gwkokab.utils.transformations
=============================

.. py:module:: gwkokab.utils.transformations


Functions
---------

.. autoapisummary::

   gwkokab.utils.transformations.Mc_eta_to_m1_m2
   gwkokab.utils.transformations.cart_to_polar
   gwkokab.utils.transformations.cart_to_spherical
   gwkokab.utils.transformations.chi_costilt_to_chiz
   gwkokab.utils.transformations.chi_p_from_components
   gwkokab.utils.transformations.chieff
   gwkokab.utils.transformations.chirp_mass
   gwkokab.utils.transformations.chirp_mass_from_m1_q
   gwkokab.utils.transformations.delta_m
   gwkokab.utils.transformations.delta_m_to_symmetric_mass_ratio
   gwkokab.utils.transformations.eta_from_q
   gwkokab.utils.transformations.log_chirp_mass
   gwkokab.utils.transformations.m1_m2_chi1_chi2_costilt1_costilt2_to_chieff
   gwkokab.utils.transformations.m1_m2_chi1_chi2_costilt1_costilt2_to_chiminus
   gwkokab.utils.transformations.m1_m2_chi1z_chi2z_to_chiminus
   gwkokab.utils.transformations.m1_m2_chieff_chiminus_to_chi1z_chi2z
   gwkokab.utils.transformations.m1_q_to_m2
   gwkokab.utils.transformations.m1_times_m2
   gwkokab.utils.transformations.m2_q_to_m1
   gwkokab.utils.transformations.m_det_z_to_m_source
   gwkokab.utils.transformations.m_source_z_to_m_det
   gwkokab.utils.transformations.mass_ratio
   gwkokab.utils.transformations.polar_to_cart
   gwkokab.utils.transformations.q_from_eta
   gwkokab.utils.transformations.reduced_mass
   gwkokab.utils.transformations.sin_tilt
   gwkokab.utils.transformations.spherical_to_cart
   gwkokab.utils.transformations.spin_costilt_from_components
   gwkokab.utils.transformations.spin_magnitude_from_components
   gwkokab.utils.transformations.symmetric_mass_ratio
   gwkokab.utils.transformations.symmetric_mass_ratio_to_delta_m
   gwkokab.utils.transformations.total_mass


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

.. py:function:: Mc_eta_to_m1_m2(Mc: jaxtyping.ArrayLike, eta: jaxtyping.ArrayLike) -> tuple[jaxtyping.ArrayLike, jaxtyping.ArrayLike]

   .. math::
       \begin{align*}
           m_1(M_c, \eta) &= \frac{M_c}{2} \eta^{-0.6} (1 + \sqrt{1 - 4\eta}) \\
           m_2(M_c, \eta) &= \frac{M_c}{2} \eta^{-0.6} (1 - \sqrt{1 - 4\eta})
       \end{align*}


.. py:function:: cart_to_polar(x: jaxtyping.ArrayLike, y: jaxtyping.ArrayLike) -> tuple[jaxtyping.ArrayLike, jaxtyping.ArrayLike]

   .. math::
       \begin{align*}
           r(x, y) &= \sqrt{x^2 + y^2} \\
           \theta(x, y) &= \arctan(y/x)
       \end{align*}


.. py:function:: cart_to_spherical(x: jaxtyping.ArrayLike, y: jaxtyping.ArrayLike, z: jaxtyping.ArrayLike) -> tuple[jaxtyping.ArrayLike, jaxtyping.ArrayLike, jaxtyping.ArrayLike]

   .. math::
       \begin{align*}
           r(x, y, z) &= \sqrt{x^2 + y^2 + z^2} \\
           \theta(x, y, z) &= \arccos\left(\frac{z}{r}\right) \\
           \phi(x, y, z) &= \arctan\left(\frac{y}{x}\right)
       \end{align*}


.. py:function:: chi_costilt_to_chiz(chi: jaxtyping.ArrayLike, costilt: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       \chi_z(\chi, \cos(\theta)) = \chi \cos(\theta)


.. py:function:: chi_p_from_components(a_1: jaxtyping.ArrayLike, cos_tilt_1: jaxtyping.ArrayLike, a_2: jaxtyping.ArrayLike, cos_tilt_2: jaxtyping.ArrayLike, mass_ratio: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       \chi_p(a_1, \cos(\theta_1), a_2, \cos(\theta_2), q) =
       \max \left(
           a_1 \sin(\theta_1),
           \frac{3 + 4q}{4 + 3q} q a_2 \sin(\theta_2)
       \right)


.. py:function:: chieff(m1: jaxtyping.ArrayLike, m2: jaxtyping.ArrayLike, chi1z: jaxtyping.ArrayLike, chi2z: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       \chi_{\text{eff}}(m_1, m_2, \chi_{1z}, \chi_{2z}) = \frac{m_1\chi_{1z} + m_2\chi_{2z}}{m_1 + m_2}


.. py:function:: chirp_mass(m1: jaxtyping.ArrayLike, m2: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       M_c(m_1, m_2) = \frac{(m_1m_2)^{3/5}}{(m_1 + m_2)^{1/5}}


.. py:function:: chirp_mass_from_m1_q(m1: jaxtyping.ArrayLike, q: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       M_c(m_1, q) = \frac{(m_1^3 q^3)^{1/5}}{(m_1 + m_1 q)^{1/5}} = m_1 \frac{q^{3/5}}{(1 + q)^{1/5}}


.. py:function:: delta_m(m1: jaxtyping.ArrayLike, m2: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       \delta_m(m_1, m_2) = \frac{m_1 - m_2}{m_1 + m_2}


.. py:function:: delta_m_to_symmetric_mass_ratio(delta_m: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       \eta(\delta_m) = \frac{1 - \delta_m^2}{4}


.. py:function:: eta_from_q(q: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       \eta(q) = \frac{q}{(1 + q)^2}


.. py:function:: log_chirp_mass(m1: jaxtyping.ArrayLike, m2: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       \log(M_c(m_1, m_2)) = 3/5\times (\log(m_1) + \log(m_2)) - \log(m_1 + m_2)/5


.. py:function:: m1_m2_chi1_chi2_costilt1_costilt2_to_chieff(*, m1: jaxtyping.ArrayLike, m2: jaxtyping.ArrayLike, chi1: jaxtyping.ArrayLike, chi2: jaxtyping.ArrayLike, costilt1: jaxtyping.ArrayLike, costilt2: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       \chi_{\text{eff}}(m_1, m_2, \chi_1, \chi_2, \cos(\theta_1), \cos(\theta_2)) =
       \frac{m_1\chi_1\cos(\theta_1) + m_2\chi_2\cos(\theta_2)}{m_1 + m_2}


.. py:function:: m1_m2_chi1_chi2_costilt1_costilt2_to_chiminus(*, m1: jaxtyping.ArrayLike, m2: jaxtyping.ArrayLike, chi1: jaxtyping.ArrayLike, chi2: jaxtyping.ArrayLike, costilt1: jaxtyping.ArrayLike, costilt2: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       \chi_{\text{minus}}(m_1, m_2, \chi_1, \chi_2, \cos(\theta_1), \cos(\theta_2)) =
       \frac{m_1\chi_1\cos(\theta_1) - m_2\chi_2\cos(\theta_2)}{m_1 + m_2}


.. py:function:: m1_m2_chi1z_chi2z_to_chiminus(m1: jaxtyping.ArrayLike, m2: jaxtyping.ArrayLike, chi1z: jaxtyping.ArrayLike, chi2z: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       \chi_{\text{minus}}(m_1, m_2, \chi_{1z}, \chi_{2z}) = \frac{m_1\chi_{1z} - m_2\chi_{2z}}{m_1 + m_2}


.. py:function:: m1_m2_chieff_chiminus_to_chi1z_chi2z(m1: jaxtyping.ArrayLike, m2: jaxtyping.ArrayLike, chieff: jaxtyping.ArrayLike, chiminus: jaxtyping.ArrayLike) -> tuple[jaxtyping.ArrayLike, jaxtyping.ArrayLike]

   .. math::
       \begin{align*}
       \chi_{1z}(m_1, m_2, \chi_{\text{eff}}, \chi_{\text{minus}}) &=
       \frac{m_1+m_2}{2m_1} \left( \chi_{\text{eff}} + \chi_{\text{minus}} \right)\\
       \chi_{2z}(m_1, m_2, \chi_{\text{eff}}, \chi_{\text{minus}}) &=
       \frac{m_1+m_2}{2m_2} \left( \chi_{\text{eff}} - \chi_{\text{minus}} \right)
       \end{align*}


.. py:function:: m1_q_to_m2(m1: jaxtyping.ArrayLike, q: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       m_2(m_1, q) = m_1q


.. py:function:: m1_times_m2(m1: jaxtyping.ArrayLike, m2: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       m_1m_2(m_1, m_2) = m_1 m_2


.. py:function:: m2_q_to_m1(m2: jaxtyping.ArrayLike, q: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       m_1(m_2, q) = \frac{m_2}{q}


.. py:function:: m_det_z_to_m_source(m_det: jaxtyping.ArrayLike, z: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       m_{\text{source}}(m_{\text{det}}, z) = \frac{m_{\text{det}}}{1 + z}


.. py:function:: m_source_z_to_m_det(m_source: jaxtyping.ArrayLike, z: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       m_{\text{det}}(m_{\text{source}}, z) = m_{\text{source}}(1 + z)


.. py:function:: mass_ratio(m1: jaxtyping.ArrayLike, m2: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       q(m_1, m_2) = \frac{m_2}{m_1}


.. py:function:: polar_to_cart(r: jaxtyping.ArrayLike, theta: jaxtyping.ArrayLike) -> tuple[jaxtyping.ArrayLike, jaxtyping.ArrayLike]

   .. math::
       \begin{align*}
           x(r, \theta) &= r \cos(\theta) \\
           y(r, \theta) &= r \sin(\theta)
       \end{align*}


.. py:function:: q_from_eta(eta: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math ::
       q(\eta) = \frac{1 - 2\eta - \sqrt{1 - 4\eta}}{2\eta}

   :param eta: Symmetric mass ratio
   :type eta: ArrayLike

   :returns: Mass ratio
   :rtype: ArrayLike


.. py:function:: reduced_mass(m1: jaxtyping.ArrayLike, m2: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       M_r(m_1, m_2) = \frac{m_1m_2}{m_1 + m_2}


.. py:function:: sin_tilt(costilt: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       \sin(\theta) = \sqrt{1 - \cos^2(\theta)}


.. py:function:: spherical_to_cart(r: jaxtyping.ArrayLike, theta: jaxtyping.ArrayLike, phi: jaxtyping.ArrayLike) -> tuple[jaxtyping.ArrayLike, jaxtyping.ArrayLike, jaxtyping.ArrayLike]

   .. math::
       \begin{align*}
           x(r, \theta, \phi) &= r \sin(\theta) \cos(\phi) \\
           y(r, \theta, \phi) &= r \sin(\theta) \sin(\phi) \\
           z(r, \theta, \phi) &= r \cos(\theta)
       \end{align*}


.. py:function:: spin_costilt_from_components(chi_x: jaxtyping.ArrayLike, chi_y: jaxtyping.ArrayLike, chi_z: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       \cos(\theta)(\chi_x, \chi_y, \chi_z) = \frac{\chi_z}{\sqrt{\chi_x^2 + \chi_y^2 + \chi_z^2}}


.. py:function:: spin_magnitude_from_components(chi_x: jaxtyping.ArrayLike, chi_y: jaxtyping.ArrayLike, chi_z: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       \chi(\chi_x, \chi_y, \chi_z) = \sqrt{\chi_x^2 + \chi_y^2 + \chi_z^2}


.. py:function:: symmetric_mass_ratio(m1: jaxtyping.ArrayLike, m2: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       \eta(m_1, m_2) = \frac{m_1m_2}{(m_1 + m_2)^2}


.. py:function:: symmetric_mass_ratio_to_delta_m(eta: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       \delta_m(\eta) = \sqrt{1 - 4\eta}


.. py:function:: total_mass(m1: jaxtyping.ArrayLike, m2: jaxtyping.ArrayLike) -> jaxtyping.ArrayLike

   .. math::
       M(m_1, m_2) = m_1 + m_2