API documentation for `kima`¶

Data¶

Most analyses will start by using the RVData class to load data from a set of files or arrays. Gaia epoch astrometry can also be read with the GAIAdata class.

Example:¶

from kima import RVData

data = RVData('filename.txt', skip=1) #(1)!

data.plot() #(2)!

With skip=1, the first line of the file will be ignored.
A very simple plot of the dataset.

kima.RVData API

Load and store RV data

init(self, filenames: collections.abc.Sequence[str], units: str = 'ms', skip: int = 0, max_rows: int = 0, delimiter: str = ' \t,', indicators: collections.abc.Sequence[str] = [], double_lined: bool = False) -> None init(self, filename: str, units: str = 'ms', skip: int = 0, max_rows: int = 0, multi: bool = False, delimiter: str = ' \t,', indicators: collections.abc.Sequence[str] = [], double_lined: bool = False) -> None init(self, t: collections.abc.Sequence[float], y: collections.abc.Sequence[float], sig: collections.abc.Sequence[float], indicators: collections.abc.Sequence[collections.abc.Sequence[float]] = [], units: str = 'ms', instrument: str = '') -> None init(self, t: collections.abc.Sequence[collections.abc.Sequence[float]], y: collections.abc.Sequence[collections.abc.Sequence[float]], sig: collections.abc.Sequence[collections.abc.Sequence[float]], indicators: collections.abc.Sequence[collections.abc.Sequence[collections.abc.Sequence[float]]] = [], units: str = 'ms', instruments: collections.abc.Sequence[str] = []) -> None

Overloaded function.

__init__(self, filenames: collections.abc.Sequence[str], units: str = 'ms', skip: int = 0, max_rows: int = 0, delimiter: str = ' \t,', indicators: collections.abc.Sequence[str] = [], double_lined: bool = False) -> None

Load RV data from a list of files.

Parameters:

Name	Type	Description	Default
`filenames`	`list`	List of filenames to load	required
`units`	`str`	Units of the data ('ms' or 'kms')	required
`skip`	`int`	Number of lines to skip at the top of the file	required
`max_rows`	`int`	Maximum number of rows to read	required
`delimiter`	`str`	Delimiter between columns	required
`indicators`	`list`	List of names for the indicator columns (should be present in all files)	required
`double_lined`	`bool`	Whether the data is for a double-lined binary	required

__init__(self, filename: str, units: str = 'ms', skip: int = 0, max_rows: int = 0, multi: bool = False, delimiter: str = ' \t,', indicators: collections.abc.Sequence[str] = [], double_lined: bool = False) -> None

Load RV data from a file.

Parameters:

Name	Type	Description	Default
`filename`	`str`	Name of the file to read	required
`units`	`str`	Units of the data ('ms' or 'kms')	required
`skip`	`int`	Number of lines to skip at the top of the file	required
`max_rows`	`int`	Maximum number of rows to read	required
`delimiter`	`str`	Delimiter between columns	required
`indicators`	`list`	List of names for the indicator columns	required
`double_lined`	`bool`	Whether the data is for a double-lined binary	required

__init__(self, t: collections.abc.Sequence[float], y: collections.abc.Sequence[float], sig: collections.abc.Sequence[float], indicators: collections.abc.Sequence[collections.abc.Sequence[float]] = [], units: str = 'ms', instrument: str = '') -> None

Load RV data from arrays for a single instrument.

Parameters:

Name	Type	Description	Default
`t`	`(list, array)`	List of observation times	required
`y`	`(list, array)`	List of RV values	required
`sig`	`(list, array)`	List of RV uncertainties	required
`indicators`	`list[list]`	Lists of indicator values	required
`units`	`str`	Units of the radial velocity data ('ms' or 'kms')	required
`instrument`	`str`	Name of the instrument	required

__init__(self, t: collections.abc.Sequence[collections.abc.Sequence[float]], y: collections.abc.Sequence[collections.abc.Sequence[float]], sig: collections.abc.Sequence[collections.abc.Sequence[float]], indicators: collections.abc.Sequence[collections.abc.Sequence[collections.abc.Sequence[float]]] = [], units: str = 'ms', instruments: collections.abc.Sequence[str] = []) -> None

Load RV data from arrays for multiple instruments.

Parameters:

Name	Type	Description	Default
`t`	`(list[list], array[array])`	Lists of observation times	required
`y`	`(list[list], array[array])`	Lists of RV values	required
`sig`	`(list[list], array[array])`	Lists of RV uncertainties	required
`indicators`	`list[list]`	Lists of indicator values (3D array)	required
`units`	`str`	Units of the radial velocity data ('ms' or 'kms')	required
`instrument`	`str`	Name of the instrument	required

`M0_epoch` `property` ¶

reference epoch for the mean anomaly

`N` `property` ¶

Total number of observations

`actind` `property` ¶

Activity indicators

`datafile` `property` ¶

The file name

`datafiles` `property` ¶

The list of file names

`double_lined` `property` ¶

if the data is for a double-lined binary

`indicator_names` `property` ¶

names of activity indicators

`instrument` `property` ¶

instrument name

`instruments` `property` ¶

instrument names

`multi` `property` ¶

Data comes from multiple instruments

`normalized_actind` `property` ¶

Activity indicators normalized to [0,1]

`obsi` `property` ¶

The instrument identifier

`sig` `property` ¶

The observed RV uncertainties

`sig2` `property` ¶

The observed secondary RV uncertainties (double-lined binary)

`skip` `property` ¶

Lines skipped when reading data

`t` `property` ¶

The times of observations

`trend_epoch` `property` ¶

reference epoch for the trend

`units` `property` ¶

Units of the RVs and uncertainties

`y` `property` ¶

The observed radial velocities

`y2` `property` ¶

The observed secondary radial velocities (double-lined binary)

`_inverse_time_indices()` `method descriptor` ¶

_inverse_time_indices(self) -> list[int]

`get_RV_max()` `method descriptor` ¶

get_RV_max(self) -> float

Get the maximum RV

`get_RV_mean()` `method descriptor` ¶

get_RV_mean(self) -> float

Get the mean RV

`get_RV_min()` `method descriptor` ¶

get_RV_min(self) -> float

Get the minimum RV

`get_RV_span()` `method descriptor` ¶

get_RV_span(self) -> float

Get the RV span

`get_RV_std()` `method descriptor` ¶

get_RV_std(self) -> float

Get the standard deviation of RVs

`get_RV_var()` `method descriptor` ¶

get_RV_var(self) -> float

Get the variance of RVs

`get_actind_max()` `method descriptor` ¶

get_actind_max(self, arg: int, /) -> float

Get the maximum value of activity indicator i

`get_actind_mean()` `method descriptor` ¶

get_actind_mean(self, arg: int, /) -> float

Get the mean of activity indicator i

`get_actind_min()` `method descriptor` ¶

get_actind_min(self, arg: int, /) -> float

Get the minimum value of activity indicator i

`get_actind_span()` `method descriptor` ¶

get_actind_span(self, arg: int, /) -> float

Get the span of activity indicator i

`get_actind_std()` `method descriptor` ¶

get_actind_std(self, arg: int, /) -> float

Get the standard deviation of activity indicator i

`get_actind_var()` `method descriptor` ¶

get_actind_var(self, arg: int, /) -> float

Get the variance of activity indicator i

`get_max_RV_span()` `method descriptor` ¶

get_max_RV_span(self) -> float

Get the maximum RV span of individual instruments

`get_t_max()` `method descriptor` ¶

get_t_max(self) -> float

Get the maximum time

`get_t_middle()` `method descriptor` ¶

get_t_middle(self) -> float

Get the middle time

`get_t_min()` `method descriptor` ¶

get_t_min(self) -> float

Get the minimum time

`get_timespan()` `method descriptor` ¶

get_timespan(self) -> float

Get the timespan

`get_trend_magnitude()` `method descriptor` ¶

get_trend_magnitude(self, degree: int, i: int = -1) -> int

Order of magnitude for trend coefficient (of degree) given the data

`get_unique_t()` `method descriptor` ¶

get_unique_t(self) -> list[float]

Get the unique times

`topslope()` `method descriptor` ¶

topslope(self) -> float

Get the maximum slope allowed by the data

kima.GAIAdata API

Load and store Gaia astrometric data

init(self, filename: str, units: str = 'ms', skip: int = 0, max_rows: int = 0, delimiter: str = ' \t,') -> None

Load astrometric data from a file

Parameters:

Name	Type	Description	Default
`filename`	`str`	Name of the file to read	required
`units`	`str`	Units of the data ('ms' or 'kms')	required
`skip`	`int`	Number of lines to skip at the top of the file	required
`max_rows`	`int`	Maximum number of rows to read	required
`delimiter`	`str`	Delimiter between columns	required

`M0_epoch` `property` ¶

reference epoch for the mean anomaly

`N` `property` ¶

Total number of observations

`datafile` `property` ¶

The file name

`pf` `property` ¶

The parallax factors

`psi` `property` ¶

The Gaia scan angles

`t` `property` ¶

The times of observations

`units` `property` ¶

Units of the Gaia data and uncertainties

`w` `property` ¶

The observed centroid positions

`wsig` `property` ¶

The observed centroid position uncertainties

Models¶

We can then create one of the several models currently implemented

Example:¶

from kima import RVmodel

model = RVmodel(fix=False, npmax=2, data=data)

kima.RVmodel API

`RVmodel()` ¶

init(self, fix: bool, npmax: int, data: kima.Data.RVData) -> None

Implements a sum-of-Keplerians model where the number of Keplerians can be free.

Parameters:

Name	Type	Description	Default
`fix`	`bool`	whether the number of Keplerians should be fixed	required
`npmax`	`int`	maximum number of Keplerians	required
`data`	`RVData`	the RV data	required

`AK_Kprior` `property` ¶

Prior for AK semi-amplitude

`AK_Pprior` `property` ¶

Prior for AK orbital period

`AK_eprior` `property` ¶

Prior for AK eccentricity

`AK_phiprior` `property` ¶

Prior for AK mean anomaly(ies)

`AK_t0prior` `property` ¶

Prior for AK center of apodizing windows (days)

`AK_tauprior` `property` ¶

Prior for AK apodization widths τ (days)

`AK_wprior` `property` ¶

Prior for AK argument of periastron

`Cprior` `property` ¶

Prior for the systemic velocity

`Jprior` `property` ¶

Prior for the extra white noise (jitter)

`KO_Kprior` `property` ¶

Prior for KO semi-amplitude

`KO_Pprior` `property` ¶

Prior for KO orbital period

`KO_eprior` `property` ¶

Prior for KO eccentricity

`KO_phiprior` `property` ¶

Prior for KO mean anomaly(ies)

`KO_wprior` `property` ¶

Prior for KO argument of periastron

`TR_Kprior` `property` ¶

Prior for TR semi-amplitude

`TR_Pprior` `property` ¶

Prior for TR orbital period

`TR_Tcprior` `property` ¶

Prior for TR mean anomaly(ies)

`TR_eprior` `property` ¶

Prior for TR eccentricity

`TR_wprior` `property` ¶

Prior for TR argument of periastron

`apodized_keplerians` `property` ¶

whether the model includes apodized Keplerian(s)

`beta_prior` `property` ¶

(Common) prior for the activity indicator coefficients

`conditional` `property` ¶

(self) -> kima.RVmodel.KeplerianConditionalPrior

`cubic_prior` `property` ¶

Prior for the cubic coefficient of the trend

`data` `property` ¶

the data

`degree` `property` ¶

degree of the polynomial trend

`directory` `property` ¶

directory where the model ran

`enforce_stability` `property` ¶

whether to enforce AMD-stability

`fix` `property` ¶

whether the number of Keplerians is fixed

`indicator_correlations` `property` ¶

include in the model linear correlations with indicators

`individual_offset_prior` `property` ¶

Common prior for the between-instrument offsets

`jitter_propto_indicator` `property` ¶

docs

`jitter_propto_indicator_index` `property` ¶

docs

`known_object` `property` ¶

whether the model includes (better) known extra Keplerian curve(s)

`n_apodized_keplerians` `property` ¶

how many apodized Keplerians

`n_known_object` `property` ¶

how many known objects

`n_transiting_planet` `property` ¶

how many transiting planets

`npmax` `property` ¶

maximum number of Keplerians

`nu_prior` `property` ¶

Prior for the degrees of freedom of the Student-t likelihood

`offsets_prior` `property` ¶

Common prior for the between-instrument offsets

`optimize_equal_times` `property` ¶

docs

`quadr_prior` `property` ¶

Prior for the quadratic coefficient of the trend

`slope_prior` `property` ¶

Prior for the slope

`star_mass` `property` ¶

stellar mass [Msun]

`stellar_jitter_prior` `property` ¶

Prior for the stellar jitter (common to all instruments)

`studentt` `property` ¶

use a Student-t distribution for the likelihood (instead of Gaussian)

`transiting_planet` `property` ¶

whether the model includes transiting planet(s)

`trend` `property` ¶

whether the model includes a polynomial trend

`set_apodized_keplerians()` `method descriptor` ¶

set_apodized_keplerians(self, arg: int, /) -> None

`set_known_object()` `method descriptor` ¶

set_known_object(self, arg: int, /) -> None

`set_loguniform_prior_Np()` `method descriptor` ¶

set_loguniform_prior_Np(self) -> None

`set_transiting_planet()` `method descriptor` ¶

set_transiting_planet(self, arg: int, /) -> None

kima.GPmodel API

`GPmodel()` ¶

init(self, fix: bool, npmax: int, data: kima.Data.RVData) -> None

Implements a model for the RVs with a sum-of-Keplerians plus a correlated noise component given by a Gaussian process.

Parameters:

Name	Type	Description	Default
`fix`	`bool`	whether the number of Keplerians should be fixed	required
`npmax`	`int`	maximum number of Keplerians	required
`data`	`RVData`	the RV data	required

`Cprior` `property` ¶

Prior for the systemic velocity

`Jprior` `property` ¶

Prior for the extra white noise (jitter)

`KO_Kprior` `property` ¶

Prior for KO semi-amplitude

`KO_Pprior` `property` ¶

Prior for KO orbital period

`KO_eprior` `property` ¶

Prior for KO eccentricity

`KO_phiprior` `property` ¶

Prior for KO mean anomaly(ies)

`KO_wprior` `property` ¶

Prior for KO argument of periastron

`Q_prior` `property` ¶

Prior for Q, the quality factor in SHO kernels

`TR_Kprior` `property` ¶

Prior for TR semi-amplitude

`TR_Pprior` `property` ¶

Prior for TR orbital period

`TR_Tcprior` `property` ¶

Prior for TR mean anomaly(ies)

`TR_eprior` `property` ¶

Prior for TR eccentricity

`TR_wprior` `property` ¶

Prior for TR argument of periastron

`beta_prior` `property` ¶

(Common) prior for the activity indicator coefficients

`conditional` `property` ¶

(self) -> kima.RVmodel.KeplerianConditionalPrior

`cubic_prior` `property` ¶

Prior for the cubic coefficient of the trend

`data` `property` ¶

the data

`degree` `property` ¶

degree of the polynomial trend

`directory` `property` ¶

directory where the model ran

`enforce_stability` `property` ¶

whether to enforce AMD-stability

`eta1_prior` `property` ¶

Prior for η1, the GP 'amplitude'

`eta2_prior` `property` ¶

Prior for η2, the GP correlation timescale

`eta3_prior` `property` ¶

Prior for η3, the GP period

`eta4_prior` `property` ¶

Prior for η4, the recurrence timescale or (inverse) harmonic complexity

`eta5_prior` `property` ¶

Prior for η5

`eta6_prior` `property` ¶

Prior for η6

`eta7_prior` `property` ¶

Prior for η7

`fix` `property` ¶

whether the number of Keplerians is fixed

`indicator_correlations` `property` ¶

include in the model linear correlations with indicators

`individual_offset_prior` `property` ¶

Common prior for the between-instrument offsets

`kernel` `property` ¶

GP kernel to use

`known_object` `property` ¶

whether the model includes (better) known extra Keplerian curve(s)

`magnetic_cycle_kernel` `property` ¶

whether to consider a (periodic) GP kernel for a magnetic cycle

`n_known_object` `property` ¶

how many known objects

`n_transiting_planet` `property` ¶

how many transiting planets

`npmax` `property` ¶

maximum number of Keplerians

`offsets_prior` `property` ¶

Common prior for the between-instrument offsets

`quadr_prior` `property` ¶

Prior for the quadratic coefficient of the trend

`slope_prior` `property` ¶

Prior for the slope

`star_mass` `property` ¶

stellar mass [Msun]

`transiting_planet` `property` ¶

whether the model includes transiting planet(s)

`trend` `property` ¶

whether the model includes a polynomial trend

`eta2_larger_eta3()` `method descriptor` ¶

eta2_larger_eta3(self, factor: float = 1.0) -> None

Constrain η2 to be larger than factor * η3

`set_known_object()` `method descriptor` ¶

set_known_object(self, arg: int, /) -> None

`set_transiting_planet()` `method descriptor` ¶

set_transiting_planet(self, arg: int, /) -> None

kima.RVFWHMmodel API

`RVFWHMmodel()` ¶

init(self, fix: bool, npmax: int, data: kima.Data.RVData) -> None

Implements a joint model for RVs and FWHM with a GP component for activity signals.

Parameters:

Name	Type	Description	Default
`fix`	`bool`	whether the number of Keplerians should be fixed	required
`npmax`	`int`	maximum number of Keplerians	required
`data`	`RVData`	the RV data	required

`Cfwhm_prior` `property` ¶

Prior for the 'systemic' FWHM

`Cprior` `property` ¶

Prior for the systemic velocity

`Jfwhm_prior` `property` ¶

Prior for the extra white noise (jitter) in the FWHM

`Jprior` `property` ¶

Prior for the extra white noise (jitter)

`KO_Kprior` `property` ¶

Prior for KO semi-amplitude

`KO_Pprior` `property` ¶

Prior for KO orbital period

`KO_eprior` `property` ¶

Prior for KO eccentricity

`KO_phiprior` `property` ¶

Prior for KO mean anomaly(ies)

`KO_wprior` `property` ¶

Prior for KO argument of periastron

`TR_Kprior` `property` ¶

Prior for TR semi-amplitude

`TR_Pprior` `property` ¶

Prior for TR orbital period

`TR_Tcprior` `property` ¶

Prior for TR mean anomaly(ies)

`TR_eprior` `property` ¶

Prior for TR eccentricity

`TR_wprior` `property` ¶

Prior for TR argument of periastron

`conditional` `property` ¶

(self) -> kima.RVmodel.KeplerianConditionalPrior

`cubic_fwhm_prior` `property` ¶

Prior for the cubic coefficient of the trend in the FWHM (in the FWHM)

`cubic_prior` `property` ¶

Prior for the cubic coefficient of the trend (in the RVs)

`data` `property` ¶

the data

`degree` `property` ¶

degree of the polynomial trend (in the RVs)

`degree_fwhm` `property` ¶

degree of the polynomial trend (in the FWHM)

`directory` `property` ¶

directory where the model ran

`enforce_stability` `property` ¶

whether to enforce AMD-stability

`eta1_fwhm_prior` `property` ¶

Prior for the GP 'amplitude' on the FWHM

`eta1_prior` `property` ¶

Prior for the GP 'amplitude' on the RVs

`eta2_fwhm_prior` `property` ¶

Prior for η2, the GP correlation timescale, on the FWHM

`eta2_prior` `property` ¶

Prior for η2, the GP correlation timescale, on the RVs

`eta3_fwhm_prior` `property` ¶

Prior for η3, the GP period, on the FWHM

`eta3_prior` `property` ¶

Prior for η3, the GP period, on the RVs

`eta4_fwhm_prior` `property` ¶

Prior for η4, the recurrence timescale or (inverse) harmonic complexity, on the FWHM

`eta4_prior` `property` ¶

Prior for η4, the recurrence timescale or (inverse) harmonic complexity, on the RVs

`fix` `property` ¶

whether the number of Keplerians is fixed

`known_object` `property` ¶

whether the model includes (better) known extra Keplerian curve(s)

`n_known_object` `property` ¶

how many known objects

`n_transiting_planet` `property` ¶

how many transiting planets

`npmax` `property` ¶

maximum number of Keplerians

`quadr_fwhm_prior` `property` ¶

Prior for the quadratic coefficient of the trend in the FWHM (in the FWHM)

`quadr_prior` `property` ¶

Prior for the quadratic coefficient of the trend (in the RVs)

`share_eta2` `property` ¶

whether the η2 parameter is shared between RVs and FWHM

`share_eta3` `property` ¶

whether the η3 parameter is shared between RVs and FWHM

`share_eta4` `property` ¶

whether the η4 parameter is shared between RVs and FWHM

`slope_fwhm_prior` `property` ¶

Prior for the slope in the FWHM (in the FWHM)

`slope_prior` `property` ¶

Prior for the slope (in the RVs)

`star_mass` `property` ¶

stellar mass [Msun]

`transiting_planet` `property` ¶

whether the model includes transiting planet(s)

`trend` `property` ¶

whether the model includes a polynomial trend (in the RVs)

`trend_fwhm` `property` ¶

whether the model includes a polynomial trend (in the FWHM)

`set_known_object()` `method descriptor` ¶

set_known_object(self, arg: int, /) -> None

`set_transiting_planet()` `method descriptor` ¶

set_transiting_planet(self, arg: int, /) -> None

kima.BINARIESmodel API

`BINARIESmodel()` ¶

init(self, fix: bool, npmax: int, data: kima.Data.RVData) -> None

Implements a sum-of-Keplerians model where the number of Keplerians can be free. This model assumes white, uncorrelated noise. This modules is tailored for the analysis of stellar binaries through the known object mode (without it this defaults to the RVmodel) The binary can have one set of RVs or two (one on each star). This model adds apsidal precession as a free parameter and accounts for GR and Tidal effects on the radial velocities.

Parameters:

Name	Type	Description	Default
`fix`	`bool, default=True`	whether the number of Keplerians should be fixed	required
`npmax`	`int, default=0`	maximum number of Keplerians	required
`data`	`RVData`	the RV data	required

`Cprior` `property` ¶

Prior for the systemic velocity

`Jprior` `property` ¶

Prior for the extra white noise (jitter)

`KO_Kprior` `property` ¶

Prior for Semi-amplitude of Binary orbit (+other known objects)

`KO_Pprior` `property` ¶

Prior for Period of Binary orbit (+other known objects)

`KO_cosiprior` `property` ¶

Prior for cosine of the inclination of Binary orbit (+other known objects) to the line-of-sight

`KO_eprior` `property` ¶

Prior for eccentricity of Binary orbit (+other known objects)

`KO_phiprior` `property` ¶

Prior for phase of Binary orbit at the reference time (+other known objects)

`KO_qprior` `property` ¶

Prior for mass ratio of Binary (+other known objects), used if double lined

`KO_wdotprior` `property` ¶

Prior for apsidal precession rate of Binary orbit (+other known objects)

`KO_wprior` `property` ¶

Prior for argument of periastron of Binary orbit (+other known objects)

`binary_mass` `property` ¶

secondary mass [Msun]

`binary_radius` `property` ¶

secondary radius [Rsun]

`conditional` `property` ¶

(self) -> kima.RVmodel.KeplerianConditionalPrior

`correction_K_precision` `property` ¶

To what precision K2 is calculated for the relativistic and tidal corrections, (default is 50 m/s and unless the orbit is very close to face-on this gives sub cm/s precision on the corrections), increasing this may speed up the sampling

`cubic_prior` `property` ¶

Prior for the cubic coefficient of the trend

`data` `property` ¶

the data

`degree` `property` ¶

degree of the polynomial trend

`directory` `property` ¶

directory where the model ran

`double_lined` `property` ¶

whether the data is for a double lined binary, and has two sets of RVs for each epoch

`eclipsing` `property` ¶

whether binary is eclipsing and the inclination can be fixed to 90, defaults to true. If false, default prior is uniform in cosi

`enforce_stability` `property` ¶

whether to enforce AMD-stability (Untested for binaries)

`fix` `property` ¶

whether the number of Keplerians is fixed

`known_object` `property` ¶

whether to include (better) known extra Keplerian curve(s), should be true for BINARIESmodel

`n_known_object` `property` ¶

how many known objects, should be >=1 for BINARIESmodel

`npmax` `property` ¶

maximum number of Keplerians

`nu_prior` `property` ¶

Prior for the degrees of freedom of the Student-t likelihood

`offsets_prior` `property` ¶

Common prior for the between-instrument offsets

`quadr_prior` `property` ¶

Prior for the quadratic coefficient of the trend

`relativistic_correction` `property` ¶

whether to perform the GR correction

`slope_prior` `property` ¶

Prior for the slope

`star_mass` `property` ¶

primary mass [Msun]

`star_radius` `property` ¶

primary radius [Rsun]

`studentt` `property` ¶

use a Student-t distribution for the likelihood (instead of Gaussian)

`tidal_correction` `property` ¶

whether to perform the tidal correction

`trend` `property` ¶

whether the model includes a polynomial trend

`use_binary_longitude` `property` ¶

Whether to sample using the mean longitude rather than mean anomaly at epoch, for use when the binary is close to circular for better sampling

TODO: kima.RVHGPMmodel API

kima.GAIAmodel API

`GAIAmodel()` ¶

init(self, fix: bool, npmax: int, data: kima.Data.GAIAdata) -> None

Analysis of Gaia epoch astrometry. Implements a sum-of-Keplerians model where the number of Keplerians can be free. This model assumes white, uncorrelated noise. Known objects are given priors for geometric elements, free planet search has the choice of geometric or Thiele-Innes elements. An option to fit for a scan-angle dependent signal is included.

Parameters:

Name	Type	Description	Default
`fix`	`bool, default=True`	whether the number of Keplerians should be fixed	required
`npmax`	`int, default=0`	maximum number of Keplerians	required
`data`	`GAIAdata`	the astrometric data	required

`Ak_prior` `property` ¶

Prior for the amplitudes of scan-angle dependent signals

`DEC` `property` ¶

Declination of the target star (degrees)

`Jprior` `property` ¶

Prior for the extra white noise (jitter)

`KO_Pprior` `property` ¶

Prior for KO orbital period(s)

`KO_Wprior` `property` ¶

Prior for KO longitude(s) of ascending node

`KO_aprior` `property` ¶

Prior for KO photocentre semi-major-axis(es)

`KO_cosiprior` `property` ¶

Prior for cosine of KO inclination(s)

`KO_eprior` `property` ¶

Prior for KO eccentricity(ies)

`KO_phiprior` `property` ¶

Prior for KO mean anomaly(ies)

`KO_wprior` `property` ¶

Prior for KO argument(s) of periastron

`RA` `property` ¶

Right Ascension of the target star (degrees)

`accela_prior` `property` ¶

Prior for the proper-acceleration in right-ascension (mas/yr^2)

`acceld_prior` `property` ¶

Prior for the proper-acceleration in declination (mas/yr^2)

`conditional` `property` ¶

(self) -> kima.GAIAmodel.GAIAConditionalPrior

`da_prior` `property` ¶

Prior for the offset in right-ascension (mas)

`data` `property` ¶

the data

`dd_prior` `property` ¶

Prior for the the offset in declination (mas)

`fix` `property` ¶

whether the number of Keplerians is fixed

`jerka_prior` `property` ¶

Prior for the proper-jerk in right-ascension (mas/yr^3)

`jerkd_prior` `property` ¶

Prior for the proper-jerk in declination (mas/yr^3)

`known_object` `property` ¶

whether the model includes (better) known extra Keplerian curve(s)

`mua_prior` `property` ¶

Prior for the proper-motion in right-ascension (mas/yr)

`mud_prior` `property` ¶

Prior for the proper-motion in declination (mas/yr)

`n_baseline_params` `property` ¶

how many baseline astrometric parameters are included the model

`n_known_object` `property` ¶

how many known objects

`n_scan_dep_components` `property` ¶

how many components of scan-angle harmonics are included

`npmax` `property` ¶

maximum number of Keplerians

`nu_prior` `property` ¶

Prior for the degrees of freedom of the Student-t likelihood

`parallax_prior` `property` ¶

Prior for the parallax

`scan_dep_signal` `property` ¶

whether the model includes a model for potential scan-angle dependent signals that could bias towards certain frequencies

`star_mass` `property` ¶

the mass of the central star (Msun)

`studentt` `property` ¶

use a Student-t distribution for the likelihood (instead of Gaussian)

`thetak_prior` `property` ¶

Prior for the phase of scan-angle dependent signals

`thiele_innes` `property` ¶

use the thiele-innes coefficients rather than geometric

`set_baseline_model()` `method descriptor` ¶

set_baseline_model(self, arg: int, /) -> None

set the number of parameters for the baseline astrometric solution, either 5 (the default astrometric solution), 7, or 9 (which include acceleration and jerk terms)

`set_known_object()` `method descriptor` ¶

set_known_object(self, arg: int, /) -> None

set how many known objects to include

`set_scan_dep_signal()` `method descriptor` ¶

set_scan_dep_signal(self, arg: int, /) -> None

set whether the model includes a model for potential scan-angle dependent signals

kima.RVGAIAmodel API

`RVGAIAmodel()` ¶

init(self, fix: bool, npmax: int, GAIAdata: kima.Data.GAIAdata, RVData: kima.Data.RVData) -> None

Combined analysis of Gaia epoch astrometry and radial velocity timeseries. Implements a sum-of-Keplerians model where the number of Keplerians can be free. This model assumes white, uncorrelated noise. Both the central star and potential planets are to be given Mass priors in Solar-Mass.

Parameters:

Name	Type	Description	Default
`fix`	`bool, default=True`	whether the number of Keplerians should be fixed	required
`npmax`	`int, default=0`	maximum number of Keplerians	required
`GAIAdata`	`GAIAdata`	the astrometric data	required
`RVdata`	`RVData`	the radial velocity data	required

`Ak_prior` `property` ¶

Prior for the amplitudes of scan-angle dependent signals

`Cprior` `property` ¶

Prior for the systemic velocity

`DEC` `property` ¶

Declination of the target star (degrees)

`GAIAdata` `property` ¶

the data

`J_GAIA_prior` `property` ¶

Prior for the extra white noise (jitter) for GAIA data

`J_RV_prior` `property` ¶

Prior for the extra white noise (jitter) for RV data

`KO_Pprior` `property` ¶

Prior for KO orbital period(s)

`KO_Wprior` `property` ¶

Prior for KO longitude(s) of ascending node

`KO_aprior` `property` ¶

Prior for KO mass(es) (M_sun)

`KO_cosiprior` `property` ¶

Prior for cosine of KO inclination(s)

`KO_eprior` `property` ¶

Prior for KO eccentricity(ies)

`KO_phiprior` `property` ¶

Prior for KO mean anomaly(ies)

`KO_wprior` `property` ¶

Prior for KO argument(s) of periastron

`RA` `property` ¶

Right Ascension of the target star (degrees)

`RVdata` `property` ¶

the data

`accela_prior` `property` ¶

Prior for the proper-acceleration in right-ascension (mas/yr^2)

`acceld_prior` `property` ¶

Prior for the proper-acceleration in declination (mas/yr^2)

`conditional` `property` ¶

(self) -> kima.RVGAIAmodel.RVGAIAConditionalPrior

`cubic_prior` `property` ¶

Prior for the cubic coefficient of the trend

`da_prior` `property` ¶

Prior for the offset in right-ascension (mas)

`dd_prior` `property` ¶

Prior for the the offset in declination (mas)

`degree` `property` ¶

degree of the polynomial trend

`directory` `property` ¶

directory where the model ran

`fix` `property` ¶

whether the number of Keplerians is fixed

`indicator_correlations` `property` ¶

include in the model linear correlations with indicators

`individual_offset_prior` `property` ¶

Common prior for the between-instrument offsets

`jerka_prior` `property` ¶

Prior for the proper-jerk in right-ascension (mas/yr^3)

`jerkd_prior` `property` ¶

Prior for the proper-jerk in declination (mas/yr^3)

`known_object` `property` ¶

whether the model includes (better) known extra Keplerian curve(s)

`mua_prior` `property` ¶

Prior for the proper-motion in right-ascension (mas/yr)

`mud_prior` `property` ¶

Prior for the proper-motion in declination (mas/yr)

`n_baseline_params` `property` ¶

how many baseline astrometric parameters are included the model

`n_known_object` `property` ¶

how many known objects

`n_scan_dep_components` `property` ¶

how many components of scan-angle harmonics are included

`npmax` `property` ¶

maximum number of Keplerians

`nu_GAIA_prior` `property` ¶

Prior for the degrees of freedom of the Student-t likelihood for GAIA data

`nu_RV_prior` `property` ¶

Prior for the degrees of freedom of the Student-t likelihood for RV data

`offsets_prior` `property` ¶

Common prior for the between-instrument offsets

`parallax_prior` `property` ¶

Prior for the parallax

`quadr_prior` `property` ¶

Prior for the quadratic coefficient of the trend

`scan_dep_signal` `property` ¶

whether the model includes a model for potential scan-angle dependent signals that could bias towards certain frequencies

`slope_prior` `property` ¶

Prior for the slope

`star_mass` `property` ¶

the mass of the central star (Msun)

`studentt` `property` ¶

use a Student-t distribution for the likelihood (instead of Gaussian)

`thetak_prior` `property` ¶

Prior for the phase of scan-angle dependent signals

`trend` `property` ¶

whether the model includes a polynomial trend

`set_baseline_model()` `method descriptor` ¶

set_baseline_model(self, arg: int, /) -> None

set the number of parameters for the baseline astrometric solution, either 5 (the default astrometric solution), 7, or 9 (which include acceleration and jerk terms)

`set_known_object()` `method descriptor` ¶

set_known_object(self, arg: int, /) -> None

`set_scan_dep_signal()` `method descriptor` ¶

set_scan_dep_signal(self, arg: int, /) -> None

set whether the model includes a model for potential scan-angle dependent signals

The model.conditional object contained in each model can be used to define the priors for the orbital parameters. Different models may use different conditionals, depending on the specific parameterisation:

RVmodel / GPmodel / RVFWHMmodel → KeplerianConditionalPrior

init(self) -> None

`Kprior` `property` ¶

Prior for the semi-amplitude(s)

`Pprior` `property` ¶

Prior for the orbital period(s)

`eprior` `property` ¶

Prior for the orbital eccentricity(ies)

`phiprior` `property` ¶

Prior for the mean anomaly(ies)

`wprior` `property` ¶

Prior for the argument(s) of periastron

GAIAmodel → GAIAConditionalPrior

init(self) -> None

`Aprior` `property` ¶

Prior thiele_innes parameter(s) A

`Bprior` `property` ¶

Prior thiele_innes parameter(s) B

`Fprior` `property` ¶

Prior thiele_innes parameter(s) F

`Gprior` `property` ¶

Prior thiele_innes parameter(s) G

`Pprior` `property` ¶

Prior for the orbital period(s)

`Wprior` `property` ¶

Prior for the longitude(s) of ascending node

`aprior` `property` ¶

Prior for the photocentre semi-major-axis(es) (mas)

`cosiprior` `property` ¶

Prior for cosine(s) of the orbital inclination

`eprior` `property` ¶

Prior for the orbital eccentricity(ies)

`phiprior` `property` ¶

Prior for the mean anomaly(ies)

`thiele_innes` `property` ¶

use a Student-t distribution for the likelihood (instead of Gaussian)

`wprior` `property` ¶

Prior for the argument(s) of periastron

TODO: RVHGPMmodel → RVHGPMConditionalPrior

Run¶

To run the sampler and estimate the posterior for the model parameters just call kima.run

Example:¶

import kima

kima.run(model, steps=1000, num_threads=4)

kima.run API

Run the DNest4 sampler with the given model

Parameters:

Name	Type	Description	Default
`m`	`(RVmodel, GPmodel, ...)`	The model	required
`steps`	`int`	How many steps to run. Default is 100.	required
`num_threads`	`int`	How many threads to use for parallel processing. Default is 1.	required
`num_particles`	`int`	Number of MCMC particles. Default is 1.	required
`new_level_interval`	`int`	Number of steps required to create a new level. Default is 2000.	required
`save_interval`	`int`	Number of steps between saves. Default is 100.	required
`thread_steps`	`int`	Number of independent steps on each thread. Default is 10.	required
`max_num_levels`	`int`	Maximum number of levels, or 0 if it should be determined automatically. Default is 0.	required
`lambda_`	`int`	Backtracking scale length, controls the degree to which particles are allowed to “backtrack” down in level during the first stage of DNS when levels are being built. Default is 10.	required
`beta`	`int`	Equal weight enforcement, see Brewer et al. (2011). Default is 100.	required
`compression`	`int`	Each subsequent level is expected to be compressed by this factor. Default is exp(1).	required
`seed`	`int`	Random number seed value, or 0 to use current time. Default is 0.	required
`print_thin`	`int`	Thinning steps for terminal output. Default is 50.	required

Distributions¶

The distributions sub-package contains the implementation of several probability distributions that can be used as priors for a model parameter. All distributions have standard parameterizations, as you would find e.g. in Wikipedia. Some distributions have a corresponding Truncated version which truncates the support of the distribution to an interval $ [{\rm lower}, {\rm upper} ]$.

Example:¶

from kima import distributions

parameter_prior = distributions.Gaussian(10, 1)

Here's a complete list of the implemented distributions:

kima.distributions API

`BivariateGaussian()` ¶

Bivariate Gaussian distribution for X and Y

init(self, mean_x: float, mean_y: float, sigma_x: float, sigma_y: float, rho: float) -> None

docs

`mean_x` `property` ¶

(self) -> float

`mean_y` `property` ¶

(self) -> float

`rho` `property` ¶

(self) -> float

`sigma_x` `property` ¶

(self) -> float

`sigma_y` `property` ¶

(self) -> float

`logpdf()` `method descriptor` ¶

logpdf(self, x: float, y: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`Cauchy()` ¶

init(self, loc: float, scale: float) -> None

Cauchy distribution

Parameters:

Name	Type	Description	Default
`loc`	`float`	location parameter	required
`scale`	`float`	scale parameter	required

`loc` `property` ¶

location parameter

`scale` `property` ¶

scale parameter

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`Exponential()` ¶

init(self, scale: float) -> None

Exponential distribution

Parameters:

Name	Type	Description	Default
`scale`	`float`	scale parameter	required

`scale` `property` ¶

(self) -> float

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`ExponentialRayleighMixture()` ¶

init(self, weight: float, scale: float, sigma: float) -> None

Mixture of Exponential and Rayleigh distributions

Parameters:

Name	Type	Description	Default
`weight`	`float`	weight parameter	required
`scale`	`float`	scale parameter	required
`sigma`	`float`	sigma parameter	required

`scale` `property` ¶

(self) -> float

`sigma` `property` ¶

(self) -> float

`weight` `property` ¶

(self) -> float

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`Fixed()` ¶

init(self, value: float) -> None

A 'Fixed' distribution (akin to a Dirac delta distribution)

Parameters:

Name	Type	Description	Default
`value`	`float`	fixed value	required

`val` `property` ¶

fixed value of the parameter

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`Gaussian()` ¶

init(self, loc: float, scale: float) -> None

Gaussian distribution

Parameters:

Name	Type	Description	Default
`loc`	`float`	location parameter (mean)	required
`scale`	`float`	scale parameter (standard deviation)	required

`loc` `property` ¶

location parameter

`scale` `property` ¶

scale parameter

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`GaussianMixture()` ¶

GaussianMixture(means: collections.abc.Sequence[float], sigmas: collections.abc.Sequence[float])

GaussianMixture(means: collections.abc.Sequence[float], sigmas: collections.abc.Sequence[float], lower: float, upper: float)

GaussianMixture(means: collections.abc.Sequence[float], sigmas: collections.abc.Sequence[float], weights: collections.abc.Sequence[float], lower: float, upper: float)

Mixture of Gaussian distributions

init(self, means: collections.abc.Sequence[float], sigmas: collections.abc.Sequence[float]) -> None init(self, means: collections.abc.Sequence[float], sigmas: collections.abc.Sequence[float], lower: float, upper: float) -> None init(self, means: collections.abc.Sequence[float], sigmas: collections.abc.Sequence[float], weights: collections.abc.Sequence[float], lower: float, upper: float) -> None

Overloaded function.

__init__(self, means: collections.abc.Sequence[float], sigmas: collections.abc.Sequence[float]) -> None

Instantiates a mixture of Gaussian distributions from lists of means and sigmas, with equal weights

__init__(self, means: collections.abc.Sequence[float], sigmas: collections.abc.Sequence[float], lower: float, upper: float) -> None

Instantiates a mixture of Gaussian distributions from lists of means and sigmas, with equal weights, truncated to [lower, upper]

__init__(self, means: collections.abc.Sequence[float], sigmas: collections.abc.Sequence[float], weights: collections.abc.Sequence[float], lower: float, upper: float) -> None

Instantiates a mixture of Gaussian distributions from lists of means, sigmas, and weights, truncated to [lower, upper]

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`HalfGaussian()` ¶

init(self, scale: float) -> None

Half-Gaussian distribution, with support in [0, inf)

Parameters:

Name	Type	Description	Default
`scale`	`float`	scale parameter (standard deviation)	required

`scale` `property` ¶

scale parameter

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`InverseGamma()` ¶

Inverse gamma distribution

init(self, alpha: float, beta: float) -> None

Inverse gamma distribution

`alpha` `property` ¶

Shape parameter α

`beta` `property` ¶

scale parameter β

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`InverseMoment()` ¶

InverseMoment prior

init(self, tau: float, kmax: float) -> None

`kmax` `property` ¶

(self) -> float

`tau` `property` ¶

(self) -> float

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`Kumaraswamy()` ¶

init(self, a: float, b: float) -> None

"Kumaraswamy distribution (similar to a Beta distribution)

Parameters:

Name	Type	Description	Default
`a`	`float`	first shape parameter	required
`b`	`float`	second shape parameter	required

`a` `property` ¶

(self) -> float

`b` `property` ¶

(self) -> float

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`Laplace()` ¶

init(self, loc: float, scale: float) -> None

"Laplace distribution

Parameters:

Name	Type	Description	Default
`loc`	`float`	location parameter	required
`scale`	`float`	scale parameter	required

`loc` `property` ¶

location parameter

`scale` `property` ¶

scale parameter

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`LogUniform()` ¶

init(self, lower: float, upper: float) -> None

"LogUniform distribution (sometimes called reciprocal or Jeffrey's distribution)

Parameters:

Name	Type	Description	Default
`lower`	`float`	lower limit (> 0)	required
`upper`	`float`	upper limit (> lower)	required

`lower` `property` ¶

(self) -> float

`upper` `property` ¶

(self) -> float

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`ModifiedLogUniform()` ¶

init(self, knee: float, upper: float) -> None

"Modified Log-Uniform distribution, with support [0, upper]

Parameters:

Name	Type	Description	Default
`knee`	`float`	knee parameter	required
`upper`	`float`	upper limit	required

`knee` `property` ¶

(self) -> float

`upper` `property` ¶

(self) -> float

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`Pareto()` ¶

Pareto distribution

init(self, min: float, alpha: float) -> None

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`RNG()` ¶

init(self, seed: int) -> None

`rand()` `method descriptor` ¶

rand(self) -> float

Uniform(0, 1)

`rand_int()` `method descriptor` ¶

rand_int(self, arg: int, /) -> int

IntegerUniform(0, N)

`randh()` `method descriptor` ¶

randh(self) -> float

Brendon's heavy-tailed distribution

`wrap(*args, **kwargs)` ¶

wrap(arg0: float, arg1: float, arg2: float, /) -> float

Wrap a number to the range [a, b]

`Rayleigh()` ¶

init(self, scale: float) -> None

Rayleigh distribution

Parameters:

Name	Type	Description	Default
`scale`	`float`	scale parameter	required

`scale` `property` ¶

(self) -> float

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`Sine()` ¶

docs

init(self) -> None

A Sine distribution with support in [0, pi]

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`SingleTransitPeriodPrior()` ¶

Prior for the orbital period when a single planet transit was observed

init(self, W: float, L: float, Pmax: float) -> None

`L` `property` ¶

Mid-transit time minus the start of the observational window

`Pmax` `property` ¶

Maximum orbital period

`W` `property` ¶

Observational window

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`Triangular()` ¶

init(self, lower: float, center: float, upper: float) -> None

Triangular distribution

Parameters:

Name	Type	Description	Default
`lower`	`float`	lower bound	required
`center`	`float`	center	required
`upper`	`float`	upper bound	required

`center` `property` ¶

(self) -> float

`lower` `property` ¶

(self) -> float

`upper` `property` ¶

(self) -> float

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`TruncatedCauchy()` ¶

init(self, loc: float, scale: float, lower: float, upper: float) -> None

Truncated Cauchy distribution

Parameters:

Name	Type	Description	Default
`loc`	`float`	location parameter	required
`scale`	`float`	scale parameter	required
`lower`	`float`	lower truncation limit	required
`upper`	`float`	upper truncation limit	required

`loc` `property` ¶

location parameter

`lower` `property` ¶

(self) -> float

`scale` `property` ¶

scale parameter

`upper` `property` ¶

(self) -> float

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`TruncatedExponential()` ¶

init(self, scale: float, lower: float, upper: float) -> None

Truncated Exponential distribution

Parameters:

Name	Type	Description	Default
`scale`	`float`	scale parameter	required
`lower`	`float`	lower truncation limit	required
`upper`	`float`	upper truncation limit	required

`lower` `property` ¶

(self) -> float

`scale` `property` ¶

(self) -> float

`upper` `property` ¶

(self) -> float

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`TruncatedGaussian()` ¶

init(self, loc: float, scale: float, lower: float, upper: float) -> None

"Gaussian distribution truncated to [lower, upper] interval

Parameters:

Name	Type	Description	Default
`loc`	`float`	location parameter (mean)	required
`scale`	`float`	scale parameter (standard deviation)	required
`lower`	`float`	lower truncation limit	required
`upper`	`float`	upper truncation limit	required

`loc` `property` ¶

location parameter

`lower` `property` ¶

lower truncation limit

`scale` `property` ¶

scale parameter

`upper` `property` ¶

upper truncation limit

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`TruncatedPareto()` ¶

Pareto distribution truncated to [lower, upper] interval

init(self, min: float, alpha: float, lower: float, upper: float) -> None

`alpha` `property` ¶

scale parameter

`lower` `property` ¶

(self) -> float

`min` `property` ¶

location parameter

`upper` `property` ¶

(self) -> float

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`TruncatedRayleigh()` ¶

Rayleigh distribution truncated to [lower, upper] interval

init(self, scale: float, lower: float, upper: float) -> None

`lower` `property` ¶

(self) -> float

`scale` `property` ¶

(self) -> float

`upper` `property` ¶

(self) -> float

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`Uniform()` ¶

init(self, lower: float, upper: float) -> None

Uniform distribution in [lower, upper]

Parameters:

Name	Type	Description	Default
`lower`	`float`	lower bound	required
`upper`	`float`	upper bound	required

`lower` `property` ¶

lower bound

`upper` `property` ¶

upper bound

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

`UniformAngle()` ¶

init(self) -> None

Uniform distribution in [0, 2*PI]

`cdf()` `method descriptor` ¶

cdf(self, x: float) -> float

Cumulative distribution function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the CDF	required

`logpdf()` `method descriptor` ¶

logpdf(self, x: float) -> float

Logarithm of the probability density function evaluated at x

Parameters:

Name	Type	Description	Default
`x`	`float`	point at which to evaluate the PDF	required

`ppf()` `method descriptor` ¶

ppf(self, q: float) -> float

Percent point function (inverse of cdf) evaluated at q

Parameters:

Name	Type	Description	Default
`q`	`float`	point at which to evaluate the PPF	required

Keplerian¶

Finally, even though it sits at the core of what kima does, there is the kima.keplerian function:

kima.keplerian API

Calculate the Keplerian curve of one planet at times t

Parameters:

Name	Type	Description	Default
`t`	`array`	Times at which to calculate the Keplerian function	required
`P`	`float`	Orbital period [days]	required
`K`	`float`	Semi-amplitude	required
`ecc`	`float`	Orbital eccentricity	required
`w`	`float`	Argument of periastron [rad]	required
`M0`	`float`	Mean anomaly at the epoch [rad]	required
`M0_epoch`	`float`	Reference epoch for the mean anomaly (M=0 at this time) [days]	required

Returns:

Name	Type	Description
`v`	`array`	Keplerian function evaluated at input times `t`

This is the default Keplerian function producing radial velocities, while other functions are specialized for Gaia astrometry:

kima.kepler.keplerian_gaia API

Calculate the Keplerian curve of one planet at times t

Parameters:

Name	Type	Description	Default
`t`	`array`	Times at which to calculate the Keplerian function	required
`psi`	`array`	Scan angle of the Gaia satellite at time t [rad]	required
`A`	`float`	Thiele-innes parameter A [mas]	required
`B`	`float`	Thiele-innes parameter B [mas]	required
`F`	`float`	Thiele-innes parameter F [mas]	required
`G`	`float`	Thiele-innes parameter G [mas]	required
`ecc`	`float`	Orbital eccentricity	required
`P`	`float`	Orbital period P [days]	required
`M0`	`float`	Mean anomaly at the epoch [rad]	required
`M0_epoch`	`float`	Reference epoch for the mean anomaly (M=0 at this time) [days]	required

Returns:

Name	Type	Description
`wk`	`array`	Gaia along-scan 'abscissa' function for a keplerian orbit evaluated at input times `t`

or for use with the BINARIESmodel including post-Keplerian corrections and apsidal precession:

kima.post_keplerian API

Calculate the Keplerian curve of the orbit of a dark companion around a star at times t with post-Keplerian additions. Suited to the orbit of a close binary star.

Parameters:

Name	Type	Description	Default
`t`	`array`	Times at which to calculate the Keplerian function	required
`P`	`float`	Orbital period [days]	required
`K`	`float`	Semi-amplitude	required
`ecc`	`float`	Orbital eccentricity	required
`w`	`float`	Argument of pericentre [rad]	required
`wdot`	`float`	Pericentre precession rate [arcsecs/year]	required
`M0`	`float`	Mean anomaly at the epoch [rad]	required
`M0_epoch`	`float`	Reference epoch for the mean anomaly (M=0 at this time) [days]	required
`cosi`	`float`	Cosine of the inclination angle of the orbit (=0 for an edge-on orbit)	required
`M1`	`float`	Mass of primary star [Msun]	required
`M2`	`float`	Mass of secondary star [Msun]	required
`R1`	`float`	Radius of primary star [Rsun] If not specfied and tidal correction included the relation R = M^0.8 will be used.	required
`GR`	`bool`	Whether to include the radial velocity corrections from General Relativity (Transverse Doppler, Light Travel-Time, and Graviatational Redshift)	required
`Tid`	`bool`	Whether to include the radial velocity correction from Tides (only suitable for circular orbits)	required
`Kprec`	`float`	What precision in m/s to calculate K2 to for the relativistic correction (defaults to 50 m/s)	required

Returns:

Name	Type	Description
`v`	`array`	Keplerian function with potential corrections evaluated at input times `t`

API documentation for kima¶

Data¶

Example:¶

M0_epoch property ¶

N property ¶

actind property ¶

datafile property ¶

datafiles property ¶

double_lined property ¶

indicator_names property ¶

instrument property ¶

instruments property ¶

multi property ¶

normalized_actind property ¶

obsi property ¶

sig property ¶

sig2 property ¶

skip property ¶

t property ¶

trend_epoch property ¶

units property ¶

y property ¶

y2 property ¶

_inverse_time_indices() method descriptor ¶

get_RV_max() method descriptor ¶

get_RV_mean() method descriptor ¶

get_RV_min() method descriptor ¶

get_RV_span() method descriptor ¶

get_RV_std() method descriptor ¶

get_RV_var() method descriptor ¶

get_actind_max() method descriptor ¶

get_actind_mean() method descriptor ¶

get_actind_min() method descriptor ¶

get_actind_span() method descriptor ¶

get_actind_std() method descriptor ¶

get_actind_var() method descriptor ¶

get_max_RV_span() method descriptor ¶

get_t_max() method descriptor ¶

get_t_middle() method descriptor ¶

get_t_min() method descriptor ¶

get_timespan() method descriptor ¶

get_trend_magnitude() method descriptor ¶

get_unique_t() method descriptor ¶

topslope() method descriptor ¶

M0_epoch property ¶

N property ¶

datafile property ¶

pf property ¶

psi property ¶

t property ¶

units property ¶

w property ¶

wsig property ¶

Models¶

Example:¶

RVmodel() ¶

AK_Kprior property ¶

AK_Pprior property ¶

AK_eprior property ¶

AK_phiprior property ¶

AK_t0prior property ¶

AK_tauprior property ¶

AK_wprior property ¶

Cprior property ¶

Jprior property ¶

KO_Kprior property ¶

KO_Pprior property ¶

KO_eprior property ¶

KO_phiprior property ¶

KO_wprior property ¶

TR_Kprior property ¶

TR_Pprior property ¶

TR_Tcprior property ¶

TR_eprior property ¶

TR_wprior property ¶

apodized_keplerians property ¶

beta_prior property ¶

conditional property ¶

cubic_prior property ¶

data property ¶

API documentation for `kima`¶

`M0_epoch` `property` ¶

`N` `property` ¶

`actind` `property` ¶

`datafile` `property` ¶

`datafiles` `property` ¶

`double_lined` `property` ¶

`indicator_names` `property` ¶

`instrument` `property` ¶

`instruments` `property` ¶

`multi` `property` ¶

`normalized_actind` `property` ¶

`obsi` `property` ¶

`sig` `property` ¶

`sig2` `property` ¶

`skip` `property` ¶

`t` `property` ¶

`trend_epoch` `property` ¶

`units` `property` ¶

`y` `property` ¶

`y2` `property` ¶

`_inverse_time_indices()` `method descriptor` ¶

`get_RV_max()` `method descriptor` ¶

`get_RV_mean()` `method descriptor` ¶

`get_RV_min()` `method descriptor` ¶

`get_RV_span()` `method descriptor` ¶

`get_RV_std()` `method descriptor` ¶

`get_RV_var()` `method descriptor` ¶

`get_actind_max()` `method descriptor` ¶

`get_actind_mean()` `method descriptor` ¶

`get_actind_min()` `method descriptor` ¶

`get_actind_span()` `method descriptor` ¶

`get_actind_std()` `method descriptor` ¶

`get_actind_var()` `method descriptor` ¶

`get_max_RV_span()` `method descriptor` ¶

`get_t_max()` `method descriptor` ¶

`get_t_middle()` `method descriptor` ¶

`get_t_min()` `method descriptor` ¶

`get_timespan()` `method descriptor` ¶

`get_trend_magnitude()` `method descriptor` ¶

`get_unique_t()` `method descriptor` ¶

`topslope()` `method descriptor` ¶

`M0_epoch` `property` ¶

`N` `property` ¶

`datafile` `property` ¶

`pf` `property` ¶

`psi` `property` ¶

`t` `property` ¶

`units` `property` ¶

`w` `property` ¶

`wsig` `property` ¶

`RVmodel()` ¶

`AK_Kprior` `property` ¶

`AK_Pprior` `property` ¶

`AK_eprior` `property` ¶

`AK_phiprior` `property` ¶

`AK_t0prior` `property` ¶

`AK_tauprior` `property` ¶

`AK_wprior` `property` ¶

`Cprior` `property` ¶

`Jprior` `property` ¶

`KO_Kprior` `property` ¶

`KO_Pprior` `property` ¶

`KO_eprior` `property` ¶

`KO_phiprior` `property` ¶

`KO_wprior` `property` ¶

`TR_Kprior` `property` ¶

`TR_Pprior` `property` ¶

`TR_Tcprior` `property` ¶

`TR_eprior` `property` ¶

`TR_wprior` `property` ¶

`apodized_keplerians` `property` ¶

`beta_prior` `property` ¶

`conditional` `property` ¶

`cubic_prior` `property` ¶

`data` `property` ¶

`degree` `property` ¶

`directory` `property` ¶

`enforce_stability` `property` ¶

`fix` `property` ¶