Module `sleplet.functions.coefficients`

Contains the abstract Coefficients class.

Classes

class Coefficients (*args: Any, **kwargs: Any)

Abstract parent class to handle harmonic/Slepian coefficients on the sphere.

Subclasses

Instance variables

var L : int: The type of the None singleton.
var coefficients : numpy.ndarray[tuple[int, ...], numpy.dtype[numpy.complex128 | numpy.float64]]: The type of the None singleton.
var extra_args : list[int] | None: The type of the None singleton.
var name : str: The type of the None singleton.
var noise : float | None: The type of the None singleton.
var reality : bool: The type of the None singleton.
var region : Region | None: The type of the None singleton.
var smoothing : int | None: The type of the None singleton.
var snr : float | None: The type of the None singleton.
var spin : int: The type of the None singleton.
var wavelet_coefficients : numpy.ndarray[tuple[int, ...], numpy.dtype[numpy.complex128 | numpy.float64]]: The type of the None singleton.
var wavelets : numpy.ndarray[tuple[int, ...], numpy.dtype[numpy.complex128 | numpy.float64]]: The type of the None singleton.

Methods

def convolve(self: Self, f_coefficient: numpy.ndarray[tuple[int, ...], numpy.dtype[numpy.complex128 | numpy.float64]], g_coefficient: numpy.ndarray[tuple[int, ...], numpy.dtype[numpy.complex128 | numpy.float64]], *, shannon: int | None = None) ‑> numpy.ndarray[tuple[int, ...], numpy.dtype[numpy.complex128 | numpy.float64]]

Perform the sifting convolution of the two inputs.

Args

f_coefficient: Input harmonic/Slepian coefficients.
g_coefficient: Input harmonic/Slepian coefficients.
shannon: The Shannon number, only used in the Slepian case.

Returns

The sifting convolution of the two inputs.

def rotate(self: Self, alpha: float, beta: float, *, gamma: float = 0) ‑> numpy.ndarray[tuple[int, ...], numpy.dtype[numpy.complex128]]

Rotates given flm on the sphere by alpha/beta/gamma.

Args

alpha: The third Euler angle, a $\alpha$ rotation about the z-axis.
beta: The second Euler angle, a $\beta$ rotation about the y-axis.
gamma: The first Euler angle, a $\gamma$ rotation about the z-axis.

Returns

The rotated spherical harmonic coefficients.

def translate(self: Self, alpha: float, beta: float, *, shannon: int | None = None) ‑> numpy.ndarray[tuple[int, ...], numpy.dtype[numpy.complex128 | numpy.float64]]

Perform the translation of the coefficients, used in the sifting convolution.

Args

alpha: The point on the 2-sphere to translate to, i.e. the $\phi$ value.
beta: The point on the 2-sphere to translate to, i.e. the $\theta$ value.
shannon: The Shannon number, only used in the Slepian case.

Returns

The translated spherical harmonic coefficients.