Adaptive trapezoid

[gomezzz]

Description

Summary of changes

• Added adaptive_trapezoid
• Added adaptive_grid

Outstanding work

• [x] Create some test functions to see if this is working (or use existing ones)
• [x] Debug the tests (currently errors are noticeably larger than for default trapezoid which does not make sense)
• [x] Optimize: There are several TODOs in the code for this (reusing computed points, allocating memory in a smarter way)
• [ ] Choose good baseline values for N_subdomains and initial N in each subdomain
• [ ] Add more logging (currently only debug in some places)
• [x] Create some code to visualize the created adaptive grids. This should help also with debugging.
• [ ] Improve refinement criterion
• [ ] Optimize for larger number of subdomains

There are a few larger topics still open then, but these probably deserve dedicated issues and PRs

• [x] Creating AdaptiveBoole and AdaptiveSimpson (should be fairly straight forward)
• Make the refinement not refine in all dimension equally, this is closely related to #123
• Implement batched grid computations to allow larger N without having out of memory problems

Above points should help remedy some of the issues, right now performance on a simple integrand (f = torch.sin(x[:,0] + (x[:,1]+1.)**2) * (x[:,2]+1.)) is worse than for vanilla trapezoid, but that is somewhat expected.

How Has This Been Tested?

• [ x ] Added new test