def plot_data(groupdata, axisdata, normdata, which_norm="L2"):
nona = "L^2" if which_norm == "L2" else "\infty"
for groupd, axisd, normd in zip(groupdata, axisdata, normdata):
# Plot the error time series for each simulation
fig = figure()
ax = fig.gca()
for cur_axisd, cur_norm in zip(axisd, normd):
# One single component in |\Psi>
if cur_norm.shape[1] == 1:
ax.plot(cur_axisd[1]*cur_axisd[0].dt, cur_norm, label=r"$\varepsilon = $" + str(cur_axisd[0].eps))
# More than one component in |\Psi>
else:
# Plot all the error norms for all components individually
for i in xrange(cur_norm.shape[1]-1):
ax.semilogy(cur_axisd[1]*cur_axisd[0].dt, cur_norm[:,i], label=r"$\varepsilon = $" + str(cur_axisd[0].eps) + r", $c_"+str(i)+r"$")
# Plot the overall summed error norm
ax.semilogy(cur_axisd[1]*cur_axisd[0].dt, cur_norm[:,-1], label=r"$\varepsilon = $" + str(cur_axisd[0].eps) +r", $\sum_i c_i$")
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.set_xlabel(r"$t$")
ax.set_ylabel(r"$\| \phi^F - \phi^H \|_{"+nona+r"}$")
ax.set_title(r"Timeseries of $\| \phi_f - \phi_h \|_{"+nona+r"}$ ")
legend()
fig.savefig("error_timevolution_"+which_norm+"_all"+GD.output_format)
close(fig)
def plot_energies(data, index=0):
print("Plotting the energies of data block '"+str(index)+"'")
timegrid, 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(timegrid, 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(timegrid, 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(timegrid, 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(timegrid, ekin[-1], label=r"$\sum_i E^{kin}_i$")
ax.plot(timegrid, epot[-1], label=r"$\sum_i E^{pot}_i$")
# Plot the overall energy of all wave packets
ax.plot(timegrid, 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(timegrid, 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)+GD.output_format)
close(fig)
def plot_data(axisdata, ekindata, epotdata, number_simulations, number_components):
colormap = ["b", "g", "r", "c", "m", "y", "b"]
# Plot the time series for each simulation
fig = figure()
ax = fig.gca()
for index in xrange(number_simulations):
for jndex in xrange(number_components):
ax.plot(
ekindata[index][:, jndex],
label=r"$" + str(index) + r": E^{kin}_" + str(jndex) + r"$",
color=colormap[2 * jndex % len(colormap)],
)
ax.plot(
epotdata[index][:, jndex],
label=r"$" + str(index) + r": E^{pot}_" + str(jndex) + r"$",
color=colormap[(2 * jndex + 1) % len(colormap)],
)
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.set_xlabel(r"Timestep")
ax.set_ylabel(r"$E$")
ax.set_title(r"Energies timeseries comparison")
legend(loc="outer right")
fig.savefig("energies_all" + GD.output_format)
close(fig)
endkindata = [array([ekindata[j][-1, i] for j in xrange(number_simulations)]) for i in xrange(number_components)]
endpotdata = [array([epotdata[j][-1, i] for j in xrange(number_simulations)]) for i in xrange(number_components)]
# Plot the comparison over versus axisdata
fig = figure()
ax = fig.gca()
# Kinetic and potential energies per component
for index in xrange(number_components):
ax.plot(axisdata, endkindata[index], label=r"$E^{kin}_" + str(index) + r"$", marker="o")
ax.plot(axisdata, endpotdata[index], label=r"$E^{pot}_" + str(index) + r"$", marker="o")
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.set_xlabel(r"$\varepsilon$")
ax.set_ylabel(r"$E$")
ax.set_title(r"Energies end of time comparison")
legend(loc="outer right")
fig.savefig("energies_comparison" + GD.output_format)
close(fig)
def plot_data(axisdata, normdata, number_simulations, number_components):
colormap = ["b", "g", "r", "c", "m", "y", "b"]
# Plot the time series for each simulation
fig = figure()
ax = fig.gca()
for index in xrange(number_simulations):
for jndex in xrange(number_components):
ax.plot(
normdata[index][:, jndex],
label=r"$" + str(index) + r":\| \psi_" + str(jndex) + r"\|$",
color=colormap[jndex % len(colormap)],
)
ax.set_ylim(0, 1.1)
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.set_xlabel(r"Timestep")
ax.set_ylabel(r"$\|\cdot\|$")
ax.set_title(r"Norms timeseries comparison")
legend(loc="outer right")
fig.savefig("norms_comparison_all" + GD.output_format)
close(fig)
enddata = [array([normdata[j][-1, i] for j in xrange(number_simulations)]) for i in xrange(number_components)]
# Plot the comparison over versus axisdata
fig = figure()
ax = fig.gca()
for jndex in xrange(number_components):
plot(
axisdata,
enddata[jndex],
label=r"$\| \psi_" + str(jndex) + r"\|$",
marker="o",
color=colormap[jndex % len(colormap)],
)
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.set_xlabel(r"$\varepsilon$")
ax.set_ylabel(r"$\|\cdot\|$")
ax.set_title(r"Norms end of time comparison")
legend(loc="outer right")
fig.savefig("norms_comparison" + GD.output_format)
close(fig)
def plot_data(times, epsdata, axisdata, normdata, which_norm="wf"):
if which_norm == "wf":
nona = "wf"
elif which_norm == "2":
nona = "L^2"
elif which_norm == "max":
nona = "max"
def guessor(x, y):
u = log(diff(x))
v = log(diff(y))
return v / u
for t, time in enumerate(times):
# Plot the convergence for all epsilon and fixed times
fig = figure()
ax = fig.gca()
for eps, ad, nd in zip(epsdata, axisdata, normdata[t]):
ax.loglog(ad, nd, "-o", label=r"$\varepsilon = "+str(eps)+"$")
# Plot a convergence indicator
ax.loglog(axisdata[0], axisdata[0]**2, "-k", label=r"$y = x^2$")
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.set_xlabel(r"Timestep size $dt$")
ax.set_ylabel(r"$$\| \phi_f - \phi_h \|_{"+nona+r"}$$")
ax.set_title(r"Error norm $\| \phi_f - \phi_h \|_{"+nona+r"}$ for time $T=" + str(time) + r"$")
legend(loc="outer right")
fig.savefig("convergence_FvP_time="+str(time)+"_"+nona+GD.output_format)
close(fig)
fig = figure()
ax = fig.gca()
for eps, ad, nd in zip(epsdata, axisdata, normdata[t]):
values = guessor(ad, nd)
ax.plot(values, "-o", label=r"$\varepsilon = "+str(eps)+"$")
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.set_title(r"guessor at time $T=" + str(time) + r"$")
legend(loc="outer right")
fig.savefig("guessor_FvP_time="+str(time)+"_"+nona+GD.output_format)
close(fig)
def plot_data(axisdata, normdata, number_simulations, number_components, timeindices=None, which_norm="wf"):
if which_norm == "wf":
nona = "L^2"
elif which_norm == "2":
nona = "L^2"
elif which_norm == "max":
nona = "max"
# Plot the time series for each simulation
fig = figure()
ax = fig.gca()
for index in xrange(number_simulations):
ax.plot(normdata[index], label=r"$\varepsilon = $" + str(axisdata[index]))
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.set_xlabel(r"Timestep $t$")
ax.set_ylabel(r"$\| \phi_f - \phi_h \|_{"+nona+r"}$")
ax.set_title(r"Timeseries of $\| \phi_f - \phi_h \|_{"+nona+r"}$")
legend(loc="outer right")
fig.savefig("convergence_"+nona+"_all"+GD.output_format)
close(fig)
# Plot the comparison over versus axisdata
for t in timeindices:
# This version works too for array of different lengths
tmp = []
for nd in normdata:
tmp.append(nd[t])
tmp = array(tmp)
fig = figure()
ax = gca()
ax.plot(axisdata, tmp, "-o", label=r"$t = " + str(t) + r"$")
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.set_xlabel(r"$\varepsilon$")
ax.set_ylabel(r"$\| \phi_f - \phi_h \|_{"+nona+r"}$")
ax.set_title(r"$\| \phi_f - \phi_h \|_{"+nona+r"}$ for different $\varepsilon$ ")
legend(loc="outer right")
fig.savefig("convergence"+str(t)+"_"+nona+"_comparison"+GD.output_format)
close(fig)
def plot_potential(grid, potential, fill=True, imgsize=(8,6)):
# Create potential and evaluate eigenvalues
potew = potential.evaluate_eigenvalues_at(grid)
# Plot the energy surfaces of the potential
fig = figure()
ax = fig.gca()
for index, ew in enumerate(potew):
if fill:
ax.fill(grid, ew, facecolor="blue", alpha=0.25)
ax.plot(grid, ew, label=r"$\lambda_"+str(index)+r"$")
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.grid(True)
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_operators(parameters, omega, grid, opT, opV, index=0):
"""Plot the propagation operators T and V
"""
# Plot the kinetic operator T
fig = figure()
ax = fig.gca()
ax.plot(omega, real(opT), label=r"$\Re T$")
ax.plot(omega, imag(opT), label=r"$\Im T$")
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.grid(True)
ax.set_xlabel(r"$\omega$")
ax.set_ylabel(r"$T\left(\omega\right)$")
legend(loc="outer right")
ax.set_title(r"The kinetic operator T")
fig.savefig("kinetic_operator_block"+str(index)+GD.output_format)
close(fig)
# Plot the potential operator V
fig = figure()
N = parameters["ncomponents"]
k = 1
for i in xrange(N):
for j in xrange(N):
ax = fig.add_subplot(N, N, k)
ax.plot(grid, real(opV[i*N+j]), label=r"$\Re V_{"+str(i)+","+str(j)+r"}$")
ax.plot(grid, imag(opV[i*N+j]), label=r"$\Im V_{"+str(i)+","+str(j)+r"}$")
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.grid(True)
#ax.set_xlim([0, parameters["ngn"]])
ax.set_xlabel(r"$x$")
ax.set_ylabel(r"$V_{"+str(i)+","+str(j)+r"}\left(x\right)$")
k += 1
fig.savefig("potential_operator_block"+str(index)+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)
def plot_energies(gid, parameters, data):
print("Plotting the energies of group '" + str(gid) + "'")
N = parameters["ncomponents"]
for datum in data:
time = datum[0]
energies_m = datum[1]
energies_c = datum[2]
ekin_m = reduce(lambda x, y: x + y, [energies_m[0][i] for i in xrange(N)])
epot_m = reduce(lambda x, y: x + y, [energies_m[1][i] for i in xrange(N)])
ekin_c = reduce(lambda x, y: x + y, [energies_c[0][i] for i in xrange(N)])
epot_c = reduce(lambda x, y: x + y, [energies_c[1][i] for i in xrange(N)])
esum = ekin_m + epot_m + ekin_c + epot_c
# Plot the energies for all components
fig = figure()
for c in xrange(N):
ax = subplot(N, 1, c + 1)
# Plot the energies of the individual wavepackets
ax.plot(time, energies_m[0][c], color="darkgreen", label=r"$E^M_{kin}$")
ax.plot(time, energies_c[0][c], color="lightgreen", label=r"$E^C_{kin}$")
ax.plot(time, energies_m[1][c], color="blue", label=r"$E^M_{pot}$")
ax.plot(time, energies_c[1][c], color="cyan", label=r"$E^C_{pot}$")
# Overall energy on component c
ax.plot(
time,
energies_m[0][c] + energies_c[0][c] + energies_m[1][c] + energies_c[1][c],
color="black",
label=r"$\sum E$",
)
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.set_xlabel(r"Time $t$")
ax.set_ylabel(r"$\Phi_" + str(c) + r"$")
ax.legend(loc="upper left")
fig.suptitle("Per-component energies of $\Psi^M$ and $\Psi^C$")
fig.savefig("energies_spawn_components_group" + str(gid) + GD.output_format)
close(fig)
# Plot the sum of the energies of mother and child
fig = figure()
ax = subplot(2, 1, 1)
ax.plot(time, ekin_m, color="green", label=r"$E_{kin}^M$")
ax.plot(time, epot_m, color="blue", label=r"$E_{pot}^M$")
ax.plot(time, ekin_m + epot_m, color="black", label=r"$E_{kin}^M + E_{pot}^M$")
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.set_xlabel(r"Time $t$")
ax.set_ylabel(r"$\Psi^M$")
ax.legend(loc="upper left")
ax = subplot(2, 1, 2)
ax.plot(time, ekin_c, color="green", label=r"$E_{kin}^C$")
ax.plot(time, epot_c, color="blue", label=r"$E_{pot}^C$")
ax.plot(time, ekin_c + epot_c, color="black", label=r"$E_{kin}^C + E_{pot}^C$")
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.set_xlabel(r"Time $t$")
ax.set_ylabel(r"$\Psi^C$")
ax.legend(loc="upper left")
fig.suptitle(r"Energies of $\Psi^M$ (top) and $\Psi^C$ (bottom)")
fig.savefig("energies_spawn_packetsum_group" + str(gid) + GD.output_format)
close(fig)
# Plot the overall sum of energies of mother and child
fig = figure()
ax = fig.gca()
ax.plot(time, ekin_m + epot_m, color="blue", label=r"$E_{kin}^M + E_{pot}^M$")
ax.plot(time, ekin_c + epot_c, color="cyan", label=r"$E_{kin}^C + E_{pot}^C$")
ax.plot(time, ekin_m + epot_m + ekin_c + epot_c, label=r"$E^M + E^C$")
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
legend(loc="outer right")
ax.set_xlabel(r"Time $t$")
ax.set_title(r"Energies of $\Psi^M$ and $\Psi^C$ and $\Psi^M + \Psi^C$")
fig.savefig("energies_spawn_sumall_group" + str(gid) + GD.output_format)
close(fig)
# Plot the drift of the sum of all energies
fig = figure()
ax = fig.gca()
ax.plot(time, esum[0] - esum)
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0, 0), axis="y")
ax.set_xlabel(r"Time $t$")
ax.set_ylabel(r"$E(t=0) - E(t)$")
ax.set_title(r"Drift of the total energy $E = E^M + E^C$")
fig.savefig("energies_spawn_sumall_drift_group" + str(gid) + GD.output_format)
close(fig)
def plot_energy(times, ekin, epot, etot):
print("Plotting the energies")
# 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(times, 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(times, 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(times, 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(times, ekin[-1], label=r"$\sum_i E^{kin}_i$")
ax.plot(times, epot[-1], label=r"$\sum_i E^{pot}_i$")
# Plot the overall energy of all wave packets
ax.plot(times, etot, label=r"$\sum_i E^{kin}_i + \sum_i E^{pot}_i$")
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.set_xlabel(r"Time $t$")
ax.set_title(r"Energies of the wavepacket $\Psi$")
legend(loc="outer right")
fig.savefig("energies_etot_canonical"+GD.output_format)
close(fig)
# Plot the difference between the computation of the overall energy
# done in the eigenbasis and the canonical basis.
etot_eig = ekin[-1] + epot[-1]
fig = figure()
ax = fig.gca()
ax.plot(times, squeeze(etot) - etot_eig, label=r"$E_{tot}^{eig} - E_{tot}^{can}$")
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.set_xlabel(r"Time $t$")
fig.savefig("etot_canonical_diff"+GD.output_format)
close(fig)
# Plot the energy drift over time
e_orig = etot[0]
fig = figure()
ax = fig.gca()
ax.plot(times, abs(e_orig-(ekin[-1]+epot[-1])), label=r"$|E_O^0 - \left( E_k^0 + E_p^0 \right) |$")
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
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 wave packet $\Psi$")
fig.savefig("energies_etot_canonical_drift"+GD.output_format)
close(fig)
def plot_norms(gid, parameters, data):
print("Plotting the norms of group '"+str(gid)+"'")
N = parameters["ncomponents"]
for datum in data:
time = datum[0]
norms_m = datum[1]
norms_c = datum[2]
overall_norm = sqrt(norms_m[-1]**2 + norms_c[-1]**2)
# Plot the norms for all components
fig = figure()
for c in xrange(N):
ax = subplot(N,1,c+1)
# Plot the norms of the individual wavepackets
ax.plot(time, overall_norm, color="black", label=r"$\sqrt{\| \Psi^M \|^2 + \| \Psi^C \|^2}$")
ax.plot(time, sqrt(norms_m[c]**2 + norms_c[c]**2), color="gray", label=r"$\sqrt{\| \Phi_"+str(c)+r"^M \|^2 + \| \Phi_"+str(c)+r"^C \|^2}$")
ax.plot(time, norms_m[c], color="blue", label=r"$\| \Phi_"+str(c)+r"^M \|$")
ax.plot(time, norms_c[c], color="cyan", label=r"$\| \Phi_"+str(c)+r"^C \|$")
ax.grid(True)
ax.set_ylim(0, 1.1*overall_norm.max())
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.set_xlabel(r"Time $t$")
ax.set_ylabel(r"$\Phi_"+str(c)+r"$")
ax.legend(loc="upper left")
fig.suptitle("Per-component norms of $\Psi^M$ and $\Psi^C$")
fig.savefig("norms_spawn_components_group"+str(gid)+GD.output_format)
close(fig)
# Plot the sum of the norms of mother and child
fig = figure()
ax = subplot(2,1,1)
ax.plot(time, overall_norm, color="black", label=r"$\sqrt{\| \Psi^M \|^2 + \| \Psi^C \|^2}$")
ax.plot(time, norms_m[-1], color="blue", label=r"$\| \Psi^M \|$")
ax.grid(True)
ax.set_ylim(0, 1.1*overall_norm.max())
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.set_xlabel(r"Time $t$")
ax.set_ylabel(r"$\Psi^M$")
ax.legend(loc="upper left")
ax = subplot(2,1,2)
ax.plot(time, overall_norm, color="black", label=r"$\sqrt{\| \Psi^M \|^2 + \| \Psi^C \|^2}$")
ax.plot(time, norms_c[-1], color="cyan", label=r"$\| \Psi^C \|$")
ax.grid(True)
ax.set_ylim(0, 1.1*overall_norm.max())
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.set_xlabel(r"Time $t$")
ax.set_ylabel(r"$\Psi^C$")
ax.legend(loc="upper left")
fig.suptitle(r"Norms of $\Psi^M$ (top) and $\Psi^C$ (bottom)")
fig.savefig("norms_spawn_sumpacket_group"+str(gid)+GD.output_format)
close(fig)
# Plot the overall sum of norms of mother and child
fig = figure()
ax = fig.gca()
ax.plot(time, overall_norm, color="black", label=r"$\sqrt{\| \Psi^M \|^2 + \| \Psi^C \|^2}$")
ax.plot(time, norms_m[-1], color="blue", label=r"$\| \Psi^M \|$")
ax.plot(time, norms_c[-1], color="cyan", label=r"$\| \Psi^C \|$")
ax.grid(True)
ax.set_ylim(0, 1.1*overall_norm.max())
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
legend(loc="outer right")
ax.set_xlabel(r"Time $t$")
ax.set_title(r"Norm of $\Psi^M$ and $\Psi^C$ and $\Psi^M + \Psi^C$")
fig.savefig("norms_spawn_sumall_group"+str(gid)+GD.output_format)
close(fig)
# Plot the drift of the sum of all norms
fig = figure()
ax = fig.gca()
ax.plot(time, overall_norm[0] - overall_norm)
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.set_xlabel(r"Time $t$")
ax.set_ylabel(r"$\|\Psi(t=0)\| - \|\Psi(t)\|$")
ax.set_title(r"Drift of the total norm $\|\Psi\| = \sqrt{\| \Psi^M \|^2 + \| \Psi^C \|^2}$")
fig.savefig("norms_spawn_sumall_drift_group"+str(gid)+GD.output_format)
close(fig)
def plot_energies(gid, parameters_o, parameters_s, data_ref, data):
print("Plotting the energies of group '"+str(gid)+"'")
N = parameters_o["ncomponents"]
timegrido = data_ref[0]
timeo = data_ref[1]
energies_o = data_ref[2]
ekin_o = reduce(lambda x,y: x+y, [ energies_o[0][i] for i in xrange(N) ])
epot_o = reduce(lambda x,y: x+y, [ energies_o[1][i] for i in xrange(N) ])
esum_o = ekin_o + epot_o
for datum in data:
timegrid = datum[0]
time = datum[1]
energies_m = datum[2]
energies_c = datum[3]
ekin_m = reduce(lambda x,y: x+y, [ energies_m[0][i] for i in xrange(N) ])
epot_m = reduce(lambda x,y: x+y, [ energies_m[1][i] for i in xrange(N) ])
ekin_c = reduce(lambda x,y: x+y, [ energies_c[0][i] for i in xrange(N) ])
epot_c = reduce(lambda x,y: x+y, [ energies_c[1][i] for i in xrange(N) ])
esum = ekin_m + epot_m + ekin_c + epot_c
indo, inds = common_timesteps(timegrido, timegrid)
# Plot the energies for all components
fig = figure()
for c in xrange(N):
ax = subplot(N,1,c+1)
# Plot the original energies
ax.plot(timeo, energies_o[0][c], color="red", label=r"$E^O_{kin}$")
ax.plot(timeo, energies_o[1][c], color="orange", label=r"$E^O_{pot}$")
ax.plot(timeo, energies_o[0][c] + energies_o[1][c], color="gray", label=r"$E^O$")
# Plot the energies of the individual wavepackets
ax.plot(time, energies_m[0][c], color="darkgreen", label=r"$E^M_{kin}$")
ax.plot(time, energies_c[0][c], color="lightgreen", label=r"$E^C_{kin}$")
ax.plot(time, energies_m[1][c], color="blue", label=r"$E^M_{pot}$")
ax.plot(time, energies_c[1][c], color="cyan", label=r"$E^C_{pot}$")
# Overall energy on component c
ax.plot(time, energies_m[0][c] + energies_c[0][c] + energies_m[1][c] + energies_c[1][c], color="black", label=r"$\sum E$")
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.set_xlabel(r"Time $t$")
ax.set_ylabel(r"$\Phi_"+str(c)+r"$")
ax.legend(loc="upper left")
fig.suptitle("Per-component energies of $\Psi^M$ and $\Psi^C$")
fig.savefig("energies_compare_components_group"+str(gid)+GD.output_format)
close(fig)
# Plot the sum of the energies of mother and child
fig = figure()
ax = subplot(2,1,1)
ax.plot(timeo, ekin_o, color="red", label=r"$E_{kin}^O$")
ax.plot(timeo, epot_o, color="orange", label=r"$E_{pot}^O$")
ax.plot(timeo, ekin_o + epot_o, color="magenta", label=r"$E^O$")
ax.plot(time, ekin_m, color="green", label=r"$E_{kin}^M$")
ax.plot(time, epot_m, color="blue", label=r"$E_{pot}^M$")
ax.plot(time, ekin_m + epot_m, color="black", label=r"$E_{kin}^M + E_{pot}^M$")
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.set_xlabel(r"Time $t$")
ax.set_ylabel(r"$\Psi^M$")
ax.legend(loc="upper left")
ax = subplot(2,1,2)
ax.plot(timeo, ekin_o, color="red", label=r"$E_{kin}^O$")
ax.plot(timeo, epot_o, color="orange", label=r"$E_{pot}^O$")
ax.plot(timeo, ekin_o + epot_o, color="magenta", label=r"$E^O$")
ax.plot(time, ekin_c, color="green", label=r"$E_{kin}^C$")
ax.plot(time, epot_c, color="blue", label=r"$E_{pot}^C$")
ax.plot(time, ekin_c + epot_c, color="black", label=r"$E_{kin}^C + E_{pot}^C$")
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.set_xlabel(r"Time $t$")
ax.set_ylabel(r"$\Psi^C$")
ax.legend(loc="upper left")
fig.suptitle(r"Energies of $\Psi^M$ (top) and $\Psi^C$ (bottom)")
fig.savefig("energies_compare_packetsum_group"+str(gid)+GD.output_format)
close(fig)
# Plot the overall sum of energies of mother and child
fig = figure()
ax = fig.gca()
ax.plot(timeo, ekin_o + epot_o, color="orange", label=r"$E_{kin}^O + E_{pot}^O$")
ax.plot(time, ekin_m + epot_m, color="blue", label=r"$E_{kin}^M + E_{pot}^M$")
ax.plot(time, ekin_c + epot_c, color="cyan", label=r"$E_{kin}^C + E_{pot}^C$")
ax.plot(time, ekin_m + epot_m + ekin_c + epot_c, color="black", label=r"$E^M + E^C$")
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
legend(loc="outer right")
ax.set_xlabel(r"Time $t$")
ax.set_title(r"Energies of $\Psi^M$ and $\Psi^C$ and $\Psi^M + \Psi^C$")
fig.savefig("energies_compare_sumall_group"+str(gid)+GD.output_format)
close(fig)
# Plot the drift of the sum of all energies
fig = figure()
ax = fig.gca()
ax.plot(timeo, esum_o[0] - esum_o, color="orange")
ax.plot(time, esum[0] - esum, color="blue")
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.set_xlabel(r"Time $t$")
ax.set_ylabel(r"$E(t=0) - E(t)$")
ax.set_title(r"Drift of the total energy $E = E^M + E^C$")
fig.savefig("energies_compare_sumall_drift_group"+str(gid)+GD.output_format)
close(fig)
# Plot difference of energies between original and spawned
# Plot the energies for all components
fig = figure()
for c in xrange(N):
ax = subplot(N,1,c+1)
# Plot the original energies
ax.plot(timeo[indo], energies_o[0][c][indo] - (energies_m[0][c][inds] + energies_c[0][c][inds]), color="green", label=r"$E^O_{kin} - E^S_{kin}$")
ax.plot(timeo[indo], energies_o[1][c][indo] - (energies_m[1][c][inds] + energies_c[1][c][inds]), color="blue", label=r"$E^O_{pot} - E^S_{pot}$")
ax.plot(timeo[indo], energies_o[0][c][indo] + energies_o[1][c][indo] -
(energies_m[0][c][inds] + energies_c[0][c][inds] + energies_m[1][c][inds] + energies_c[1][c][inds]), color="red", label=r"$E^O - E^S$")
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
ax.set_xlabel(r"Time $t$")
ax.set_ylabel(r"$\Phi_"+str(c)+r"$")
ax.legend(loc="upper left")
fig.suptitle("Per-component energy difference $E^O - E^S$")
fig.savefig("energies_compare_components_diff_group"+str(gid)+GD.output_format)
close(fig)
# Plot the overall sum of energies of mother and child
fig = figure()
ax = fig.gca()
ax.plot(timeo[indo], ekin_o[indo] - (ekin_m[inds] + ekin_c[inds]), color="green", label=r"$E_{kin}^O + E_{kin}^S$")
ax.plot(timeo[indo], epot_o[indo] - (epot_m[inds] + epot_c[inds]), color="blue", label=r"$E_{pot}^O + E_{pot}^S$")
ax.plot(timeo[indo], ekin_o[indo] + epot_o[indo] - (ekin_m[inds] + epot_m[inds] + ekin_c[inds] + epot_c[inds]), color="red", label=r"$E^O + E^S$")
ax.grid(True)
ax.ticklabel_format(style="sci", scilimits=(0,0), axis="y")
legend(loc="outer right")
ax.set_xlabel(r"Time $t$")
ax.set_title(r"Energy difference $E^O - E^S$")
fig.savefig("energies_compare_sumall_diff_group"+str(gid)+GD.output_format)
close(fig)
