Support block banded cholesky

[dlfivefifty]

No description provided.

[dlfivefifty]

@TSGut @MikaelSlevinsky This might be useful especially for 2D stuff. Should be fairly straightforward to get it working adaptively as well.

FYI for 2D finite-difference matrix it roughly matches the speed of UMFPack which I think is a "success":

julia> @time cholesky(Symmetric(Δ));
  0.360270 seconds (359.21 k allocations: 204.490 MiB)

julia> @time cholesky(sparse(Δ));
  0.379772 seconds (5.49 k allocations: 88.902 MiB)

[dlfivefifty]

Actually... this has a different complexity than UMF pack so when n becomes large UMFPack is still much faster...

[dlfivefifty]

But it would be pretty easy to add hierarchical multi-threading combined with the rank-update formula....but adding support for multi-threading should be done to all BlockArrays.jl (and dependencies) linalg routines.

[codecov]

Codecov Report

Merging #130 (ebca6dc) into master (a77af6f) will decrease coverage by 0.10%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master     #130      +/-   ##
==========================================
- Coverage   87.00%   86.90%   -0.11%     
==========================================
  Files          10       10              
  Lines        1185     1191       +6     
==========================================
+ Hits         1031     1035       +4     
- Misses        154      156       +2     

Impacted Files	Coverage Δ
src/BlockBandedMatrices.jl	0.00% <ø> (ø)
src/interfaceimpl.jl	96.05% <ø> (-2.54%)	⬇️
src/linalg.jl	83.14% <100.00%> (+0.19%)	⬆️

---

Continue to review full report at Codecov.

Legend - Click here to learn more
Δ = absolute <relative> (impact), ø = not affected, ? = missing data
Powered by Codecov. Last update a77af6f...ebca6dc. Read the comment docs.

[MikaelSlevinsky]

Should I retract my rocket?

[dlfivefifty]

Probably... at least until we add multithreading. (Actually that might be a bigger part of why UMFPack seems to have better complexity.)