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Ran 18 Aug 2024 11:15AM UTC

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Committed 18 Aug 2024 04:20AM UTC coverage: 87.831% (+0.04%) from 87.789%

Job # #37874.1

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push

local

Committed by

web-flow

Commit Message

Avoid using zero for the eltype in `tr(::Matrix)` (#55519)

This lets us compute the `tr` for `Matrix`es where the `eltype` does not
have a zero, but we may sum over the diagonal.
E.g. the following works after this:
```julia
julia> M = fill([1 2; 3 4], 2, 2)
2×2 Matrix{Matrix{Int64}}:
 [1 2; 3 4]  [1 2; 3 4]
 [1 2; 3 4]  [1 2; 3 4]

julia> tr(M)
2×2 Matrix{Int64}:
 2  4
 6  8
```

Also, using linear indexing over Cartesian appears to provide a slight
speed-up for small to mid-sized matrices:
```julia
julia> A = rand(1000,1000);

julia> @btime tr($A);
  1.796 μs (0 allocations: 0 bytes) # nightly
  1.524 μs (0 allocations: 0 bytes) # This PR
```

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