Nested Sampling

Nested Main:

ForMoSA.nested_sampling.nested_sampling.import_obsmod(global_params)

Function to import spectra (model and data) before the inversion

Parameters:

global_params (object) – Class containing every input from the .ini file.

Returns:

Return a list of lists with the wavelengths, flux, errors, covariance matrix,

transmission, star flux, systematics, grid indices and the grids for both spectroscopic and photometric data.

Return type:

• main_file (list(array))

Authors: Simon Petrus, Matthieu Ravet and Allan Denis

ForMoSA.nested_sampling.nested_sampling.launch_nested_sampling(global_params)

Function to launch the nested sampling. We first perform LogL function check-ups. Then the free parameters are counted and the data imported. Finally, depending on the nested sampling methode chosen in the config file, we perform the inversion. (Methods succesfully implemented are Nestle and PyMultinest)

Parameters:

global_params (object) – Class containing every input from the .ini file.

Returns:

None

Author: Simon Petrus and Matthieu Ravet

ForMoSA.nested_sampling.nested_sampling.loglike(theta, theta_index, global_params, main_file, for_plot='no')

Function that calculates the logarithm of the likelihood. The evaluation depends on the choice of likelihood. (If this function is used on the plotting module, it returns the outputs of the modif_spec function)

Parameters:

• theta (list) – Parameter values randomly picked by the nested sampling

• theta_index (list) – Index for the parameter values randomly picked

• global_params (object) – Class containing every input from the .ini file.

• main_file (list(list)) – List containing the wavelengths, flux, errors, covariance, and grid information

• for_plot (str) – Default is ‘no’. When this function is called from the plotting functions module, we use ‘yes’

Returns:

Final evaluated loglikelihood for both spectra and photometry.

Return type:

• FINAL_logL (float)

Authors: Simon Petrus, Matthieu Ravet and Allan Denis

ForMoSA.nested_sampling.nested_sampling.prior_transform(theta, theta_index, lim_param_grid, global_params)

Function that define the priors to be used for the inversion. We check that the boundaries are consistent with the grid extension.

Parameters:

• theta (list) – Parameter values randomly picked by the nested sampling

• theta_index (list) – Index for the parameter values randomly picked

• lim_param_grid (list) – Boundaries for the parameters explored

• global_params (object) – Class containing every input from the .ini file.

Returns:

List containing all the prior information

Return type:

• prior (list)

Author: Simon Petrus, Matthieu Ravet, Allan Denis

Modify Spectra:

ForMoSA.nested_sampling.nested_modif_spec.modif_spec(global_params, theta, theta_index, obs_dict, flx_mod_spectro, flx_mod_photo, wav_mod_spectro, res_mod_obs_spectro, indobs=0)

Modification of the interpolated synthetic spectra with the different extra-grid parameters. It can perform : Re-calibration on the data, Doppler shifting, Application of a substellar extinction, Application of a rotational velocity, Application of a circumplanetary disk (CPD).

Parameters:

• global_params (object) – Class containing each parameter

• theta (list) – Parameter values randomly picked by the nested sampling

• theta_index (list) – Parameter index identificator

• obs_dict (dict) – Dictionay containing all the observationnal entries (photometry, spectroscopy and/or optional)

• flx_mod_spectro (array) – New flux of the interpolated synthetic spectrum (spectroscopy)

• flx_mod_photo (array) – New flux of the interpolated synthetic spectrum (photometry)

• wav_mod_spectro (array) – Wavelength array of the model (can be different from wav_obs_spectro)

• res_mod_obs_spectro (array) – Spectroscopic resolution of the model interpolated onto wav_obs_spectro

• indobs (int) – Index of the current observation looping

Returns:

New dictionay containing all the observationnal entries (photometry, spectroscopy and/or optional) - flx_mod_spectro (array): New flux of the interpolated synthetic spectrum (spectroscopy) - flx_mod_photo (array): New flux of the interpolated synthetic spectrum (photometry) - flx_mod_spectro_nativ (array): New flux of the interpolated synthetic spectrum NOT RESAMPLED (spectroscopy) - contributions (array): Contributions from the high-contrast model - scale_spectro (float): Spectroscopic flux scaling factor - scale_photo (float): Photometric flux scaling factor

Return type:

• obs_dict (dict)

Author: Simon Petrus, Paulina Palma-Bifani, Allan Denis and Matthieu Ravet

Prior Functions:

ForMoSA.nested_sampling.nested_prior_functions.gaussian_prior(prior_fct_arg, theta)

Gaussian prior for nested sampling.

Parameters:

• prior_fct_arg (list) – Two-values list with uniform prior boundaries.

• theta (list) – Parameter values randomly picked by the nested sampling

Returns:

Evaluated prior

Return type:

• Evaluated (float)

Author: Simon Petrus

ForMoSA.nested_sampling.nested_prior_functions.loguniform_prior(prior_fct_arg, theta)

LogUniform prior for nested sampling.

Parameters:

• prior_fct_arg (list) – Two-values list with loguniform prior boundaries.

• theta (list) – Parameter values randomly picked by the nested sampling

Returns:

Evaluated prior

Return type:

• Evaluated (float)

Author: Simon Petrus

ForMoSA.nested_sampling.nested_prior_functions.uniform_prior(prior_fct_arg, theta)

Uniform prior for nested sampling.

Parameters:

• prior_fct_arg (list) – Two-values list with uniform prior boundaries.

• theta (list) – Parameter values randomly picked by the nested sampling

Returns:

Evaluated prior

Return type:

• Evaluated (float)

Author: Simon Petrus

Likelihood Functions:

ForMoSA.nested_sampling.nested_logL_functions.logL_CCF_Brogi(flx_obs, flx_mod)

Function to compute logL based on the CCF mapping from Brogi et al. 2019 under the assumption of gaussian and spectrally constant noise.

Parameters:

• flx_obs (array) – flux of the observation as a function of wavelength

• flx_mod (array) – flux of the model as a function of wavelength

Returns:

the loglikelihood value

Return type:

• logL (float)

Author: Matthieu Ravet

ForMoSA.nested_sampling.nested_logL_functions.logL_CCF_Zucker(flx_obs, flx_mod)

Function to compute logL based on the CCF mapping from Zucker 2003 under the assumption of gaussian and spectrally constant noise.

Parameters:

• flx_obs (array) – flux of the observation as a function of wavelength

• flx_mod (array) – flux of the model as a function of wavelength

Returns:

the loglikelihood value

Return type:

• logL (float)

Author: Matthieu Ravet

ForMoSA.nested_sampling.nested_logL_functions.logL_CCF_custom(flx_obs, flx_mod, err_obs)

Function to compute logL based on the custom CCF mapping from Me under the assumption of gaussian and spectrally constant noise.

Parameters:

• flx_obs (array) – flux of the observation as a function of wavelength

• flx_mod (array) – flux of the model as a function of wavelength

• err_obs (array) – errors of the observation as a function of wavelength

Returns:

the loglikelihood value

Return type:

• logL (float)

Author: Matthieu Ravet

ForMoSA.nested_sampling.nested_logL_functions.logL_chi2(delta_flx, err, log_det, full=False)

Function to compute logL based on the upper limits chi2 under the assumption of gaussian and spectrally uncorrelated noise.

Parameters:

• delta_flx (array) – residual data-model as a function of wavelength

• err (array) – error (=standard deviation) of the observed spectrum as a function of wavelength

• log_det (float) – Log-determinant of the error bars

• full (bool) – True or False to add the usual constant terms

Returns:

the loglikelihood value

Return type:

• logL (float)

Author: Matthieu Ravet & Alice Radcliffe

ForMoSA.nested_sampling.nested_logL_functions.logL_chi2_covariance(delta_flx, inv_cov, log_det, full=False)

Function to compute logL based on the generalized chi2 under the assumption of gaussian and spectrally correlated noise.

Parameters:

• delta_flx (array) – residual data-model as a function of wavelength

• inv_cov (n-array) – inverse of the covariance matrix of the observed spectrum as a function of wavelength

• full (bool) – True or False to add the usual constant terms

• log_det (float) – Log-determinant of the covariance matrix

Returns:

the loglikelihood value

Return type:

• logL (float)

Author: Matthieu Ravet

ForMoSA.nested_sampling.nested_logL_functions.logL_chi2_noisescaling(delta_flx, err, log_det, full=False)

Function to compute logL based on the chi2 with a fitted noise scaling s (marginalized) under the assumption of gaussian and spectrally uncorrelated noise.

Parameters:

• delta_flx (array) – residual data-model as a function of wavelength

• err (array) – error (=standard deviation) of the observed spectrum as a function of wavelength

• full (bool) – True or False to add the usual constant terms

• log_det (float) – Log-determinant of the error bars matrix

Returns:

the loglikelihood value

Return type:

• logL (float)

Author: Allan Denis and Matthieu Ravet

ForMoSA.nested_sampling.nested_logL_functions.logL_chi2_noisescaling_covariance(delta_flx, inv_cov, log_det, full=False)

Function to compute logL based on the chi2 with a fitted noise scaling s (marginalized) under the assumption of gaussian and spectrally correlated noise.

Parameters:

• delta_flx (array) – residual data-model as a function of wavelength

• inv_cov (n-array) – inverse of the covariance matrix of the observed spectrum as a function of wavelength

• full (bool) – True or False to add the usual constant terms

• log_det (float) – Log-determinant of the covariance matrix

Returns:

the loglikelihood value

Return type:

• logL (float)

Author: Allan Denis and Matthieu Ravet

High-contrast Models:

ForMoSA.nested_sampling.nested_highcont_models.hc_model(global_params, obs_dict, flx_mod_spectro, indobs)

For high-contrast companions, where the star speckles signal contaminate the data

Parameters:

• global_params (object) – Class containing each parameter used in ForMoSA

• obs_dict (dict) – Dictionay containing all the observationnal entries (photometry, spectroscopy and/or optional)

• flx_mod_spectro (array) – Model flux of the companion

• indobs (int) – Index of the current observation loop

Returns:

Results of the high-constrast model - flx_mod_spectro (array): Model of the high-constrast model - flx_mod_spectro (array): Model of the high-constrast model - speckles (array): Speckles contribution

Return type:

• contributions (array)

Authors: Allan Denis

ForMoSA.nested_sampling.nested_highcont_models.hc_model_estimate_speckles(flx_obs_spectro, flx_cont_obs_spectro, star_flx_obs_spectro, star_flx_cont_obs_spectro, flx_mod_spectro, flx_cont_mod_spectro, err, bounds, system_obs_spectro)

high-constrast model of planet and star contributions

Parameters:

• flx_obs_spectro (array) – Flux of the data

• flx_cont_obs_spectro (array) – Continuum of the data

• star_flx_obs_spectro (array) – Flux of the star data

• star_flx_cont_obs_spectro (array) – Continuum of the star data

• flx_mod_spectro (array) – Model of the companion

• flx_cont_mod_spectro (array) – Continuum of the model of the companion

• weights (array) – Weights to apply to the data

• bounds (tuple) – Bounds to be applied to the estimated parameters

• system_obs_spectro (array) – Systematics

Returns:

Results of the high-constrast model - flx_mod_spectro (array): Model of the high-constrast model - speckles (array): Speckles contribution

Return type:

• results.x (array)

Authors: Allan Denis

ForMoSA.nested_sampling.nested_highcont_models.hc_model_remove_speckles(flx_obs_spectro, flx_cont_obs_spectro, star_flx_obs_spectro, star_flx_cont_obs_spectro, flx_mod_spectro, flx_cont_mod_spectro, err_obs_spectro)

high-constrast

Parameters:

• flx_obs_spectro (array) – Flux of the data

• flx_cont_obs_spectro (array) – Continuum of the data

• star_flx_obs_spectro (array) – Flux of the star data

• star_flx_cont_obs_spectro (array) – Continuum of the star data

• flx_mod_spectro (array) – Model of the companion

• flx_cont_mod_spectro (array) – Continuum of the model of the companion

• err_obs_spectro (array) – Noise of the data

Returns:

High-resolution content of planet model - speckles (array): Speckles contribution - systematics (float): Not taken into account here

Return type:

• flx_mod_spectro (array)

Authors: Allan Denis