Lattice rules for (hyper)cubic grids
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- Dominant language
- Python
- Stars
- 101
- Forks
- 40
- PR merge metrics
- No merged PRs in 30d
Description
Among the most efficient ways to integrate of a (hyper)cube are the lattice rules. There are several choices here, but probabilty the embedded lattice rules are the easiest to implement, and they have been tabulated.
For a (simpler) lead reference, I recommend the early paper from Sloan.
It would be good to use lattice rules as an alternative for integration over a cube or (after an affine transformation) an arbitrary parallelepiped. I'm much less sure that higher-dimensions are supported, but it is easy to support arbitrary-dimensional integration on a parallelepiped (beyond $d=3000$, which is more than enough!) with a lattice rule. Interpolation is also relatively straightforward, as it is a generalization of the current structure with specially selected vectors.
Contributor guide
First steps
- Read the whole issue, then the project's contributing guide.
- Comment on the issue to say you are picking it up — it saves two people doing the same work.
- Fork the repository and make your change on a branch.
- Open a pull request that references the issue number.
Research direction
No files or tests are named. Start by locating the existing cube and parallelepiped integration entry points and reviewing the cited lattice-rule references; done means a lattice-rule alternative is supported for those domains, with the supported dimensional range and interpolation scope made explicit.
Written by the indexing model from the issue text.
Assessment
- Tech stack
- python
- Domain
- data
- Issue type
- Feature
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Quiet
- Clarity
- Needs clarification
- Newbie friendliness
- 30/100