import jax
jax.config.update("jax_enable_x64", True)
def _rho_xx(p_xx, p_xy, p_xz, p_x0, p_yy, p_yz, p_y0, p_zz, p_z0, p_00):
return p_xx - p_xz**2 / (4.0 * p_zz)
def _rho_xy(p_xx, p_xy, p_xz, p_x0, p_yy, p_yz, p_y0, p_zz, p_z0, p_00):
return p_xy - (p_xz * p_yz) / (2.0 * p_zz)
def _rho_x0(p_xx, p_xy, p_xz, p_x0, p_yy, p_yz, p_y0, p_zz, p_z0, p_00):
return p_x0 - (p_xz * p_z0) / (2.0 * p_zz)
def _rho_yy(p_xx, p_xy, p_xz, p_x0, p_yy, p_yz, p_y0, p_zz, p_z0, p_00):
return p_yy - p_yz**2 / (4.0 * p_zz)
def _rho_y0(p_xx, p_xy, p_xz, p_x0, p_yy, p_yz, p_y0, p_zz, p_z0, p_00):
return p_y0 - (p_yz * p_z0) / (2.0 * p_zz)
def _rho_00(p_xx, p_xy, p_xz, p_x0, p_yy, p_yz, p_y0, p_zz, p_z0, p_00):
return p_00 - p_z0**2 / (4.0 * p_zz)
[docs]
@jax.jit
def planet_2d_coeffs(
p_xx, p_xy, p_xz, p_x0, p_yy, p_yz, p_y0, p_zz, p_z0, p_00, **kwargs
):
"""Compute the coefficients that describe the planet as an implicit 2D surface from the
observer's perspective.
This function transforms the coefficients that describe the planet's 3D shape into
a new set of coefficients that describe its projected outline as seen from
z=infinity. The input p coefficients satisfy the equation:
.. math::
p_{xx} x^2 + p_{xy} xy + p_{xz} xz + p_{x0} x + p_{yy} y^2 + p_{yz} yz + p_{y0} y + p_{zz} z^2 + p_{z0} z + p_{00} = 1
Args:
p_xx (Array): Coefficient representing xx interaction in the 3D model.
p_xy (Array): Coefficient representing xy interaction in the 3D model.
p_xz (Array): Coefficient representing xz interaction in the 3D model.
p_x0 (Array): Coefficient representing x0 interaction in the 3D model.
p_yy (Array): Coefficient representing yy interaction in the 3D model.
p_yz (Array): Coefficient representing yz interaction in the 3D model.
p_y0 (Array): Coefficient representing y0 interaction in the 3D model.
p_zz (Array): Coefficient representing zz interaction in the 3D model.
p_z0 (Array): Coefficient representing z0 interaction in the 3D model.
p_00 (Array): Coefficient representing 00 interaction in the 3D model.
**kwargs: Unused additional keyword arguments. These are included to allow for
flexibility in providing additional data that may be ignored during the
computation but included for interface consistency.
Returns:
dict:
A dictionary with keys representing different transformed coefficient
names ('rho_xx', 'rho_xy', 'rho_x0', 'rho_yy', 'rho_y0', 'rho_00') and
their corresponding values. These coefficients describe the outline of the
planet as an implicit curve that satisfies the equation:
.. math::
\\rho_{xx} x^2 + \\rho_{xy} xy + \\rho_{x0} x + \\rho_{yy} y^2 + \\rho_{y0} y + \\rho_{00} = 1
"""
return {
"rho_xx": _rho_xx(p_xx, p_xy, p_xz, p_x0, p_yy, p_yz, p_y0, p_zz, p_z0, p_00),
"rho_xy": _rho_xy(p_xx, p_xy, p_xz, p_x0, p_yy, p_yz, p_y0, p_zz, p_z0, p_00),
"rho_x0": _rho_x0(p_xx, p_xy, p_xz, p_x0, p_yy, p_yz, p_y0, p_zz, p_z0, p_00),
"rho_yy": _rho_yy(p_xx, p_xy, p_xz, p_x0, p_yy, p_yz, p_y0, p_zz, p_z0, p_00),
"rho_y0": _rho_y0(p_xx, p_xy, p_xz, p_x0, p_yy, p_yz, p_y0, p_zz, p_z0, p_00),
"rho_00": _rho_00(p_xx, p_xy, p_xz, p_x0, p_yy, p_yz, p_y0, p_zz, p_z0, p_00),
}
