Implement efficient sparse array comparisons

[eschnett]

Closes #226.

[codecov-commenter]

Codecov Report

Merging #227 (fd508a1) into main (f51b64c) will increase coverage by 0.03%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##             main     #227      +/-   ##
==========================================
+ Coverage   92.11%   92.15%   +0.03%     
==========================================
  Files          11       11              
  Lines        7203     7223      +20     
==========================================
+ Hits         6635     6656      +21     
+ Misses        568      567       -1     

Impacted Files	Coverage Δ
src/sparsematrix.jl	95.35% <100.00%> (+0.02%)	⬆️
src/higherorderfns.jl	96.69% <0.00%> (+0.02%)	⬆️
src/linalg.jl	84.58% <0.00%> (+0.08%)	⬆️

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[SobhanMP]

Is there a need to check zero(eltype(A)) == zero(eltype(B)) ? or is this assumed to be true regardless?

[rayegun]

SparseMatrixCSC assumes that the fill value is zero(T) broadly speaking, IIRC.

[eschnett]

@SobhanMP Yes, that needs to be checked, since e.g. 0 == [0] isn't true.

[SobhanMP]

@Wimmerer yes but are all zeros equal?

[SobhanMP]

gotta say the github font is bad 😅 .

[eschnett]

Saved by the colour coding?

[SobhanMP]

so i compared the number of operations with flattened arrays and it seems that this patch does less comparison than sparse sparse comparison. let me check a few things tonight. otherwise looks good.

[ViralBShah]

If all good, then please merge.

[SobhanMP]

in the end i think it's best to not compare zero, for the sake of compability with ==. i also made the test stricter. i.e. nnz(A) + nnz(B) + 1 operations at max. also some style upgrade.

@ViralBShah do you know how it would be possible to make a benchmark for this package. to track performance degradations?

[eschnett]

I think we should compare the zeros:

julia> fill(0,1,1) == fill([0;;],1,1)
false

julia> sparse(fill(0,1,1)) == sparse(fill([0;;],1,1))
true

That's a bug in the current sparse array comparisons.

[eschnett]

Opened #234 for the issue above.

[SobhanMP]

i'll go ahead an merge this, if any one has any opinion, i guess we can move to #234