gaiasupdate.constants module

Module that defines central constants and variables used in this package.

gaiasupdate.constants.TCB_REFERENCE_EPOCH

Barycentric Coordinate Time reference epoch 2010-01-01T00:00:00 (TCB).

Type:

Astropy time

gaiasupdate.constants.DR4_REFERENCE_EPOCH

Gaia Data Release 4 reference epoch 2017.5 julian year (TCB).

Type:

Astropy time

gaiasupdate.epoch_astrometry module

Module to facilitate the handling of Gaia Epoch Astrometry.

class gaiasupdate.epoch_astrometry.EpochAstrometryDataFrameArchive(pandas_obj)

Bases: GaiaCentroidDataFrame

Extension for Epoch Astrometric Data in public Gaia Archive format.

class gaiasupdate.epoch_astrometry.EpochAstrometryDataFrameCu9(pandas_obj)

Bases: GaiaCentroidDataFrame

Extension for Epoch Astrometric Data in CU9 format (internal use).

class gaiasupdate.epoch_astrometry.GaiaCentroidDataFrame(pandas_obj)

Bases: object

Extension for Gaia epoch astrometry data from centroids.

check_if_is_exploded(epoch_data)

Check whether the dataframe is already exploded.

Parameters:

input (pandas dataframe) – Dataframe to check whether it is exploded.

Returns:

True or False if the dataframe is exploded or not.

Return type:

Boolean

static explode_ccdlevel_columns(df_input)

Convert the columns holding arrays of CCD-transit information into dataframe rows, also fixing issues in certain columns.

Note

A new column ‘component_index’ is introduced to keep track of the device where the CCD transit was recorded.

Parameters:

df_input (pandas dataframe) – Dataframe containing GaiaCentroidDataFrame.

Returns:

Dataframe with rows exploded to hold one device data per row.

Return type:

Pandas dataframe

filter_by_query(query)

Filter out the dataframe a string ‘query’.

Parameters:

query (str) – String containing a query to filter data in the dataframe.

Returns:

Dataframe filtered using the ‘query’ argument.

Return type:

Pandas dataframe

filter_null_from_column(column)

Filter out rows where the specified ‘column’ contains nulls.

Parameters:

column (str) – Column name to be filtered.

Returns:

Dataframe without any rows where ‘column’ contains null entries.

Return type:

Pandas dataframe

filter_on_ccdprocflags(flags_to_keep: ndarray)

Filter out rows where ‘ccdprocflags’ column values are in argument list ‘flags_to_keep’.

Parameters:

flags_to_keep (narray) – List of values accepted in the ‘ccdprocflags’ column.

Returns:

Dataframe without any entry with ‘ccdprocflag’ value in the list ‘flags_to_keep’.

Return type:

Pandas dataframe

filter_on_multipeak()

Filter out rows where ‘multipeak’ column is True.

Returns:

Dataframe without any entry with ‘multipeak’ column set to True.

Return type:

Pandas dataframe

filter_on_used_by_agis(scan_direction='al')

Filter out rows containing observations not used by AGIS.

Parameters:

scan_direction (str, optional) – Scan direction to use, either ‘al’ (along scan) or ‘ac’ (across scan). Default: ‘al’.

Returns:

Dataframe filtered following column mask ‘used_by_agis_al’ or ‘used_by_agis_ac’.

Return type:

Pandas dataframe

filter_out_skymapper()

Filter out rows corresponding to SkyMapper (SM) data.

Returns:

Dataframe without any SkyMapper data.

Return type:

Pandas dataframe

fix_blended_column()

Fix the ‘blended’ column, filling it with NaN and set as float type.

get_design_equation_parameters(model='6p_constrained_colour', scan_direction='Al') → OrderedDict

Compute and return the design equation parameters.

s : pandas dataframe with the lpcs of the source s

t0 : the reference epoch in obmt ns (see obmt decodeur)

withDeltat : if true use the lpc extra deltat time to reference epoch in year

return : D,h the design matrix [alpha0,delta0,varpi,mualphastar,mudelta] and right hand side [w]

Parameters:

• model (str) – Model corresponding to the number of astrometric parameters to solve. Default: ‘5p_single_source’.

• scan_direction (str, optional) – Scan direction to use, either ‘al’ (along scan) or ‘ac’ (across scan). Default: ‘al’.

Returns:

Ordered dictionary containing the astrometric parameters computed.

Return type:

OrderedDict

set_dtypes_for_exploded_columns(column_dtypes)

After exploding object-dtype columns their dtype needs to be set explicitly.

Parameters:

column_types (dict) – Dictionary of key/value wich corresponds to column/type.

Returns:

Dataframe containing the columns/types as defined in ‘column_types’ argument.

Return type:

Pandas dataframe

set_relative_time()

Set new columns for relative time in years and days, including the barycentric correction.

Note

GAIA-C3-TN-LU-LL-061 available at Public DPAC documents.

set_scan_angle_derived_columns()

Add new columns to dataframe that correspond to scan-angle coefficients.

sort_by_column(column_name)

Sort the epoch data dataframe by the specified column.

Parameters:

column_name (str) – Sort dataframe by ‘column_name’ in ascending order.

class gaiasupdate.epoch_astrometry.GaiaEpochAstrometry(epoch_data: DataFrame, source_id=None, explode=True, is_exploded=False)

Bases: object

Class for Gaia Epoch Astrometric Data.

classmethod from_dataframe(df, **kwargs)

Extract data from dataframe and return astropy table.

Parameters:

df (pandas dataframe) – Data in pandas dataframe format.

Returns:

Astropy table containing the dataframe data.

Return type:

Astropy table

n_filtered_ccd_transits = None

class gaiasupdate.epoch_astrometry.GaiaEpochAstrometryArchive(epoch_data: DataFrame, source_id=None, explode=True, is_exploded=False)

Bases: GaiaEpochAstrometry

Class for Gaia Epoch Astrometric Data in Gaia Archive format.

classmethod archive_to_cu9(df)

Convert dataframe from Gaia Archive format to CU9 format.

Parameters:

df (Pandas dataframe) – Dataframe containing data in Gaia Archive format.

Returns:

Dataframe containing data in CU9 format.

Return type:

Pandas dataframe

classmethod astropy_table_to_df(df)

Convert series in astropy table in flat df.

Parameters:

df (Pandas dataframe) – Dataframe containing data.

Returns:

Dataframe with series from astropy flatten.

Return type:

Pandas dataframe

classmethod supdate(df, sourceid, model=None, compute_excess_noise=False)

Run compute_source_parameters_like_dr4 from Archive data.

Parameters:

• df (Pandas dataframe) – Dataframe containing data in Gaia Archive format.

• source_id (long int) – Gaia identifier of the source.

• model (str, optional) – Model corresponding to the number of astrometric parameters to solve. Default: ‘6p_constrained_colour’.

• compute_excess_noise (boolean, optional) – Whether to fit the excess_noise of the observation or use computed by AGIS.

Returns:

The astrometric parameters computed for the source.

Return type:

dict

class gaiasupdate.epoch_astrometry.GaiaEpochAstrometryCu9(epoch_data: DataFrame, source_id=None, explode=True, is_exploded=False)

Bases: GaiaEpochAstrometry

Class for Gaia Epoch Astrometric Data in MDB format.

classmethod filter_columns_for_computation(df)

Dismiss the unneeded columns during the computation.

Parameters:

df (pandas dataframe) – Dataframe containing data.

Returns:

Dataframe that containg only the columns needed for source update computation, the rest are dropped.

Return type:

Pandas dataframe

classmethod supdate(df, sourceid, model=None, compute_excess_noise=False)

Run compute_source_parameters_like_dr4 on CU9 internal format.

Parameters:

• df (pandas dataframe) – Dataframe containing data.

• source_id (long int) – Gaia identifier of the source.

• model (str, optional) – Model corresponding to the number of astrometric parameters solve. Default: 6p_constrained_colour.

• compute_excess_noise (boolean, optional) – Whether to fit the excess_noise of the observation or use computed by AGIS.

Returns:

The astrometric parameters computed for the source.

Return type:

dict

class gaiasupdate.epoch_astrometry.GaiaSourceEpochAstrometry(epoch_data: DataFrame, source_id=None, explode=True, is_exploded=False)

Bases: GaiaEpochAstrometry

Class for Gaia Epoch Astrometric Data corresponding to an individual source.

compute_perspective_acceleration(convergence_threshold=1e-09)

Compute a source update with perspective acceleration and return results.

Parameters:

convergence_threshold (float, optional) – Convergence threshold. Default: 1e-9.

Returns:

Dictionary containing the results of the computation.

Return type:

dict

compute_source_update(model='5p_single_source')

Execute source update for model ‘5p_single_source’.

Parameters:

model (str) – Model corresponding to the number of astrometric parameters to solve. Default: ‘5p_single_source’.

Returns:

The astrometric parameters computed for the source.

Return type:

dict

compute_source_update_iteratively(initial_parameters, fit_perspective_acceleration=False, n_iterations_max=10, solver='least_squares', convergence_threshold=1e-09)

Return iterative source update which allows us to account for perspective acceleration.

Parameters:

• initial_parameters (narray) – Initial parameters to start the iteration.

• fit_perspective_acceleration (boolean, optional) – Whether to fit for perspective acceleration. Default: False

• n_iterations_max (int, optional) – Number of maximum iterations to perform. Default: 10.

• solver (str, optional) – Solver to be used. Default: least_squares.

• convergence_threshold (float, optional) – Maximum convergence threshold. Default: 1e-9.

Returns:

The parameters of the solution.

Return type:

dict

Note

Equations were implemented following GAIA-C3-TN-LU-LL-061 (Appendix E) available at Public DPAC documents.

classmethod from_dataframe(df, source_id, **kwargs)

Extract data from dataframe and return astropy table for a specific source_id.

Parameters:

• df (Pandas dataframe) – Data in pandas format.

• source_id (long int) – Gaia identifier of the source.

Returns:

Data in Astropy table format for a specific source_id.

Return type:

Astropy table

class gaiasupdate.epoch_astrometry.GaiaSourceEpochAstrometryArchive(epoch_data: DataFrame, source_id=None, explode=True, is_exploded=False)

Bases: GaiaEpochAstrometryArchive, GaiaSourceEpochAstrometry

Class for Gaia Epoch Astrometric Data in the Gaia Archive format corresponding to an individual source.

classmethod from_gacs_datalink(source_id, format='votable', gaia_data_server='https://gea.esac.esa.int/', credentials_file=None, data_release='Gaia DR4_INT4', data_structure='RAW', retrieval_type='EPOCH_ASTROMETRY')

Query Gaia Archive to retrive EpochAstrometry data of a specific object.

Parameters:

• source_id (long int) – Gaia identifier of the source being queried.

• format (str, optional) – Format of the data to be retrieved. It can be VOTable, CSV, ECSV, FITS or parquet

• gaia_data_server (str, optional) – URL of the Archive data server. Default is https://gea.esac.esa.int/

• credentials_file (str, optional) – Local path of the txt file containing the user Archive credentials.

Returns:

Table that contains the epoch astrometry data requested to the Gaia Archive.

Return type:

Astropy table

get_design_parameters(filter_on_used_by_agis=True, **kwargs)

Compute the design parameters using class-specific column names.

Parameters:

filter_on_used_by_agis (boolean, optional) – Select whether to follow the selection strategy as AGIS for the parameters computation. Default: True

Returns:

design parameters – Dictionary containing the design_matrix_coefficients and auxiliary data.

Return type:

OrderedDict

class gaiasupdate.epoch_astrometry.GaiaSourceEpochAstrometryCu9(epoch_data: DataFrame, source_id=None, explode=True, is_exploded=False)

Bases: GaiaEpochAstrometryCu9, GaiaSourceEpochAstrometry

Class for Gaia Epoch Astrometric Data in CU9 format corresponding to an individual source.

compute_source_parameters(model=None, compute_excess_noise=False)

Compute the astrometric source paramaters.

Parameters:

• model (str, optional) – Model corresponding to the number of astrometric parameters to solve. Default: 6p_constrained_colour.

• compute_excess_noise (boolean, optional. Default: False.) – Whether to fit the excess noise or to use the provided with the epoch astrometry data.

Returns:

The astrometric parameters computed for the specified source.

Return type:

dict

compute_source_parameters_like_dr4()

Compute the astrometric source paramaters with a DR4-like configuration.

This will generate the best-possible reproduction of the DR4 astrometric parameters.

Returns:

The astrometric parameters computed for the specified source.

Return type:

dict

get_design_parameters(filter_on_used_by_agis=False, **kwargs)

Compute the design parameters using class-specific column names.

Parameters:

filter_on_used_by_agis (boolean, optional) – Select whether to follow the selection strategy as AGIS for the parameters computation. Default: False.

gaiasupdate.metrics module

Module providing statistical metrics and an auxiliary class.

class gaiasupdate.metrics.SolutionStatistic(parameters)

Bases: object

Convenience class for handling solutions of linear equations systems.

gaiasupdate.metrics.akaike_information_criterion(n_parameters, ln_likelihood)

Return AIC.

Parameters:

• n_parameters (int) – Number of parameters.

• n_measurements (int) – Number of measurements.

Returns:

Akaike information criterion

Return type:

float

gaiasupdate.metrics.bayesian_information_criterion(n_parameters, n_measurements, ln_likelihood)

Return BIC.

Parameters:

• n_parameters (int) – Number of parameters.

• n_measurements (int) – Number of measurements.

• ln_likelihood (float) – Logarithm of the likelihood

Returns:

Bayesian information criterion

Return type:

float

gaiasupdate.metrics.chi_squared(residuals, variance)

Return chi2 fit quality metric.

Parameters:

• residuals (narray) – Array of residuals.

• variance (narray) – Array of variances.

Returns:

chi2 fit quality metric

Return type:

float

gaiasupdate.metrics.f_test_of_additional_parameter(n_measurements: int, n_parameters_1: int, chi2_1: float, n_parameters_2: int, chi2_2: float) → float

Return F-Test probability that the simpler model is correct.

Note

e.g. n_parameters_1 = 5. is the number of PPM parameters

e.g. n_parameters_2 = n_parameters_1 + 7. is the number of PPM + orbital parameters

Parameters:

• n_measurements (int) – Number of data points

• n_parameters_1 (int) – Number of parameters of the simpler model

• chi2_1 (float) – chi^2 corresponding to the simpler model

• n_parameters_2 (int) – Number of parameters of the model with more parameters n_parameters_2 > p1

• chi2_2 (float) – chi^2 corresponding to the model with more parameters

Returns:

Probability.

Return type:

float

gaiasupdate.metrics.gaia_f2(chi2, nu)

Return F2, a goodness-of-fit statistic.

Note

In the Gaia archive this is called astrometric_gof_al, see the Archive documentation.

Parameters:

• chi2 (float) – goodness-of-fit statistic chi^2.

• nu (int) – number of degrees of freedom.

Returns:

Gaia f2, which is a goodness of fit statistic.

Return type:

float

gaiasupdate.metrics.log_likelihood(residuals, variance)

Return the log(likelihood).

Parameters:

• residuals (narray) – Array of residuals.

• variance (narray) – Array of variances.

Returns:

ln_likelihood

Return type:

float

gaiasupdate.metrics.log_likelihood_0(variance)

Return lnL0 term.

Parameters:

variance (narray) – Array of variances.

Returns:

lnL0

Return type:

float

gaiasupdate.solver module

Module for solving systems of linear equations.

These methods are equivalent to the Java implementation in the Gaia AGIS processing software.

Note

credit authors that contributed to this code: Sahlmann, Bombrun, Lindegren

class gaiasupdate.solver.DesignEquation(parameters: dict)

Bases: object

Class to handle and solve linear equation systems like AGIS does.

basic_source_update_calculator_solve(cholesky: bool = False, total_variance: ndarray = None) → Tuple[ndarray, ndarray, ndarray, ndarray]

Use matrix inversion to solve the linear equations using least-squares.

Note

Modelled after gaia.cu3.agistools.algo.gis.source.BasicSourceUpdateCalculator.solve()

See also solve_linear_equations function.

Parameters:

• cholesky (boolean, optional) – Cholesky decomposition. Default: False.

• total_variance (narray, optional) – Total variance array. Default: None.

Returns:

• narray – normals_full, which is the same as parameter_covariance_matrix_formal_inverse.

• narray – rhs, right-hand side of the normal equations.

• narray – Array of parameters.

• narray – Array of residuals.

calculate_downweights(residuals)

Return downweights for a given array of residuals.

Note

See gaia.cu3.agistools.algo.gis.source.RobustSourceUpdateCalculator.calculateDownweights. Calculates downweights for a given array of residuals, using the current variances and excess source noise. This implements algorithm P2, i.e. Eq. (20) in GAIA-C3-TN-LU-LL-083.

Parameters:

residuals (ndarray) – Array of residuals.

Returns:

Array of downweights.

Return type:

ndarray

calculate_estimate()

Calculate the solution estimate.

Note

See gaia.cu3.agistools.algo.gis.source.RobustSourceUpdateCalculator.calculateEstimate()

Returns:

• narray – Excess source noise.

• narray – Excess source noise significance.

calculate_excess_source_noise()

Compute and return excess source noise.

Note

Calculates and sets the excess source noise and significance for the currently set (fixed) variances and downweights. This implements algorithm P1 in GAIA-C3-TN-LU-LL-083.

See corresponding Java code: gaia.cu3.agistools.algo.gis.source.RobustSourceUpdateCalculator.calculateExcessSourceNoise()

Returns:

• float – The source excess noise.

• float – The source excess noise significance.

compute_n_outliers()

Compute the number of outliers based on weights and threshold.

Note

See gaia.cu3.agistools.algo.gis.source.SourceUpdateStatistics.getNOut()

Returns:

n_outliers

Return type:

narray

compute_residuals(parameters)

Compute the residuals given the input parameters.

Parameters:

parameters (narray) – Array of parameters corresponding to a solution of the system of equations.

Returns:

The computed residuals.

Return type:

narray

construct_full_normals(total_variance=None)

Replicate Java method constructFullNormals.

Note

gaia.cu3.agistools.algo.gis.source.BasicSourceUpdateCalculator.constructFullNormals()

Parameters:

total_variance (narray, optional) – Array of total variances.

Returns:

• narray – Parameter covariance matrix formal inverse.

• narray – rhs, right-hand side of the normal equations.

property excess_source_noise

Return current excess source noise.

get_downweights(multiply_by_prior: bool)

Return array of the currently defined downweights.

Returns:

Array of downweights.

Return type:

ndarray

get_improved_estimate_of_excess_source_variance(dof)

Return an improved estimate of the excess source noise.

Note

This uses the currently set data, variances and downweights. It implements a single iteration of algorithm P1 in GAIA-C3-TN-LU-LL-083.

See the Java method getImprovedEstimateOfExcessSourceVariance(int dof).

Parameters:

dof (int) – degrees of freedom

Returns:

Applied change in excess source variance.

Return type:

float

get_index_keep()

Return the indices of the measurements that are not outliers.

static get_initial_dispersion_estimate(data)

Return initial dispersion estimate of the input dataset.

Note

See gaia.cu3.agistools.algo.gis.source.RobustSourceUpdateCalculator.getInitialDispersionEstimate(double[])

Parameters:

data (ndarray) – Input dataset.

Returns:

Initial dispersion estimate of the input.

Return type:

ndarray

get_postfit_residuals()

Return post-fit residuals.

Note

See Java method gaia.cu3.agistools.algo.gis.source.BasicSourceUpdateCalculator.getPostfitResiduals()

get_prefit_residuals()

Return pre-fit residuals.

Note

See Java method gaia.cu3.agistools.algo.gis.source.BasicSourceUpdateCalculator.getPrefitResiduals()

get_updates()

Return the updates from the latest call to solve().

Note

See Java method gaia.cu3.agistools.algo.gis.source.BasicSourceUpdateCalculator.getUpdates()

get_weighted_ssr_and_derivative()

Return weighted sum of squared residuals and its derivative.

property n_degrees_of_freedom

Return current degrees of freedom.

property n_effective_degrees_of_freedom

Return current effective degrees of freedom.

property n_measurements

Return current number of measurements.

property n_parameters

Return current number of parameters.

property observation_variances

Return the observation variances.

Note

This is the sum of observation uncertainties and axcess attitude/observation noise, see Eq. 62ff of Lindegren at al. 2012:

sigmaTilde_l^2 = sigma_l^2 + epsilon_a^2(t_l),

where obsSigma = the sigmas of the observations

epsilonA = Any contribution from the excess attitude noise and excess calibration noise (but not the excess source noise).

See Java method setObservationVariances(double[] obsSigma, double[] epsilonA)

Returns:

The observation variances.

Return type:

ndarray

solve(solver='agis', **kwargs)

Solve the equations and return results.

Parameters:

• solver (str) – the solver to be used, default is ‘agis’

• kwargs (dict) – keyword arguments passed on to the solver code

Returns:

Solution parameters and auxiliary information

Return type:

dict

solve_least_squares()

Solve equations with a standard least-square solver.

Returns:

Dictionary containing information about the solution.

Return type:

dict

solve_like_agis(total_variance: ndarray = None) → dict

Solve linear equations like AGIS.

Parameters:

total_variance (float) – Total variance.

Returns:

Dictionary with information on the solution.

Return type:

dict

gaiasupdate.solver.agis_weight_function(z)

Evaluate AGIS weight function as defined in Eq. 66 of Lindegren et al. 2012.

Parameters:

z (ndarray) – Input data array

Returns:

An array on weights

Return type:

ndarray

gaiasupdate.solver.agis_weights(residuals, uncertainties, excess_noise, weight_threshold=0.2)

Return the residual down weight factors and identify outliers.

Note

See procedure P2 in GAIA-C3-TN-LU-LL-083 (Eq. 21) from the Archive documentation.

astrometric_n_good_obs_al : Number of good observations AL (short) Number of AL observations (= CCD transits) that were not strongly downweighted in the astrometric solution of the source. Strongly downweighted observations (with downweighting factor 𝑤<0.2) are instead counted in astrometric_n_bad_obs_al.

The sum of astrometric_n_good_obs_al and astrometric_n_bad_obs_al equals astrometric_n_obs_al, the total number of AL observations used in the astrometric solution of the source.

Parameters:

• residuals (narray) – Array of residuals.

• uncertainties (narray) – Array of uncertainties.

• excess_noise (narray.) – Array of excess noises.

• weight_threshold (float) – Cutoff below which measurements are considered to be outliers.

Returns:

• ndarray – Array of weights.

• int – Number of outliers.

• ndarray – Array of the good indices.

gaiasupdate.solver.decay_downweight(z: ndarray, scale_factor: float = 1.0) → ndarray

Return weight.

See gaia.cu3.agistools.algo.observations.DecayDownweight.downweight(double, double).

Parameters:

• z (ndarray) – The input data array.

• scale_factor (float) – The scale factor

Returns:

Array of decay downweights

Return type:

ndarray

gaiasupdate.solver.estimate_excess_noise(residuals, sigmas, weights, nu)

Estimate the excess noise from given residuals.

See Equation 64 of Lindegren at al. 2012, A&A, 538, A78.

Parameters:

• residuals (narray) – Array of residuals.

• sigmas (narray) – Array of sigmas.

• weights (narray) – Array of weights.

• nu (int) – Number of degrees of freedom.

Returns:

Array containing the excess noise estimation.

Return type:

narray

gaiasupdate.solver.get_sextiles(x)

Return sextiles of input array.

Note

Emulate gaia.cu3.agistools.algo.gis.source.RobustSourceUpdateCalculator.getSextiles(double[])

The sextiles are returned as an array of length 5 (say, double[] sext), with sext[0] = the 1st (lowest) sextile and sext[4] = the 5th (highest) sextile. sext[2] is the median, and (sext[4]-sext[0])/2 is half the intersextile range, which can be used as a robust estimate of the standard deviation.

If the length of the input array x is <= 3, then sext[0] and sext[4] equal the minimum and maximum x values, respectively. If the length is 1, then all sextiles equal the single x value.

Parameters:

x (ndarray) – An array containg the input values.

Returns:

Array containing the sextiles.

Return type:

ndarray

gaiasupdate.solver.huber_downweight(z: ndarray, scale_factor: float = 1.0) → ndarray

Return weight.

See gaia.cu3.agistools.algo.observations.HuberDownweight

Parameters:

• z (ndarray) – The input data array.

• scale_factor (float) – The scale factor

Returns:

Array of Huber downweights

Return type:

ndarray

gaiasupdate.solver.robust_dispersion_estimate(residuals)

Return half the intersextile range according to procedure P3 of LL83 (Eq. 22).

Parameters:

residuals (ndarray) – Array of residuals.

Returns:

The dispersion estimate.

Return type:

float

gaiasupdate.solver.solve_linear_equations(design_matrix_coefficients: ndarray, dependent_variable: ndarray, dependent_variable_error: ndarray, weights: ndarray = None, excess_noise: float = 0)

Use matrix inversion to solve the linear equations using least-squares.

Note

Weights and excess noise can be accounted for as described in procedure 4 of GAIA-C3-TN-LU-LL-083.

Parameters:

• design_matrix_coefficients (ndarray) – The normal matrix.

• dependent_variable (ndarray) – The measurements.

• dependent_variable_error (ndarray) – The measurement uncertainties.

• weights (ndarray, optionl) – The measurement weights.

• excess_noise (float, optional) – The excess noise, a term that is added in quadrature to the measurement uncertainty.

Returns:

• ndarray – The solution parameters.

• ndarray – The residuals, i.e. observed minus calculated values.

• ndarray – Inverse of the solution parameter covariance matrix.

gaiasupdate.utils module

Module with basic utilities.

gaiasupdate.utils.decode_ccd_proc_flag_to_description(flag: int) → ndarray

Return array of strings corresponding to the CCD processing flag.

Parameters:

flag (int) – Processing flag.

Returns:

Array containing CCD processing flags decoded.

Return type:

narray

gaiasupdate.utils.decode_transit_acquisition_flag_to_description(flag: int) → ndarray

Return array of strings corresponding to the CCD processing flag.

Parameters:

flag (int) – Processing flag.

Returns:

Array containing the transit aquisition flags decoded.

Return type:

narray

gaiasupdate.utils.fov_from_transit_id(transit_id: int) → int

Extract the FoV information from a transit_id.

Parameters:

transit_id (int) – Transit identifier.

Returns:

Gaia field of view (1 or 2).

Return type:

int

Note

See GAIA-C3-TN-UB-JP-011, page 9 available at Public DPAC documents.