Add associated Legendre function calculations #505
Conversation
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Allocate the output array out of the loop. This way we can do it once only when evaluating the spherical harmonics. Pre-compute the square roots of integers that we use in the loops. Doesn't work well if the square roots are calculated at the module level (probably a numba thing).
Results are bad beyond that even with the scaling
|
@santisoler and @MarkWieczorek this is ready now. I added the Holmes and Featherstone scaling and tested until degree 2800. I was surprised that calculating the derivatives on rescaled functions works well. That's nice because it means we can keep them separate and use the derivative functions to calculate higher order derivatives (which would appear in gravity gradients). If you could both have a quick look I'd really appreciate it. And thanks for all the information and code examples @MarkWieczorek! It really helped. |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment
Add this suggestion to a batch that can be applied as a single commit.
This suggestion is invalid because no changes were made to the code.
Suggestions cannot be applied while the pull request is closed.
Suggestions cannot be applied while viewing a subset of changes.
Only one suggestion per line can be applied in a batch.
Add this suggestion to a batch that can be applied as a single commit.
Applying suggestions on deleted lines is not supported.
You must change the existing code in this line in order to create a valid suggestion.
Outdated suggestions cannot be applied.
This suggestion has been applied or marked resolved.
Suggestions cannot be applied from pending reviews.
Suggestions cannot be applied on multi-line comments.
Suggestions cannot be applied while the pull request is queued to merge.
Suggestion cannot be applied right now. Please check back later.
The numba-based functions calculate the associated Legendre functions (unnormalized, Schmidt normalized, and fully normalized) and their derivatives$\dfrac{\partial P_n^m}{\partial \theta}(\cos\theta)$ . The derivatives functions can be used to calculate higher order derivatives as well. Values are tested against analytical solutions for the first 4 degrees as well as an identity for the Schmidt functions and the Legendre equation for the Schmidt and fully normalized functions. The values are returned as 2D numpy arrays. This is a bit of a waste of memory but it's much easier to use than storing these in sparse matrices or 1D arrays. But it should be acceptable since we're unlikely to ever go over ~2700 degree so the waste is in the order of a few Mb at worse.
Relevant issues/PRs:
Related to #504