The `AIMS` program

A module which contains the main program for AIMS as well as various classes which intervene when calculating the priors and likelihood function:

Distribution: a class which represents a probability distribution
Prior_list: a class with a list of priors
Mode: a class used to represent observed modes
Combination: a class used to represent a linear frequency combination
Combination_function: a class used to represent functions of frequency combinations
Likelihood: a class used to represent the likelihood function
Probability: a class which groups the priors and likelihood function together

This module relies on the emcee package to apply an MCMC algorithm which will return a representative sample of models for a given set of seismic an classic constraints.

Warning

In various places in this module, for instance in the Prior_list and Likelihood classes, various methods return what is described as a \(\chi^2\) value. Technically, these are not \(\chi^2\) values, but rather \(-\chi^2/2\), i.e. the argument of the exponential function which intervenes in the Gaussian probability distribution.

class AIMS.Combination[source]

A class which contains indices and coefficients which represent a linear combination of frequencies.

add_coeff(j, coeff)[source]

Append the given index and coefficient to the list of indices and coefficients.

Parameters

j (int) – index of the mode
coeff (float) – coefficient used in the frequency combination

coeff: Coefficients of the linear combination of frequencies.

find_values(freq)[source]

Find the value associated with this frequency combination using the input frequencies.

Parameters: freq (float array like) – list of frequencies

index: Indices in of the linear combination of frequencies.

print_me()[source]: Print frequency combination.

value: Value of the linear combination of frequencies.

class AIMS.Combination_function(_name, _function, _gradient_function, _offset=0.0)[source]

A class which applies functions to linear frequency combinations.

add_combination(combination)[source]

Append a frequency combination to this combination function.

Parameters: combination (Combination) – a linear frequency combination

combinations: The frequency combinations which intervene in the function.

find_values(freq)[source]

Find the value and gradient of this frequency combination function for the input set of frequencies.

Parameters: freq (float array like) – list of frequencies

function: The function which is applied to the frequency combinations.

gradient: The gradient of the frequency combination function at the observed frequencies.

gradient_function: The gradient of the function which is applied to the frequency combinations.

name: Human-readable name of the frequency combination function

offset: Additive offset for the frequency combination function.

print_me()[source]: Print frequency combination function.

value: Value of the frequency combination function at the observed frequencies.

class AIMS.Distribution(_type, _values)[source]

A class which represents a probability distribution, and can yield its value for a given input parameter, or provide a random realisation.

Note

Derived from a class originally written by G. Davies.

Parameters

_type (string) – type of probability function (current options include “Gaussian”, “Truncated_gaussian”, “Uniform”, “IMF1”, “IMF2”, “Uninformative”, “Above”, “Below”)
_values (list of floats) – list of parameters relevant to the probability function

property error_bar

Returns an error bar based on the distribution. This does not necessarily correspond to the one-sigma value but rather to what is the most convenient value.

Returns: the error bar
Return type: float

property mean

Returns the mean value of the probability distribution.

Returns: the mean value of the probability distribution
Return type: float

property nparams

Return the number of relevant parameters for a given distribution.

Returns: the number of relevant parameters
Return type: int

print_me()[source]: Print type and parameters of probability distribution.

re_centre(value)[source]

Re-centre the probability distribution around the input value.

Parameters: value (float) – new value around which to centre the distribution

re_normalise(value)[source]

Re-normalise the probability distribution so that its characteristic width corresponds to the input value.

Parameters: value (float) – new value around for the chacteristic width

realisation(size=None)[source]

Return random values which statistically follow the probability distribution.

Parameters: size (int or tuple of ints) – shape of random variates
Returns: a set of random realisations
Return type: float

to_string()[source]

Produce nice string representation of the distribution.

Returns: nice string representation of the distribution
Return type: string

type: Type of probability function (“Uniform”, “Gaussian”, “Truncated_gaussian”, “IMF1”, “IMF2”, “Uninformative”, “Above”, or “Below”)

values: List of parameters relevant to probability function

class AIMS.Likelihood[source]

A class which described the likelihood function and allows users to evaluate it.

Rkkinv: Inverse of R matrix from the WhoSGlAd method (see Eqs. (D.5) and (D.10) from Farnir et al. (2019))

Note

The first index corresponds to the p vector whereas the second index corresponds to the normalised q vector.

add_combinations(string, num_list, den_list=[], target_ell=None)[source]

This finds the indices of modes which intervene in a frequency combination or ratio, as specified by the mandatory and optional arguments. These indices, the relevant coefficients, the numerator, the denominator, and the resultant value of the combination are stored in the combination_functions variable.

Parameters

string (string) – name of the frequency combination
num_list (list of (int,int,float)) – list of relative mode identifications and coefficients used to define a frequency combination or the numerator of a frequency ratio. This list contains tuples of the form (delta n, delta l, coeff).
den_list (list of (int,int,float)) – list of relative mode identifications and coefficients used to define the denominator of a frequency ratio. If absent, then, it is assumed that a linear combination of frequencies is represented. The form is the same as for num_list.
target_ell (int) – this is used to impose a specific l value on the first selected mode.

add_constraint(constraint)[source]

Add a supplementary constraint to the list of constraints.

Parameters: constraint ((string, Distribution)) – supplementary constraint

add_dnu_constraint(string, l_targets=[0])[source]

Add the large frequency separation as a contraint. The coefficients are obtained via a least-squares approach. The approach taken here has two advantages:

Correlations between the large frequency separation and other seismic constraints will be taken into account.
The same modes will be used in the same way, both for the observations and the models.

Parameters

string (string) – name of this seismic constraint
l_targets (list of int) – specifies for which l values the large frequency separation is to be calculated. If None is supplied, all modes will be used.

Note

This uses an analytical approach and is therefore the prefered method.

add_dnu_constraint_matrix(string, l_targets=[0])[source]

Add the large frequency separation as a contraint. The coefficients are obtained via a least-squares approach. The approach taken here has two advantages:

Correlations between the large frequency separation and other seismic constraints will be taken into account.
The same modes will be used in the same way, both for the observations and the models.

Parameters

string (string) – name of this seismic constraint
l_targets (list of int) – specifies for which l values the large frequency separation is to be calculated. If None is supplied, all modes will be used.

Note

This uses a matrix approach and is therefore not the prefered method.

add_nu_min_constraint(string, target_ell=0, pos=0, min_n=False)[source]

Add the minimun frequencies/modes of a specific ell value as a seismic constraint. Typically, such constraints are used as an “anchor” when combined with constraints based on frequency ratios.

Parameters

string (string) – name of the seismic constraint
target_ell (int) – ell value of the minimum frequency/mode
pos (int) – position of desired frequency (0 = lowest, 1 = second lowest …)
min_n (boolean) – if False, look for minimum observational frequency. If True, look for minimum radial order.

add_seismic_constraint(string)[source]

Add seismic contraints based on the keyword given in string.

Parameters

string (string) –

keyword which specifies the type of constraint to be added. Current options include:

nu: individual frequencies
nu0: individual frequencies (radial modes only)
nu_min0: radial mode with minimum frequency
nu_min1: radial mode with second lowest frequency
nu_min2: radial mode with third lowest frequency
r02: \(r_{02}\) frequency ratios
r01: \(r_{01}\) frequency ratios
r10: \(r_{10}\) frequency ratios
dnu: individual large frequency separations (using all modes)
dnu0: individual large frequency separations (using radial modes only)
d2nu: second differences (using all modes)
avg_dnu: average large frequency separation (using all modes)
avg_dnu0: average large frequency separation (using radial modes only)
whosglad_dnu: WhoSGlAd version of average large frequency separation (all modes)
whosglad_dnu0: WhoSGlAd version of average large frequency separation (l=0 modes)
whosglad_dnu1: WhoSGlAd version of average large frequency separation (l=1 modes)
whosglad_r01: WhoSGlAd version of average r01 frequency ratio
whosglad_r02: WhoSGlAd version of average r02 frequency ratio
whosglad_Delta01: WhoSGlAd Delta01 seismic constraint
whosglad_Delta02: WhoSGlAd Delta02 seismic constraint
whosglad_eps0: WhoSGlAd average frequency offset (l=0 modes)
whosglad_eps1: WhoSGlAd average frequency offset (l=1 modes)
whosglad_AHe: WhoSGlAd amplitude indicator for helium content
whosglad_Abcz: WhoSGlAd amplitude indicator for the base of the convection zone

add_whosglad_AHe_constraint(string, maxpower=2)[source]

Add a seismic constraint which provides a normalised He glitch amplitude using the WhoSGlAd method (Farnir et al. 2019). This approach has the advantage of leading to (near) orthogonal seismic indicators.

Parameters

string (string) – name of this seismic constraint
maxpower (int) – maximum power in Pj(n)=n^j polynomial

add_whosglad_Abcz_constraint(string, maxpower=2)[source]

Add a seismic constraint which provides a normalised glitch amplitude for the base of the convection zone using the WhoSGlAd method (Farnir et al. 2019). This approach has the advantage of leading to (near) orthogonal seismic indicators.

Parameters

string (string) – name of this seismic constraint
maxpower (int) – maximum power in Pj(n)=n^j polynomial

add_whosglad_Delta_constraint(string, l_target, maxpower=2)[source]

Add a ratio of large frequency separations as a contraint using the WhoSGlAd method (Farnir et al. 2019). This approach has the advantage of leading to (near) orthogonal seismic indicators.

Parameters

string (string) – name of this seismic constraint
l_target (int) – specifies for which l to calculate the average Delta constraint.
maxpower (int) – maximum power in Pj(n)=n^j polynomial

add_whosglad_dnu_constraint(string, l_targets=[0], maxpower=2)[source]

Add an average large frequency separation as a contraint using the WhoSGlAd method (Farnir et al. 2019). This approach has the advantage of leading to (near) orthogonal seismic indicators.

Parameters

string (string) – name of this seismic constraint
l_targets (list of int) – specifies for which l values the large frequency separation is to be calculated. If None is supplied, all modes will be used.
maxpower (int) – maximum power in Pj(n)=n^j polynomial

add_whosglad_epsilon_constraint(string, l_target, maxpower=2)[source]

Add an average frequency offset as a contraint using the WhoSGlAd method (Farnir et al. 2019). This approach has the advantage of leading to (near) orthogonal seismic indicators.

Parameters

string (string) – name of this seismic constraint
l_target (int) – specifies for which l to calculate the average epsilon offset.
maxpower (int) – maximum power in Pj(n)=n^j polynomial

add_whosglad_ratio_constraint(string, l_target, maxpower=2)[source]

Add an average frequency ratio as a contraint using the WhoSGlAd method (Farnir et al. 2019). This approach has the advantage of leading to (near) orthogonal seismic indicators.

Parameters

string (string) – name of this seismic constraint
l_target (int) – specifies for which l to calculate the average frequency ratio.
maxpower (int) – maximum power in Pj(n)=n^j polynomial

apply_constraints(my_model)[source]

Calculate a \(\chi^2\) value for the set of constraints (excluding seismic constraints based on mode frequencies).

Parameters: my_model (model.Model) – model for which the \(\chi^2\) value is being calculated
Returns: the \(\chi^2\) value deduced from classic constraints
Return type: float

assign_n(my_model)[source]

Assign the radial orders based on proximity to theoretical frequencies from an input model.

Parameters: my_model (model.Model) – input model

classic_weight: Absolute weight to be applied to classic constraints (incl. nu_max constraint).

clear_seismic_constraints()[source]: This clears the seismic constraints. Specifically, the list of seismic combinations, and associated covariance matrix and its inverse are reinitialised.

coeff

2D float array with the coefficients for each frequency combination. The indices are:

The index of the term

The cumulative index of the frequency combination

combination_functions: This contains functions of frequency combinations.

compare_frequency_combinations(my_model, mode_map, a=[])[source]

This finds a \(\chi^2\) value based on a comparison of frequency combination functions, as defined in the combination_function variable.

Parameters

my_model (model.Model) – model for which the \(\chi^2\) value is being calculated
mode_map (list of int) – a mapping which relates observed modes to theoretical ones
a (array-like) – parameters of surface correction terms

Returns

the \(\chi^2\) value for the seismic constraints

Return type

float

Note

I’m assuming none of the modes are missing (i.e. that mode_map doesn’t contain the value -1)

constraints: List of constraints which intervene in the likelihood function.

construct_whosglad_basis(maxpower=2, glitchpower=- 5)[source]

Construct orthogonal basis for the smooth component of a pulsation spectrum using the Gram-Schmidt orthonormalisation method as described in the WhoSGlAd method (Farnir et al. 2019).

Parameters

maxpower (int) – maximum power in Pj(n)=n^j polynomial
glitchpower (int) – lower power used in Helium glitch component

cov: Covariance matrix which intervenes when calculating frequency combinations.

create_combination_arrays()[source]: Create array form of frequency combination functions to be used with a fortran based routine for calculating the seismic chi^2 value.

create_mode_arrays()[source]: Create arrays with mode parameters (n, l, freq), which can be interfaced with fortran methods more easily.

dot_product_whosglad(v1, v2)[source]

Dot product used for constructing an orthonormal set of seismic indicators using the WhoSGlAd method (Farnir et al. 2019).

Parameters

v1 (float np.array) – a vector of frequencies (or some polynomial of the radial order)
v2 (float np.array) – a vector of frequencies (or some polynomial of the radial order)

Returns

the dot product between v1 and v2

Return type

float

evaluate(my_model)[source]

Calculate ln of likelihood function (i.e. a \(\chi^2\) value) for a given model.

Parameters: my_model (model.Model) – model for which the \(\chi^2\) value is being calculated
Returns: the \(\chi^2\) value, optionally the optimal surface amplitudes (depending on the value of AIMS_configure.surface_option), integers to indicate whether the model was rejected due to classic or seismic contraints
Return type: float, np.array (optional), int, int

Note

This avoids model interpolation and can be used to gain time.

find_covariance()[source]: This prepares the covariance matrix and its inverse based on the frequency combinations in combination_functions.

Warning

This method should be called after all of the methods which add to the list of frequency combinations.

find_l_list(l_targets, npowers=2)[source]

Find a list of l values with the following properties:

each l value only occurs once
each l value given in the parameter l_targets is in the result l list, except if there is less than npowers modes with this l value
if the parameter l_targets is None, look for all l values with npowers or more modes associated with them

Parameters

l_targets (list of int) – input list of l values
npowers (int) – the number of powers in the fit

Returns

new list of l values with the above properties

Return type

list of int

find_map(my_model, use_n)[source]

This finds a map which indicates the correspondance between observed modes and theoretical modes from my_model.

Parameters

my_model – model for which the \(\chi^2\) value is being calculated
use_n (boolean) – specify whether to use the radial order when finding the map from observed modes to theoretical modes. If False, the map is based on frequency proximity.

Returns

the correspondance between observed and theoretical modes from the above model, and the number of observed modes which weren’t mapped onto theoretical modes

Return type

list of int, int

Note

a value of -1 is used to indicate that no theoretical mode corresponds to a particular observed mode.
only zero or one observed mode is allowed to correspond to a theoretical mode

find_vec(a_combination_function)[source]

This finds a set of coefficients which intervene when constructing the coviance matrix for frequency combination functions.

Parameters: a_combination_function (Combination_function) – variable which specifies the frequency combination function.
Returns: the above set of coefficients
Return type: np.array

find_weights()[source]: Find absolute weights for seismic and classic constraints based on options in AIMS_configure.py.

find_weights_new()[source]: Find absolute weights for seismic and classic constraints based on options in AIMS_configure.py.

fvalues: Array with the observed frequencies

get_optimal_surface_amplitudes(my_model, mode_map)[source]

Find optimal surface correction amplitude, for the surface correction specified by surface_option.

Parameters

my_model (model.Model) – the model for which we’re finding the surface correction amplitude
mode_map (list of int) – a mapping which relates observed modes to theoretical ones

Returns

optimal surface correction amplitudes

Return type

np.array

guess_dnu(with_n=False)[source]

Guess the large frequency separation based on the radial modes.

Parameters: with_n (boolean) – specifies whether to use the n values already stored with each mode, when calculating the large frequency separation.
Returns: the large frequency separation
Return type: float

guess_n()[source]

Guess the radial order of the observed pulsations modes.

This method uses the large frequency separation, as calculated with guess_dnu(), to estimate the radial orders. These orders are subsequently adjusted to avoid multiple modes with the same identification. The resultant radial orders could be off by a constant offset, but this is not too problematic when computing frequency combinations or ratios.

indices

2D int array with the mode indices for each frequency combination. The indices are:

The index of the term

The cumulative index of the frequency combination

invcov: Inverse of covariance matrix, Likelihood.cov.

lvalues: Array with the l values of the observed modes

modes: List of pulsation modes (of type Mode).

ncoeff: The number of terms in each frequency combination. The index is a cumulative index that uniquely designates one of the frequency combinations from one of the frequency combination functions. It is also the same as the second index in the coeff and indices variables.

ncomb: 1D int array which specifies the number of frequency combinations within each frequency combination function

nvalues: Array with the n values of the observed modes

qk: Normalised q vectors from the WhoSGlAd method (Farnir et al. 2019).

read_constraints(filename, factor=1.0)[source]

Read a file with pulsation data and constraints.

Parameters

filename (string) – name of file with pulsation data.
factor (float) – multiplicative factor for pulsation frequencies. Can be used for conversions.

seismic_weight: Absolute weight to be applied to seismic constraints

sort_modes()[source]: Sort the modes. The ordering will depend on the value of use_n from the AIMS_configure.py file.

class AIMS.Mode(_n, _l, _freq, _dfreq)[source]

A class which describes an observed pulsation mode.

Parameters

_n (int) – radial order of observed mode
_l (int) – harmonic degree of observed mode.
_freq (float) – pulsation frequency (in \(\mathrm{\mu Hz}\)).
_dfreq (float) – error bar on pulsation frequency (in \(\mathrm{\mu Hz}\)).

Warning

Negative values are not accepted for _l, _freq, or _dfreq.

dfreq: Error bar on pulsation frequency (in \(\mathrm{\mu Hz}\)).

freq: Pulsation frequency (in \(\mathrm{\mu Hz}\)).

l: Harmonic degree of observed mode.

match(a_mode)[source]

Check to see if input mode has the same (n,l) values as the current mode.

Parameters: a_mode (Mode) – input mode which is being compared with current mode.
Returns: True if the input mode has the same (n,l) values as the current mode.
Return type: boolean

n: Radial order of observed mode.

print_me()[source]: Print the mode in a human readable form.

class AIMS.Prior_list[source]

A class which contains a list of priors as well as convenient methods for adding priors and for evaluating them.

add_prior(aPrior)[source]

Add a prior to the list.

Parameters: aPrior (Distribution) – prior which is to be added to the list.

priors: A list of probability distributions which correspond to priors.

realisation(size=None)[source]

Return an array with realisations for each prior. The last dimension will correspond to the different priors.

Parameters: size (int or tuple of ints) – shape of random variates (for each prior)
Returns: a set of realisations
Return type: numpy float array

class AIMS.Probability(_priors, _likelihood)[source]

A class which combines the priors and likelihood function, and allows the the user to evalute ln of the product of these.

Parameters

_priors (Prior_list) – input set of priors
_likelihood (Likelihood) – input likelihood function

evaluate(my_model)[source]

Evalulate the ln of the product of the priors and likelihood function, i.e. the probability, for a given model, to within an additive constant.

Parameters: my_model (model.Model) – input model
Returns: the ln of the probability, integers indicating if the model has bee rejected based on classic constraints, seismic constraints, and/or priors
Return type: float, int, int, int

Note

This avoids model interpolation and can be used to gain time.

is_outside(params)[source]

Test to see if the given set of parameters lies outside the grid of models. This is done by evaluate the probability and seeing if the result indicates this.

Parameters: params (array-like) – input set of parameters
Returns: True if the set of parameters corresponds to a point outside the grid.
Return type: boolean

likelihood: The likelihood function.

priors: The set of priors.

AIMS.accepted_parameters = []: list of parameters associated with accepted models

AIMS.append_osm_parameter(config_osm, name, value, step, rate, bounds)[source]

Add a parameter in xlm format in the file with the classic constraints for OSM.

Parameters

config_osm (lxml.etree._Element) – XLM etree element to which to add the parameter
name (string) – name of the parameter
value (float) – value of the parameter
step (float) – parameter step (this intervenes when numerically calculating derivatives with respect to this parameter)
rate (float) – parameter rate (this corresponds to a tolerance on this parameter)
bounds (float tuple) – bounds on the parameter

AIMS.append_osm_surface_effects(modes_osm, name, numax, values)[source]

Add a method with which to calculate surface effects to the OSM contraint file.

Parameters

modes_osm (lxml.etree._Element) – XML element to which to add the surface effects method
name (string) – name of the method
numax (float) – value of numax
values (float tuple) – values which intervene in the method

AIMS.autocorr_time = []: integrated autocorrelelation time (this is useful for testing convergence)

AIMS.best_MCMC_model = None: best model from the MCMC run

AIMS.best_MCMC_params = None: parameters for the model best_MCMC_model

AIMS.best_MCMC_result = -1e+300: ln(probability) result for the model best_MCMC_model

AIMS.best_age_range = 0.0: Age range on track with best_model_model

AIMS.best_grid_model = None: best model from a scan of the entire grid

AIMS.best_grid_params = None: parameters for the model best_grid_model

AIMS.best_grid_result = -1e+300: ln(probability) result for the model best_grid_model

AIMS.check_configuration()[source]

Test the version of the EMCEE package and set the mc2 variable accordingly.

Test the values of the variables in check_configuration to make sure they’re acceptable. If an unacceptable value is found, then this will stop AIMS and explain what variable has an erroneous value.

AIMS.find_a_blob(params)[source]

Find a blob (i.e. supplementary output parameters) for a given set of parameters (for one model). The blob also includes the log(P) value as a first entry.

Parameters: params (array-like) – input set of parameters
Returns: list of supplementary output parameters
Return type: list of floats

AIMS.find_best_model()[source]: Scan through grid of models to find “best” model for a given probability function (i.e. the product of priors and a likelihood function).

AIMS.find_best_model_in_track(ntrack)[source]

Scan through an evolutionary track to find “best” model for prob, the probability function (i.e. the product of priors and a likelihood function).

Parameters: ntrack (int) – number of the evolutionary track
Returns: the ln(probability) value, the “best” model, the parameters of accepted models, the parameters of rejected models, the age range of the track, and the numbers of models rejected due to classic constraints, seismic contraints, and priors
Return type: (float, model.Model, 2D float list, 2D float list, float, int, int, int)

AIMS.find_blobs(samples)[source]

Find blobs (i.e. supplementary output parameters) from a set of samples (i.e. for multiple models).

Parameters: samples (list/array of array-like) – input set of samples
Returns: set of supplementary output parameters
Return type: np.array

AIMS.grid = None: grid of models

AIMS.grid_params_MCMC = (): parameters used in the MCMC run (excluding surface correction parameters)

AIMS.grid_params_MCMC_with_surf = (): parameters used in the MCMC run (including surface correction parameters)

AIMS.init_walkers()[source]

Initialise the walkers used in emcee.

Returns: array of starting parameters
Return type: np.array

AIMS.interpolation_tests(filename)[source]

Carry out various interpolation tests and write results in binary format to file.

Parameters: filename (string) – name of file in which to write test results.

Note

The contents of this file may be plotted using methods from plot_interpolation_test.py.

AIMS.load_binary_data(filename)[source]

Read a binary file with a grid of models.

Parameters: filename (string) – name of file with grid in binary format
Returns: the grid of models
Return type: model.Model_grid

AIMS.log0 = -1e+300: a large negative value used to represent ln(0)

AIMS.mc2 = None: True if emcee’s version is 2 or prior

AIMS.my_map = None: pointer to the map function (either the parallel or sequential versions)

AIMS.ndims = 0: number of dimensions for MCMC parameters (includes nsurf)

AIMS.nreject_classic = 0: Number of models rejected because of classic constraints

AIMS.nreject_prior = 0: Number of models rejected based on priors

AIMS.nreject_seismic = 0: Number of models rejected because of seismic constraints

AIMS.nsurf = 0: number of surface term parameters

AIMS.output_folder = None: folder in which to write the results

AIMS.plot_distrib_iter(percentiles, labels, folder)[source]

Plot individual distribution of walkers as a function of iterations.

Parameters

percentiles (np.array) – array with percentiles from emcee run
labels (list of strings) – labels for the different dimensions in parameters space
folder (string) – specify name of file in which to save plots of walkers.

Warning

This method must be applied before the samples are reshaped, and information on individual walkers lost.

AIMS.plot_distrib_iter_old(samples, labels, folder)[source]

Plot individual distribution of walkers as a function of iterations.

Parameters

samples (np.array) – samples from the emcee run
labels (list of strings) – labels for the different dimensions in parameters space
folder (string) – specify name of file in which to save plots of walkers.

Warning

This method must be applied before the samples are reshaped, and information on individual walkers lost.

AIMS.plot_echelle_diagram(my_model, my_params, model_name)[source]

Produce an echelle diagram for input model.

Parameters

my_model (model.Model) – model for which we’re making an echelle diagram
my_params (array-like) – parameters of the model
model_name (string) – name used to describe this model. This is also used when naming the file with the echelle diagram.

AIMS.plot_frequencies(grid)[source]

Plot frequencies along an evolutionary track. For debugging purposes only.

Parameters: grid (Model_grid) – grid of models

AIMS.plot_frequency_diff(my_model, my_params, model_name, scaled=False)[source]

Make a diagram with frequency differences.

Parameters

my_model (model.Model) – model for which we’re plotting frequencie differences
my_params (array-like) – parameters of the model
model_name (string) – name used to describe this model. This is also used when naming the file with the plot.
scaled (boolean) – if True, scale frequency differences by frequency error bars

AIMS.plot_histograms(samples, names, fancy_names, truths=None)[source]

Plot a histogram based on a set of samples.

Parameters

samples (np.array) – samples form the emcee run
names (list of strings) – names of the quantities represented by the samples. This will be used when naming the file with the histogram
fancy_names (list of strings) – name of the quantities represented by the samples. This will be used as the x-axis label in the histogram.
truths (list of floats) – reference values (typically the true values or some other important values) to be added to the histograms as a vertical line

AIMS.plot_walkers(samples, labels, filename, nw=3)[source]

Plot individual walkers.

Parameters

samples (np.array) – samples from the emcee run
labels (list of strings) – labels for the different dimensions in parameters space
filename (string) – specify name of file in which to save plots of walkers.
nw (int) – number of walkers to be plotted

Warning

This method must be applied before the samples are reshaped, and information on individual walkers lost.

AIMS.pool = None: pool from which to carry out parallel computations

AIMS.prob = None: Probability type object that represents the probability function which includes the likelihood and priors

AIMS.rejected_parameters = []: list of parameters associated with rejected models

AIMS.run_emcee(p0)[source]

Run the emcee program.

Parameters: p0 (np.array) – the initial set of walkers
Returns: the emcee sampler for the MCMC run, array with walker percentiles as a function of iteration number
Return type: emcee sampler object, np.array

AIMS.statistical_model = None: model corresponding to statistical parameters

AIMS.statistical_params = None: parameters for the model statistical_model

AIMS.statistical_result = -1e+300: ln(probability) result for the model statistical_model

AIMS.string_to_title(string)[source]

Create fancy title from string.

Parameters: string (string) – string from which the title is created.
Returns: the fancy string title
Return type: string

AIMS.swap_dimensions(array)[source]

Swaps the two first dimensions of an array. This is useful for handling the different conventions used to store the samples in emcee3 and ptemcee.

Parameters: array (np.array) – input array
Returns: array with swapped dimensions
Return type: np.array

AIMS.threshold = -1e+290: threshold for “accepted” models. Needs to be greater than log0

AIMS.tight_ball_distributions = None: Prior_list type object with the distributions for the initial tight ball

AIMS.write_LEGACY_summary(filename, KIC, labels, samples)[source]

Write a one line summary of the statistical properties based on a sequence of realisations to a file. The format matches that of the LEGACY project.

The results include:

average values for each variable (statistical mean)
error bars for each variable (standard mean deviation)

Parameters

filename (string) – name of file in which to write the statistical properties
KIC (string) – KIC number of the star
labels (list of strings) – names of relevant variables
samples (np.array) – samples for which statistical properties are calculated

AIMS.write_SPInS_file_cgs(filename)[source]: Write list file compatible with SPInS. The quantities mass, luminosity, and radius are provided in cgs.

Note

The header in the output file might need to be edited by hand.

AIMS.write_SPInS_file_solar(filename)[source]: Write list file compatible with SPInS. The quantities mass, luminosity, and radius are provided solar units.

Note

The header in the output file might need to be edited by hand.

AIMS.write_binary_data(infile, outfile)[source]

Read an ascii file with a grid of models, and write corresponding binary file.

Parameters

infile (string) – input ascii file name
outfile (string) – output binary file name

AIMS.write_combinations(filename, samples)[source]

Produce a list of linear combinations of grid models (based on interpolation) corresponding to the provided model parameters.

Parameters

filename (string) – name of the file to which to write the model combinations
samples (np.array) – set of model parameters for which we would like to obtain the grid models and interpolation coefficients

AIMS.write_list_file(filename)[source]: Write list file from which to generate binary grid. Various filters can be included to reduce the number of models.

Note

This code is intended for developpers, not first time users.

AIMS.write_model(my_model, my_params, my_result, model_name, extended=False)[source]

Write text file with caracteristics of input model.

Parameters

my_model (model.Model) – model for which we’re writing a text file
my_params (array-like) – parameters of the model
my_result (float) – ln(P) value obtained for the model
model_name (string) – name used to describe this model. This is also used when naming the text file.
extended – if set to True, all of the theoretical modes are saved in the text file, including those not matched to observations

AIMS.write_osm_don(filename, my_model)[source]

Write file with choice of physical ingredients to be used by CESAM or CESTAM and OSM.

Parameters

filename (string) – name of file which will contain the physical ingredients
my_model (model.Model) – model from which which is derived various physical constraints/settings

Note

Written by B. Herbert.

AIMS.write_osm_frequencies(filename, my_model)[source]

Write file with frequencies for Optimal Stellar Model (OSM), written by R. Samadi.

Parameters

filename (string) – name of file which will contain the frequencies
my_model (model.Model) – model from which are derived the radial orders

Note

Written by B. Herbert.

AIMS.write_osm_xml(filename, my_params, my_model)[source]

Write file with classic constraints for OSM

Parameters

filename (string) – name of file with classic constraints
my_model (model.Model) – model used in deriving some of the constraints

Note

Originally written by B. Herbert. Includes some modifications.

AIMS.write_percentiles(filename, labels, samples)[source]

Write percentiles based on a sequence of realisations to a file. The results include:

+/- 2 sigma error bars (using the 2.5th and 97.5th percentiles) +/- 1 sigma error bars (using the 16th and 84th percentiles) the median value (i.e. the 50th percentile)

Parameters

filename (string) – name of file in which to write the percentiles
labels (list of strings) – names of relevant variables
samples (np.array) – samples for which statistical properties are calculated

AIMS.write_readme(filename, elapsed_time)[source]

Write parameters relevant to this MCMC run.

Parameters: filename (string) – name of file in which to write the statistical properties

AIMS.write_samples(filename, labels, samples)[source]

Write raw samples to a file.

Parameters

filename (string) – name of file in which to write the samples
labels (list of strings) – names of relevant variables (used to write a header)
samples (array-like) – samples for which statistical properties are calculated

AIMS.write_statistics(filename, labels, samples)[source]

Write statistical properties based on a sequence of realisations to a file. The results include:

average values for each variable (statistical mean)
error bars for each variable (standard mean deviation)
correlation matrix between the different variables

Parameters

filename (string) – name of file in which to write the statistical properties
labels (list of strings) – names of relevant variables
samples (np.array) – samples for which statistical properties are calculated

The AIMS program

The `AIMS` program