Add derivative check for Jacobian of residual

[tmigot]

JuliaSmoothOptimizers/NLPModelsTest.jl#101

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 92.54%. Comparing base (9585863) to head (e8d8059).
Report is 3 commits behind head on main.

❗ Current head e8d8059 differs from pull request most recent head 64a857d

Please upload reports for the commit 64a857d to get more accurate results.

Additional details and impacted files

@@           Coverage Diff           @@
##             main      #85   +/-   ##
=======================================
  Coverage   92.54%   92.54%           
=======================================
  Files           5        5           
  Lines         295      295           
=======================================
  Hits          273      273           
  Misses         22       22           

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[tmigot]

@amontoison the issue here is that the jacobian of the residual is most likely not correct so the test won't pass :s

[amontoison]

Is it possible to isolate which components are wrong?
First do we have the correct sparsity pattern?

[dpo]

The Jacobian was computed explicitly here: https://www.gerad.ca/en/papers/G-2020-42. That should be what’s implemented.

[dpo]

@amontoison Could you have your test print the errors?

[amontoison]

@amontoison Could you have your test print the errors?

@tmigot You opened the PR and know better than me what is implemented in NLPModelsTest.jl.
Is it possible?

[tmigot]

You can compare the obtained result with auto diff eventually ? https://jso.dev/ADNLPModels.jl/dev/mixed/ you can build an ADNLSModel from a BundleAdjustmentModel.

jacobian_residual_check returns a Dict{Tuple{Int, Int}, Float64} where the Tuple is the indices of the Jacobian matrix and Float64 the error when it is nonzero. In other words, those are the wrong indices.

[dpo]

The error will be nonzero, because it's finite differences (except in special cases), so it's the magnitude of the error that we should look at.

[amontoison]

I checked the Jacobians with ADNLPModels.jl and it's only correct when we use x = nlp.meta.x0.
Something is wrong in the function coord_residual implemented in this package.
In #92, I added an option in the benchmarks to also check the Jacobian.