torch_harmonics.random_fields.GaussianRandomFieldS2#

class torch_harmonics.random_fields.GaussianRandomFieldS2(
nlat,
alpha=2.0,
tau=3.0,
sigma=None,
radius=1.0,
grid='equiangular',
dtype=torch.float32,
)[source]#

Bases: Module

Gaussian random field on the sphere via Karhunen–Loève expansion.

Samples realisations of a centred Gaussian random field on \(S^2\) whose covariance operator has the Matérn-like power spectrum

\[C_l = \sigma^2 \left(\frac{l(l+1)}{R^2} + \tau^2\right)^{-\alpha}\]

where \(l\) is the spherical harmonic degree. The field is generated by drawing i.i.d. standard-normal spectral coefficients, scaling them by \(\sqrt{C_l}\), and transforming to the spatial domain with an inverse SHT.

Larger alpha produces smoother fields (steeper spectral roll-off); tau controls the transition scale between the flat low-\(l\) plateau and the power-law decay.

Parameters:

  • nlat (int) – Number of latitudinal grid points (nlon is set to 2 * nlat).

  • alpha (float, optional) – Spectral exponent (smoothness). Must be > 1 when sigma is not given. Default 2.0.

  • tau (float, optional) – Inverse correlation length scale. Default 3.0.

  • sigma (float, optional) – Overall amplitude. If None (default), computed from alpha and tau so that the field variance is \(\mathcal{O}(1)\).

  • radius (float, optional) – Radius of the sphere. Default 1.0.

  • grid (str, optional) – Grid type for the inverse SHT ("equiangular", "legendre-gauss", etc.). Default "equiangular".

  • dtype (torch.dtype, optional) – Floating-point dtype. Default torch.float32.

Examples

>>> import torch
>>> from torch_harmonics.random_fields import GaussianRandomFieldS2
>>> grf = GaussianRandomFieldS2(nlat=128, alpha=2.5, tau=5.0)
>>> samples = grf(4)          # 4 independent realisations
>>> samples.shape
torch.Size([4, 128, 256])
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