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[WIP]: minimal general matern kernel. #392

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[WIP]: minimal general matern kernel. #392

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daniel-dodd
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@daniel-dodd daniel-dodd commented Sep 19, 2023

@astfalckl would be great to get your thoughts on this. If we could get a simple example showing where the general Matern offers that greater spectral flexibility - that would be excellent.

Type of changes

  • Bug fix
  • [ x] New feature
  • Documentation / docstrings
  • Tests
  • Other

Checklist

  • I've formatted the new code by running poetry run pre-commit run --all-files --show-diff-on-failure before committing.
  • I've added tests for new code.
  • I've added docstrings for the new code.

Description

This adds a Matérn kernel for general smoothness parameter. #391

TODO:

  • Needs testing, and check for consistency with our Matern12, Matern32, Matern52 kernels.
  • Performance is slow. While we know this will be slower, how much slower should this be?
  • Update docstrings and provide the general matern formula (currently this has just robbed the docstring from one of the other integer Materns).
  • Perhaps document on an example where this important - i.e., show a nice spectral_density example.
  • Why are we passing nu = 2 * nu in the spectral density for the Matern12, Matern32, Matern52 kernels this seems rather weird (I mimic this for my implementation)? Also why do we not define the spectral density with the lengthscale and variance? Instead these terms seem to appear in basis function computation - I would expect to get the spectral density of my Kernel for my given variance and lengthscale if I called spectral_density? @thomaspinder

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