Deflating Schur algorithm for quasi1D Green functions #161
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draft heavy wip debugging wip wip Jordan chain works new method for Jordan compromise: r0 = 1 wip one example down working! atol = 0 defaults to Wimmer refactor + fastpaths fixes improved rank-defect handling cleanup fix type instabilities from schur another fix in recursion consistency fix safety cutoff in jordan loop C1 deflate method remove debug print Deflating Schur hessenberg approach reducing allocations reduce more allocations elliminate more allocations cleanup fix memory overwrite + bugfix optimize 1=>n green by using dense invG simplify again, inplace lu! for g(1=>n) same in-place opt for local-infinite-fastpath in-place optimizations on top of the QR C1 deflate removed debug print tweak show greens remove redundant shiftw! remove SpecialFunctions dep cover the case with zero h_+- flatten/unflatten greens r x r Jordan reconstruction with tests unflatten! fix test fix
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Codecov Report
@@ Coverage Diff @@
## master #161 +/- ##
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- Coverage 71.28% 71.09% -0.20%
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Files 16 16
Lines 3382 3494 +112
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+ Hits 2411 2484 +73
- Misses 971 1010 +39
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Closes #154
This implements a deflating Schur algorithm that is far more precise, performant and stable than the one in master. It is developed in detail in a paper to be submitted, will post here when available. I just post a plot from the paper here
I leave some branches open for a while with alternative algorithms that were explored in developing this.
When writing tests for this I realized that the fact that
unitcellsometimes changes the shape of the unit cell (probably because of #117) and the algorithm enlarges the unit cell usingunticellwhen there are next-nearest-cell hoppings, the result can be wrong. Must fixunitcellin a future PR to always preserve cell shape, at least in 1D.