waveformtools.spherical

Methods to handle functions on a sphere.

Functions

decompose_in_SWSHs(waveform, gridinfo[, ...])

Decompose a given function on a sphere in Spin Weighted Spherical Harmonics

quad_on_sphere(integrand, gridinfo[, kind])

Integrate on a sphere using the scipy.quad method

waveformtools.spherical.decompose_in_SWSHs(waveform, gridinfo, spin_weight=- 2, ell_max=8, emm_list='all')[source]

Decompose a given function on a sphere in Spin Weighted Spherical Harmonics

Parameters:
waveform: list

A list that contains as its items the waveform defined on the sphere as an array of shape [ntheta, nphi]. Each item in the list may denote an instant of time or frequency.

spin_weight: int, optional

The spin weight of the waveform. It defaults to -2 for a gravitational waveform.

ell_max: int, optional

The maximum value of the :math:`ell’ polar quantum number. Defaults to 6=8.

gridinfo: class instance

The class instance that contains the properties of the spherical grid.

Returns:
SWSH_coeffs: list

The SWSH coefficients of the waveform. It may be a list composed of a single floating point number or a 1d array (denoting time or frequency dimension). The waveform can have angular as well as time dimentions. The nesting order will be that, given the list `non_boosted_waveform’, each item refers to a one dimensional array in time/ frequency of SWSH coefficients.

Notes

Assumes that the sphere on which this decomposition is carried out is so far out that the coordinate system is spherical polar and the poper area is the same as its co-ordinate area.

waveformtools.spherical.quad_on_sphere(integrand, gridinfo, kind='third')[source]

Integrate on a sphere using the scipy.quad method

Parameters:
integrand: 2d array

The two dimensional integrand array defined on the sphere.

info: class instance

The class instance that contains the properties of the spherical grid.

kind: str

The interpolation order to use in integration.

Returns
——-
final_integralfloat

The given integrand integrated over the sphere.

final_errs: float

The accumulated errors.

Notes

Assumes that the sphere is a unit round sphere.