Module `sleplet.slepian_methods`

Methods to work with Slepian coefficients.

Functions

def choose_slepian_method(L: int, region: Region) ‑> SlepianFunctions

Initialise Slepian object depending on input.

Args

L: The spherical harmonic bandlimit.
region: The Slepian region.

Raises

ValueError: Invalid region_type, likely cause is invalid mask_name.

Returns

The given Slepian object.

def compute_s_p_omega(L: int, slepian: SlepianFunctions) ‑> numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128]]

Compute $S_{p}(\omega)$ for a given region.

Args

L: The spherical harmonic bandlimit.
slepian: The given Slepian object.

Returns

The complex $S_{p}(\omega)$ values.

def slepian_forward(L: int, slepian: SlepianFunctions, *, f: numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128]] | None = None, flm: numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]] | None = None, mask: numpy.ndarray[typing.Any, numpy.dtype[numpy.float64]] | None = None, n_coeffs: int | None = None) ‑> numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128]]

Compute the Slepian forward transform for all coefficients.

Args

L: The spherical harmonic bandlimit.
slepian: The given Slepian object.
f: The field value.
flm: The spherical harmonic coefficients.
mask: A boolean mask of the Slepian region.
n_coeffs: The number of Slepian coefficients to use.

Returns

The Slepian coefficients of the inputs.

def slepian_inverse(f_p: numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]], L: int, slepian: SlepianFunctions) ‑> numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128]]

Compute the Slepian inverse transform up to the Shannon number.

Args

f_p: The Slepian coefficients.
L: The spherical harmonic bandlimit.
slepian: The given Slepian object.

Returns

The values on the sphere in pixel space.

def slepian_mesh_forward(mesh_slepian: MeshSlepian, *, u: numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]] | None = None, u_i: numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]] | None = None, mask: bool = False, n_coeffs: int | None = None) ‑> numpy.ndarray[typing.Any, numpy.dtype[numpy.float64]]

Compute the Slepian forward transform for all coefficients on the mesh.

Args

mesh_slepian: The Slepian mesh object containing the eigensolutions.
u: The signal field value on the mesh.
u_i: The Fourier coefficients of the mesh.
mask: Whether to use the mask to compute the coefficients.
n_coeffs: The number of Slepian coefficients to use.

Returns

The Slepian coefficients on the mesh.

def slepian_mesh_inverse(mesh_slepian: MeshSlepian, f_p: numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]) ‑> numpy.ndarray[typing.Any, numpy.dtype[numpy.complex128 | numpy.float64]]

Compute the Slepian inverse transform on the mesh up to the Shannon number.

Args

mesh_slepian: The Slepian mesh object containing the eigensolutions.
f_p: The Slepian wavelet coefficients.

Returns

The value of a function on the mesh in pixel space.