Unitcell stress test: coordination should not change with full-rank supercells

[pablosanjose]

This is the result of a stress test on the unitcell routines to catch edge cases. We want to guarantee that any unitcell(h, sc) with any full-rank sc does not change the coordination of the resulting Hamiltonian. To achieve that we needed to correct some bugs and edge cases. Long story short, we were assuming supercell definitions that were slightly different when building the superlattice and the Hamiltonian (position-based vs dn-based). Now both should be consistent (position-based). We also need to be strict about which sites end up in the final lattice: they should be only those within the bounds of the supercell, no hanging sites. Also, we needed to be a little more conservative in the scan of dn space when building the supercell.

Now tests over a full range of full-rank supercells generate the correct lattices, with identical coordination.

[pablosanjose]

The fast paths for unitcells (unitell(h, 3) and unitcell(h, 3,3,3)) was still using the dn-based criterion for supercell construction, that then conflicted with the hamiltonian construction (position-based). We remove the fastpaths for now. An advantage is that the definition of the supercell does not depend on whether we're using the fastpath: it's always the sites located within the supercell bounding box, drawn so that the site position average mean(r) is at the center of the supercell.

[pablosanjose]

The above strict definition of supercell has some unexpected consequences, such as unitcell(lat) != lat.unitcell. The reason is that lat.unitcell can have site positions outside the bounding box of the unitcell, as defined by the Bravais vectors. In this case, the outlying sites will be folded back onto the unitcell, yielding a different set of positions.

Thinking about all possible edge cases this seems unavoidable. If we allow sites outside the unitcell bounding box (as we should), one needs to be very disciplined about how supercells are built. Otherwise one can easily end up not finding the outliers in a dn search to build the final supercell (i.e. in the folding-back process). Hence, the current version of _cell_iter goes to great pains to (1) always cover a minimum dn bounding box that covers the supercell unit and (2) persist in the dn search if a site folds down to a dn that is not in the already searched domain.

[codecov-io]

Codecov Report

Merging #117 into master will increase coverage by 0.11%.
The diff coverage is 98.11%.

@@            Coverage Diff             @@
##           master     #117      +/-   ##
==========================================
+ Coverage   62.00%   62.11%   +0.11%     
==========================================
  Files          16       16              
  Lines        2845     2856      +11     
==========================================
+ Hits         1764     1774      +10     
- Misses       1081     1082       +1     

Impacted Files	Coverage Δ
src/Quantica.jl	100.00% <ø> (ø)
src/lattice.jl	81.81% <97.36%> (+0.22%)	⬆️
src/hamiltonian.jl	79.62% <100.00%> (+0.05%)	⬆️

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