argmin-rs/sphrs

Spherical harmonics and solid harmonics in Rust

sphrs's Issues

Implement parallel evaluation of several positions using rayon

Due to the low computation time of a single SH they may not parallelize well when evaluated at several positions. Evaluating an HarmonicsSet in parallel may however increase performance and should be easy to implement (using rayon). This feature should be behind a feature gate.

Write macro for loop unrolling in `eval_internal` of `HarmonicsSet`

Loop unrolling improved performance of eval_internal by about a factor of 2. Currently loop unrolling is done manually up to degree 20. Automatic unrolling with a macro would be more convenient and less error prone.

Differences with scipy.special.sph_harm for high degrees

There are significant differences between the complex SH provided by scipy.special.sph_harm and those provided by sphrs for high degrees. For example, the conjugate of the computed SH at the point Coordinates::spherical(1f64, 1.7453292519943295, 1.3962634015954636) are

degree 11 and order 11:
scipy: 0.4405634627748642+0.16035198675529674j
sphrs: 3.561861287727778+1.2964114873179975j

degree 12 and order 12:
scipy: -0.23561802283529287+0.4081023867296495j
sphrs: -56.973351046253434+98.68073868956799j

degree 13 and order 13:
scipy: -0.3622756435535203-0.3039853588902706j
sphrs: -1770.9169188717583-1485.975733470897j

The dramatic increase in the values returned by sphrs makes me think of numerical instability, but I couldn't pinpoint the issue.

Perform extensive benchmarks

Compare to other implementations and add the results to the documentation.

Test solid harmonics

Currently there are no tests for solid harmonics. A comparison to a reference solution would be useful.

Implement (more) hardcoded (complex) spherical harmonics

Performance is substantially improved by hardcoding spherical harmonics. Currently only real spherical harmonics are implemented hardcoded (up to dregree 3 only).

Write macros for benchmarks

The benchmarks currently involve a lot of duplicated code which could be simplified with macros.