qnm.nearby

Find a nearby root of the coupled radial/angular Teukolsky equations.

TODO Documentation.

Classes

NearbyRootFinder(*args, **kwargs)

Object to find and store results from simultaneous roots of radial and angular QNM equations, following the Leaver and Cook-Zalutskiy approach.

class qnm.nearby.NearbyRootFinder(*args, **kwargs)

Object to find and store results from simultaneous roots of radial and angular QNM equations, following the Leaver and Cook-Zalutskiy approach.

Parameters:

a: float [default: 0.]

Dimensionless spin of black hole, 0 <= a < 1.

s: int [default: -2]

Spin of field of interest

m: int [default: 2]

Azimuthal number of mode of interest

A_closest_to: complex [default: 4.+0.j]

Complex value close to desired separation constant. This is intended for tracking the l-number of a sequence starting from the analytically-known value at a=0

l_max: int [default: 20]

Maximum value of l to include in the spherical-spheroidal matrix for finding separation constant and mixing coefficients. Must be sufficiently larger than l of interest that angular spectral method can converge. The number of l’s needed for convergence depends on a.

omega_guess: complex [default: .5-.5j]

Initial guess of omega for root-finding

tol: float [default: sqrt(double epsilon)]

Tolerance for root-finding omega

cf_tol: float [defailt: 1e-10]

Tolerance for continued fraction calculation

n_inv: int [default: 0]

Inversion number of radial infinite continued fraction, which selects overtone number of interest

Nr: int [default: 300]

Truncation number of radial infinite continued fraction. Must be sufficiently large for convergence.

Nr_min: int [default: 300]

Floor for Nr (for dynamic control of Nr)

Nr_max: int [default: 4000]

Ceiling for Nr (for dynamic control of Nr)

r_N: complex [default: 1.]

Seed value taken for truncation of infinite continued fraction. UNUSED, REMOVE

Methods

__call__(x)	Internal function for usage with optimize.root, for an instance of this class to act like a function for root-finding.
clear_results()	Clears the stored results from last call of do_solve()
do_solve()	Try to find a root of the continued fraction equation, using the parameters that have been set in set_params().
get_cf_err()	Return the continued fraction error and the number of iterations in the last evaluation of the continued fraction.
set_params(*args, **kwargs)	Set the parameters for root finding.
set_poles([poles])	Set poles to multiply error function.

__call__(x)

Internal function for usage with optimize.root, for an instance of this class to act like a function for root-finding. optimize.root only works with reals so we pack and unpack complexes into float[2]

clear_results()

Clears the stored results from last call of do_solve()

do_solve()

Try to find a root of the continued fraction equation, using the parameters that have been set in set_params().

get_cf_err()

Return the continued fraction error and the number of iterations in the last evaluation of the continued fraction.

Returns:

cf_err: float

n_frac: int

set_params(*args, **kwargs)

Set the parameters for root finding. Parameters are described in the class documentation. Finally calls clear_results().

set_poles(poles=[])

Set poles to multiply error function.

Parameters:

poles: array_like as complex numbers [default: []]