Matrix constructor for triangular

[jishnub]

This reduces TTFX as well as improves performance. This is because we add specialized functions to avoid the branches in getindex for a triangular matrix.

julia> using LinearAlgebra

julia> U4 = UpperTriangular(ones(4,4));

julia> @time Array(U4); # TTFX
  0.087534 seconds (193.27 k allocations: 9.706 MiB, 99.88% compilation time) # nightly
  0.049869 seconds (91.45 k allocations: 4.531 MiB, 99.78% compilation time) # this PR

julia> U = UpperTriangular(ones(2000,2000));

julia> @btime Array($U);
  3.205 ms (3 allocations: 30.52 MiB) # master
  2.764 ms (3 allocations: 30.52 MiB) # this PR

[dkarrasch]

What's the rationale here?

[jishnub]

The idea here is that we remove the branches in getindex, and move the conditions to the loop ranges instead (we loop over the stored and non-stored rows separately). We also hardcode the zero element corresponding to the non-stored indices instead of relying on getindex, whereas for the stored indices, we forward the indexing to the parent. This makes the copy simpler to compile, as well as faster to execute.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 92.04%. Comparing base (830ea2f) to head (bef96b4).
Report is 7 commits behind head on master.

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #1282   +/-   ##
=======================================
  Coverage   92.03%   92.04%           
=======================================
  Files          34       34           
  Lines       15499    15515   +16     
=======================================
+ Hits        14265    14281   +16     
  Misses       1234     1234           

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[jishnub]

Should we go ahead with this?