rangle|$"
#ax.plot(timegrid, real(datum), label=label_i)
#ax.plot(timegrid, imag(datum), label=label_i)
ax.plot(timegrid, abs(datum), label=label_i)
# Plot the sum of all autocorrelations
ax.plot(timegrid, abs(autocorrelations[-1]), color=(1,0,0), label=r"$\sum_i {|\langle \Phi_i(0) | \Phi_i(t) \rangle|}$")
ax.set_xlim(min(timegrid), max(timegrid))
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.set_title(r"Autocorrelations of $\Psi$")
legend(loc="upper right")
ax.set_xlabel(r"Time $t$")
ax.set_ylim(0, 1.1)
fig.savefig("autocorrelations_block"+str(index)+GD.output_format)
close(fig)
# Plot the autocorrelations
N = len(autocorrelations) -1
fig = figure()
# Plot the autocorrelations of the individual wavepackets
for i, datum in enumerate(autocorrelations[:-1]):
ax = fig.add_subplot(N, 1, i+1)
label_ir = r"$\Re \langle \Phi_"+str(i)+r"(0) | \Phi_"+str(i)+r"(t) \rangle$"
label_ii = r"$\Im \langle \Phi_"+str(i)+r"(0) | \Phi_"+str(i)+r"(t) \rangle$"
label_im = r"$|\langle \Phi_"+str(i)+r"(0) | \Phi_"+str(i)+r"(t) \rangle|$"
ax.plot(timegrid, real(datum), label=label_ir)
ax.plot(timegrid, imag(datum), label=label_ii)
ax.plot(timegrid, abs(datum), label=label_im)
ax.set_xlim(min(timegrid), max(timegrid))
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.set_xlabel(r"Time $t$")
legend(loc="upper right")
ax.set_ylim(0, 1.1)
ax.set_title(r"Autocorrelations of $\Psi$")
fig.savefig("autocorrelations_per_component_block"+str(index)+GD.output_format)
close(fig)
def plot_energies(data, index=0):
print("Plotting the energies of data block '"+str(index)+"'")
timegridk, timegridp, ekin, epot = data
# Plot the energies
fig = figure()
ax = fig.gca()
# Plot the kinetic energy of the individual wave packets
for i, kin in enumerate(ekin[:-1]):
ax.plot(timegridk, kin, label=r"$E^{kin}_"+str(i)+r"$")
# Plot the potential energy of the individual wave packets
for i, pot in enumerate(epot[:-1]):
ax.plot(timegridp, pot, label=r"$E^{pot}_"+str(i)+r"$")
# Plot the sum of kinetic and potential energy for all wave packets
for i, (kin, pot) in enumerate(zip(ekin, epot)[:-1]):
ax.plot(timegridk, kin + pot, label=r"$E^{kin}_"+str(i)+r"+E^{pot}_"+str(i)+r"$")
# Plot sum of kinetic and sum of potential energy
ax.plot(timegridk, ekin[-1], label=r"$\sum_i E^{kin}_i$")
ax.plot(timegridp, epot[-1], label=r"$\sum_i E^{pot}_i$")
# Plot the overall energy of all wave packets
ax.plot(timegridk, ekin[-1] + epot[-1], label=r"$\sum_i E^{kin}_i + \sum_i E^{pot}_i$")
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.grid(True)
ax.set_xlabel(r"Time $t$")
legend(loc="outer right")
ax.set_title(r"Energies of the wavepacket $\Psi$")
fig.savefig("energies_block"+str(index)+GD.output_format)
close(fig)
# Plot the energy drift
e_orig = (ekin[-1]+epot[-1])[0]
data = abs(e_orig-(ekin[-1]+epot[-1]))
fig = figure()
ax = fig.gca()
ax.plot(timegridk, data, label=r"$|E_O^0 - \left( E_k^0 + E_p^0 \right) |$")
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.grid(True)
ax.set_xlabel(r"Time $t$")
ax.set_ylabel(r"$|E_O^0 - \left( E_k^0 + E_p^0 \right) |$")
ax.set_title(r"Energy drift of the wavepacket $\Psi$")
fig.savefig("energy_drift_block"+str(index)+"_lin"+GD.output_format)
close(fig)
fig = figure()
ax = fig.gca()
ax.semilogy(timegridk, data, label=r"$|E_O^0 - \left( E_k^0 + E_p^0 \right) |$")
ax.grid(True)
ax.set_xlabel(r"Time $t$")
ax.set_ylabel(r"$|E_O^0 - \left( E_k^0 + E_p^0 \right) |$")
ax.set_title(r"Energy drift of the wavepacket $\Psi$")
fig.savefig("energy_drift_block"+str(index)+"_log"+GD.output_format)
close(fig)
def plot_autocorrelations(data, blockid=0, view=None, path='.'):
print("Plotting the autocorrelations of data block '%s'" % blockid)
timegrid, autocorrelations, dt = data
if dt is None:
xlbl = r"Timesteps $n$"
dt = 1.0
else:
xlbl = r"Time $t$"
# Filter
time = timegrid * dt
time = where(timegrid < 0, nan, time)
# View
if view[0] is None:
view[0] = nanmin(time)
if view[1] is None:
view[1] = nanmax(time)
if view[2] is None:
view[2] = 0.0
if view[3] is None:
view[3] = 1.1
# Plot the autocorrelations
fig = figure()
ax = fig.gca()
# Plot the autocorrelations of the individual wavepackets
for i, datum in enumerate(autocorrelations[:-1]):
ax.plot(time,
abs(datum),
label=r"$|\langle \Phi_{%d}(0) | \Phi_{%d}(t) \rangle|$" %
(i, i))
# Plot the sum of all autocorrelations
ax.plot(time,
abs(autocorrelations[-1]),
color=(1, 0, 0),
label=r"$\sum_i {|\langle \Phi_i(0) | \Phi_i(t) \rangle|}$")
ax.grid(True)
ax.set_xlim(view[:2])
ax.set_ylim(view[2:])
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.set_title(r"Autocorrelations of $\Psi$")
legend(loc="upper right")
ax.set_xlabel(xlbl)
fig.savefig(
os.path.join(
path, "autocorrelations_block" + str(blockid) + GD.output_format))
close(fig)
# Plot the autocorrelations
N = len(autocorrelations) - 1
fig = figure()
# Plot the autocorrelations of the individual wavepackets
for i, datum in enumerate(autocorrelations[:-1]):
ax = fig.add_subplot(N, 1, i + 1)
ax.plot(time,
real(datum),
label=r"$\Re \langle \Phi_{%d}(0) | \Phi_{%d}(t) \rangle$" %
(i, i))
ax.plot(time,
imag(datum),
label=r"$\Im \langle \Phi_{%d}(0) | \Phi_{%d}(t) \rangle$" %
(i, i))
ax.plot(time,
abs(datum),
label=r"$|\langle \Phi_{%d}(0) | \Phi_{%d}(t) \rangle|$" %
(i, i))
ax.grid(True)
ax.set_xlim(view[:2])
ax.set_ylim(view[2:])
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.set_xlabel(xlbl)
legend(loc="upper right")
ax.set_title(r"Autocorrelations of $\Psi$")
fig.savefig(
os.path.join(
path, "autocorrelations_per_component_block" + str(blockid) +
GD.output_format))
close(fig)
def plot_energies(data, blockid=0, view=None, path='.'):
print("Plotting the energies of data block '{}'".format(blockid))
timegridk, timegridp, ekin, epot, dt = data
if dt is None:
xlbl = r"Timesteps $n$"
dt = 1.0
else:
xlbl = r"Time $t$"
# Filter
timek = timegridk * dt
timep = timegridp * dt
timek = where(timegridk < 0, nan, timek)
timep = where(timegridp < 0, nan, timep)
# View
if view[0] is None:
view[0] = min(nanmin(timek), nanmin(timep))
if view[1] is None:
view[1] = max(nanmax(timek), nanmax(timep))
# Plot the energies
fig = figure()
ax = fig.gca()
# Plot the kinetic energy of the individual wave packets
for i, kin in enumerate(ekin[:-1]):
ax.plot(timek, kin, label=r"$E^{kin}_{%d}$" % i)
# Plot the potential energy of the individual wave packets
for i, pot in enumerate(epot[:-1]):
ax.plot(timep, pot, label=r"$E^{pot}_{%d}$" % i)
# Plot the sum of kinetic and potential energy for all wave packets
for i, (kin, pot) in enumerate(list(zip(ekin, epot))[:-1]):
ax.plot(timek,
kin + pot,
label=r"$E^{kin}_{%d}+E^{pot}_{%d}$" % (i, i))
# Plot sum of kinetic and sum of potential energy
ax.plot(timek, ekin[-1], label=r"$\sum_i E^{kin}_i$")
ax.plot(timep, epot[-1], label=r"$\sum_i E^{pot}_i$")
# Plot the overall energy of all wave packets
ax.plot(timek,
ekin[-1] + epot[-1],
label=r"$\sum_i E^{kin}_i + \sum_i E^{pot}_i$")
ax.set_xlim(view[:2])
if None not in view[2:]:
ax.set_ylim(view[2:])
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.grid(True)
ax.set_xlabel(xlbl)
legend(loc="outer right")
ax.set_title(r"Energies of the wavepacket $\Psi$")
fig.savefig(
os.path.join(path, "energies_block" + str(blockid) + GD.output_format))
close(fig)
# Plot the energy drift
e_orig = (ekin[-1] + epot[-1])[0]
data = abs(e_orig - (ekin[-1] + epot[-1]))
fig = figure()
ax = fig.gca()
ax.plot(timek, data, label=r"$|E_O^0 - \left( E_k^0 + E_p^0 \right) |$")
ax.set_xlim(view[:2])
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.grid(True)
ax.set_xlabel(xlbl)
ax.set_ylabel(r"$|E_O^0 - \left( E_k^0 + E_p^0 \right) |$")
ax.set_title(r"Energy drift of the wavepacket $\Psi$")
fig.savefig(
os.path.join(
path,
"energy_drift_block" + str(blockid) + "_lin" + GD.output_format))
close(fig)
fig = figure()
ax = fig.gca()
ax.semilogy(timek,
data,
label=r"$|E_O^0 - \left( E_k^0 + E_p^0 \right) |$")
ax.set_xlim(view[:2])
ax.grid(True)
ax.set_xlabel(xlbl)
ax.set_ylabel(r"$|E_O^0 - \left( E_k^0 + E_p^0 \right) |$")
ax.set_title(r"Energy drift of the wavepacket $\Psi$")
fig.savefig(
os.path.join(
path,
"energy_drift_block" + str(blockid) + "_log" + GD.output_format))
close(fig)
def plot_norms(data, blockid=0, view=None, path='.'):
print("Plotting the norms of data block '{}'".format(blockid))
timegrid, norms, dt = data
# Filter
time = timegrid * dt
time = where(timegrid < 0, nan, time)
if dt is None:
xlbl = r"Timesteps $n$"
dt = 1.0
else:
xlbl = r"Time $t$"
# View
if view[0] is None:
view[0] = nanmin(time)
if view[1] is None:
view[1] = nanmax(time)
if view[2] is None:
view[2] = 0.0
if view[3] is None:
view[3] = 1.1 * max(norms[-1])
# Plot the norms
fig = figure()
ax = fig.gca()
# Plot the norms of the individual wavepackets
for i, norm in enumerate(norms[:-1]):
label_i = r"$\| \Phi_{%d} \|$" % i
ax.plot(time, norm, label=label_i)
# Plot the sum of all norms
ax.plot(time, norms[-1], color=(1, 0, 0), label=r"${\sqrt{\sum_i {\| \Phi_i \|^2}}}$")
ax.grid(True)
ax.set_xlim(view[:2])
ax.set_ylim(view[2], view[3])
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.set_title(r"Norms of $\Psi$")
legend(loc="outer right")
ax.set_xlabel(xlbl)
fig.savefig(os.path.join(path, "norms_block"+str(blockid)+GD.output_format))
close(fig)
fig = figure()
ax = fig.gca()
# Plot the squared norms of the individual wavepackets
for i, norm in enumerate(norms[:-1]):
label_i = r"$\| \Phi_{%d} \|^2$" % i
ax.plot(time, norm**2, label=label_i)
# Plot the squared sum of all norms
ax.plot(time, norms[-1]**2, color=(1, 0, 0), label=r"${\sum_i {\| \Phi_i \|^2}}$")
ax.grid(True)
ax.set_xlim(view[:2])
ax.set_ylim(view[2], view[3]**2)
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.set_title(r"Squared norms of $\Psi$")
legend(loc="outer right")
ax.set_xlabel(xlbl)
fig.savefig(os.path.join(path, "norms_sqr_block"+str(blockid)+GD.output_format))
close(fig)
# Plot the difference from the theoretical norm
fig = figure()
ax = fig.gca()
ax.plot(time, abs(norms[-1][0] - norms[-1]), label=r"$\|\Psi\|_0 - \|\Psi\|_t$")
ax.grid(True)
ax.set_xlim(view[:2])
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.set_title(r"Drift of $\| \Psi \|$")
legend(loc="outer right")
ax.set_xlabel(xlbl)
ax.set_ylabel(r"$\|\Psi\|_0 - \|\Psi\|_t$")
fig.savefig(os.path.join(path, "norms_drift_block"+str(blockid)+GD.output_format))
close(fig)
fig = figure()
ax = fig.gca()
ax.semilogy(time, abs(norms[-1][0] - norms[-1]), label=r"$\|\Psi\|_0 - \|\Psi\|_t$")
ax.set_xlim(view[:2])
ax.grid(True)
ax.set_title(r"Drift of $\| \Psi \|$")
legend(loc="outer right")
ax.set_xlabel(xlbl)
ax.set_ylabel(r"$\|\Psi\|_0 - \|\Psi\|_t$")
fig.savefig(os.path.join(path, "norms_drift_block"+str(blockid)+"_log"+GD.output_format))
close(fig)
def plot_norms(data, index=0):
print("Plotting the norms of data block '"+str(index)+"'")
timegrid, norms = data
# Plot the norms
fig = figure()
ax = fig.gca()
# Plot the norms of the individual wavepackets
for i, datum in enumerate(norms[:-1]):
label_i = r"$\| \Phi_"+str(i)+r" \|$"
ax.plot(timegrid, datum, label=label_i)
# Plot the sum of all norms
ax.plot(timegrid, norms[-1], color=(1,0,0), label=r"${\sqrt{\sum_i {\| \Phi_i \|^2}}}$")
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.set_title(r"Norms of $\Psi$")
legend(loc="outer right")
ax.set_xlabel(r"Time $t$")
ax.set_ylim([0,1.1*max(norms[:-1])])
fig.savefig("norms_block"+str(index)+GD.output_format)
close(fig)
fig = figure()
ax = fig.gca()
# Plot the squared norms of the individual wavepackets
for i, datum in enumerate(norms[:-1]):
label_i = r"$\| \Phi_"+str(i)+r" \|^2$"
ax.plot(timegrid, datum**2, label=label_i)
# Plot the squared sum of all norms
ax.plot(timegrid, norms[-1]**2, color=(1,0,0), label=r"${\sum_i {\| \Phi_i \|^2}}$")
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.set_title(r"Squared norms of $\Psi$")
legend(loc="outer right")
ax.set_xlabel(r"Time $t$")
ax.set_ylim([0,1.1*max(norms[-1]**2)])
fig.savefig("norms_sqr_block"+str(index)+GD.output_format)
close(fig)
# Plot the difference from the theoretical norm
fig = figure()
ax = fig.gca()
ax.plot(timegrid, abs(norms[-1][0] - norms[-1]), label=r"$\|\Psi\|_0 - \|\Psi\|_t$")
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.set_title(r"Drift of $\| \Psi \|$")
legend(loc="outer right")
ax.set_xlabel(r"Time $t$")
ax.set_ylabel(r"$\|\Psi\|_0 - \|\Psi\|_t$")
fig.savefig("norms_drift_block"+str(index)+GD.output_format)
close(fig)
fig = figure()
ax = fig.gca()
ax.semilogy(timegrid, abs(norms[-1][0] - norms[-1]), label=r"$\|\Psi\|_0 - \|\Psi\|_t$")
ax.grid(True)
ax.set_title(r"Drift of $\| \Psi \|$")
legend(loc="outer right")
ax.set_xlabel(r"Time $t$")
ax.set_ylabel(r"$\|\Psi\|_0 - \|\Psi\|_t$")
fig.savefig("norms_drift_block"+str(index)+"_log"+GD.output_format)
close(fig)
def plot_norms(data, blockid=0, view=None, path='.'):
print("Plotting the norms of data block '{}'".format(blockid))
timegrid, norms, dt = data
if dt is None:
xlbl = r"Timesteps $n$"
dt = 1.0
else:
xlbl = r"Time $t$"
# Filter
time = timegrid * dt
time = where(timegrid < 0, nan, time)
# View
if view[0] is None:
view[0] = nanmin(time)
if view[1] is None:
view[1] = nanmax(time)
if view[2] is None:
view[2] = 0.0
if view[3] is None:
view[3] = 1.1 * max(norms[-1])
# Plot the norms
fig = figure()
ax = fig.gca()
# Plot the norms of the individual wavepackets
for i, norm in enumerate(norms[:-1]):
label_i = r"$\| \Phi_{%d} \|$" % i
ax.plot(time, norm, label=label_i)
# Plot the sum of all norms
ax.plot(time,
norms[-1],
color=(1, 0, 0),
label=r"${\sqrt{\sum_i {\| \Phi_i \|^2}}}$")
ax.grid(True)
ax.set_xlim(view[:2])
ax.set_ylim(view[2], view[3])
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.set_title(r"Norms of $\Psi$")
legend(loc="outer right")
ax.set_xlabel(xlbl)
fig.savefig(
os.path.join(path, "norms_block" + str(blockid) + GD.output_format))
close(fig)
fig = figure()
ax = fig.gca()
# Plot the squared norms of the individual wavepackets
for i, norm in enumerate(norms[:-1]):
label_i = r"$\| \Phi_{%d} \|^2$" % i
ax.plot(time, norm**2, label=label_i)
# Plot the squared sum of all norms
ax.plot(time,
norms[-1]**2,
color=(1, 0, 0),
label=r"${\sum_i {\| \Phi_i \|^2}}$")
ax.grid(True)
ax.set_xlim(view[:2])
ax.set_ylim(view[2], view[3]**2)
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.set_title(r"Squared norms of $\Psi$")
legend(loc="outer right")
ax.set_xlabel(xlbl)
fig.savefig(
os.path.join(path,
"norms_sqr_block" + str(blockid) + GD.output_format))
close(fig)
# Plot the difference from the theoretical norm
fig = figure()
ax = fig.gca()
ax.plot(time,
abs(norms[-1][0] - norms[-1]),
label=r"$\|\Psi\|_0 - \|\Psi\|_t$")
ax.grid(True)
ax.set_xlim(view[:2])
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.set_title(r"Drift of $\| \Psi \|$")
legend(loc="outer right")
ax.set_xlabel(xlbl)
ax.set_ylabel(r"$\|\Psi\|_0 - \|\Psi\|_t$")
fig.savefig(
os.path.join(path,
"norms_drift_block" + str(blockid) + GD.output_format))
close(fig)
fig = figure()
ax = fig.gca()
ax.semilogy(time,
abs(norms[-1][0] - norms[-1]),
label=r"$\|\Psi\|_0 - \|\Psi\|_t$")
ax.set_xlim(view[:2])
ax.grid(True)
ax.set_title(r"Drift of $\| \Psi \|$")
legend(loc="outer right")
ax.set_xlabel(xlbl)
ax.set_ylabel(r"$\|\Psi\|_0 - \|\Psi\|_t$")
fig.savefig(
os.path.join(
path,
"norms_drift_block" + str(blockid) + "_log" + GD.output_format))
close(fig)
def plot_norms(data, index=0):
print("Plotting the norms of data block '" + str(index) + "'")
timegrid, norms = data
# Plot the norms
fig = figure()
ax = fig.gca()
# Plot the norms of the individual wavepackets
for i, datum in enumerate(norms[:-1]):
label_i = r"$\| \Phi_" + str(i) + r" \|$"
ax.plot(timegrid, datum, label=label_i)
# Plot the sum of all norms
ax.plot(timegrid,
norms[-1],
color=(1, 0, 0),
label=r"${\sqrt{\sum_i {\| \Phi_i \|^2}}}$")
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.set_title(r"Norms of $\Psi$")
legend(loc="outer right")
ax.set_xlabel(r"Time $t$")
ax.set_ylim([0, 1.1 * max(norms[:-1])])
fig.savefig("norms_block" + str(index) + GD.output_format)
close(fig)
fig = figure()
ax = fig.gca()
# Plot the squared norms of the individual wavepackets
for i, datum in enumerate(norms[:-1]):
label_i = r"$\| \Phi_" + str(i) + r" \|^2$"
ax.plot(timegrid, datum**2, label=label_i)
# Plot the squared sum of all norms
ax.plot(timegrid,
norms[-1]**2,
color=(1, 0, 0),
label=r"${\sum_i {\| \Phi_i \|^2}}$")
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.set_title(r"Squared norms of $\Psi$")
legend(loc="outer right")
ax.set_xlabel(r"Time $t$")
ax.set_ylim([0, 1.1 * max(norms[-1]**2)])
fig.savefig("norms_sqr_block" + str(index) + GD.output_format)
close(fig)
# Plot the difference from the theoretical norm
fig = figure()
ax = fig.gca()
ax.plot(timegrid,
abs(norms[-1][0] - norms[-1]),
label=r"$\|\Psi\|_0 - \|\Psi\|_t$")
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.set_title(r"Drift of $\| \Psi \|$")
legend(loc="outer right")
ax.set_xlabel(r"Time $t$")
ax.set_ylabel(r"$\|\Psi\|_0 - \|\Psi\|_t$")
fig.savefig("norms_drift_block" + str(index) + GD.output_format)
close(fig)
fig = figure()
ax = fig.gca()
ax.semilogy(timegrid,
abs(norms[-1][0] - norms[-1]),
label=r"$\|\Psi\|_0 - \|\Psi\|_t$")
ax.grid(True)
ax.set_title(r"Drift of $\| \Psi \|$")
legend(loc="outer right")
ax.set_xlabel(r"Time $t$")
ax.set_ylabel(r"$\|\Psi\|_0 - \|\Psi\|_t$")
fig.savefig("norms_drift_block" + str(index) + "_log" + GD.output_format)
close(fig)
def plot_energies(data, index=0):
print("Plotting the energies of data block '" + str(index) + "'")
timegridk, timegridp, ekin, epot = data
# Plot the energies
fig = figure()
ax = fig.gca()
# Plot the kinetic energy of the individual wave packets
for i, kin in enumerate(ekin[:-1]):
ax.plot(timegridk, kin, label=r"$E^{kin}_" + str(i) + r"$")
# Plot the potential energy of the individual wave packets
for i, pot in enumerate(epot[:-1]):
ax.plot(timegridp, pot, label=r"$E^{pot}_" + str(i) + r"$")
# Plot the sum of kinetic and potential energy for all wave packets
for i, (kin, pot) in enumerate(zip(ekin, epot)[:-1]):
ax.plot(timegridk,
kin + pot,
label=r"$E^{kin}_" + str(i) + r"+E^{pot}_" + str(i) + r"$")
# Plot sum of kinetic and sum of potential energy
ax.plot(timegridk, ekin[-1], label=r"$\sum_i E^{kin}_i$")
ax.plot(timegridp, epot[-1], label=r"$\sum_i E^{pot}_i$")
# Plot the overall energy of all wave packets
ax.plot(timegridk,
ekin[-1] + epot[-1],
label=r"$\sum_i E^{kin}_i + \sum_i E^{pot}_i$")
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.grid(True)
ax.set_xlabel(r"Time $t$")
legend(loc="outer right")
ax.set_title(r"Energies of the wavepacket $\Psi$")
fig.savefig("energies_block" + str(index) + GD.output_format)
close(fig)
# Plot the energy drift
e_orig = (ekin[-1] + epot[-1])[0]
data = abs(e_orig - (ekin[-1] + epot[-1]))
fig = figure()
ax = fig.gca()
ax.plot(timegridk,
data,
label=r"$|E_O^0 - \left( E_k^0 + E_p^0 \right) |$")
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.grid(True)
ax.set_xlabel(r"Time $t$")
ax.set_ylabel(r"$|E_O^0 - \left( E_k^0 + E_p^0 \right) |$")
ax.set_title(r"Energy drift of the wavepacket $\Psi$")
fig.savefig("energy_drift_block" + str(index) + "_lin" + GD.output_format)
close(fig)
fig = figure()
ax = fig.gca()
ax.semilogy(timegridk,
data,
label=r"$|E_O^0 - \left( E_k^0 + E_p^0 \right) |$")
ax.grid(True)
ax.set_xlabel(r"Time $t$")
ax.set_ylabel(r"$|E_O^0 - \left( E_k^0 + E_p^0 \right) |$")
ax.set_title(r"Energy drift of the wavepacket $\Psi$")
fig.savefig("energy_drift_block" + str(index) + "_log" + GD.output_format)
close(fig)
def plot_autocorrelations(data, blockid=0, view=None, path='.'):
print("Plotting the autocorrelations of data block '%s'" % blockid)
timegrid, autocorrelations, dt = data
if dt is None:
xlbl = r"Timesteps $n$"
dt = 1.0
else:
xlbl = r"Time $t$"
# Filter
time = timegrid * dt
time = where(timegrid < 0, nan, time)
# View
if view[0] is None:
view[0] = nanmin(time)
if view[1] is None:
view[1] = nanmax(time)
if view[2] is None:
view[2] = 0.0
if view[3] is None:
view[3] = 1.1
# Plot the autocorrelations
fig = figure()
ax = fig.gca()
# Plot the autocorrelations of the individual wavepackets
for i, datum in enumerate(autocorrelations[:-1]):
ax.plot(time, abs(datum), label=r"$|\langle \Phi_{%d}(0) | \Phi_{%d}(t) \rangle|$" % (i, i))
# Plot the sum of all autocorrelations
ax.plot(time, abs(autocorrelations[-1]), color=(1, 0, 0), label=r"$\sum_i {|\langle \Phi_i(0) | \Phi_i(t) \rangle|}$")
ax.grid(True)
ax.set_xlim(view[:2])
ax.set_ylim(view[2:])
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.set_title(r"Autocorrelations of $\Psi$")
legend(loc="upper right")
ax.set_xlabel(xlbl)
fig.savefig(os.path.join(path, "autocorrelations_block" + str(blockid) + GD.output_format))
close(fig)
# Plot the autocorrelations
N = len(autocorrelations) - 1
fig = figure()
# Plot the autocorrelations of the individual wavepackets
for i, datum in enumerate(autocorrelations[:-1]):
ax = fig.add_subplot(N, 1, i + 1)
ax.plot(time, real(datum), label=r"$\Re \langle \Phi_{%d}(0) | \Phi_{%d}(t) \rangle$" % (i, i))
ax.plot(time, imag(datum), label=r"$\Im \langle \Phi_{%d}(0) | \Phi_{%d}(t) \rangle$" % (i, i))
ax.plot(time, abs(datum), label=r"$|\langle \Phi_{%d}(0) | \Phi_{%d}(t) \rangle|$" % (i, i))
ax.grid(True)
ax.set_xlim(view[:2])
ax.set_ylim(view[2:])
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.set_xlabel(xlbl)
legend(loc="upper right")
ax.set_title(r"Autocorrelations of $\Psi$")
fig.savefig(os.path.join(path, "autocorrelations_per_component_block" + str(blockid) + GD.output_format))
close(fig)
def plot_energies(data, blockid=0, view=None, path='.'):
print("Plotting the energies of data block '{}'".format(blockid))
timegridk, timegridp, ekin, epot, dt = data
if dt is None:
xlbl = r"Timesteps $n$"
dt = 1.0
else:
xlbl = r"Time $t$"
# Filter
timek = timegridk * dt
timep = timegridp * dt
timek = where(timegridk < 0, nan, timek)
timep = where(timegridp < 0, nan, timep)
# View
if view[0] is None:
view[0] = min(nanmin(timek), nanmin(timep))
if view[1] is None:
view[1] = max(nanmax(timek), nanmax(timep))
# Plot the energies
fig = figure()
ax = fig.gca()
# Plot the kinetic energy of the individual wave packets
for i, kin in enumerate(ekin[:-1]):
ax.plot(timek, kin, label=r"$E^{kin}_{%d}$" % i)
# Plot the potential energy of the individual wave packets
for i, pot in enumerate(epot[:-1]):
ax.plot(timep, pot, label=r"$E^{pot}_{%d}$" % i)
# Plot the sum of kinetic and potential energy for all wave packets
for i, (kin, pot) in enumerate(list(zip(ekin, epot))[:-1]):
ax.plot(timek, kin + pot, label=r"$E^{kin}_{%d}+E^{pot}_{%d}$" % (i, i))
# Plot sum of kinetic and sum of potential energy
ax.plot(timek, ekin[-1], label=r"$\sum_i E^{kin}_i$")
ax.plot(timep, epot[-1], label=r"$\sum_i E^{pot}_i$")
# Plot the overall energy of all wave packets
ax.plot(timek, ekin[-1] + epot[-1], label=r"$\sum_i E^{kin}_i + \sum_i E^{pot}_i$")
ax.set_xlim(view[:2])
if None not in view[2:]:
ax.set_ylim(view[2:])
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.grid(True)
ax.set_xlabel(xlbl)
legend(loc="outer right")
ax.set_title(r"Energies of the wavepacket $\Psi$")
fig.savefig(os.path.join(path, "energies_block" + str(blockid) + GD.output_format))
close(fig)
# Plot the energy drift
e_orig = (ekin[-1] + epot[-1])[0]
data = abs(e_orig - (ekin[-1] + epot[-1]))
fig = figure()
ax = fig.gca()
ax.plot(timek, data, label=r"$|E_O^0 - \left( E_k^0 + E_p^0 \right) |$")
ax.set_xlim(view[:2])
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.grid(True)
ax.set_xlabel(xlbl)
ax.set_ylabel(r"$|E_O^0 - \left( E_k^0 + E_p^0 \right) |$")
ax.set_title(r"Energy drift of the wavepacket $\Psi$")
fig.savefig(os.path.join(path, "energy_drift_block" + str(blockid) + "_lin" + GD.output_format))
close(fig)
fig = figure()
ax = fig.gca()
ax.semilogy(timek, data, label=r"$|E_O^0 - \left( E_k^0 + E_p^0 \right) |$")
ax.set_xlim(view[:2])
ax.grid(True)
ax.set_xlabel(xlbl)
ax.set_ylabel(r"$|E_O^0 - \left( E_k^0 + E_p^0 \right) |$")
ax.set_title(r"Energy drift of the wavepacket $\Psi$")
fig.savefig(os.path.join(path, "energy_drift_block" + str(blockid) + "_log" + GD.output_format))
close(fig)