OCFit

The class for fitting O-C according to different models: LiTE for the 3rd and also the 4th body, combination of mass-transfer and LiTE for the 3rd and also the 4th body, apsidal motion and models based on Agol et al. (2005).

Initialization

`OCFit.OCFit(t, oc, err = None)`

For initialization these classes, it is necessary to give observed times of minima (O) and the values of O-C. The values of O-C could be obtained using the classes FitLinear and FitQuad. It is also possible to set the errors of O-C.

Parameter	Type	Description
t	numpy.array or list	Observed times of minima.
oc	numpy.array or list	Values of O-C in days.
err	numpy.array or list, optional	Errors of O-C.

Setting the parameters for fitting

`OCFit.OCFit.?`

It is necessary to set some parameters of model and fitting routine after initialization. They are mainly the limits and steps of parameters, values of fixed parameters, the list of parameters for fitting and model of O-C which will be used for fitting.

Parameter	Type	Description
limits	dictionary	Limits of fitted parameters. It is necessary to set the list with a lower and upper limit for each fitted parameter. The names of parameters are said in a description of the specific model.
steps	dictionary	Steps of fitted parameters. It is necessary to set the size of the step for each fitted parameter. The names of parameters are said in the description of the specific model.
fit_params	list	The list of parameters which will be fitted. The names of parameters are said in the description of the specific model.
params	dictionary, optional	The values of fixed parameters. The names of parameters are said in the description of the specific model.
model	string, optional	Setting model which will be used for fitting of O-C. The name of the model is the same as the name of the function for calculation it. The default model is LiTE3.

Working with weights of data points

If it is possible, it is better to work directly with errors of data points and no with weights! In the case of work with weight (w), the errors could be computed as 1/w. But in many cases, these errors are really over-estimated.

During working with weights is very good to follow this instruction:

during initialization set errors as 1/w
fitting using FitGA
re-normalization of errors using AddWeight
fitting by MC method using FitMCMC
in the saving data by function SaveRes enter the weights in parameter weight
in the plotting figures enter weights in parameter weight and eventually use also trans_weight = True

General notes to the work with the class OCFit

The base of successful fitting is to choose an appropriate model. It is useful to minimize the number of model parameter and also a number of fitted parameters. It means, not use a model with a lot of parameters while many of them are fixed if it is not really necessary. Using of such complicated model unnecessarily extends computing time and sometimes also decrease the quality of results. Because of this fact, it is sometimes more appropriate to work with residue and not with original data, e. g. for fitting O-C influenced by LiTE from 3rd and also the 4th body. Eventually, firstly remove linear / quadratic trend using functions from FitLinear and FitQuad and in the next step fit more complicated changes. It is also useless to fit a parameter which has near zero value, has no influence on the shape of the model curve and its value is on the level of its uncertainty. A good example is quadratic therm Q in the models LiTE3Quad and LiTE34Quad. In the case, that there is not quadratic but the only linear trend in data it is useful to fix it on value 0. By its removing from fitted parameters the precision of the fitting improves and now it is also possible to decrease the number of iterations of fitting routines.

The second key point is to set a suitable interval of parameters for fitting. In many cases, they could be wide enough. However, their reduction increases the precision of fitting and reduce the number of necessary iterations. The values of eccentricity e and longitude of pericenter w could be found in whole logically possible intervals, i. e. from 0 to 1 for eccentricity and from 0 to 2π for the longitude of pericenter. For other parameters (such as period of 3rd body P3), it is possible to estimate the interval from the O-C diagram. On the other hand, the value of linear ephemeris t0 and P should be set really small interval because the shape of O-C diagram is very sensitive to the value of linear ephemeris. Very wide interval often leads to completely wrong results of fitting. Depending on the specific O-C diagram the width of the searching intervals for linear ephemeris should not exceed 1-2 hours. It is the best, if it is possible, avoid fitting of complex models together with linear ephemeris.

For successful fitting, it is even necessary to set a sufficient number of iterations for each of fitting algorithms. When genetic algorithms (GA) are used, it should be sufficient to set a number of generations and a size of one generation to >= 100 − 200× number of fitted parameters. Like some universal settings, it could be used to set both to the value 1000. For the first test of fitting with GA, it is enough to set both parameters to 100. In a case of Monte Carlo method, the sufficient number of iterations depends on the quality of input data, the precision of started values and type of model, it is mainly in the range from 1E5 to 1E7. Some universal value should be 1E6. Many times, it is needful to remove at least 1E3 of the first values and use binning with the size 10 – 100. For the first estimation, it is enough to use only 1000 iterations without removing values and with unity binning.

Available functions

AvailableModels

`OCFit.OCFit.AvailableModels()`

Displaying available model of O-C. The list with names of all models is also saved in variable availableModels.

ModelParams

`OCFit.OCFit.ModelParams(model = None, allModels = False)`

Displaying the parameters of selected model of O-C or all available models. If no parameter is given, the parameters of model set in variable model are displayed.

Parameter	Type	Description
model	string, optional	Name of selected model.
allModels	boolean, optional	Display parameters of all available models.

LiTE

`OCFit.OCFit.LiTE(t, a_sin_i3, e3, w3, t03, P3)`

Function for calculation of O-C based on model of Light-time effect (LiTE). Details are in Irwin (1952). It is not function for fitting model but only auxiliary function!

Parameter	Type	Description
t	numpy.array	Times for calculation the values of O-C.
a_sin_i3	float	Value of a sin i3 in AU.
e3	float	Eccentricity of the orbit of the 3rd body.
w3	float	Longitude of pericenter of the orbit of the 3rd body in radians.
t03	float	Time of pericenter passage of the 3rd body.
P3	float	Period of the 3rd body in days.

Output	numpy.array	Values of O-C calculated from LiTE model.

AgolInPlanet

`OCFit.OCFit.AgolInPlanet(t, P, a, w, e, mu3, r3, w3, t03, P3)`

Function for calculation of O-C based on the model of perturbations caused by inner planet according to paper Agol et al. (2005, their eq. (12)). Set model = 'AgolInPlanet' for using this model. The names of parameters for fitting, setting limits, steps and values of parameters are same as the name of input parameters of this function (except time t).

Parameter	Type	Description
t	numpy.array	Times for calculation the values of O-C.
P	float	Period of transiting exoplanet in days.
a	float	Semi-major axis of orbits of transiting exoplanet in AU.
w	float	Longitude of pericenter of transiting exoplanet in radians.
e	float	Eccentricity of the orbit of transiting exoplanet.
mu3	float	Reduced mass of the 3rd body (inner planet).
r3	float	Radius of the orbit of the 3rd body.
w3	float	Longitude of pericenter of the 3rd body.
t03	float	Time of pericenter passage of the 3rd body.
P3	float	Period of the 3rd body in days.

Output	numpy.array	Values of O-C calculated from the model.

AgolInPlanetLin

`OCFit.OCFit.AgolInPlanetLin(t, t0, P, a, w, e, mu3, r3, w3, t03, P3)`

Function for calculation of O-C based on the model of perturbations caused by inner planet according to paper Agol et al. (2005, their eq. (12)) combined with the linear model of O-C. The function Epoch has to be used before using this model. Set model = 'AgolInPlanetLin' for using this model. The names of parameters for fitting, setting limits, steps and values of parameters are same as the name of input parameters of this function (except time t).

Parameter	Type	Description
t	numpy.array	Times for calculation the values of O-C.
t0	float	Time of reference transit.
P	float	Period of transiting exoplanet in days.
a	float	Semi-major axis of orbits of transiting exoplanet in AU.
w	float	Longitude of pericenter of transiting exoplanet in radians.
e	float	Eccentricity of the orbit of transiting exoplanet.
mu3	float	Reduced mass of the 3rd body (inner planet).
r3	float	Radius of the orbit of the 3rd body.
w3	float	Longitude of pericenter of the 3rd body.
t03	float	Time of pericenter passage of the 3rd body.
P3	float	Period of the 3 rd body in days in days.

Output	numpy.array	Values of O-C calculated from the model.

AgolExPlanet

`OCFit.OCFit.AgolExPlanet(t, P, mu3, e3, t03, P3)`

Function for calculation of O-C based on the model of perturbations caused by exterior planet according to paper Agol et al. (2005, their eq. (25)). Set model = 'AgolExPlanet' for using this model. The names of parameters for fitting, setting limits, steps and values of parameters are same as the name of input parameters of this function (except time t).

Parameter	Type	Description
t	numpy.array	Times for calculation the values of O-C.
P	float	Period of transiting exoplanet in days.
mu3	float	Reduced mass of the 3rd body (exterior planet).
e3	float	Eccentricity of the orbit of the 3rd body.
t03	float	Time of pericenter passage of the 3rd body.
P3	float	Period of the 3rd body.

Output	numpy.array	Values of O-C calculated from the model.

AgolExPlanetLin

`OCFit.OCFit.AgolExPlanetLin(t, t0, P, mu3, e3, t03, P3)`

Function for calculation of O-C based on model of perturbations caused by exterior planet according to paper Agol et al. (2005, their eq. (25)) combined with the linear model of O-C. The function Epoch has to be used before using this model. Set model = 'AgolExPlanetLin' for using this model. The names of parameters for fitting, setting limits, steps and values of parameters are same as the name of input parameters of this function (except time t).

Parameter	Type	Description
t	numpy.array	Times for calculation the values of O-C.
t0	float	Time of reference transit.
P	float	Period of transiting exoplanet in days.
mu3	float	Reduced mass of the 3rd body (exterior planet).
e3	float	Eccentricity of the orbit of the 3rd body.
t03	float	Time of pericenter passage of the 3rd body.
P3	float	Period of the 3rd body in days.

Output	numpy.array	Values of O-C calculated from the model.

LiTE3

`OCFit.OCFit.LiTE3(t, a_sin_i3, e3, w3, t03, P3)`

Function for calculation of O-C based on the model of LiTE caused by the presence of the 3rd body. Details are in Irwin (1952). Set model = 'LiTE3' for using this model. The names of parameters for fitting, setting limits, steps and values of parameters are same as the name of input parameters of this function (except time t).

Parameter	Type	Description
t	numpy.array	Times for calculation the values of O-C.
a_sin_i3	float	Value of a sin i3 in AU.
e3	float	Eccentricity of the orbit of the 3rd body.
w3	float	Longitude of pericenter of the orbit of the 3rd body in radians.
t03	float	Time of pericenter passage of the 3rd body.
P3	float	Period of the 3rd body in days.

Output	numpy.array	Values of O-C calculated from the model.

LiTE3Quad

`OCFit.OCFit.LiTE3Quad(t, t0, P, Q, a_sin_i3, e3, w3, t03, P3)`

Function for calculation of O-C based on the model of LiTE caused by the presence of the 3rd body combined with the quadratic model of O-C. Details are in Irwin (1952). The function Epoch has to be used before using this model. Set model = 'LiTE3Quad' for using this model. The names of parameters for fitting, setting limits, steps and values of parameters are same as the name of input parameters of this function (except time t).

Parameter	Type	Description
t	numpy.array	Times for calculation the values of O-C.
t0	float	Time of reference minimum.
P	float	Period of Eclipsing binary in days.
Q	float	Quadratic term.
a_sin_i3	float	Value of a sin i3 in AU.
e3	float	Eccentricity of the orbit of the 3rd body.
w3	float	Longitude of pericenter of the orbit of the 3rd body in radians.
t03	float	Time of pericenter passage of the 3rd body.
P3	float	Period of the 3rd body in days.

Output	numpy.array	Values of O-C calculated from the model.

LiTE34

`OCFit.OCFit.LiTE34(t, a_sin_i3, e3, w3, t03, P3, a_sin_i4, e4, w4, t04, P4)`

Function for calculation of O-C based on the model of LiTE caused by the presence of the 3rd and the 4th body. Details are in Irwin (1952). Set model = 'LiTE34' for using this model. The names of parameters for fitting, setting limits, steps and values of parameters are same as the name of input parameters of this function (except time t).

Parameter	Type	Description
t	numpy.array	Times for calculation the values of O-C.
a_sin_i3	float	Value of a sin i3 in AU.
e3	float	Eccentricity of the orbit of the 3rd body.
w3	float	Longitude of pericenter of the orbit of the 3rd body in radians.
t03	float	Time of pericenter passage of the 3rd body.
P3	float	Period of the 3rd body in days.
a_sin_i4	float	Value of a sin i4 in AU.
e4	float	Eccentricity of the orbit of the 4th body.
w4	float	Longitude of pericenter of the orbit of the 4th body in radians.
t04	float	Time of pericenter passage of the 4th body.
P4	float	Period of the 4th body in days.

Output	numpy.array	Values of O-C calculated from the model.

LiTE34Quad

`OCFit.OCFit.LiTE34Quad(t, t0, P, Q, a_sin_i3, e3, w3, t03, P3, a_sin_i4, e4, w4, t04, P4)`

Function for calculation of O-C based on the model of LiTE caused by the presence of the 3rd and the 4th body combined with the quadratic model of O-C. Details are in Irwin (1952). The function Epoch has to be used before using this model. Set model = 'LiTE34Quad' for using this model. The names of parameters for fitting, setting limits, steps and values of parameters are same as the name of input parameters of this function (except time t).

Parameter	Type	Description
t	numpy.array	Times for calculation the values of O-C.
t0	float	Time of reference minimum.
P	float	Period of Eclipsing binary in days.
Q	float	Quadratic term.
a_sin_i3	float	Value of a sin i3 in AU.
e3	float	Eccentricity of the orbit of the 3rd body.
w3	float	Longitude of pericenter of the orbit of the 3rd body in radians.
t03	float	Time of pericenter passage of the 3rd body.
P3	float	Period of the 3rd body in days.
a_sin_i4	float	Value of a sin i4 in AU.
e4	float	Eccentricity of the orbit of the 4th body.
w4	float	Longitude of pericenter of the orbit of the 4th body in radians.
t04	float	Time of pericenter passage of the 4th body.
P4	float	Period of the 4th body in days.

Output	numpy.array	Values of O-C calculated from the model.

Apsidal

`OCFit.OCFit.Apsidal(t, t0, P, w0, dw, e, min_type)`

Function for calculation of O-C based on the model of apsidal motion. Details are in Giménez & Bastero (1995). The function Epoch has to be used before using this model. Set model = 'Apsidal' for using this model. The names of parameters for fitting, setting limits, steps and values of parameters are same as the name of input parameters of this function (except time t and types of minima min_type).

Parameter	Type	Description
t	numpy.array	Times for calculation the values of O-C.
t0	float	Time of reference minimum.
P	float	Period of Eclipsing binary in days.
w0	float	Initial longitude of pericenter in radians.
dw	float	Angular velocity of line of apsides in radians per period.
e	float	Eccentricity of the orbit.
min_type	numpy.array	Type of minima (0 = primary, 1 = secondary).

Output	numpy.array	Values of O-C calculated from model.

Model

`OCFit.OCFit.Model(t = None, params = None, min_type = None)`

Function for calculation of selected model of O-C based on a given set of parameters in given times. Parameters are given using dictionary and their names are same as names used for setting the model (see descriptions of individual models). If some of the parameters of this function are not given, the corresponding parameter from the class will be used.

Parameter	Type	Description
t	numpy.array or float, optional	Times for calculation the values of O-C.
params	dictionary, optional	Set of model parameters.
min_type	numpy.array or float, optional	Type of minima (0 = primary, 1 = secondary).

Output	numpy.array	Values of O-C calculated from model.

KeplerEQ

`OCFit.OCFit.KeplerEQ(M, e, eps = 1e-10)`

Function for solving the Kepler’s equation. Newton-Raphson iteration scheme is used for solving. The expression S9 from the paper Odell & Gooding (1986) is used as a started value. The solution converges for all values of e and M. Computing time starts rapidly raise for e>=0.9. Because of it, the function KeplerEQMarkley is used in this case.

Parameter	Type	Description
M	numpy.array or float	Values of mean anomaly in radians.
e	float	Eccentricity of the orbit.
eps	float, optional	Required accuracy of the solution.

Output	numpy.array or float	Values of eccentric anomaly in radians.

KeplerEQMarkley

`OCFit.OCFit.KeplerEQMarkley(M, e)`

Function for solving the Kepler’s equation. Non-iterative algorithm from the paper Markley (1995) is used for solving. Computing time is nearly the same, not depending on the given values of e and M. The calculation using this algorithm is faster like using function KeplerEQ for e>=0.9 but it is better to use the function KeplerEQ for small values of eccentricity.

Parameter	Type	Description
M	numpy.array or float	Values of mean anomaly in radians.
e	float	Eccentricity of the orbit.

Output	numpy.array or float	Values of eccentric anomaly in radians.

Epoch

`OCFit.OCFit.Epoch(t0, P, t = None)`

Calculation of epoch of all observed minima. This function has to be used before fitting the model containing a linear or quadratic model or model of apsidal motion, eventually plotting the figures with x-axis in epochs. Obtained epochs are saved to variable epoch.

Parameter	Type	Description
t0	float	Time of reference minimum.
P	float	Period in days.
t	numpy.array or float, optional	Times of minima.

Output	numpy.array	Calculated epochs.

PhaseCurve

`OCFit.FitLinear.PhaseCurve(P, t0, plot = False)`

Calculation of the phase curve on the basis of the given linear ephemeris. The final phase curve could be displayed on a figure.

Parameter	Type	Description
P	float	Period.
t0	float	Time of reference minimum.
plot	boolean, optional	Plot also a figure or only calculated phase curve.

Output	numpy.array	Phases and values of O-C.

FitGA

`OCFit.OCFit.FitGA(generation, size, mut = 0.5, SP = 2, plot_graph = False, visible = True, n_thread = 1, db = None)`

Fitting values of O-C using genetic algorithms (GA). For using this function, it is necessary to set limits and steps of all fitted parameters. Fitting using GA is good to obtain the first estimation of values of parameters which could be used for fitting using MC by function FitMCMC.

It is necessary to set a suitable number of generations and their size in variables generation and size. A total number of the conducted calculation of model is generation x size. The fitting routine could be improved by setting the correct probability of mutations and the value of selective pressure.

It is possible to save the obtained set of individuals in all generations to file and analyse it using function InfoGA.

More detailed information about using GA could be found in Hartmann & Rieger (2002) or Weise (2011).

Parameter	Type	Description
generation	integer	Number of generations.
size	integer	Size of one generation, i. e. the number of individual in one generation.
mut	float, optional	Probability of mutations (in the range from 0 to 1).
SP	float, optional	Value of selective pressure (details in Razali & Geraghty (2011)).
plot_graph	boolean, optional	Plotting figure with progress of chi2 error in individual generations.
visible	boolean, optional	Display a progress of fitting.
n_thread	integer, optional	Number of thread for multithreading.
db	string, optional	Name of the file for saving the fitting.

Output	dictionary	Values of fitted parameters.

InfoGA

`OCFit.OCFit.InfoGA(db, eps = False)`

Function for detail analysis of results of GA obtained using FitGA. For each of the fitted parameters, the figure displaying its values through individual generations is generated. The figure with the progress of the chi2 error in individual generations and the file with summary information about fitting is also created.

Parameter	Type	Description
db	string	Name of the file with saved fitting.
eps	boolean, optional	Save figures also in eps format.

FitMCMC

`OCFit.OCFit.FitMCMC(n_iter, burn = 0, binn = 1, visible = True, db = None)`

The function for fitting O-C diagram using Markov chain Monte Carlo (MCMC) method. It is necessary to have installed package pymc (Patil et al., 2010). Running of this function is possible only if the initial values of fitted parameters were calculated. They could be obtained from fitting using function FitGA or by manually setting them in params.

It is necessary to set a suitable number of iterations in a variable n_iter. Sometimes, it is also necessary to set some other parameters for MCMC. In case that the initial values of parameters are not close to their optimal values to which MC method converge, it is necessary to set using parameter burn a number of MC steps which are removed. Now, the only values in equilibrium are used for the calculation of mean values and errors. The next problem could be a strong correlation between following MC steps. It is possible to reduce it by binning the generated sequence of MC steps. The size of one block is set up through parameter binn.

Obtained MC sampling could be saved to file and analysed by function InfoMCMC.

If the errors of data points were not given during initialization of class, it is necessary to calculate it using function CalcErr. Eventually, if the weights are available, it is necessary to transform them into the errors using function AddWeight. In a case, that fitting using FitGA gives good results but fitting using the MCMC method worsen them, it could be a problem in over-estimated errors of data points. It is possible to normalise them using CorrectErr.

More details about using the MCMC method could be found in Brooks et al. (2011).

Parameter	Type	Description
n_iter	float	Number of MC steps.
burn	float, optional	Number of MC steps which will be reject from calculation.
binn	float, optional	The size of one block for binning.
visible	boolean, optional	Display progress of fitting and summary of results from `pymc`.
db	string, optional	Name of file for saving MC sampling.

Output	dictionary, dictionary	Values and errors of fitted parameters.

InfoMCMC

`OCFit.OCFit.InfoMCMC(db, eps = False, geweke = False)`

Function for detail analysis of MCMC sampling obtained by FitMCMC. It will be generated a plot with a trace of fitting and common plot with trace and histogram for each of the fitted parameters. An also, the file with brief information about sampling, obtained values and errors of the parameter will be created. It is also possible to plot figures for Geweke analysis (details in Geweke (1992)).

Few common figures for all fitted parameters will be generated, too. There are histograms, deviances, correlation plots and 2D histograms displaying the confidence regions. For 2D histograms, the function ConfInt is used, everyone else is generated by the class TraceAnalysis from PyAstronomy.

The last output is a table with correlation coefficients between fitted parameters.

Parameter	Type	Description
db	string	Name of file with saved MC sampling.
eps	boolean, optional	Save figures also in eps format.
geweke	boolean, optional	Geweke analysis.

CalcErr

`OCFit.OCFit.CalcErr()`

Calculation of errors of input data on a basis of values of fitted parameters. This function could not be used before fitting the data. For all point, the same error will be assigned. The size of error will be set that the value of reduced squared error chi2r will be equal to 1.

It is necessary to use this function before fitting using the MC method by function FitMCMC if the errors of input data were not given during initialization. It is possible to fit data using genetic algorithms by function FitGA. It is assumed that actual values of parameters give the model O-C close to the real data.

Parameter	Type	Description

Output	numpy.array	Calculated errors.

CorrectErr

`OCFit.OCFit.CorrectErr()`

Re-normalization of given errors of input data on a basis of values of fitted parameters. This function could not be used before fitting the data. The size of error will be set that the value of reduced squared error chi2r will be equal to 1. For plotting the figure, original values of errors are used.

It is useful to use this function before fitting using the MC method by function FitMCMC if the errors of input data are wrong calculated (under- or over-estimated). It is possible to fit data using genetic algorithms by function FitGA. It is assumed that actual values of parameters give model O-C close to the real data.

Parameter	Type	Description

Output	numpy.array	Calculated errors.

AddWeight

`OCFit.OCFit.AddWeight(w)`

Adding the weights and normalization of errors on a basis of values of fitted parameters. This function could not be used before fitting the data. The size of error will be set that the value of reduced squared error chi2r will be equal to 1.

It is necessary to use this function before fitting using the MC method by function FitMCMC. It is possible to fit data using genetic algorithms by function FitGA. It is assumed that actual values of parameters give model O-C close to the real data.

Parameter	Type	Description
w	numpy.array	Weights of points.

Output	numpy.array	Calculated errors.

Amplitude

`OCFit.OCFit.Amplitude()`

Function for calculation of amplitude of O-C based on the used model and set up parameters. If the function FitMCMC was used, the uncertainty will be also calculated. Obtained value is saved to variable paramsMore and error to variable paramsMore_err.

Parameter	Type	Description

Output	dictionary	Calculated amplitude and error.

Summary

`OCFit.OCFit.Sumarry(name = None)`

Summary of values and errors of fitted parameters. It is possible to save the output to file or display it on the screen.

Parameter	Type	Description
name	string, optional	Name of output file.

Chi2

`OCFit.OCFit.Chi2(params)`

Function for calculation of chi2 error for given set of parameters and setted up model.

Parameter	Type	Description
params	dictionary	Set of parameters of the model.

Output	float	Calculated chi2 error.

MassFun

`OCFit.OCFit.MassFun()`

Function for calculation of mass function for models based on LiTE. If the function FitMCMC was used, the uncertainty will be also calculated. Obtained value is saved to variable paramsMore and error to variable paramsMore_err.

Parameter	Type	Description

Output	dictionary	Calculated mass function and error.

AbsoluteParam

`OCFit.OCFit.AbsoluteParam(M, i = 90, M_err = 0, i_err = 0)`

Calculation of mass of the 3rd body and semi-mayor axes for models based on LiTE or Agol's models. If the function FitMCMC was used, the uncertainties will be also calculated. Obtained values are saved to variable paramsMore and errors to variable paramsMore_err.

Parameter	Type	Description
M	float	Mass of eclipsing binary.
i	float	Inclination of orbit of the 3rd body.
M_err	float	Uncertainty of mass of eclipsing binary.
i_err	float	Uncertainty of orbital inclination of the 3rd body.

Output	dictionary	Values of calculated parameters and errors.

ParamsApsidal

`OCFit.OCFit.ParamsApsidal()`

Calculation of other parameters of the system for the model of apsidal motion. If the function FitMCMC was used, the uncertainties will be also calculated. Obtained values are saved to variable paramsMore and errors to variable paramsMore_err.

Parameter	Type	Description

Output	dictionary	Values of calculated parameters and errors.

Plot

`OCFit.OCFit.Plot(name = None, no_plot = 0, no_plot_err = 0, params = None, eps = False, oc_min = True, time_type = 'JD', offset = 2400000, trans = True, title = None, epoch = False, min_type = False, weight = None, trans_weight = False, model2 = False, with_res = False, bw = False, double_ax = False, legend = None, fig_size = None)`

Plotting original values of O-C and curve of O-C calculated from the fit. It is possible to calculate model curve also for different values of parameters. Parameters are entered to params, it is a dictionary with parameters of the model. Eventually, it is possible to plot curve calculated from fitted values of parameters together with curve calculated from given set of parameters, set model2 = True to do this. In this case, green line is fitted model and red is given model.

It is possible to save the figure to png file (eventually also to eps) or only display it on the screen. Outlier points or points with big error could not be plotted. Values of O-C could be displayed in minutes or in days. It is possible to set different type of Julian date displayed on x-label. The date could be transformed by subtraction of given offset. If the date was already transformed before, it is necessary to disable transformation of x-values (trans = False) but the value of the used offset is suitable to set due to the label on the x-axis. It is also possible to use epochs on the x-axis or also have two axes with Julian dates and epochs together. In the case, if the values of O-C of primary and also secondary minima are available, it is possible to distinguish it using the parameter min_type = True. Primary minima are displayed be full circle and the secondary by an empty circle. If the weights of points are available, they could be shown on the figures by entering them to weight. Weights are divided into these categories: 0-3, 3-5, 5-8, 8-10. In the case, that the weights are not in this interval, it is necessary to transform them by setting trans_weight = True. If the errors of data points were set up during initialization of the class and now the weights are given to weight, there will be plotted figure on according to given weights without error bars.

Parameter	Type	Description
name	string, optional	Name of file (without extension) where the figure will be saved.
no_plot	integer, optional	Number of outlier points which will not be plotted.
no_plot_err	integer, optional	Number of points with the biggest errors which will not be plotted.
params	dictionary, optional	Parameters of the model.
eps	boolean, optional	Save figure also to eps file. (It is necessary to set the name to variable name!)
oc_min	boolean, optional	Values of O-C display in minutes, not in days.
time_type	string, optional	Type of Julian date (JD, HJD, BJD).
offset	float, optional	Value of offset of dates due to shortening values on x axis.
trans	boolean, optional	Transform x values by the offset.
title	string, optional	Title of the figure.
epoch	boolean, optional	Axis x in epochs.
min_type	boolean, optional	Distinguishing primary and secondary minima.
weight	numpy.array, optional	Weights of points.
trans_weight	boolean, optional	Transformation of weights to the range 0 – 10.
model2	boolean, optional	Plot model curve of O-C for given and fitted values of parameters.
bw	boolean, optional	Black and white figure.
double_ax	boolean, optional	Double x axis - dates + epochs.
with_res	boolean, optional	Common figure with residue.
legend	list, optional	List of labels for legend (give '', if the label could not be displayed; the 2nd model given trough params is the last one).
fig_size	tuple, optional	Custom figure size - e.g. (12,6).

PlotRes

`OCFit.OCFit.PlotRes(name = None, no_plot = 0, no_plot_err = 0, params = None, eps = False, oc_min = True, time_type = 'JD', offset = 2400000, trans = True, title = None, epoch = False, min_type = False, weight = None, trans_weight = False, bw = False, double_ax=False, fig_size = None)`

Plotting residue (new values of O-C) between original values of O-C and O-Cs calculated from the fit. It is possible to calculate residue also for different set of parameters. Parameters are entered to params, it is a dictionary with parameters of the model.

It is possible to save the figure to png file (eventually also to eps) or only display it on the screen. Outlier points or points with big error could not be plotted. Values of O-C could be displayed in minutes or in days. It is possible to set different type of Julian date displayed on x-label. The date could be transformed by subtraction of given offset. If the date was already transformed before, it is necessary to disable transformation of x-values (trans = False) but the value of the used offset is suitable to set due to the label on the x-axis. It is also possible to use epochs on the x-axis or also have two axes with Julian dates and epochs together. In the case, if the values of O-C of primary and also secondary minima are available, it is possible to distinguish it using the parameter min_type = True. Primary minima are displayed be full circle and the secondary by an empty circle. If the weights of points are available, they could be shown on the figures by entering them to weight. Weights are divided into these categories: 0-3, 3-5, 5-8, 8-10. In the case, that the weights are not in this interval, it is necessary to transform them by setting trans_weight = True. If the errors of data points were set up during initialization of the class and now the weights are given to weight, there will be plotted figure on according to given weights without error bars.

Parameter	Type	Description
name	string, optional	Name of file (without extension) where the figure will be saved.
no_plot	integer, optional	Number of outlier points which will not be plotted.
no_plot_err	integer, optional	Number of points with the biggest errors which will not be plotted.
params	dictionary, optional	Parameters of the model.
eps	boolean, optional	Save figure also to eps file. (It is necessary to set the name to variable name!)
oc_min	boolean, optional	Values of O-C display in minutes, not in days.
time_type	string, optional	Type of Julian date (JD, HJD, BJD).
offset	float, optional	Value of offset of dates due to shortening values on x axis.
trans	boolean, optional	Transform x values by the offset.
title	string, optional	Title of the figure.
epoch	boolean, optional	Axis x in epochs.
min_type	boolean, optional	Distinguishing primary and secondary minima.
weight	numpy.array, optional	Weights of points.
trans_weight	boolean, optional	Transformation of weights to the range 0 – 10.
bw	boolean, optional	Black and white figure.
double_ax	boolean, optional	Double x axis - dates + epochs.
fig_size	tuple, optional	Custom figure size - e.g. (12,6).

Save

`OCFit.OCFit.Save(path)`

Saving the parameters of the class OCFit to file. It is possible to use the class OCFitLoad or function Load for loading them, again.

Parameter	Type	Description
path	string	Name of the file to save parameters of the class.

Load

`OCFit.OCFit.Load(path)`

Loading the parameters of the class OCFit saved by function Save from the file. It is also possible to use the class OCFitLoad with the name of the file as only one input parameters. It includes all the functions of the class OCFit.

Parameter	Type	Description
path	string	Name of the file with saved parameters of the class.

SaveModel

`OCFit.OCFit.SaveModel(name, E_min = None, E_max = None, n = 1000, params = None, t0 = None, P = None)`

Saving the model curve of O-C calculated on the basis of the fit to file. It is possible to calculate the model curve also for a different set of parameters. Parameters are entered to params, it is a dictionary with parameters of the model. The data are in columns: observed times of minima, epochs, model values of O-C.

Parameter	Type	Description
name	string	Name of output file.
E_min	float, optional	Minimal epoch (if not given, minimal epoch of the data).
E_max	float, optional	Maximal epoch (if not given, maximal epoch of the data).
n	integer, optional	Number of points for calculation of model O-C.
params	dictionary, optional	Set of model parameters.
t0	float, optional	Time of reference minimum (necessary, if t0 is not in model).
P	float, optional	Period of system (necessary, if t0 is not in model).

SaveRes

`OCFit.OCFit.SaveRes(name, params = None, t0 = None, P = None, weight = None)`

The saving residue (new values of O-C) between original values of O-C and O-Cs calculated from the fit to file. It is possible to calculate residue also for the different set of parameters. Parameters are entered to params, it is a dictionary with parameters of the model. The data are in columns: observed times of minima, epochs, new values of O-C (residue), errors (if given) or weight (if given).

Parameter	Type	Description
name	string	Name of output file.
params	dictionary, optional	Set of model parameters.
t0	float, optional	Time of reference minimum (necessary, if t0 is not in model).
P	float, optional	Period of system (necessary, if t0 is not in model).
weight	numpy.array, optional	Weights of data points.

Example

from OCFit import OCFit, FitLinear

import numpy as np

#generating data

E = np.arange(0, 100, 1) #epochs

#simulation of observed times, LiTE with amplitude 72 min. and period 1125 d

P = 15

t0 = 1540

t = P*E + t0 + 0.05*np.sin(2*np.pi/(5*P)*E)+ np.random.normal(scale = 0.01, size = E.shape)

err = 0.01*np.ones(E.shape) #errors of 'observed' times

#usage of FitLinear for calculation of O-C

#initialization using estiamtion (original values) of linear ephemeris

#for long time range of observation, the value of period has to be close

#to the right value, otherwise the primary and secondary minims could be mixed

lin = FitLinear(t, t0, P, err = err)

oc = lin.oc #O-C calculated from original ephemeris

#WARNING! FitLinear sorts input data. "oc" is sorted now! Combination of

#sorted and unsorted data ("t", "err") leads to bad O-C diagram.

#Next to lines sort all data.

t = t[lin._order]

err = err[lin._order]

#initialization of class OCFit and O-C calculated using FitLinear

fit=OCFit(t,oc,err = err)

fit.Epoch(t0,P) #calculating epochs

#setting the model and parameters for fitting

fit.model='LiTE3'

fit.fit_params=['a_sin_i3', 'e3', 'w3', 't03', 'P3']

fit.limits={'a_sin_i3': [5, 10], 'e3': [0, 1], 'w3': [0, 2*np.pi],'t03': [1540, 3000], 'P3': [900, 1300]}

fit.steps={'a_sin_i3': 1e-2, 'e3': 1e-2, 'w3': 1e-2, ’t03’: 10, 'P3': 10}

#fitting using GA without displaying fitting progress

fit.FitGA(100,100,visible=False)

#sumarry of results after GA

fit.Summary()

#fitting using MCMC without displaying fitting progress

fit.FitMCMC(1e3,visible=False)

#sumarry of results after MC

fit.Summary()

#plotting figure

#figure with original O-C with fit without transformation of x axis

#together with residue and 2nd axis in epochs

fit.Plot(trans = False,with_res=True,double_ax=True)