Keep a non-finite value times an unstored zero in the sparse outer product x .* y'

[ViralBShah]

x .* y' for sparse vectors drops a non-finite product with an unstored zero: Inf * 0 and NaN * 0 are NaN in the dense result and an unstored zero in the sparse one. kron(x, y') goes through the same broadcast and has the same defect.

Before

julia> x, y = sparsevec([Inf, 0.0]), sparsevec([0.0, 1.0]);

julia> Array(x .* y')
2×2 Matrix{Float64}:
 0.0  Inf
 0.0  0.0

julia> Array(x) .* Array(y)'
2×2 Matrix{Float64}:
 NaN    Inf
   0.0   0.0

After

julia> Array(x .* y')
2×2 Matrix{Float64}:
 NaN    Inf
   0.0   0.0

Array(kron(x, y')) changes in the same way and now equals kron(Array(x), Array(y)').

The outer-product shortcut _outer multiplies stored entries with stored entries alone, which is the product only when every stored entry times a zero is a zero. _copy(*, x, y') now checks that with _outerkeepszeros, an O(nnz) pass over both vectors, and otherwise takes the general broadcast kernel. Both branches return the same SparseMatrixCSC type, so the result stays inferable.

x .* y' with 10^3 stored Float64 entries in each vector of length 10^4 (10^6 stored results), minimum of 20 runs on a shared machine:

	time	allocations
main	2.87 ms	9 (16087432 bytes)
this PR	2.77 ms	9 (16087432 bytes)

Left out: x .* y' for an eltype without zero, such as a vector of matrices, throws a MethodError as it does on main.

Split from #1022. Backport candidate: a wrong result, also on Julia 1.13.

Written by Claude Code.

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 94.76%. Comparing base (6324de6) to head (74b08f0).
⚠️ Report is 4 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #1077      +/-   ##
==========================================
- Coverage   94.76%   94.76%   -0.01%     
==========================================
  Files          16       16              
  Lines        9947     9965      +18     
==========================================
+ Hits         9426     9443      +17     
- Misses        521      522       +1     

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[ViralBShah]

Reviewed by Codex at 92fed66.

No actionable findings in the non-finite outer-product fix. A sweep of 9,604 cases with finite values, infinities, NaNs, stored zeros and dropped zeros found no nonzero/NaN discrepancies against dense results. The guard correctly sends either operand’s non-finite zero products through general broadcasting.