#PyRSM PyRSM_Lite is a simplified version of the PyRSM python package for exoplanets detection which applies the Regime Switching Model (RSM) framework on ADI (and ADI+SDI) sequences (see Dahlqvist et al. A&A, 2020, 633, A95). The RSM map algorithm relies on one or several PSF subtraction techniques to process one or multiple ADI sequences (or ADI+SDI) before computing a final probability map. Considering the large set of parameters needed for the computation of the RSM detection map (parameters for the selected PSF-subtraction techniques as well as the RSM algorithm itself), a parameter selection framework called auto-RSM (Dahlqvist et al., A&A, 2021, 656, A54) is proposed to automatically select the optimal parametrization. The proposed multi-step parameter optimization framework can be divided into three main steps, (i) the selection of the optimal set of parameters for the considered PSF-subtraction techniques, (ii) the optimization of the RSM approach parametrization, and (iii) the selection of the optimal set of PSF-subtraction techniques and ADI sequences to be considered when generating the final detection map.

The add_cube and add_model methods allows to consider several ADI or ADI+SDI sequences and models to generate the cube of residuals used to compute the RSM map. The cube should be provided by the same instrument or rescaled to a unique pixel size. A specific PSF should be provided for each cube. In the case of ADI+SDI, a single psf should be provided per cube (typically the PSF averaged over the set of frequencies, as the package does not acomodate yet 3-dimensionnal PSF). Five different models and two forward model variants are available. Each model can be parametrized separately. The method like_esti allows the estimation of a cube of likelihoods containing for each pixel and each frame the likelihood of being in the planetary or the speckle regime. These likelihood cubes are then used by the probmap_esti method to provide the final probability map based on the RSM framework.

The second set of methods regroups the four main methods used by the auto-RSM/auto-S/N framework. The opti_model method allows the optimization of the PSF subtraction techniques parameters based on the minimisation of the average annulus-wise contrast. The opti_RSM method takes care of the optimization of the parameters of the RSM framework (all related to the computation of the likelihood associated to every pixels and frames). The third method opti_combination, relies on a greedy selection algorithm to define the optimal set of ADI sequences and PSF-subtraction techniques to consider when generating the final detection map using the RSM approach. Finally, the opti_map method allows to compute the final RSM detection map. The optimization of the parameters can be done using the reversed parallactic angles, blurring potential planetary signals while keeping the main characteristics of the speckle noise. An S/N map based code is also proposed and encompasses the opti_model, the opti_combination and the opti_map methods. For the last two methods, the SNR parameter should be set to True.

The last set of methods regroups the methods allowing the computation of contrast curves and the characterization of a detected astrophysical signals. The contrast_curve method allows the computation of a contrast curve at a pre-defined completeness level (see Dahlqvist et al. 2021 for more details), while the contrast_matrix method provided contrast curves for a range of completeness levels defined by the number of fake companion injected (completeness level from 1/n_fc to 1-1/n_fc with n_fc the number of fake companions). This last method provides a good representation of the contrast/completeness distribution but requires a longer computation time. The target_charact method allows the estimation of the photometry and astrometry of a detected signal (see Dahlqvist et al. 2022 for more details)

A jupyter notebook tutorial as well as a dataset of 51 Eridani B is provided in the folder example to test the PyRSM class. A list of parameters for the PyRSM class and for the main functions are given below:

Setup and tutorial

The package may be installed via pip install using the command:

pip install https://github.com/vortex-exoplanet/RSM_lite/releases/download/0.1.0/PyRSM_Lite.tar.gz

A jupyter notebook tutorial as well as a test dataset of 51 Eridani B is provided here. A post-processing pipeline for treating ADI or ADI+SDI sequences is also provided.

##PyRSM class

• fwhm: int Full width at half maximum for the instrument PSF
• minradius : int Center radius of the first annulus considered in the RSM probability map estimation. The radius should be larger than half the value of the 'crop' parameter
• maxradius : int Center radius of the last annulus considered in the RSM probability map estimation. The radius should be smaller or equal to half the size of the image minus half the value of the 'crop' parameter
• interval: list of float or int, optional List of values taken by the delta parameter defining, when mutliplied by the standard deviation, the strengh of the planetary signal in the Regime Switching model. Default is [1]. The different delta paramaters are tested and the optimal value is selected via maximum likelmihood.
• pxscale : float Value of the pixel in arcsec/px. Only used for printing plots when 'showplot=True' in like_esti.
• ncore : int, optional Number of processes for parallel computing. By default ('ncore=1') the algorithm works in single-process mode.
• max_r_fm: int, optional Largest radius for which the forward model version of KLIP or LOCI are used, when relying on forward model versions of RSM. Forward model versions of RSM have a higher performance at close separation, considering their computation time, their use should be restricted to small angular distances. Default is None, i.e. the foward model version are used for all considered angular distance.
• inv_ang: bool, optional If True, the sign of the parallactic angles of all ADI sequence is flipped for the entire optimization procedure. Default is True.
• opti_type: str, optional 'Contrast' for an optimization based on the average contrast and 'RSM' for an optimization based on the ratio of the peak probability of the injected fake companion on the peak (noise) probability in the remaining of the considered annulus (much higher computation time). Default is 'Contrast'.
• trunc: int, optional Maximum angular distance considered for the full-frame parameter optimization. Defaullt is None.
• imlib : str, optional See the documentation of the 'vip_hci.preproc.frame_rotate' function.
• interpolation : str, optional See the documentation of the 'vip_hci.preproc.frame_rotate' function.

##add_cube

• psf : numpy ndarray 2d 2d array with the normalized PSF template, with an odd shape. The PSF image must be centered wrt to the array! Therefore, it is recommended to run the function 'normalize_psf' to generate a centered and flux-normalized PSF template.
• cube : numpy ndarray, 3d or 4d Input cube (ADI sequences), Dim 1 = temporal axis, Dim 2-3 = spatial axis Input cube (ADI + SDI sequences), Dim 1 = temporal axis, Dim 2=wavelength Dim 3-4 = spatial axis
• pa : numpy ndarray, 1d Parallactic angles for each frame of the ADI sequences.
• scale_list: numpy ndarray, 1d, optional Scaling factors in case of IFS data (ADI+mSDI cube). Usually, the scaling factors are the central channel wavelength divided by the shortest wavelength in the cube (more thorough approaches can be used to get the scaling factors). This scaling factors are used to re-scale the spectral channels and align the speckles. Default is None

##add_model

• model : str Selected ADI-based post-processing techniques used to generate the cubes of residuals feeding the Regime Switching model. 'APCA' for annular PCA, NMF for Non-Negative Matrix Factorization, LLSG for Local Low-rank plus Sparse plus Gaussian-noise decomposition, LOCI for locally optimized combination of images and'KLIP' for Karhunen-Loeve Image Projection. There exitsts a foward model variant of KLIP and LOCI called respectively 'FM KLIP' and 'FM LOCI'.

• delta_rot : float, optional Factor for tunning the parallactic angle threshold, expressed in FWHM. Default is 0.5 (excludes 0.5xFHWM on each side of the considered frame).

• delta_sep : float, optional The threshold separation in terms of the mean FWHM (for ADI+mSDI data). Default is 0.1.

• asize : int, optional Width in pixels of each annulus.When a single. Default is 5.

• n_segments : int, optional The number of segments for each annulus. Default is 1 as we work annulus-wise.

• ncomp : int, optional Number of components used for the low-rank approximation of the speckle field with 'APCA', 'KLIP' and 'NMF'. Default is 20.

• rank : int, optional
  Expected rank of the L component of the 'LLSG' decomposition. Default is 5.

• tolerance: float, optional Tolerance level for the approximation of the speckle field via a linear combination of the reference images in the LOCI algorithm. Default is 1e-2.

• interval: list of float or int, optional List of values taken by the delta parameter defining, when mutliplied by the standard deviation, the strengh of the planetary signal in the Regime Switching model. Default is [5]. The different delta paramaters are tested and the optimal value is selected via maximum likelmihood.

• var: str, optional Model used for the residual noise variance estimation. Five different approaches are proposed: 'ST', 'FR', and 'FM'. While all six can be used when intensity='Annulus', only the last three can be used when intensity='Pixel'. When using ADI+SDI dataset only 'FR' and 'FM' can be used. Default is 'ST'.

  'ST': consider every frame and pixel in the selected annulus with a width equal to asize (default approach)

  'FR': consider the pixels in the selected annulus with a width equal to asize but separately for every frame.

  'FM': consider the pixels in the selected annulus with a width equal to asize but separately for every frame. Apply a mask one FWHM on the selected pixel and its surrounding.

• modtocube: bool, optional Parameter defining if the concatenated cube feeding the RSM model is created considering first the model or the different cubes. If 'modtocube=False', the function will select the first cube then test all models on it and move to the next one. If 'modtocube=True', the model will select one model and apply it to every cubes before moving to the next model. Default is True.

• crop_size: int, optional Part of the PSF tempalte considered is the estimation of the RSM map

• crop_range: int, optional Range of crop sizes considered in the estimation of the RSM map, starting with crop_size and increasing the crop size incrementally by 2 pixels up to a crop size of crop_size + 2 x (crop_range-1).

• opti_bound: list, optional List of boundaries used for the parameter optimization. - For APCA: [[L_ncomp,U_ncomp],[L_nseg,U_nseg],[L_delta_rot,U_delta_rot]] Default is [[15,45],[1,4],[0.25,1.5]] - For NMF: [[L_ncomp,U_ncomp]] Default is [[2,20]] - For LLSG: [[L_ncomp,U_ncomp],[L_nseg,U_nseg]] Default is [[1,10],[1,4]] - For LOCI: [[L_tolerance,U_tolerance],[L_delta_rot,U_delta_rot]] Default is [[1e-3,1e-2],[0.25,1.5]] - For FM KLIP: [[L_ncomp,U_ncomp],[L_delta_rot,U_delta_rot]] Default is [[15,45],[0.25,1.5]] - For FM LOCI: [[L_tolerance,U_tolerance],[L_delta_rot,U_delta_rot]] Default is [[1e-3,1e-2],[0.25,1.5]] with L_ the lower bound and U_ the Upper bound.

##like_esti

• showplot: bool, optional If True, provides the plots of the final residual frames for the selected ADI-based post-processing techniques along with the final RSM map. Default is False.
• fulloutput: bool, optional If True, provides the selected distribution, the fitness erros and the mixval (for distri='mix') for every annulus in respectively obj.distrisel, obj.fiterr and obj.mixval (the length of these lists are equall to maxradius - minradius, the size of the matrix for each annulus depends on the approach selected for the variance estimation, see var in add_model)
• verbose : bool, optional If True prints intermediate info. Default is True.

##prob_esti

• modtocube: bool, optional Parameter defining if the concatenated cube feeding the RSM model is created considering first the model or the different cubes. If 'modtocube=False', the function will select the first cube then test all models on it and move to the next one. If 'modtocube=True', the model will select one model and apply it to every cubes before moving to the next model. Default is True.
• ns: float , optional Number of regime switches. Default is one regime switch per annulus but smaller values may be used to reduce the impact of noise or disk structures on the final RSM probablity map.
• sel_crop: list of int or None, optional Selected crop sizes from proposed crop_range (crop size = crop_size + 2 x (sel_crop)). A specific sel_crop should be provided for each mode. Default is crop size = [crop_size]
• estimator: str, optional Approach used for the probability map estimation either a 'Forward' model (approach used in the original RSM map algorithm) which consider only the past observations to compute the current probability or 'Forward-Backward' model which relies on both past and future observations to compute the current probability
• colmode:str, optional Method used to generate the final probability map from the three-dimensionnal cube of probabilities generated by the RSM approach. It is possible to chose between the 'mean', the 'median' of the 'max' value of the probabilities along the time axis. Default is 'median'.
• ann_center:int, optional Selected annulus if the probabilities are computed for a single annulus (Used by the optimization framework). Default is None
• sel_cube: list of arrays,optional List of selected PSF-subtraction techniques and ADI sequences used to generate the final probability map. [[i1,j1],[i2,j2],...] with i1 the first considered PSF-subtraction technique and j1 the first considered ADI sequence, i2 the second considered PSF-subtraction technique, etc. Default is None whih implies that all PSF-subtraction techniques and all ADI sequences are used to compute the final probability map.

##opti_model

• optimisation_model: str, optional Approach used for the paramters optimal selection via the maximization of the contrast for APCA, LOCI, KLIP and KLIP FM. The optimization is done either via a Bayesian approach ('Bayesian') or using Particle Swarm optimization ('PSO'). Default is PSO.
• param_optimisation: dict, optional dictionnary regrouping the parameters used by the Bayesian or the PSO optimization framework. For the Bayesian optimization we have 'opti_iter' the number of iterations, ,'ini_esti' number of sets of parameters for which the loss function is computed to initialize the Gaussian process, random_search the number of random searches for the selection of the next set of parameters to sample based on the maximisation of the expected immprovement. For the PSO optimization, 'w' is the inertia factor, 'c1' is the cognitive factor and 'c2' is the social factor, 'n_particles' is the number of particles in the swarm (number of point tested at each iteration), 'opti_iter' the number of iterations,'ini_esti' number of sets of parameters for which the loss function is computed to initialize the PSO. {'c1': 1, 'c2': 1, 'w':0.5,'n_particles':10 ,'opti_iter':15,'ini_esti':10, 'random_search':100}
• filt: True, optional If True, a Hampel Filter is applied on the set of parameters for the annular mode in order to avoid outliers due to potential bright artefacts.

##opti_RSM

• estimator: str, optional Approach used for the probability map estimation either a 'Forward' model (approach used in the original RSM map algorithm) which consider only the past observations to compute the current probability or 'Forward-Backward' model which relies on both past and future observations to compute the current probability
• colmode:str, optional Method used to generate the final probability map from the three-dimensionnal cube of probabilities generated by the RSM approach. It is possible to chose between the 'mean', the 'median' of the 'max' value of the probabilities along the time axis. Default is 'median'.

##RSM_combination

• estimator: str, optional Approach used for the probability map estimation either a 'Forward' model (approach used in the original RSM map algorithm) which consider only the past observations to compute the current probability or 'Forward-Backward' model which relies on both past and future observations to compute the current probability
• colmode:str, optional Method used to generate the final probability map from the three-dimensionnal cube of probabilities generated by the RSM approach. It is possible to chose between the 'mean', the 'median' of the 'max' value of the probabilities along the time axis. Default is 'median'.
• threshold: bool, optional When True a radial treshold is computed on the final detection map with parallactic angles reversed. For a given angular separation, the radial threshold is defined as the maximum probability observed within the annulus. The radia thresholds are checked for outliers and smoothed via a Hampel filter. Only used when relying on the auto-RSM framework. Default is True.
• contrast_sel: str,optional Contrast and azimuth definition for the optimal likelihood cubes/ residuall cubes selection. If 'Max' ('Min' or 'Median'), the largest (smallest or median) contrast obtained during the PSF-subtraction techniques optimization will be chosen along the corresponding azimuthal position for the likelihood cubes selection. Default is 'Max'.
• combination: str,optional Type of greedy selection algorithm used for the selection of the optimal set of cubes of likelihoods/cubes of residuals (either 'Bottom-Up' or 'Top-Down'). For more details see Dahlqvist et al. (2021). Default is 'Bottom-Up'.
• SNR: bool,optional If True, the auto-S/N framework is used, resulting in an optimizated final S/N map when using subsequently the opti_map. If False the auto-RSM framework is used, providing an optimized probability map when using subsequently the opti_map.

##opti_map

• estimator: str, optional Approach used for the probability map estimation either a 'Forward' model (approach used in the original RSM map algorithm) which consider only the past observations to compute the current probability or 'Forward-Backward' model which relies on both past and future observations to compute the current probability
• colmode:str, optional Method used to generate the final probability map from the three-dimensionnal cube of probabilities generated by the RSM approach. It is possible to chose between the 'mean', the 'median' of the 'max' value of the probabilities along the time axis. Default is 'median'.
• threshold: bool, optional When True the radial treshold is computed during the RSM_combination is applied on the final detection map with the original parallactic angles. Only used when relying on the auto-RSM framework. Default is True.
• Full: bool,optional If True, the entire set of ADI-sequences and PSF-subtraction techniques are used to generate the final detection map. If performed after RSM_combination, the obtained optimal set is repkaced by the entire set of cubes. Please make ure you have saved the optimal set via the save_parameter function. Default is 'False'.
• SNR: bool,optional If True, the auto-S/N framework is used, resulting in an optimizated final S/N map when using subsequently the opti_map. If False the auto-RSM framework is used, providing an optimized probability map when using subsequently the opti_map.

##contrast_curve

• an_dist: list or ndarray List of angular separations for which a contrast has to be estimated.
• ini_contrast: list or ndarray Initial contrast for the range of angular separations included in an_dist. The number of initial contrasts shoul be equivalent to the number of angular separations.
• probmap: numpy 2d ndarray Detection map provided by the RSM algorithm via opti_map or probmap_esti.
• inv_ang: bool, optional If True, the sign of the parallactic angles of all ADI sequence is flipped for the computation of the contrast. Default is False.
• threshold: bool, optional If an angular separation based threshold has been used when generating the detection map, the same set of thresholds should be considered as well during the contrast computation. Default is False.
• psf_oa: bool, optional, optional Saturated PSF of the host star used to compute the scaling factor allowing the conversion between contrasts and fluxes for the injection of fake companions during the computation of the contrast. If no Saturated PSF is provided, the ini_contrast should be provided in terms of flux instead of contrast. Default is None.
• estimator: str, optional Approach used for the probability map estimation either a 'Forward' model (approach used in the original RSM map algorithm) which consider only the past observations to compute the current probability or 'Forward-Backward' model which relies on both past and future observations to compute the current probability
• colmode:str, optional Method used to generate the final probability map from the three-dimensionnal cube of probabilities generated by the RSM approach. It is possible to chose between the 'mean', the 'median' of the 'max' value of the probabilities along the time axis. Default is 'median'.
• n_fc: int, optional Number of azimuths considered for the computation of the True positive rate/completeness, (number of fake companions injected separately). The number of azimuths is defined such that the selected completeness is reachable (e.g. 95% of completeness requires at least 20 fake companion injections). Default 20.
• completeness: float, optional The completeness level to be achieved when computing the contrasts, i.e. the True positive rate reached at the threshold associated to the first false positive (the first false positive is defined as the brightest speckle present in the entire detection map). Default 95.

##contrast_matrix

• an_dist: list or ndarray List of angular separations for which a contrast has to be estimated.
• ini_contrast: list or ndarray Initial contrast for the range of angular separations included in an_dist. The number of initial contrasts shoul be equivalent to the number of angular separations.
• probmap: numpy 2d ndarray Detection map provided by the RSM algorithm via opti_map or probmap_esti.
• inv_ang: bool, optional If True, the sign of the parallactic angles of all ADI sequence is flipped for the computation of the contrast. Default is False.
• threshold: bool, optional If an angular separation based threshold has been used when generating the detection map, the same set of thresholds should be considered as well during the contrast computation. Default is False.
• psf_oa: bool, optional, optional Saturated PSF of the host star used to compute the scaling factor allowing the conversion between contrasts and fluxes for the injection of fake companions during the computation of the contrast. If no Saturated PSF is provided, the ini_contrast should be provided in terms of flux instead of contrast. Default is None.
• estimator: str, optional Approach used for the probability map estimation either a 'Forward' model (approach used in the original RSM map algorithm) which consider only the past observations to compute the current probability or 'Forward-Backward' model which relies on both past and future observations to compute the current probability
• colmode:str, optional Method used to generate the final probability map from the three-dimensionnal cube of probabilities generated by the RSM approach. It is possible to chose between the 'mean', the 'median' of the 'max' value of the probabilities along the time axis. Default is 'median'.
• n_fc: int, optional Number of azimuths considered for the computation of the True positive rate/completeness, (number of fake companions injected separately). The range of achievable completenness depends on the number of considered azimuths (the minimum completeness is defined as 1/n_fc an the maximum is 1-1/n_fc). Default 20.

#target_characterisation

• expected_pos: list or ndarray (Y,X) position of the detected planetary candidate.
• psf_oa: bool, optional Saturated PSF of the host star used to compute the scaling factor allowing the conversion between contrasts and fluxes. If no Saturated PSF is provided, the photometry will be provided in terms of flux not contrast. Default is None.
• ns: float , optional Number of regime switches. Default is one regime switch per annulus but smaller values may be used to reduce the impact of noise or disk structures on the final RSM probablity map. The number of regime switches my be increase in the case of faint sources to ease their characterization. Default is 1.
• loss_func: str, optional Loss function used for the computation of the source astrometry and photometry. If 'value', it relies on the minimization of the average probability within a 2 FWHM aperture centered on the expected position of the source. If 'prob', it considers the entire annulus for the computation of the background noise statistics and use a Gaussian distribution to determine the probability that the probabilities associated with the planetary candidates in the detection map belongs to the background noise distribution. Default is 'value'.
• optimisation_model: str, optional Approach used for the astrometry and photometry estimation (minimisation of the probabilities within a 2 FWHM aperture centered on the detected source). The optimization is done either via a Bayesian approach ('Bayesian') or using Particle Swarm optimization('PSO'). Default is PSO.
• param_optimisation: dict, optional dictionnary regrouping the parameters used by the Bayesian or the PSO optimization framework. For the Bayesian optimization we have 'opti_iter' the number of iterations, ,'ini_esti' number of sets of parameters for which the loss function is computed to initialize the Gaussian process, random_search the number of random searches for the selection of the next set of parameters to sample based on the maximisation of the expected immprovement. For the PSO optimization, 'w' is the inertia factor, 'c1' is the cognitive factor and 'c2' is the social factor, 'n_particles' is the number of particles in the swarm (number of point tested at each iteration), 'opti_iter' the number of iterations,'ini_esti' number of sets of parameters for which the loss function is computed to initialize the PSO. {'c1': 1, 'c2': 1, 'w':0.5,'n_particles':10 ,'opti_iter':15,'ini_esti':10,'random_search':100}
• photo_bound: list, optional Photometry range considered during the estimation. The range, expressed in terms of contrast (or flux if psf_oa is not provided), is given by the first two number, while the third number gives the number of tested values within this range. The fourth number gives the admissible error after the initial estimation of the photometry and is used by the PSO or Bayesian optimisation function to defined the range of possible values for the photometry (initial value +- admissible error). Default [1e-5,1e-4,10,2e-5].
• ci_esti: str, optional Parameters determining if a confidence interval should be computed for the photometry and astrometry.The erros associated with the photometry and astrometry can be estimated via the inversion of the hessian matrix ('hessian') or via the BFGS minimisation approach ('BFGS') which allows to further improve the precision of the estimates but requires more computation time. Default is None, implying no computation of confidence intervals.
• first_guess: boolean, optional Define if an initialisation of the algorrithm is done via a standard negfc (using the VIP function firstguess) before applying the PSO or Bayesian optimisation. This initialisation is useful when the target is very bright. It relies on PCA approach, SNR ratio maps and negative fake companion injection to estimate the photometry and astrometry. Default is False.