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Workflow to solve v_inner boundary

The source code for this workflow can be found at: https://github.com/tardis-sn/tardis/blob/master/tardis/workflows/v_inner_solver.py.

This workflow demonstrates how to use the TARDIS modules to perform targeted tasks. This workflow is built on top of the SimpleTARDISWorkflow to solve the v_inner boundary, in addition to the remaining radiative properties.

import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
from astropy import units as u

from tardis.workflows.v_inner_solver import InnerVelocitySolverWorkflow
from tardis.io.configuration.config_reader import Configuration

/home/runner/work/tardis/tardis/tardis/__init__.py:17: UserWarning: Astropy is already imported externally. Astropy should be imported after TARDIS.
  warnings.warn(

config = Configuration.from_yaml('../tardis_example.yml')

This code modifies the TARDIS example configuration to include convergence information for the inner boundary velocity solver.

config.montecarlo.convergence_strategy['v_inner_boundary'] = {
    'damping_constant' : 0.5,
    'threshold' : 0.01,
    'type' : 'damped',
    'store_iteration_properties' : True
    }

config.montecarlo.convergence_strategy.stop_if_converged = True
config.model.structure.velocity.start = 5000 * u.km/u.s # Decrease start velocity from 11000 km/s in example file, to search over a wider range
config.model.structure.velocity.num = 50 # Increase number of shells from 20 in example file, to provide more granularity

workflow = InnerVelocitySolverWorkflow(
    config, tau=2.0/3,
    mean_optical_depth="rosseland"
)

workflow.run()

Shell No.	t_rad	next_t_rad	w	next_w
0	1.44e+04 K	1.59e+04 K	0.0531	0.486
5	1.44e+04 K	1.66e+04 K	0.0407	0.214
10	1.43e+04 K	1.68e+04 K	0.0323	0.125
15	1.42e+04 K	1.63e+04 K	0.0262	0.0918
20	1.42e+04 K	1.57e+04 K	0.0217	0.0755
25	1.41e+04 K	1.5e+04 K	0.0183	0.0669

Shell No.	t_rad	next_t_rad	w	next_w
0	1.59e+04 K	1.25e+04 K	0.486	0.458
5	1.66e+04 K	1.38e+04 K	0.214	0.158
10	1.68e+04 K	1.39e+04 K	0.125	0.0934
15	1.63e+04 K	1.38e+04 K	0.0918	0.0658
20	1.57e+04 K	1.34e+04 K	0.0755	0.0551
25	1.5e+04 K	1.29e+04 K	0.0669	0.0481

Shell No.	t_rad	next_t_rad	w	next_w
0	1.25e+04 K	1.14e+04 K	0.458	0.511
5	1.38e+04 K	1.26e+04 K	0.158	0.194
10	1.39e+04 K	1.29e+04 K	0.0934	0.109
15	1.38e+04 K	1.28e+04 K	0.0658	0.0744
20	1.34e+04 K	1.25e+04 K	0.0551	0.0606
25	1.29e+04 K	1.19e+04 K	0.0481	0.0548

Shell No.	t_rad	next_t_rad	w	next_w
0	1.14e+04 K	1.12e+04 K	0.511	0.504
5	1.26e+04 K	1.19e+04 K	0.194	0.222
10	1.29e+04 K	1.21e+04 K	0.109	0.132
15	1.28e+04 K	1.21e+04 K	0.0744	0.0908
20	1.25e+04 K	1.19e+04 K	0.0606	0.072
25	1.19e+04 K	1.14e+04 K	0.0548	0.0649

Shell No.	t_rad	next_t_rad	w	next_w
0	1.12e+04 K	1.09e+04 K	0.504	0.529
5	1.19e+04 K	1.15e+04 K	0.222	0.232
10	1.21e+04 K	1.17e+04 K	0.132	0.139
15	1.21e+04 K	1.16e+04 K	0.0908	0.101
20	1.19e+04 K	1.13e+04 K	0.072	0.0824
25	1.14e+04 K	1.09e+04 K	0.0649	0.0717

Shell No.	t_rad	next_t_rad	w	next_w
0	1.09e+04 K	1.09e+04 K	0.529	0.507
5	1.15e+04 K	1.12e+04 K	0.232	0.237
10	1.17e+04 K	1.13e+04 K	0.139	0.151
15	1.16e+04 K	1.12e+04 K	0.101	0.108
20	1.13e+04 K	1.1e+04 K	0.0824	0.087
25	1.09e+04 K	1.06e+04 K	0.0717	0.0775

Shell No.	t_rad	next_t_rad	w	next_w
0	1.45e+04 K	1.09e+04 K	0.0563	0.56
5	1.13e+04 K	1.12e+04 K	0.263	0.256
10	1.13e+04 K	1.12e+04 K	0.16	0.16
15	1.13e+04 K	1.11e+04 K	0.112	0.114
20	1.1e+04 K	1.08e+04 K	0.0908	0.0942
25	1.07e+04 K	1.05e+04 K	0.0797	0.08
30	1.03e+04 K	1.03e+04 K	0.0733	0.0713

Shell No.	t_rad	next_t_rad	w	next_w
0	1.09e+04 K	1.09e+04 K	0.56	0.578
5	1.12e+04 K	1.12e+04 K	0.256	0.263
10	1.12e+04 K	1.13e+04 K	0.16	0.161
15	1.11e+04 K	1.11e+04 K	0.114	0.118
20	1.08e+04 K	1.09e+04 K	0.0942	0.0969
25	1.05e+04 K	1.06e+04 K	0.08	0.0818
30	1.03e+04 K	1.03e+04 K	0.0713	0.0734

Shell No.	t_rad	next_t_rad	w	next_w
0	1.09e+04 K	1.1e+04 K	0.578	0.562
5	1.12e+04 K	1.13e+04 K	0.263	0.256
10	1.13e+04 K	1.14e+04 K	0.161	0.156
15	1.11e+04 K	1.12e+04 K	0.118	0.118
20	1.09e+04 K	1.09e+04 K	0.0969	0.0953
25	1.06e+04 K	1.06e+04 K	0.0818	0.081
30	1.03e+04 K	1.03e+04 K	0.0734	0.0724

Shell No.	t_rad	next_t_rad	w	next_w
0	1.1e+04 K	1.09e+04 K	0.562	0.579
5	1.13e+04 K	1.14e+04 K	0.256	0.254
10	1.14e+04 K	1.14e+04 K	0.156	0.157
15	1.12e+04 K	1.12e+04 K	0.118	0.117
20	1.09e+04 K	1.09e+04 K	0.0953	0.0962
25	1.06e+04 K	1.06e+04 K	0.081	0.0813
30	1.03e+04 K	1.03e+04 K	0.0724	0.0725

Plot the spectrum

spectrum = workflow.spectrum_solver.spectrum_real_packets
spectrum_virtual = workflow.spectrum_solver.spectrum_virtual_packets
spectrum_integrated = workflow.spectrum_solver.spectrum_integrated

%matplotlib inline
plt.figure(figsize=(10, 6.5))

spectrum.plot(label="Normal packets")
spectrum_virtual.plot(label="Virtual packets")
spectrum_integrated.plot(label='Formal integral')

plt.xlim(500, 9000)
plt.title("TARDIS example model spectrum")
plt.xlabel(r"Wavelength [$\AA$]")
plt.ylabel(r"Luminosity density [erg/s/$\AA$]")
plt.legend()
plt.show()

Plot the convergence process

%matplotlib inline

# extract plasma states
t_rad = workflow.iterations_t_rad
t_inner = workflow.iterations_t_inner
w = workflow.iterations_w
taus = workflow.iterations_mean_optical_depth
v_inner = workflow.iterations_v_inner_boundary

# remove all nans, or rows where all values are nan
t_rad = t_rad[~np.all(np.isnan(t_rad), axis=1)]
t_inner = t_inner[~np.isnan(t_inner)]
w = w[~np.all(np.isnan(w), axis=1)]
taus = taus[~np.all(np.isnan(taus), axis=1)]
v_inner = v_inner[~np.isnan(v_inner)]

# initialize figure
fig,axes =  plt.subplots(2,2,figsize=(12,8))
plt.subplots_adjust(wspace=0.4,hspace=0.3)

# get the raw velocity grid
vel = workflow.simulation_state.geometry.v_inner

# pick a colormap for the iterations
cmap = plt.get_cmap('plasma',taus.shape[0])

# plot v inner change
v_inner_plot = axes[0,0]
v_inner_plot.plot(v_inner,marker="o",color="b")
v_inner_plot.set_xlabel("Iterations", fontsize=14)
v_inner_plot.set_ylabel("v_inner (cm/s)", fontsize=14)
v_inner_plot.grid(alpha=0.3)
v_inner_plot.tick_params(axis='y', colors='blue')
v_inner_plot.yaxis.label.set_color('blue')

# plot t inner change in same subplot
t_inner_plot = axes[0][0].twinx()
t_inner_plot.plot(t_inner,marker="s",color="r")
t_inner_plot.set_ylabel("t_inner (K)", fontsize=14)
t_inner_plot.tick_params(axis='y', colors='red')
t_inner_plot.yaxis.label.set_color('red')

# plot the tau change
tau_plot = axes[0][1]
for i, tau in enumerate(taus):
    tau_plot.plot(vel[-len(tau):], tau, color=cmap(i/taus.shape[0]),label=f"itr {i+1}",alpha=0.7)
tau_plot.scatter(workflow.simulation_state.v_inner_boundary.value, np.log(2.0 / 3.0), color="k",marker="o")
tau_plot.axhline(np.log(2.0 / 3.0), color='black', linestyle='--')
tau_plot.axvline(workflow.simulation_state.v_inner_boundary.value, color='k', linestyle='--')
tau_plot.set_xlabel("Velocity (cm/s)", fontsize=14)
tau_plot.set_ylabel("log(tau)", fontsize=14)
tau_plot.grid(alpha=0.3)
tau_plot.set_title("1 Loop of all together - without resetting plasma", fontsize=14)

# plot t radiative change
t_rad_plot = axes[1][0]
for i in range(len(taus)):
    t_rad_plot.plot(vel[-len(t_rad[i]):], t_rad[i],color=cmap(i/taus.shape[0]),label=f"itr {i+1}",alpha=0.7)
t_rad_plot.set_xlabel("Velocity (cm/s)", fontsize=14)
t_rad_plot.set_ylabel("t_rad", fontsize=14)
t_rad_plot.grid(alpha=0.3)

# plot dilution factor change
w_plot = axes[1][1]
for i in range(len(taus)):
    w_plot.plot(vel[-len(w[i]):], w[i],color=cmap(i/taus.shape[0]),label=f"itr {i+1}",alpha=0.7)
w_plot.set_xlabel("Velocity (cm/s)", fontsize=14)
w_plot.set_ylabel("dilution_factor", fontsize=14)
w_plot.grid(alpha=0.3)

# add colorbar for iteration number
norm = mpl.colors.Normalize(vmin=1, vmax=len(taus))
sm = mpl.cm.ScalarMappable(cmap=cmap, norm=norm)
cbar = fig.colorbar(sm, ax=axes, orientation='vertical', fraction=0.025, pad=0.02)
cbar.set_label('Iteration Number', fontsize=12)