Reimplementation of local band-to-tridiagonal

[rasolca]

Implementation without let_value.
To me it looks simpler and more readable compared to other attempt with let_value (see #939), but introduce a little trick with a shared_ptr to allow to share the vector of tiles.

The new implementation is 45-50% faster (tested 20k, 30k and 40k).

[msimberg]

Nice @rasolca! Any idea about the scaling so far (I'm just eager to hear the results, don't worry if you don't have that yet)?

For the let_value version, would you mind opening a PR with it (even if we end up closing it in favour of this one)? It's easier to compare and comment in a PR.

[rasolca]

Nice @rasolca! Any idea about the scaling so far (I'm just eager to hear the results, don't worry if you don't have that yet)?

Not yet... still trying to make the local let_value version working.

For the let_value version, would you mind opening a PR with it (even if we end up closing it in favour of this one)? It's easier to compare and comment in a PR.

#939

[rasolca]

cscs-ci run

[msimberg]

Approved modulo the formatting violations.

[rasolca]

cscs-ci run

[codecov-commenter]

Codecov Report

Merging #938 (188f562) into master (3d86f2b) will increase coverage by 1.53%.
The diff coverage is 98.62%.

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@@            Coverage Diff             @@
##           master     #938      +/-   ##
==========================================
+ Coverage   93.20%   94.73%   +1.53%     
==========================================
  Files         136      122      -14     
  Lines        8327     7504     -823     
  Branches     1081     1023      -58     
==========================================
- Hits         7761     7109     -652     
+ Misses        391      240     -151     
+ Partials      175      155      -20     

Impacted Files	Coverage Δ
include/dlaf/eigensolver/band_to_tridiag/mc.h	98.08% <98.57%> (+0.44%)	⬆️
include/dlaf/eigensolver/band_to_tridiag.h	51.51% <100.00%> (ø)
include/dlaf/eigensolver/eigensolver/impl.h	77.77% <100.00%> (ø)

... and 34 files with indirect coverage changes