Add sparse jacobian

[tmigot]

I will split this into several PRs as it is a large change

• Add c in backend constructors
• Add get_nln_nnzj and get_nln_nnzh functions
• Extend ADModelBackend to NLS functions
• Add sparse jacobian!

[codecov]

Codecov Report

Base: 99.44% // Head: 99.45% // Increases project coverage by +0.01% 🎉

Coverage data is based on head (9e87cd7) compared to base (6e45688).
Patch coverage: 100.00% of modified lines in pull request are covered.

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #83      +/-   ##
==========================================
+ Coverage   99.44%   99.45%   +0.01%     
==========================================
  Files           7        8       +1     
  Lines         715      740      +25     
==========================================
+ Hits          711      736      +25     
  Misses          4        4              

Impacted Files	Coverage Δ
src/ADNLPModels.jl	100.00% <ø> (ø)
src/ad.jl	96.29% <ø> (+0.14%)	⬆️
src/nlp.jl	100.00% <ø> (ø)
src/nls.jl	100.00% <ø> (ø)
src/sparse_derivatives.jl	100.00% <100.00%> (ø)

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[tmigot]

I also added a complementary tests with problems from OptimizationProblems.jl:

using ADNLPModels, LinearAlgebra, NLPModels, NLPModelsJuMP, OptimizationProblems

for prob in intersect(names(ADNLPProblems), names(PureJuMP))
  if prob == :hs61
    continue
  end
  if occursin("tetra", string(prob)) || occursin("triangle", string(prob))
    continue # too slow
  end
  nlp = eval(Meta.parse("ADNLPProblems.$(prob)()"))
  model = MathOptNLPModel(eval(Meta.parse("PureJuMP.$(prob)()")))
  if nlp.meta.ncon > 0
    x = nlp.meta.x0
    test = Matrix(jac(nlp, x)) ≈ Matrix(jac(model, x))
    if !test
      println("$prob : $(nlp.meta.nvar), $(nlp.meta.ncon)")
      @show norm(Matrix(jac(nlp, x)) - Matrix(jac(model, x)))
    end
  end
end

and all the tests passed (after this JuliaSmoothOptimizers/OptimizationProblems.jl#223).

[github-actions]

Package name	latest	stable
CaNNOLeS.jl
DCISolver.jl
DerivativeFreeSolvers.jl
JSOSolvers.jl
NLPModelsIpopt.jl
OptimizationProblems.jl
Percival.jl
QuadraticModels.jl
SolverBenchmark.jl
SolverTools.jl

[github-actions]

Package name	latest	stable
CaNNOLeS.jl
DCISolver.jl
DerivativeFreeSolvers.jl
JSOSolvers.jl
NLPModelsIpopt.jl
OptimizationProblems.jl
Percival.jl
QuadraticModels.jl
SolverBenchmark.jl
SolverTools.jl

[dpo]

We really have to update the config of that dratted probot. I didn't even have a chance to look at this PR!

[tmigot]

Sorry for that, if you have some feedback on this I can open a new PR to fix it.

#91 should help with the bot.