gwkokab.models.redshift
=======================

.. py:module:: gwkokab.models.redshift


Classes
-------

.. autoapisummary::

   gwkokab.models.redshift.MadauDickinsonRedshiftModel
   gwkokab.models.redshift.PowerlawRedshiftModel


Package Contents
----------------

.. py:class:: MadauDickinsonRedshiftModel(z_max: jax.Array, kappa: jax.Array, gamma: jax.Array, z_peak: jax.Array, *, validate_args: Optional[bool] = None)

   Bases: :py:obj:`_RedshiftModel`


   Redshift distribution for compact binary mergers modeled after the Madau-
   Dickinson star formation rate, modulated by the cosmological volume element.

   The probability density function is defined as:

   .. math::
       p(z) \propto \frac{dV_c/dz(z) \cdot (1 + z)^{\kappa - 1}}{1 + \left(\\frac{1 + z}{1 + z_{peak}}\right)^{\gamma}}, \
       \qquad 0 \leq z \leq z_{max}

   where:
     - dV_c/dz is the differential comoving volume element,
     - gamma is the high-redshift slope,
     - kappa is the low-redshift slope,
     - z_max is the upper redshift cutoff.
     - z_peak is the redshift at which the merger rate peaks,

   This distribution is normalized numerically on a fixed redshift grid.


   .. py:method:: log_psi_of_z(z: jax.Array) -> jax.Array

      Evaluate the psi function at a given redshift.

      .. math::

          \ln\psi(z) = \kappa \ln(1 + z) + \ln\left(1 + (1 + z_{peak})^{\gamma}\right)
          - \ln\left((1 + z_{peak})^{\gamma} + (1 + z)^{\gamma}\right)

      :param z: Redshift(s) to evaluate.
      :type z: ArrayLike

      :returns: Values of the psi function.
      :rtype: ArrayLike



.. py:class:: PowerlawRedshiftModel(z_max: jax.Array, kappa: jax.Array, *, validate_args: Optional[bool] = None)

   Bases: :py:obj:`_RedshiftModel`


   Redshift distribution for compact binary mergers modeled as a power law modulated
   by the cosmological volume element.

   The probability density function is defined as:

   .. math::
       p(z) \propto \frac{dV_c/dz(z) \cdot (1 + z)^{\kappa - 1}}}, \qquad 0 \leq z \leq z_{max}

   where:
     - dV_c/dz is the differential comoving volume element,
     -  is the redshift evolution power-law index,
     - z_max is the upper redshift cutoff.

   This distribution is normalized numerically on a fixed redshift grid.

   :param kappa: The power-law exponent :math:`\kappa`.
   :type kappa: float
   :param z_max: The maximum redshift (upper limit of the support).
   :type z_max: float


   .. py:method:: log_psi_of_z(z: jax.Array) -> jax.Array

      Evaluate the psi function at a given redshift.

      .. math::

          \ln\psi(z) = \kappa \ln(1 + z)

      :param z: Redshift(s) to evaluate.
      :type z: ArrayLike

      :returns: Values of the psi function.
      :rtype: ArrayLike