Utilities#

Plotting, quadrature, and helper functions.

Quadrature#

torch-harmonics supports several quadrature rules for the latitudinal direction. Each corresponds to a grid keyword accepted by the SHT and convolution layers:

Grid string	Quadrature rule	Nodes	Key properties
`"equiangular"`	Clenshaw–Curtis	Equally spaced in \(\theta\) (including poles)	Default grid. Exact for polynomials up to degree \(N-1\). Simple, FFT-friendly.
`"legendre-gauss"`	Gauss–Legendre	Roots of \(P_N(\cos\theta)\)	Exact for polynomials up to degree \(2N-1\). Optimal accuracy per node, but nodes are non-uniform.
`"lobatto"`	Gauss–Lobatto	Roots of \(P'_{N-1}(\cos\theta)\), plus endpoints	Exact for polynomials up to degree \(2N-3\). Includes both poles, useful when pole values are needed.
`"equiangular-trapezoidal"`	Trapezoidal	Equally spaced	Supports periodic grids. Lower-order accuracy but simplest structure.

The longitudinal direction always uses equispaced nodes (see precompute_longitudes).

`precompute_longitudes`
`precompute_latitudes`
`legendre_gauss_weights`	Helper routine which returns the Legendre-Gauss nodes and weights on the interval [a, b]
`lobatto_weights`	Helper routine which returns the Legendre-Gauss-Lobatto nodes and weights on the interval [a, b]
`clenshaw_curtiss_weights`	Computation of the Clenshaw-Curtis quadrature nodes and weights.
`trapezoidal_weights`	Helper routine which returns equiangular-trapezoidal nodes with trapezoidal weights on the interval [a, b]

Plotting#

`plot_sphere`	Plots a function defined on the sphere using pcolormesh
`imshow_sphere`	Displays an image on the sphere

Truncation#

truncate_sht

Determine the maximum spherical harmonic degree and order for an SHT based on the spatial grid.

Debugging#

torch_harmonics.distributed.config#: Module-level configuration for torch_harmonics.distributed. Env vars are used as defaults but can be overridden programmatically, e.g.:

from torch_harmonics.distributed import config config.debug = True

The config object exposes a single boolean property, debug. When enabled, the distributed primitives perform extra shape-verification checks on every collective call, which is useful for diagnosing partitioning mismatches.

from torch_harmonics.distributed import config

# enable programmatically
config.debug = True

# or via environment variable (before importing)
# TORCH_HARMONICS_DISTRIBUTED_DEBUG=1