PDF Functions

PDF fuctions for exoSpin :

ExoSpin - PDF important functions

@authors : I. Abdoulwahab & P. Palma-Bifani & G. Chauvin & A. Simonnin

pdf_functions.ip_complex_pdf(v_kde, vsini_kde, v_range, n)[source]

Evaluate the companion spin axis PDF by using M. Bryan et al. 2020 method.

Parameters:

  • v_kde (scipy.stats.gaussian_kde) – A 1D KDE of companion velocity.

  • vsini_kde (scipy.stats.gaussian_kde) – A 1D KDE of companion rotational velocity.

  • v_range (numpy.ndarray) – 1D array representing the domain where the velocities will be evaluated.

  • n (int) – Number of evaluated points.

Returns:

1D array representing the PDF of companion spin axis.

Return type:

(numpy.ndarray)

Raises:

ValueError – The number of evaluted points must be greater than 1 and v_range must be a 1D array.

pdf_functions.kde(data)[source]

From your data, the function returns a 1D Kernel Density Estimation.

Parameters:

data (numpy.ndarray) – A 1D array that contains the data that will be estimated.

Returns:

A 1D Kernel Density Estimation object.

Return type:

(scipy.stats.gaussian_kde)

Raises:

ValueError – If data are not a 1D array of if data is empty.

pdf_functions.pdf(kde, domain)[source]

Evaluate the Kernel Density Estimation (KDE) over a specified interval and return a normalized PDF.

Parameters:

  • kde (scipy.stats.gaussian_kde) – A 1D Kernel Density Estimation object.

  • domain (numpy.ndarray) – 1D array representing the domain where the KDE will be evaluated.

Returns:

1D array of KDE values evaluated at each point in the interval and normalized.

Return type:

(numpy.ndarray)

Raises:

ValueError – If interval is not a 1D array.

pdf_functions.proj_obli_complex_pdf(io_kde, ip_pdf, n)[source]

Evaluate the companion projected obliquity PDF.

Parameters:

  • io_kde (scipy.stats.gaussian_kde) – A 1D KDE of orbital inclination.

  • ip_pdf (numpy.ndarray) – 1D array of KDE evaluated values of the companion spin axis

  • n (int) – Number of evaluated points

Returns:

1D array representing the PDF of companion spin axis.

Return type:

(numpy.ndarray)

Raises:

ValueError – The number of evaluted points must be greater than 1

pdf_functions.true_obli_complex_pdf(io_pdf, ip_pdf, lambda_pdf, nb)[source]

Evaluate the companion true obliquity PDF.

Parameters:

  • io_pdf (numpy.ndarray) – 1D array of KDE evaluated values of the orbital inclination.

  • ip_pdf (numpy.ndarray) – 1D array of KDE evaluated values of the companion spin axis.

  • omega_o_pdf (numpy.ndarray) – 1D array of KDE evaluated values of the star inclination.

  • nb (int) – Number of evaluated points.

Returns:

1D array representing the PDF of companion true obliquity.

Return type:

(numpy.ndarray)

Raises:

ValueError – The number of evaluted points must be greater than 1.