You can interact with this notebook online: Launch notebook

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(

Initializing tabulator and plotly panel extensions for widgets to work

Auto-detected Sphinx build environment

Auto-detected Sphinx build environment

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	0.482
5	1.44e+04 K	1.67e+04 K	0.0407	0.208
10	1.43e+04 K	1.68e+04 K	0.0323	0.124
15	1.42e+04 K	1.64e+04 K	0.0262	0.0907
20	1.42e+04 K	1.58e+04 K	0.0217	0.0738
25	1.41e+04 K	1.52e+04 K	0.0183	0.0648

Shell No.	t_rad	next_t_rad	w	next_w
0	1.59e+04 K	1.25e+04 K	0.482	0.46
5	1.67e+04 K	1.38e+04 K	0.208	0.158
10	1.68e+04 K	1.4e+04 K	0.124	0.0932
15	1.64e+04 K	1.38e+04 K	0.0907	0.0658
20	1.58e+04 K	1.35e+04 K	0.0738	0.0538
25	1.52e+04 K	1.29e+04 K	0.0648	0.049

Shell No.	t_rad	next_t_rad	w	next_w
0	1.25e+04 K	1.14e+04 K	0.46	0.511
5	1.38e+04 K	1.26e+04 K	0.158	0.195
10	1.4e+04 K	1.28e+04 K	0.0932	0.11
15	1.38e+04 K	1.27e+04 K	0.0658	0.0777
20	1.35e+04 K	1.24e+04 K	0.0538	0.0619
25	1.29e+04 K	1.2e+04 K	0.049	0.0541

Shell No.	t_rad	next_t_rad	w	next_w
0	1.14e+04 K	1.12e+04 K	0.511	0.507
5	1.26e+04 K	1.19e+04 K	0.195	0.22
10	1.28e+04 K	1.21e+04 K	0.11	0.132
15	1.27e+04 K	1.21e+04 K	0.0777	0.0902
20	1.24e+04 K	1.17e+04 K	0.0619	0.075
25	1.2e+04 K	1.14e+04 K	0.0541	0.0653

Shell No.	t_rad	next_t_rad	w	next_w
0	1.12e+04 K	1.08e+04 K	0.507	0.539
5	1.19e+04 K	1.15e+04 K	0.22	0.232
10	1.21e+04 K	1.16e+04 K	0.132	0.144
15	1.21e+04 K	1.15e+04 K	0.0902	0.103
20	1.17e+04 K	1.11e+04 K	0.075	0.0866
25	1.14e+04 K	1.08e+04 K	0.0653	0.0752

Shell No.	t_rad	next_t_rad	w	next_w
0	1.08e+04 K	1.09e+04 K	0.539	0.506
5	1.15e+04 K	1.12e+04 K	0.232	0.24
10	1.16e+04 K	1.13e+04 K	0.144	0.148
15	1.15e+04 K	1.12e+04 K	0.103	0.11
20	1.11e+04 K	1.09e+04 K	0.0866	0.0885
25	1.08e+04 K	1.06e+04 K	0.0752	0.0787

Shell No.	t_rad	next_t_rad	w	next_w
0	1.45e+04 K	1.08e+04 K	0.0563	0.562
5	1.12e+04 K	1.12e+04 K	0.264	0.252
10	1.13e+04 K	1.12e+04 K	0.159	0.158
15	1.12e+04 K	1.11e+04 K	0.116	0.115
20	1.1e+04 K	1.08e+04 K	0.0925	0.0935
25	1.07e+04 K	1.05e+04 K	0.0801	0.0804
30	1.03e+04 K	1.02e+04 K	0.0731	0.0717

Shell No.	t_rad	next_t_rad	w	next_w
0	1.08e+04 K	1.09e+04 K	0.562	0.584
5	1.12e+04 K	1.12e+04 K	0.252	0.263
10	1.12e+04 K	1.13e+04 K	0.158	0.159
15	1.11e+04 K	1.12e+04 K	0.115	0.115
20	1.08e+04 K	1.09e+04 K	0.0935	0.0954
25	1.05e+04 K	1.06e+04 K	0.0804	0.0828
30	1.02e+04 K	1.03e+04 K	0.0717	0.0733

Shell No.	t_rad	next_t_rad	w	next_w
0	1.09e+04 K	1.09e+04 K	0.584	0.57
5	1.12e+04 K	1.13e+04 K	0.263	0.259
10	1.13e+04 K	1.13e+04 K	0.159	0.161
15	1.12e+04 K	1.11e+04 K	0.115	0.12
20	1.09e+04 K	1.08e+04 K	0.0954	0.0986
25	1.06e+04 K	1.06e+04 K	0.0828	0.0806
30	1.03e+04 K	1.03e+04 K	0.0733	0.0726

Shell No.	t_rad	next_t_rad	w	next_w
0	1.09e+04 K	1.09e+04 K	0.57	0.576
5	1.13e+04 K	1.13e+04 K	0.259	0.255
10	1.13e+04 K	1.13e+04 K	0.161	0.158
15	1.11e+04 K	1.11e+04 K	0.12	0.118
20	1.08e+04 K	1.09e+04 K	0.0986	0.0952
25	1.06e+04 K	1.07e+04 K	0.0806	0.0799
30	1.03e+04 K	1.04e+04 K	0.0726	0.0715

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)