synthpop.modules.initial_mass_function.piecewise_powerlaw
=========================================================

.. py:module:: synthpop.modules.initial_mass_function.piecewise_powerlaw

.. autoapi-nested-parse::

   Initial mass function for a piecewise power law, e.g.:
       
           For M ≤ m1:    ξ(M) ∝ M^-a0
           
           For m1 < M ≤ m2:    ξ(M) ∝ M^-a1
           
           For m2 < M:           ξ(M) ∝ M^-a2
           
   The number of splitpoints is modifiable.



Classes
-------

.. autoapisummary::

   synthpop.modules.initial_mass_function.piecewise_powerlaw.PiecewisePowerlaw


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

.. py:class:: PiecewisePowerlaw(min_mass=None, max_mass=None, alphas: tuple[float] = 1, splitpoints: tuple[float] = (), **kwargs)

   Bases: :py:obj:`synthpop.modules.initial_mass_function._initial_mass_function.InitialMassFunction`


   Initial mass function generator for a piecewise power law

   Attributes:
   -----------
   min_mass : float
       lower initial mass limit
   max_mass : float
       upper initial mass limit
   alphas : ndarray [float]
       power law indices for the mass chunks from lower mass to higher
   splitpoints : ndarray [float]
       mass values where pieces split;
       length must be length alphas minus 1


   .. py:attribute:: imf_name
      :value: 'Piecewise Powerlaw'



   .. py:attribute:: alphas
      :value: 1



   .. py:attribute:: splitpoints
      :value: ()



   .. py:method:: get_functions(alphas, splitpoints)


   .. py:method:: get_imf_parts(m_upper, m_lower, a, alpha)


   .. py:method:: get_F_parts(m_upper, m_lower, a, alpha) -> Callable


   .. py:method:: get_F_inv_parts(m_upper, m_lower, p_upper, p_lower, a, alpha)


   .. py:method:: imf(m_in)

      Initial mass function

      Parameters
      ----------
      m_in: initial mass

      Returns
      -------
      prob: probability at the initial mass




   .. py:method:: F_imf(m_in)

      Integral of the initial mass function from 0 to m_in

      Parameters
      ----------
      m_in: initial mass

      Returns
      -------
      F: integral




   .. py:method:: F_imf_inverse(p_in)

      Inverse of F_imf

      Parameters
      ----------
      p_in : cumulative likelihood

      Returns
      -------
      met



   .. py:attribute:: grid_max
      :value: 10000



   .. py:attribute:: grid_min
      :value: 0