Retrievals: Basic Retrieval Tutorial
Written by Evert Nasedkin and Paul Mollière
References: - Mollière+ (2019) - Mollière+ (2020)
What is a retrieval?
Let’s start with the basics! An atmospheric retrieval is the process through which we fit a model of a spectrum to data. The model usually incorporates elements of chemistry and radiative transfer in order to compute a spectrum - see the getting started page for an example.
If you’re here, we’re going to assume that you already have an exoplanet emission or transmission spectrum, and you want to learn something about the planet’s properties. We’ll use the petitRADTRANS (pRT) package, a 1D atmospheric radiative transfer tool, combined with a sampler which will allow us to statistically measure the properties of the planet of interest. As inputs for this, you’ll need a 1D spectrum with error bars (or a covariance matrix), and a model function that generates a
synthetic spectrum. We have a few example datasets included in petitRADTRANS/retrieval/examples/, and several forward models implemented in petitRADTRANS/retrieval/models.py, which you can use directly, or as templates to build your own model.
In this example we will make use of an HST transmission spectrum, located locally in petitRADTRANS/retrieval/examples/transmission/observations/HST/hst_example_clear_spec.txt, or online. This dataset is included when you install pRT, and we’ll automatically locate the data and output files throughout the notebook. The outputs of the
retrieval example will be a best-fit spectrum, an atmospheric pressure-temperature profile, and the posterior distributions of all of the parameters of your model atmosphere. Of course, you do not have to use pRT’s retrieval package to run retrievals with pRT-generated spectra, but we believe that what is described below may be sufficient for most people, and will thus save you from most of the tedious implementation work.
Getting started
You should already have an installation of pRT on your machine, please see the installation manual if you have not installed it yet. pyMultiNest - and therefore Multinest is also required. Multinest allows for easy scaling of the retrievals to run on large clusters, but can also be installed locally on your laptop to run small retrievals, such as this example.
Ultranest is required if you want to use that as your sampler rather than pyMultiNest. See the Ultranest documentation for why you might want to choose this method. Using nested sampling rather than MCMC is faster, handles multimodal cases better, and directly provides the Bayesian evidence, which allows for easier model comparison. However, we’ve found that in general pyMultinest is faster than Ultranest, and generally recommend its
use.
In this tutorial, we will outline the process of setting up a RetrievalConfig object, which is the class used to set up a pRT retrieval. The basic process will always be to set up the configuration, and then pass it to the Retrieval class to run the retrieval using pyMultiNest. Several standard plotting outputs will also be produced by the retrieval class. Most of the classes and functions used in this tutorial have more advanced features than what will be explained here, so it’s highly recommended to take a look at the code and API documentation. There should be enough flexibility built in to cover most typical retrieval studies, but if you have feature requests please get in touch, or open an issue on gitlab.
[4]:
# Let's start by importing everything we need.
import os
# To not have numpy start parallelizing on its own
os.environ["OMP_NUM_THREADS"] = "1"
# You may need to set the input data path so that pRT knows where the opacities are stored.
#os.environ["pRT_input_data_path"] = "/path/to/petitRADTRANS/petitRADTRANS/input_data/"
import numpy as np
import matplotlib.pyplot as plt
from petitRADTRANS import Radtrans
from petitRADTRANS import nat_cst as nc
# Import the class used to set up the retrieval.
from petitRADTRANS.retrieval import Retrieval, RetrievalConfig
# Import Prior functions, if necessary.
from petitRADTRANS.retrieval.util import gaussian_prior
# Import an atmospheric model function
from petitRADTRANS.retrieval.models import isothermal_transmission
Let’s start with a simple model. We’ll use an isothermal temperature profile, and use free chemistry - allowing the chemical abundances to vary freely within fixed boundaries, but requiring them to be vertically constant throughout the atmosphere. The basic process for every retrieval will be the same. We need to set up a `RetrievalConfig <https://gitlab.com/mauricemolli/petitRADTRANS/-/blob/master/petitRADTRANS/retrieval/retrieval_config.py>`__ object, adding in the
`Data <https://gitlab.com/mauricemolli/petitRADTRANS/-/blob/master/petitRADTRANS/retrieval/data.py>`__ objects that we want to fit together with the `Parameter <https://gitlab.com/mauricemolli/petitRADTRANS/-/blob/master/petitRADTRANS/retrieval/parameter.py>`__ objects and their priors, which we can use to customize our retrieval.
Lets start out by setting up a simple run definition. We’ll add the data AFTER we define the model function below. We start out by initialising the object, and then adding each of the parameters of interest to the RetrievalConfig. Full details of the parameters can be found in the API documentation.
[5]:
# Lets start out by setting up a simple run definition
# We'll add the data AFTER we define the model function below
# Full details of the parameters can be found in retrieval_config.py
# Since our retrieval has already ran before, we'll set the mode to 'evaluate' so we can make some plots.
RunDefinition = RetrievalConfig(retrieval_name = "hst_example_clear_spec",
run_mode = "evaluate", # This must be 'retrieval' to run PyMultiNest
AMR = False, # We won't be using adaptive mesh refinement for the pressure grid
scattering = False) # This would turn on scattering when calculating emission spectra.
# Scattering is automatically included for transmission spectra.
# Let's start with the parameters that will remain fixed during the retrieval
RunDefinition.add_parameter('Rstar', # name
False, # is_free_parameter, So Rstar is not retrieved here.
value = 0.651*nc.r_sun)
# Log of the surface gravity in cgs units.
# The transform_prior_cube argument transforms a uniform random sample x, drawn between 0 and 1.
# to the physical units we're using in pRT.
RunDefinition.add_parameter('log_g',
True, # is_free_parameter: we are retrieving log(g) here
transform_prior_cube_coordinate = \
lambda x : 2.+3.5*x) # This means that log g
# can vary between 2 and 5.5
# Note that logg is usually not a free parameter in retrievals of
# transmission spectra, at least it is much better constrained as being
# assumed here, as the planetary mass and radius are usually known.
# Planet radius in cm
RunDefinition.add_parameter('R_pl',
True,
transform_prior_cube_coordinate = \
lambda x : ( 0.2+0.2*x)*nc.r_jup_mean) # Radius varies between 0.2 and 0.4
# Interior temperature in Kelvin
RunDefinition.add_parameter('Temperature',
True,
transform_prior_cube_coordinate = \
lambda x : 300.+2000.*x)
# Let's include a grey cloud as well to see what happens, even though we assumed a clear atmosphere.
RunDefinition.add_parameter("log_Pcloud",
True,
transform_prior_cube_coordinate = \
lambda x : -6.0+8.0*x) # The atmosphere can thus have an opaque cloud
# between 1e-6 and 100 bar
Opacities
petitRADTRANS can be setup to use line-by-line opacities at \(\lambda/\Delta \lambda = 10^6\), or a lower resolution correlated-k mode (which we use here). The names of each species in these lists much match the names of the pRT opacity data folders. See the standard list here.
In addition to the line opacities, pRT also accounts for Rayleigh scattering, collision-induced absorption (CIA) opaticies, and opacities for various condensate cloud species. If a cloud species is used, it will have a set of parameters added in order to retrieve the cloud abundance. We give such an example below. The parameters added depend on the model chosen.
If you aren’t sure which species are available, the RetrievalConfig class has a few functions that will list the currently available line, CIA and cloud opacities, see the API documentation.
exo-k
If you set the model resolution for your data, and do not have existing c-k tables at that resolution, exo-k will be used to bin the higher resolution tables down to a lower resolution. This must be run on a single core. To ensure that the retrieval runs properly, the retrieval will end if exo-k is used, so that the remainder of the retrieval can be restarted and run with multiple cores. This isn’t an elegant solution, and will be improved in a future release.
[6]:
RunDefinition.list_available_line_species()
RunDefinition.set_rayleigh_species(['H2', 'He'])
RunDefinition.set_continuum_opacities(['H2-H2', 'H2-He'])
# Here we setup the line species for a free retrieval, setting the prior bounds with the abund_lim parameter
# The retrieved value is the log mass fraction.
# RunDefinition.set_line_species(["CH4", "H2O", "CO2", "CO_all_iso"], free=True, abund_lim = (-6.0,0.0))
# Let's use the most up-to-date line lists
RunDefinition.set_line_species(["CH4", "H2O_Exomol", "CO2", "CO_all_iso_HITEMP"], eq=False, abund_lim = (-6.0,0.0))
correlated-k opacities
Si
CrH
Ti+
AlH
H2O_Exomol
Fe
O3
CO_13_HITEMP
O
VO
C2H2
CO_12_HITEMP
SiO
MgO
K_lor_cut
HCN
FeH
OH
AlO
K_allard
Mg
SO2
Fe+
CO_all_iso_Chubb
SiO2
CO_13_Chubb
H2O_HITEMP
O2
H2S
H2O
O+
SH
MgH
Al+
VO_Plez
CO_all_iso_HITEMP
Si+
Mg+
PH3
analytics
C2H4
CO2
Na_lor_cut
TiO_48_Exomol
V
Na_burrows
Ca
TiO_48_Plez
K_burrows
Ca+
NaH
Na_allard
CO_all_iso
TiO_all_Plez
Ti
Li
Al
CH4
CaH
TiO_all_Exomol
V+
NH3
line-by-line opacities
CO2_main_iso
Cr
H2O_main_iso
K
Fe+
TiO_all_iso_exo
H2S_main_iso
HCN_main_iso
CH4_main_iso
VO
NH3_main_iso
TiO_all_iso
CO_main_iso
Na
Fe
Model Functions
In addition to setting up a retrieval with a standard mode, you may also want to write your own model to be used in the retrieval setup. pRT has a wide range of built in model functions, which we recommend using as opposed to writing your own, but we’ll include a simple example here to show what’s going on behind the scenes. For further documentation on the built in models, check out this tutorial page. This function will be passed as the
model_generating_function argument when you add_data to the RetrievalConfig class. Here we will outline a simple, cloud-free transmission spectrum model using free retrieval chemistry and an isothermal P-T profile to demonstrate.
Four parameters are required. A pRT object which is created is from the Radtrans class in pRT and a dictionary of parameters, which is stored in the RetrievalConfig class that we defined above. The remaining three parameters deal with plotting and adaptive mesh refinement, which we won’t use in this example.
In general, the built in model functions require cgs units, apart from pressure which is given in bar.
For this tutorial we are reimplementing a simplified version the isothermal_transmission model, available in petitRADTRANS.retrieval.models.
[7]:
from petitRADTRANS.physics import isothermal
from petitRADTRANS.retrieval.util import calc_MMW, compute_gravity
# Now we can define the atmospheric model we want to use
def retrieval_model_spec_iso(pRT_object, \
parameters, \
PT_plot_mode = False,
AMR = False):
"""
retrieval_model_eq_transmission
This model computes a transmission spectrum based on free retrieval chemistry
and an isothermal temperature-pressure profile.
parameters
-----------
pRT_object : object
An instance of the pRT class, with optical properties as defined in the RunDefinition.
parameters : dict
Dictionary of required parameters:
Rstar : Radius of the host star [cm]
log_g : Log of surface gravity
R_pl : planet radius [cm]
Temperature : Isothermal temperature [K]
species : Log abundances for each species used in the retrieval
log_Pcloud : optional, cloud base pressure of a grey cloud deck.
PT_plot_mode : bool
Return only the pressure-temperature profile for plotting. Evaluate mode only.
AMR :
Adaptive mesh refinement. Use the high resolution pressure grid around the cloud base.
returns
-------
wlen_model : np.array
Wavlength array of computed model, not binned to data [um]
spectrum_model : np.array
Computed transmission spectrum R_pl**2/Rstar**2
"""
contribution = False
if "contribution" in parameters.keys():
contribution = parameters["contribution"].value
# Make the P-T profile
pressures = pRT_object.press/1e6 # Convert from bar to cgs; internally pRT uses cgs
# Note how we access the values of the Parameter class objects
temperatures = isothermal(pressures,parameters['Temperature'].value)
# If in evaluation mode, and PTs are supposed to be plotted
if PT_plot_mode:
return pressures, temperatures
# Make the abundance profiles
abundances = {}
msum = 0.0 # Check that the total massfraction of all species is <1
for species in pRT_object.line_species:
spec = species.split('_R_')[0] # Dealing with the naming scheme
# for binned down opacities (see below).
abundances[species] = 10**parameters[spec].value * np.ones_like(pressures)
msum += 10**parameters[spec].value
if msum > 1.0:
return None, None
abundances['H2'] = 0.766 * (1.0-msum) * np.ones_like(pressures)
abundances['He'] = 0.234 * (1.0-msum) * np.ones_like(pressures)
# Find the mean molecular weight in each layer
MMW = calc_MMW(abundances)
gravity, R_pl = compute_gravity(parameters)
# Calculate the spectrum
pRT_object.calc_transm(temperatures,
abundances,
gravity,
MMW,
P0_bar=0.01,
R_pl = R_pl,
Pcloud = 10**parameters['log_Pcloud'].value,
contribution = contribution)
# Transform the outputs into the units of our data.
wlen_model = nc.c/pRT_object.freq/1e-4 # wlen in micron
spectrum_model = (pRT_object.transm_rad/parameters['Rstar'].value)**2.
if contribution:
return wlen_model, spectrum_model, pRT_object.contr_tr
return wlen_model, spectrum_model
Data
With the model set up, we can read in the data. The data must be a 1D spectrum with error bars or a covariance matrix. The input format for ASCII data is
# Wavelength [micron], Flux [W/m2/micron or (Rp/Rstar)^2], Flux Error [W/m2/micron or (Rp/Rstar)^2]
Optionally, there can also be an additional column to specify the wavelength bins, which would then have the format:
# Wavelength [micron], Bins [micron], Flux [W/m2/micron or (Rp/Rstar)^2], Flux Error [W/m2/micron or (Rp/Rstar)^2]
The file can be comma or space separated, and by default ‘#’ is the comment character. The wavelength column must be sorted and is in ascending order. If you write your own model function, the units of your data can vary from this template, but the units of your data and the output of your model function must match. Throughout our documentation we will use W/m2/micron for emission spectra and (Rp/Rstar)^2 for consistency between our model functions and the example data.
The fits file requirements are more strict. An extension labelled ‘SPECTRUM’ is required, with three fields in a binary table: ‘WAVELENGTH’, ‘FLUX’ and ‘COVARIANCE’. An example of this is the HR8799e_spectra.fits file included in petitRADTRANS/retrieval/examples/emission/, see pRT’s gitlab page. A function called fits_output() is included in retrieval.util to provide an example of how to generate this type of file.
The Data class is arguably the most important part of setting up the retrieval. Not only do you input your data here, but you also choose your model function and resolution. This means that you can design a retrieval around different datatypes and retrieve simultaneously on both - for example, if you want the day and nightside of a planet, or want to combine the eastward and westward limbs of a transmission spectrum with different models.
By adjusting the resolution you can also speed up the retrieval. By default, pRT uses the correlated-k method for computing opacities, which works up to \(\lambda/\Delta \lambda = 1000\). Here you need to pick 'c-k' as opacity_mode, see below. Often low resolution data does not require this resolution, and the computation can be sped up using the model_resolution parameter, which will use the exo-k package to bin down the correlated-k tables.
If you use the 'lbl' (line-by-line) mode, pRT can compute opacities up to \(\lambda/\Delta \lambda = 10^6\), though this is quite slow. By setting the model_resolution parameter, pRT will sample the high resolution line list at the specified resolution. In this case you must make sure that the downsampled calculations match the binned-down results of the \(\lambda/\Delta \lambda = 10^6\) mode at the required data resolution.
The Data class can also handle photometric data, which is described in the emission tutorial.
[8]:
# Finally, we associate the model with the data, and we can run our retrieval!
import petitRADTRANS # need to get the name for the example data
path_to_data = petitRADTRANS.__file__.split('__init__.py')[0] # Default location for the example
RunDefinition.add_data('HST', # Simulated HST data
path_to_data + \
'retrieval/examples/transmission/observations/HST/hst_example_clear_spec.txt', # Where is the data
model_generating_function = retrieval_model_spec_iso, # The atmospheric model to use
opacity_mode = 'c-k',
data_resolution = 60, # The spectral resolution of the data
model_resolution = 120) # The resolution of the c-k tables for the lines
# This model is a noise-free, clear atmosphere transmission spectrum for a sub-neptune type planet
# The model function used to calculate it was slightly different, and used different opacity tables
# than what we'll use in the retrieval, but the results don't significantly change.
# In general, it is also useful to use the data_resolution and model_resolution arguments.
# The data_resolution argument will convolve the generated model spectrum by the instrumental
# resolution prior to calculating the chi squared value.
#
# The model_resolution function uses exo-k to generate low-resolution correlated-k opacity tables
# in order to speed up the radiative transfer calculations.
# We recommend choosing a model_resolution of about 2x the data_resolution.
Plotting
Let’s set up some plotting details so that we can generate nice outputs.
Each parameter can be added to the corner plot, its label changed, and the values transformed to more digestible units (e.g., the planet radius in jupiter radii, rather than cm). We can also set the bounds and scaling on the best-fit spectrum plot and the limits for the P-T profile plot. With this complete, our retrieval is ready to go.
Most parameters include a default setting, so the plots will be created even if you don’t set any plotting parameters, but the outputs might not be very informative. In general, the possible arguments to plot_kwargs follow the naming conventions of matplotlib arguments and functions, with some additions. Full details of the plotting can be found in the Retrieval class, see the API documentation.
[9]:
##################################################################
# Define what to put into corner plot if run_mode == 'evaluate'
##################################################################
RunDefinition.parameters['R_pl'].plot_in_corner = True
RunDefinition.parameters['R_pl'].corner_label = r'$R_{\rm P}$ ($\rm R_{Jup}$)'
RunDefinition.parameters['R_pl'].corner_transform = lambda x : x/nc.r_jup_mean
RunDefinition.parameters['log_g'].plot_in_corner = True
RunDefinition.parameters['log_g'].corner_ranges = [2., 5.]
RunDefinition.parameters['log_g'].corner_label = "log g"
RunDefinition.parameters['Temperature'].plot_in_corner = True
RunDefinition.parameters['Temperature'].corner_label ="Temp"
RunDefinition.parameters['log_Pcloud'].plot_in_corner = True
RunDefinition.parameters['log_Pcloud'].corner_label =r"log P$_{\rm cloud}$"
RunDefinition.parameters['log_Pcloud'].corner_ranges = [-6, 2]
# Adding all of the chemical species in our atmosphere to the corner plot
for spec in RunDefinition.line_species:
if 'all_iso' in spec:
# CO is named CO_all_iso, watch out
RunDefinition.parameters[spec].corner_label = 'CO'
RunDefinition.parameters[spec].plot_in_corner = True
RunDefinition.parameters[spec].corner_ranges = [-6.2,0.2]
# Note, the post_equal_weights file has the actual abundances.
# If the retrieval is rerun, it will contain the log10(abundances)
#RunDefinition.parameters[spec].corner_transform = lambda x : np.log10(x)
##################################################################
# Define axis properties of spectral plot if run_mode == 'evaluate'
##################################################################
RunDefinition.plot_kwargs["spec_xlabel"] = 'Wavelength [micron]'
RunDefinition.plot_kwargs["spec_ylabel"] = r'$(R_{\rm P}/R_*)^2$ [ppm]'
RunDefinition.plot_kwargs["y_axis_scaling"] = 1e6 # so we have units of ppm
RunDefinition.plot_kwargs["xscale"] = 'linear'
RunDefinition.plot_kwargs["yscale"] = 'linear'
# Use at least ~100 samples to plot 3 sigma curves
RunDefinition.plot_kwargs["nsample"] = 10
##################################################################
# Define from which observation object to take P-T
# in evaluation mode (if run_mode == 'evaluate'),
# add PT-envelope plotting options
##################################################################
RunDefinition.plot_kwargs["take_PTs_from"] = 'HST'
RunDefinition.plot_kwargs["temp_limits"] = [150, 3000]
RunDefinition.plot_kwargs["press_limits"] = [1e1, 1e-6]
# If in doubt, define all of the plot_kwargs used here.
Running the retrieval
At this point, we are ready to run the retrieval! All we need to do is pass the RunDefinition we just created to the Retrieval class and call its run() method. There are a few additional parameters that can be adjusted, but the defaults should work well for almost all use cases. In general it may not be wise to run a retrieval on your laptop, as it can be quite computationally expensive. However, the included HST example should be able to be run fairly easily! (less than an hour). We
only use 40 live points in the example so that it runs in a reasonable length of time, but we highly recommend using more live points for your own retrievals! If you want to run the retrieval on a cluster, or just on multiple cores on your local machine, set use_MPI=True. You should copy the contents of this notebook into a single .py file, which then you can run using mpiexec -n $NUMBER_OF_CORES python my_retrieval_file.py, substituting in the number of cores you want to use to run
the retrieval.
Most of the various parameters used to control pyMultiNest or Ultranest can be set in the retrieval.run() function, see the API documentation.
[10]:
# If you want to run the retrieval, you need to choose a different output directory name,
# due to pRT requirements.
output_dir = f"{path_to_data}retrieval/examples/transmission/"
retrieval = Retrieval(RunDefinition,
output_dir=output_dir,
use_MPI = False, # Run locally, don't need to use MPI for massive parallelisation
sample_spec=False, # Output the spectrum from nsample random samples.
pRT_plot_style=True, # We think that our plots look nice.
ultranest=False) # Let's use pyMultiNest rather than Ultranest
retrieval.run(n_live_points=40, # PMN number of live points. 400 is good for small retrievals, 4000 for large
const_efficiency_mode=False, # Turn PMN const efficiency mode on or off (recommend on for large retrievals)
resume=True) # Continue retrieval from where it left off.)
#retrieval.plot_all(contribution = True) # We'll make all the plots individually for now. Uncomment to automatically generate plots
Starting retrieval hst_example_clear_spec
Setting up PRT Objects
/Users/nasedkin/python-packages/petitRADTRANS/petitRADTRANS/radtrans.py:119: FutureWarning: pRT_input_data_path was set by an environment variable. In a future update, the path to the petitRADTRANS input_data will be set within a .ini file that will be automatically generated into the user home directory (OS agnostic), inside a .petitradtrans directory
warnings.warn(f"pRT_input_data_path was set by an environment variable. In a future update, the path to "
Read line opacities of CH4_R_120...
Done.
Read line opacities of H2O_Exomol_R_120...
Done.
Read line opacities of CO2_R_120...
Done.
Read line opacities of CO_all_iso_HITEMP_R_120...
Done.
Read CIA opacities for H2-H2...
Read CIA opacities for H2-He...
Done.
Best fit likelihood = 172.62
Best fit 𝛘^2 = 0.75
Best fit 𝛘^2/n_wlen = 0.04
Best fit 𝛘^2 = 0.75
Best fit 𝛘^2/DoF = 0.06
No errors detected in the model function!
analysing data from /Users/nasedkin/python-packages/petitRADTRANS/petitRADTRANS/retrieval/examples/transmission/out_PMN/hst_example_clear_spec_.txt
Best fit likelihood = 172.62
Best fit 𝛘^2 = 0.75
Best fit 𝛘^2/n_wlen = 0.04
Best fit 𝛘^2 = 0.75
Best fit 𝛘^2/DoF = 0.06
marginal likelihood:
ln Z = 159.4 +- 0.1
parameters:
log_g 2.685 +- 0.097
R_pl 1608627572 +- 66486542
Temperature 690 +- 166
log_Pcloud 0.3 +- 1.1
CH4 -2.25 +- 0.66
H2O_Exomol -2.08 +- 0.80
CO2 -3.6 +- 1.5
CO_all_iso_HITEMP-3.4 +- 1.6
Once the retrieval is complete, we can use the plotAll() function to generate plots of the best fit spectrum, the pressure-temperature profile and the corner plots. A standard output file will be produced when the retrieval is run, describing the prior boundaries, the data used in the retrieval, and if the retrieval is finished it will include the best fit and median model parameters. Check out this file, together with the other outputs in
petitRADTRANS/retrieval/examples/transmission/evaluate_hst_example_clear_spec.
Let’s make some plots to see how our retrieval went! We need to start by reading in the results. If we want to read results from multiple retrievals, use the ret_names argument. Currently, only the corner plots make use of this feature.
[11]:
# These are dictionaries in case we want to look at multiple retrievals.
# The keys for the dictionaries are the retrieval_names
sample_dict, parameter_dict = retrieval.get_samples()
# Pick the current retrieval to look at.
samples_use = sample_dict[retrieval.retrieval_name]
parameters_read = parameter_dict[retrieval.retrieval_name]
Best Fit Spectrum
Here we will plot the best fit spectrum, together with the data used in the retrieval and the residuals between the two. Using the mode parameter, it is also possible to plot the spectrum using the 'median' fit instead of the maximum likelihood sample. The chi squared value presented in the figure is the reduced chi square, that is the chi square divided by the degrees of freedom (number of data points - number of parameters).
[12]:
# Plotting the best fit spectrum
# This will generate a few warnings, but it's fine.
fig,ax,ax_r = retrieval.plot_spectra(samples_use, parameters_read, refresh = True, mode = 'bestfit')
plt.show()
Plotting Best-fit spectrum
Best fit likelihood = 172.62
Read line opacities of CH4...
Done.
Read line opacities of H2O_Exomol...
Done.
Read line opacities of CO2...
Done.
Read line opacities of CO_all_iso_HITEMP...
Read CIA opacities for H2-H2...
Read CIA opacities for H2-He...
Done.
Best fit 𝛘^2/DoF = 0.05
/Users/nasedkin/python-packages/petitRADTRANS/petitRADTRANS/retrieval/retrieval.py:2372: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.
plt.tight_layout()
Pressure-Temperature profile
Here we show the retrieved pressure-temperature profile throughout the atmosphere. The contours show the 1, 2 and 3 sigma confidence intervals in temperature around the median retrieved profile. The opacity shading and dashed line show the region of the atmosphere that contributes to the observed spectrum, highlighting which part of the pressure profile is being probed.
[20]:
# Plotting the PT profile
fig,ax =retrieval.plot_PT(sample_dict,parameters_read, contribution = True)
plt.show()
/Users/nasedkin/anaconda3/lib/python3.7/site-packages/ipykernel/ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
and should_run_async(code)
/Users/nasedkin/python-packages/petitRADTRANS/petitRADTRANS/radtrans.py:121: FutureWarning: pRT_input_data_path was set by an environment variable. In a future update, the path to the petitRADTRANS input_data will be set within a .ini file that will be automatically generated into the user home directory (OS agnostic), inside a .petitradtrans directory
FutureWarning)
Plotting PT profiles
Best fit likelihood = 172.62
Best fit likelihood = 172.62
Read line opacities of CH4...
Done.
Read line opacities of H2O_Exomol...
Done.
Read line opacities of CO2...
Done.
Read CIA opacities for H2-H2...
Read CIA opacities for H2-He...
Done.
Corner plot
Here we show the corner plot for the retrieval, which shows the marginal posterior probability distributions for each parameter (though it is also possibe to plot only a subset of the parameters). The corner plot produces 1, 2 and 3 sigma contours for the 2D plots, and highlights the 1 sigma confidence interval in the histograms for each parameter. Optional, there are several kwarg parameters that can be used to customise the plotting aesthetics.
[21]:
# Corner plot
retrieval.plot_corner(sample_dict,parameter_dict,parameters_read,title_kwargs = {"fontsize" : 10})
plt.show()
/Users/nasedkin/anaconda3/lib/python3.7/site-packages/ipykernel/ipkernel.py:287: DeprecationWarning: `should_run_async` will not call `transform_cell` automatically in the future. Please pass the result to `transformed_cell` argument and any exception that happen during thetransform in `preprocessing_exc_tuple` in IPython 7.17 and above.
and should_run_async(code)
(2014, 9)
Making corner plot
Contact
If you need any additional help, don’t hesitate to contact Evert Nasedkin.
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