simplify objective functions

[oscardssmith]

since the log(A_ij) is constant, there's no need to include it in the linear objectives, which allows for simplifying the loop dramatically (at least when the matrix has no zeros)

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 92.87%. Comparing base (ce4a3f2) to head (a8cf11a).
⚠️ Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #15      +/-   ##
==========================================
+ Coverage   92.84%   92.87%   +0.03%     
==========================================
  Files           5        5              
  Lines         852      856       +4     
==========================================
+ Hits          791      795       +4     
  Misses         61       61              

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[timholy]

You're right this is a good simplification (although it's the constraints that make it slow), but we need to handle the case where A has zeros. I think precomputing sum(iszero, A; dims=1 or 2) might enable this?

[oscardssmith]

I think we're need both. It would be somewhat surprising to me if going from an O(mn) to O(m+n) size objective didn't speed things up a bit.

[timholy]

Clearly I need more test coverage for the A[i, j] = 0 case...try this:

julia> A = [
       8 20 18;
       20 10 0;
       18 0 5
       ];

julia> a = symcover_lmin(A)
3-element Vector{Float64}:
 6.324555320336757
 3.1622776601683795
 2.8460498941515415

julia> cover_lobjective(a, A)
2.0918640616783923

julia> a = symcover_lmin_bad(A)
3-element Vector{Float64}:
 8.04984471899924
 3.1622776601683795
 2.23606797749979

julia> cover_lobjective(a, A)
2.574290210922684

where symcover_lmin_bad is the implementation here.

[oscardssmith]

Now this recovers the correct cover.

[timholy]

Thanks! This is great!