pyseobnr.eob.dynamics.initial_conditions_aligned_ecc_opt.find_root_cons

pyseobnr.eob.dynamics.initial_conditions_aligned_ecc_opt.find_root_cons(z: tuple[float, float] | list[float] | np.array, pr_star: float, dot_prstar: float, m_1: float, m_2: float, chi_1: float, chi_2: float, omega_inst: float, H: Hamiltonian, count: int = 0) → tuple[float, float, bool, int]

Finds the roots for the conservative equations. First, the function tries with the root-finding method ‘hybr’ with a ‘factor’ of 0.01 to avoid giving large steps in the root-finding procedure. If this is not successful, then tries the other available methods. This function is useful when the root-solver struggles to find a solution.

Parameters:

• z (tuple) – 2-uple containing the unknowns r and pphi

• pr_star (float) – Radial momentum in tortoise coordinates

• dot_prstar (float) – Time derivative of the radial momentum in tortoise coordinates

• m_1 (float) – Mass of the primary

• m_2 (float) – Mass of the secondary

• chi_1 (float) – z-component of the dimensionless spin vector of the primary

• chi_2 (float) – z-component of the dimensionless spin vector of the secondary

• omega_inst (float) – Desired starting instantaneous orbital frequency, in geometric units

• H (Hamiltonian) – The Hamiltonian to use (an instance of Hamiltonian class)

• count (int) – Counter of attempts to find solutions for the initial conditions

Returns:

(r, pphi, successful_root, count). The initial conditions: (r, pphi),

whether there was a successful root (successful_root) and the number of attempts to find the solution (count)

Return type:

tuple