reggae.asymptotic
=================

.. py:module:: reggae.asymptotic


Classes
-------

.. autoapisummary::

   reggae.asymptotic.asymptotic


Module Contents
---------------

.. py:class:: asymptotic

   .. py:method:: _pair(nu0, h, w, d02)

      Define a pair as the sum of two Lorentzians.

      A pair is assumed to consist of an l=0 and an l=2 mode. The widths are
      assumed to be identical, and the height of the l=2 mode is scaled
      relative to that of the l=0 mode. The frequency of the l=2 mode is the
      l=0 frequency minus the small separation.

      Parameters
      ----------
      nu0 : float
          Frequency of the l=0 (muHz).
      h : float
          Height of the l=0 (SNR).
      w : float
          The mode width (identical for l=2 and l=0) (log10(muHz)).
      d02 : float
          The small separation (muHz).

      Returns
      -------
      pair_model : array
          The SNR as a function of frequency of a mode pair.




   .. py:method:: _lor(nu0, h, w)

      Lorentzian to describe a mode.

      Parameters
      ----------
      nu0 : float
          Frequency of lorentzian (muHz).
      h : float
          Height of the lorentizan (SNR).
      w : float
          Full width of the lorentzian (muHz).

      Returns
      -------
      mode : ndarray
          The SNR as a function frequency for a lorentzian.




   .. py:method:: _get_nmax(dnu, numax, eps)

      Compute radial order at numax.

      Compute the radial order at numax, which in this implimentation of the
      asymptotic relation is not necessarily integer.

      Parameters
      ----------
      numax : float
          Frequency of maximum power of the p-mode envelope (muHz).
      dnu : float
          Large separation of l=0 modes (muHz).
      eps : float
          Epsilon phase term in asymptotic relation.

      Returns
      -------
          nmax : float
              non-integer radial order of maximum power of the p-mode envelope




   .. py:method:: _get_n_p(nmax)

      Compute radial order numbers.

      Get the enns that will be included in the asymptotic relation fit.
      These are all integer.

      Parameters
      ----------
      nmax : float
          Frequency of maximum power of the p-mode envelope.
      norders : int
          Total number of radial orders to consider.

      Returns
      -------
      enns : ndarray
              Numpy array of norders radial orders (integers) around nu_max
              (nmax).



   .. py:method:: _P_envelope(nu, hmax, numax, width)

      Power of the seismic p-mode envelope

      Computes the power at frequency nu in the p-mode envelope from a Gaussian
      distribution. Used for computing mode heights.

      Parameters
      ----------
      nu : float
          Frequency (muHz).
      hmax : float
          Height of p-mode envelope (SNR).
      numax : float
          Frequency of maximum power of the p-mode envelope (muHz).
      width : float
          Width of the p-mode envelope (muHz).

      Returns
      -------
      h : float
          Power at frequency nu (SNR)




   .. py:method:: _get_freq_range(numax)

      Get frequency range around numax for model

      Returns a boolean array corresponding to the frequency bins that span
      the p-mode envelope.

      The range is set to be -/+ Dnu from the lowest/heighest radial order.

      Parameters
      ----------
      numax : float
          Frequency of maximum power of the p-mode envelope (muHz).

      Returns
      -------
      idx : bool
          Boolean array pick out the frequency range of the p-mode envelope.



   .. py:method:: _asymptotic_relation(numax, dnu, eps, alpha)

      Compute the l=0 mode frequencies from the asymptotic relation for
      p-modes

      Parameters
      ----------
      numax : float
          Frequency of maximum power of the p-mode envelope (muHz).
      dnu : float
          Large separation of l=0 modes (muHz).
      eps : float
          Epsilon phase term in asymptotic relation (unitless).
      alpha : float
          Curvature factor of l=0 ridge (second order term, unitless).

      Returns
      -------
      nu0s : ndarray
          Array of l=0 mode frequencies from the asymptotic relation (muHz).



   .. py:method:: asymptotic_model(theta_asy)

      Constructs a spectrum model from the asymptotic relation.

      The asymptotic relation for p-modes with angular degree, l=0, is
      defined as:

      $nu_nl = (n + \epsilon + lpha/2(n - nmax)^2) * \log{dnu}$ ,

      where nmax = numax / dnu - epsilon.

      We separate the l=0 and l=2 modes by the small separation d02.

      Parameters
      ----------
      dnu : float
          Large separation log10(muHz)
      lognumax : float
          Frequency of maximum power of the p-mode envelope log10(muHz)
      eps : float
          Phase term of the asymptotic relation (unitless)
      alpha : float
          Curvature of the asymptotic relation log10(unitless)
      d02 : float
          Small separation log10(muHz)
      loghmax : float
          Gaussian height of p-mode envelope log10(SNR)
      logenvwidth : float
          Gaussian width of the p-mode envelope log10(muHz)
      logmodewidth : float
          Width of the modes (log10(muHz))
      *args : array-like
          List of additional parameters (Teff, bp_rp) that aren't actually
          used to construct the spectrum model, but just for evaluating the
          prior.

      Returns
      -------
      model : ndarray
          spectrum model around the p-mode envelope