Utilities

Utilities#

Miscellaneous Utilities#

Helper functions used throughout the package (type conversions, array normalization, percentile computations, etc.).

ForMoSA.utils.misc.decoupe(second)[source]#

Re-arranged a number of seconds in the hours-minutes-seconds format.

Parameters:

second (float) – number of second

Returns:

  • float : hours

  • float : minutes

  • float : seconds

Notes

Authors: Simon Petrus

ForMoSA.utils.misc.find_nearest(array, value)[source]#

Return the indice of the closest values from a desire value in an array.

Parameters:

  • array (array) – Array to explore

  • value (float) – Desire value

Returns:

int

Index of the closest values from the desire value

Notes

Authors: Simon Petrus

ForMoSA.utils.misc.format_grid(grid, attr, free_comp, weights)[source]#

Format PCA or NMF outputs into a single xarray

Parameters:

  • grid (np.ndarray) – Original grid

  • attr (dict) – Original grid attributs

  • free_comp (int) – Number of free components in the new grid (= PCA component used during PCA + 1 (nfs))

  • weights (np.ndarray) – PCA or NMF weights grid

Returns:

xarray

Xarray of the PCA or NMF weights grid

Notes

Authors: Matthieu Ravet

ForMoSA.utils.misc.get_weighted_percentile(n, data, weights=None)[source]#

Return the weighted nth percentile(s) of the data

Parameters:

n (float | list | array) – Percentile(s) between 0 and 100

dataarray

Data array, shape (N,) or (N, M)

weightsarray | None

Weights array of shape (N,). If None, uniform weights are used.

Returns:

percentilesarray

Weighted percentile values. - shape (len(n),) if data is 1D - shape (len(n), M) if data is 2D

Notes

Authors: Allan Denis

ForMoSA.utils.misc.scale_to_one_significant_digit(flux)[source]#

Returns a tuple (scaled_flux, factor) such that flux ≈ scaled_flux * 10**factor

Notes

Authors: Allan Denis

ForMoSA.utils.misc.from_recarray_to_dic(data)[source]#

Transform a recarray (from a fits file) into a dictionary

Parameters:

data (FITS_rec) – Data from a fits file

Returns:

data_dict (dic) – Dictionary representation of the data

Notes

Authors: Allan Denis

ForMoSA.utils.misc.normalize_list(value, name, converter=None)[source]#

Normalize value to a list and apply optional conversion.

Parameters:

  • value (Any) – Value to normalize

  • name (str) – Parameter name (for error messages)

  • converter (callable) – Function applied to each element if provided

Returns:

list – Normalized list

Notes

Authors: Allan Denis

ForMoSA.utils.misc.to_float_if_possible(v)[source]#

Convert value to float if possible.

Parameters:

v (Any) – Value to convert

Returns:

float – Float if conversion succeeds, otherwise original value

Notes

Authors: Allan Denis

Spectra Utilities#

Spectral manipulation routines: resolution degradation, Doppler shift, rotational broadening, reddening, continuum estimation, and more.

ForMoSA.utils.spec.calc_ck(flx_mod, flx_obs, err_obs, r_picked, d_picked, analytic='no', bounds=(-inf, inf))[source]#

Calculation of the dilution factor Ck and re-normalization of the synthetic spectrum.

Parameters:

  • flx_mod (ndarray) – Flux of the model spectrum

  • flx_obs (ndarray) – Flux of the data

  • err_obs (ndarray) – Error of the data

  • r_picked (float) – Radius (Rjup)

  • d_picked (float) – Distance (pc)

  • analytic (str) – If ‘yes’, compute Ck by linear least-squares fitting, else use alpha*(R/d)^2

  • bounds (tuple[float, float]) – Bounds for the Least Squares

Return type:

tuple[ndarray, float]

Returns:

  • flx_mod_ck (np.ndarray) – Scaled model flux

  • ck (float) – Scaling coefficient

Notes

Authors: Simon Petrus and Allan Denis

ForMoSA.utils.spec.convolve_and_sample(wv_channels, sigmas_wvs, model_wvs, model_fluxes, num_sigma=3, force_int=True)[source]#

Simulate the observations of a model. Convolves the model with a variable Gaussian LSF, sampled at each desired spectral channel.

Parameters:

  • wv_channels (list) – the wavelengths values desired

  • sigmas_wvs (list) – the LSF gaussian standard deviation of each wv_channels [IN UNITS OF model_wvs]

  • model_wvs (ndarray) – the wavelengths of the model

  • model_fluxes (ndarray) – the fluxes of the model

  • num_sigma (int) – number of +/- sigmas to evaluate the LSF to.

  • force_int (bool) – False by default. If True, will force interpolation onto wv_channels when the kernel is singular

Return type:

ndarray

Returns:

array

the fluxes in each of the wavelength channels

Notes

Authors: Jason Wang

ForMoSA.utils.spec.resolution_decreasing(wav_input, flx_input, res_input, wav_output, res_output)[source]#

Decrease the resolution of a spectrum by convolving with a Gaussian kernel.

Parameters:

  • wav_input (ndarray) – Wavelength grid of the input

  • flx_input (ndarray) – Flux of the input

  • res_input (ndarray) – Spectral resolution at wav_input

  • wav_output (ndarray) – Desired output wavelength grid

  • res_output (ndarray) – Spectral resolution at wav_output

Return type:

ndarray

Returns:

array

Flux at lower resolution, resampled to wav_output

Notes

Authors: Simon Petrus

ForMoSA.utils.spec.continuum_estimate(wav_input, flx_input, res_input, wav_cont_bounds, res_cont)[source]#

Decrease the resolution of a spectrum (data or model). The function calculates the FWHM as a function of the wavelengths of the custom spectral resolution (estimated for the continuum). It then calculates a sigma to decrease the resolution of the spectrum to this custom FWHM for each wavelength using a gaussian filter and resample it on the wavelength grid of the data.

Parameters:

  • wav_input (ndarray) – Wavelength grid of the spectrum for which you want to estimate the continuum

  • flx_input (ndarray) – Flux of the spectrum for which you want to estimate the continuum

  • res_input (ndarray) – Spectral resolution of the spectrum for which you want to estimate the continuum

  • wav_cont_bounds (str) – Wavelength bounds where you want to estimate the continuum

  • res_cont (float) – Approximate resolution of the continuum

Return type:

ndarray

Returns:

np.ndarray

Estimated continuum of the spectrum re-sampled on the data wavelength grid

Notes

Authors: Simon Petrus, Matthieu Ravet

ForMoSA.utils.spec.doppler_fct(wav_mod_spectro, flx_mod_spectro, res_mod_spectro, rv_picked)[source]#

Application of a Doppler shifting to the interpolated synthetic spectrum using the function pyasl.dopplerShift. The side effects of the Doppler shifting are taking into account by using a model interpolated on a larger wavelength grid as the wavelength grid of the data. After the Doppler shifting, the model is then cut to the wavelength of the data.

Parameters:

  • wav_mod_spectro (ndarray) – Wavelength grid of the model

  • flx_mod_spectro (ndarray) – Flux of the interpolated synthetic spectrum

  • res_mod_spectro (ndarray) – Resolution of the model

  • rv_picked (float) – Radial velocity randomly picked by the nested sampling (in km.s-1)

Return type:

tuple[ndarray, ndarray, ndarray]

Returns:

array

Wavelength grid after Doppler shifting

array

New flux of the interpolated synthetic spectrum

array

New resolution of the interpolated synthetic spectrum

Notes

Authors: Simon Petrus, Allan Denis and Matthieu Ravet

ForMoSA.utils.spec.reddening_fct(wav, flx, av_picked)[source]#

Application of a sythetic interstellar extinction to the interpolated synthetic spectrum using the function extinction.fm07.

Parameters:

  • wav (ndarray) – Wavelength grid of the model

  • flx (ndarray) – Flux of the interpolated synthetic spectrum

  • av_picked (float) – Extinction randomly picked by the nested sampling (in mag)

Return type:

tuple[ndarray, ndarray]

Returns:

array

New flux of the interpolated synthetic spectrum

Notes

Authors: Simon Petrus

ForMoSA.utils.spec.vsini_fct(wav_mod_spectro, flx_mod_spectro, res_mod_obs_spectro, ld_picked, vsini_picked, vsini_type)[source]#

Application of a rotational velocity (line broadening) to the interpolated synthetic spectrum

Parameters:

  • wav_mod_spectro (ndarray) – Wavelength grid of the model

  • flx_mod_spectro (ndarray) – Flux of the interpolated synthetic spectrum (spectroscopy)

  • res_mod_obs_spectro (ndarray) – Resolution of the model as a function of the wavelength grid of the data

  • ld_picked (float) – Limb darkening randomly picked by the nested sampling

  • vsini_picked (float) – v.sin(i) randomly picked by the nested sampling (in km.s-1)

  • vsini_type (str) – Vsin(i) function to use

Return type:

tuple[ndarray, ndarray]

Returns:

array

New flux of the broadened synthetic spectrum (spectroscopy)

array

New resolution of the broadened synthetic spectrum (photometry)

Notes

Authors: Allan Denis

ForMoSA.utils.spec.vsini_fct_rot_broad(wav_mod_spectro, flx_mod_spectro, ld_picked, vsini_picked)[source]#

Application of a rotation velocity (line broadening) to the interpolated synthetic spectrum using the function extinction.fm07.

Parameters:

  • wav_mod_spectro (ndarray) – Wavelength grid of the model

  • flx_mod_spectro (ndarray) – Flux of the interpolated synthetic spectrum

  • ld_picked (ndarray) – Limb darkening randomly picked by the nested sampling

  • vsini_picked (float) – v.sin(i) randomly picked by the nested sampling (in km.s-1)

Return type:

ndarray

Returns:

array

New flux of the interpolated synthetic spectrum

Notes

Authors: Simon Petrus

ForMoSA.utils.spec.vsini_fct_fast_rot_broad(wav_mod_spectro, flx_mod_spectro, ld_picked, vsini_picked)[source]#

Application of a rotation velocity (line broadening) to the interpolated synthetic spectrum using the function extinction.fm07.

Parameters:

  • wav_mod_spectro (ndarray) – Wavelength grid of the model

  • flx_mod_spectro (ndarray) – Flux of the interpolated synthetic spectrum

  • ld_picked (ndarray) – Limb darkening randomly picked by the nested sampling

  • vsini_picked (float) – v.sin(i) randomly picked by the nested sampling (in km.s-1)

Return type:

ndarray

Returns:

array

New flux of the interpolated synthetic spectrum

Notes

Authors: Simon Petrus

ForMoSA.utils.spec.vsini_fct_accurate(wav_mod_spectro, flx_mod_spectro, ld_picked, vsini_picked, nr=50, ntheta=100, dif=0.0)[source]#

A routine to quickly rotationally broaden a spectrum in linear time. Adapted from Carvalho & Johns-Krull 2023 https://ui.adsabs.harvard.edu/abs/2023RNAAS…7…91C/abstract

Parameters:

  • wav_mod_spectro (ndarray) – Wavelength grid of the model

  • flx_mod_spectro (ndarray) – Flux of the interpolated synthetic spectrum

  • ld_picked (ndarray) – Limb darkening randomly picked by the nested sampling

  • vsini_picked (ndarray) – v.sin(i) randomly picked by the nested sampling (in km.s-1)

  • nr (int) – (default = 10) The number of radial bins on the projected disk

  • ntheta (int) –

    (default = 100) The number of azimuthal bins in the largest radial annulus

    note: the number of bins at each r is int(r*ntheta) where r < 1

  • dif (float) –

    (default = 0) The differential rotation coefficient, applied according to the law Omeg(th)/Omeg(eq) = (1 - dif/2 - (dif/2) cos(2 th)).

    Dif = .675 nicely reproduces the law proposed by Smith, 1994, A&A, Vol. 287, p. 523-534, to unify WTTS and CTTS. Dif = .23 is similar to observed solar differential rotation. Note: the th in the above expression is the stellar co-latitude, not the same as the integration variable used below. This is a disk integration routine.

Return type:

ndarray

Returns:

array

New flux of the interpolated synthetic spectrum

Notes

Authors: Allan Denis

ForMoSA.utils.spec.vsini_fct_accurate_fast_rot_broad(wav_mod_spectro, flx_mod_spectro, ld_picked, vsini_picked)[source]#

Application of a rotation velocity (line broadening) to the interpolated synthetic spectrum using the Carvalho & Johns-Krull (2023) approach

Parameters:

  • wav_mod_spectro (ndarray) – Wavelength grid of the model

  • flx_mod_spectro (ndarray) – Flux of the interpolated synthetic spectrum

  • ld_picked (float) – Limb darkening randomly picked by the nested sampling

  • vsini_picked (float) – v.sin(i) randomly picked by the nested sampling (in km.s-1)

Return type:

ndarray

Returns:

array

New flux of the interpolated synthetic spectrum

Notes

Authors: Simon Petrus, Arthur Vigan and Allan Denis

ForMoSA.utils.spec.bb_cpd_fct(wav, flx, distance, bb_t_picked, bb_r_picked)[source]#

Function to add the effect of a cpd (circum planetary disc) to the models.

Parameters:

  • wav (ndarray) – Wavelength grid of the model

  • flx (ndarray) – Flux of the interpolated synthetic spectrum

  • distance (ndarray) – Distance from the observation in pc units

  • bb_t_picked (ndarray) – Temperature value randomly picked by the nested sampling in K units

  • float) (bb_r_picked)

  • bb_r_picked (ndarray)

Return type:

tuple[ndarray, ndarray]

Returns:

array

New flux of the interpolated synthetic spectrum

Notes

Authors: Paulina Palma-Bifani

ForMoSA.utils.spec.fit_linear_model(components, flx_obs, err_obs=None, bounds=None, fixed_coeffs=None)[source]#

Generic weighted linear model fitter.

Solve:

flx_obs = sum_i c_i * components

Parameters:
Return type:

dict

Returns:

dict with keys – coeffs reconstructed model

Notes

Authors: Allan Denis

ForMoSA.utils.spec.build_linear_components(flx_mod=None, transm=None, flx_cont_mod=None, star_flx_obs=None, flx_cont_obs=None, star_flx_cont_obs=None, system_obs=None, analytic='yes', ck_value=None, bounds=None)[source]#

Build linear components, fixed coefficients and bounds for fit_linear_model().

Parameters:

  • flx_mod (ndarray | None) – Model flux

  • transm (ndarray | None) – Transmission function

  • flx_cont_mod (ndarray | None) – Model continuum flux

  • star_flx_obs (ndarray | None) – Stellar flux

  • flx_cont_obs (ndarray | None) – Observed continuum flux

  • star_flx_cont_obs (ndarray | None) – Observation star flux continuum

  • system_obs (ndarray | None) – Systematics model

  • analytic (str) – ‘yes’ to fit for the model, ‘no’ to apply a constant scaling law

  • ck_value (float | None) – Fixed scaling coefficient if scaling_mode is “fixed”

  • bounds (tuple | None) – Bounds for the optimization

Returns:

  • components (list[np.ndarray]) – Model components

  • fixed_coeffs (dict[int, float]) – Fixed coefficients

  • labels (list[str]) – Labels for each component

Notes

Authors: Allan Denis

ForMoSA.utils.spec.compute_ccf(wav_mod_spectro, flx_mod_spectro, wav_obs_spectro, flx_obs_spectro, err_obs_spectro, res_mod_spectro, res_obs_spectro, res_cont, wav_fit, star_flx_obs_spectro=array([], dtype=float64), transm_obs_spectro=array([], dtype=float64), system_obs_spectro=array([], dtype=float64), rv_grid=array([-300., -298.99833055, -297.9966611, -296.99499165, -295.9933222, -294.99165275, -293.98998331, -292.98831386, -291.98664441, -290.98497496, -289.98330551, -288.98163606, -287.97996661, -286.97829716, -285.97662771, -284.97495826, -283.97328881, -282.97161937, -281.96994992, -280.96828047, -279.96661102, -278.96494157, -277.96327212, -276.96160267, -275.95993322, -274.95826377, -273.95659432, -272.95492487, -271.95325543, -270.95158598, -269.94991653, -268.94824708, -267.94657763, -266.94490818, -265.94323873, -264.94156928, -263.93989983, -262.93823038, -261.93656093, -260.93489149, -259.93322204, -258.93155259, -257.92988314, -256.92821369, -255.92654424, -254.92487479, 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102.67111853, 103.67278798, 104.67445743, 105.67612688, 106.67779633, 107.67946578, 108.68113523, 109.68280467, 110.68447412, 111.68614357, 112.68781302, 113.68948247, 114.69115192, 115.69282137, 116.69449082, 117.69616027, 118.69782972, 119.69949917, 120.70116861, 121.70283806, 122.70450751, 123.70617696, 124.70784641, 125.70951586, 126.71118531, 127.71285476, 128.71452421, 129.71619366, 130.71786311, 131.71953255, 132.721202, 133.72287145, 134.7245409, 135.72621035, 136.7278798, 137.72954925, 138.7312187, 139.73288815, 140.7345576, 141.73622705, 142.73789649, 143.73956594, 144.74123539, 145.74290484, 146.74457429, 147.74624374, 148.74791319, 149.74958264, 150.75125209, 151.75292154, 152.75459098, 153.75626043, 154.75792988, 155.75959933, 156.76126878, 157.76293823, 158.76460768, 159.76627713, 160.76794658, 161.76961603, 162.77128548, 163.77295492, 164.77462437, 165.77629382, 166.77796327, 167.77963272, 168.78130217, 169.78297162, 170.78464107, 171.78631052, 172.78797997, 173.78964942, 174.79131886, 175.79298831, 176.79465776, 177.79632721, 178.79799666, 179.79966611, 180.80133556, 181.80300501, 182.80467446, 183.80634391, 184.80801336, 185.8096828, 186.81135225, 187.8130217, 188.81469115, 189.8163606, 190.81803005, 191.8196995, 192.82136895, 193.8230384, 194.82470785, 195.8263773, 196.82804674, 197.82971619, 198.83138564, 199.83305509, 200.83472454, 201.83639399, 202.83806344, 203.83973289, 204.84140234, 205.84307179, 206.84474124, 207.84641068, 208.84808013, 209.84974958, 210.85141903, 211.85308848, 212.85475793, 213.85642738, 214.85809683, 215.85976628, 216.86143573, 217.86310518, 218.86477462, 219.86644407, 220.86811352, 221.86978297, 222.87145242, 223.87312187, 224.87479132, 225.87646077, 226.87813022, 227.87979967, 228.88146912, 229.88313856, 230.88480801, 231.88647746, 232.88814691, 233.88981636, 234.89148581, 235.89315526, 236.89482471, 237.89649416, 238.89816361, 239.89983306, 240.9015025, 241.90317195, 242.9048414, 243.90651085, 244.9081803, 245.90984975, 246.9115192, 247.91318865, 248.9148581, 249.91652755, 250.91819699, 251.91986644, 252.92153589, 253.92320534, 254.92487479, 255.92654424, 256.92821369, 257.92988314, 258.93155259, 259.93322204, 260.93489149, 261.93656093, 262.93823038, 263.93989983, 264.94156928, 265.94323873, 266.94490818, 267.94657763, 268.94824708, 269.94991653, 270.95158598, 271.95325543, 272.95492487, 273.95659432, 274.95826377, 275.95993322, 276.96160267, 277.96327212, 278.96494157, 279.96661102, 280.96828047, 281.96994992, 282.97161937, 283.97328881, 284.97495826, 285.97662771, 286.97829716, 287.97996661, 288.98163606, 289.98330551, 290.98497496, 291.98664441, 292.98831386, 293.98998331, 294.99165275, 295.9933222, 296.99499165, 297.9966611, 298.99833055, 300.]), rv_sini_map=False, normalize=True)[source]#

Function to compute the ccf between a template and data

Parameters:

  • wav_mod_spectro (ndarray) – Wavelength grid of the template

  • flx_mod_spectro (ndarray) – Flux of the template

  • wav_obs_spectro (ndarray) – Wavelength grid of the data

  • flx_obs_spectro (ndarray) – Flux of the data

  • err_obs_spectro (ndarray) – Error of the data

  • res_mod_spectro (ndarray) – Resolution of the template

  • res_obs_spectro (ndarray) – Resolution of the data

  • res_cont (float) – Resolution of the continuum

  • wav_fit (str | ndarray) – Wavelengths used for fitting

  • star_flx_obs_spectro (ndarray) – Star flux of the data

  • transm_obs_spectro (ndarray) – Transmission

  • system_obs_spectro (ndarray) – Systematics

  • rv_grid (ndarray) – Grid of RV for the CCF function

  • rv_vsini_map (bool) – Whether to use this function to compute a rv / vsini map

  • normalize (bool) – Whether to normalize ccf

  • rv_sini_map (bool)

Returns:

ccf_normnp.ndarray

CCF function normalized by the SNR

acf_normnp.ndarray

ACF function rescaled and shifted at the peak of the RV

star_ccf_normnp.ndarray

CCF function with star data

rv_peakfloat

Peak of the RV

Notes

Authors: Arthur Vigan and Allan Denis

ForMoSA.utils.spec.compute_ccf_single_rv(rv, wav_mod_spectro, flx_mod_spectro, flx_mod_spectro_no_rv_hf, res_mod_spectro, wav_obs_spectro, flx_obs_spectro, flx_cont_obs_spectro, flx_obs_spectro_hf, res_obs_spectro, wav_cont, res_cont, err_obs_spectro, transm_obs_spectro=1, star_flx_obs_spectro=array([], dtype=float64), star_flx_cont_obs_spectro=1, star_flx_obs_spectro_hf=array([], dtype=float64), system_obs_spectro=array([], dtype=float64), speckles=1, ld=0.6)[source]#

Function to compute the correlation between template and data for a specific rv value

Parameters:

  • rv (float) – rv value

  • vsini (float) – vsini value

  • wav_mod_spectro (ndarray) – Wavelength grid of the template

  • flx_mod_spectro (ndarray) – Flux of the template

  • flx_mod_spectro_no_rv_hf (ndarray) – High frequency content of the flux of the model at 0 rv

  • res_mod_spectro (ndarray) – Resolution of the template interpolated onto the wavelength grid of the data

  • wav_obs_spectro (ndarray) – Wavelength grid of the data

  • flx_obs_spectro (ndarray) – The flux of the data

  • flx_cont_obs_spectro (ndarray) – Continuum of the flux of the data

  • res_obs_spectro (ndarray) – Resolution of the data

  • wav_cont (str) – Wavelength used for the continuum

  • res_cont (ndarray) – Resolution of the continuum

  • err_obs_spectro (ndarray) – Error of the flux

  • transm_obs_spectro (int | ndarray) – Transmission

  • star_flx_obs_spectro (ndarray) – Flux of the star

  • star_flx_cont_obs_spectro (int | ndarray) – Continuum of the flux of the star

  • system_obs_spectro (ndarray) – Systematics

  • speckles (int | ndarray) – Speckles

  • flx_obs_spectro_hf (ndarray)

  • star_flx_obs_spectro_hf (ndarray)

  • ld (float)

Return type:

tuple[float, float, float]

Returns:

ccffloat

Correlation between the template and the data

acffloat

Autocorrelation between the template and itself

ccf_starfloat

Correlation between the template and the star data

Notes

Authors: Arthur Vigan and Allan Denis