Separate out Matern kernels

[sbfnk]

Description

This PR closes #760 and #828.

It splits out spectral densities of Matern Kernels of order 1/2, 3/2 and 5/2.

It would be good for someone to check both the maths (which I've updated in the vignette) and code are correct.

Initial submission checklist

• My PR is based on a package issue and I have explicitly linked it.
• I have tested my changes locally (using devtools::test() and devtools::check()).
• I have added or updated unit tests where necessary.
• I have updated the documentation if required and rebuilt docs if yes (using devtools::document()).
• I have followed the established coding standards (and checked using lintr::lint_package()).
• I have added a news item linked to this PR.

After the initial Pull Request

• I have reviewed Checks for this PR and addressed any issues as far as I am able.

[github-actions]

This is how benchmark results would change (along with a 95% confidence interval in relative change) if 8db04a5 is merged into main:

• ✔️default: 22.9s -> 23.1s [-12.64%, +14.1%]
• ✔️no_delays: 28.2s -> 29.2s [-6.41%, +13.73%]
• ✔️random_walk: 10.2s -> 9.95s [-7.91%, +3.37%]
• ✔️stationary: 22s -> 7.31s [-146.77%, +13.19%]
• ✔️uncertain: 38.6s -> 39s [-8.36%, +10.75%]
  Further explanation regarding interpretation and methodology can be found in the documentation.

[github-actions]

This is how benchmark results would change (along with a 95% confidence interval in relative change) if 3e43cdb is merged into main:

• 🚀default: 23.3s -> 20.2s [-24.81%, -1.84%]
• ✔️no_delays: 28.3s -> 26.8s [-13.05%, +2.86%]
• ✔️random_walk: 10s -> 9.82s [-7.49%, +3.81%]
• ✔️stationary: 13s -> 13.7s [-16.99%, +27.53%]
• ✔️uncertain: 38.2s -> 51.7s [-46.64%, +116.91%]
  Further explanation regarding interpretation and methodology can be found in the documentation.

[seabbs]

This looks right to me based but I also convinced myself the other approach was correct so take that with a pinch of salt.

[github-actions]

This is how benchmark results would change (along with a 95% confidence interval in relative change) if f8228d0 is merged into main:

• ✔️default: 23.6s -> 24.3s [-8.87%, +14.41%]
• ✔️no_delays: 26.9s -> 28.7s [-3.93%, +17.11%]
• ✔️random_walk: 9.61s -> 10.1s [-1.32%, +11.29%]
• ✔️stationary: 14s -> 12.6s [-26.8%, +6.8%]
• ✔️uncertain: 36.5s -> 36.1s [-9.92%, +7.7%]
  Further explanation regarding interpretation and methodology can be found in the documentation.