healpix_analyse.alm

Attributes

ArrayLike

Classes

AlmCoeffs	Container for local complex spherical harmonic coefficients.
AlmTransform	Local FFT-oriented spherical harmonic transform on a HEALPix patch.

Module Contents

healpix_analyse.alm.ArrayLike

class healpix_analyse.alm.AlmCoeffs

Container for local complex spherical harmonic coefficients.

Parameters:

• alm (torch.Tensor) – Complex coefficient tensor with shape [K] or [B, K].

• l (torch.Tensor) – Degree indices with shape [K].

• m (torch.Tensor) – Order indices with shape [K]. Only m >= 0 is stored in V1.

• meta (dict) – Metadata associated with the transform.

alm: torch.Tensor

l: torch.Tensor

m: torch.Tensor

meta: Dict[str, Any]

property n_modes: int

property is_batched: bool

clone() → AlmCoeffs

to(device: str | torch.device | None = None, dtype: torch.dtype | None = None) → AlmCoeffs

cpu() → AlmCoeffs

cuda() → AlmCoeffs

class healpix_analyse.alm.AlmTransform(cell_ids: ArrayLike, level: int, indexing_scheme: str = '2D_array', ellipsoid: str = 'sphere', method: str = 'fft', dtype: torch.dtype = torch.float32, device: str | torch.device | None = None, debug: bool = False, lon: numpy.ndarray = None, lat: numpy.ndarray = None, weights: numpy.array = None)

Local FFT-oriented spherical harmonic transform on a HEALPix patch.

This implementation follows a two-stage local solver:

1. local Fourier analysis on each observed iso-latitude ring,

2. local Legendre analysis over the observed ring colatitudes.

The design avoids explicit dense Y_lm evaluation over all pixels. It is intended as a practical starting point for large local patches and keeps only m >= 0 coefficients.

Parameters:

• level (int) – HEALPix level such that nside = 2**level.

• cell_ids (array-like) – HEALPix cell identifiers at the given level.

• indexing_scheme (str, default "ring") – The indexing scheme for the cell IDs.

• ellipsoid ({"sphere", "WGS84"}, default "sphere") – Geometry model.

• method ({"fft", "alm"}, default "fft", Alm approximation, alm option under development.) – Analysis mode used in the Legendre stage.

• dtype (torch.dtype, default torch.float32) – Real dtype for maps and geometry.

• device (str or torch.device, optional) – Execution device. If None, uses CUDA when available, else CPU.

• debug (bool, default False) – Whether to store diagnostic timing information.

Notes

Current assumptions: - all input cells are at the same HEALPix level, - reconstruction is only performed on the same input cells, - input maps are real-valued.

level

indexing_scheme = ''

ellipsoid = ''

method = ''

dtype = Ellipsis

cdtype = Ellipsis

device

debug = False

cell_ids

pixel_shift

phase_shift

compute_phase_shift(x0, dim=-1)

Applique un décalage spatial x0 à un signal via sa FFT déjà calculée.

Parameters:

• x0 (float or torch.Tensor) – Décalage à appliquer dans l’espace réel. Convention: f(x - x0) <-> F(k) * exp(-i 2π k x0)

• dim (int) – Dimension correspondant à la FFT 1D.

Returns:

torch.Tensor – Facteur de phase.

fft(data_: ArrayLike, pbc: bool = True) → ArrayLike

abstractmethod ifft(data: ArrayLike) → ArrayLike

Reconstruct a map on the same local HEALPix cells.

Not implemented yet. The inverse needs the Legendre-projection stage that fft() does not currently compute (see the TODO next to its second FFT stage), and relies on ring bookkeeping (self.n_rings, self.idx_ring, self.weights, self.xa, self.N_k) that __init__ does not currently set. Rather than fail on a missing attribute or silently return a wrong map, this raises explicitly until that work lands.