Add derivative check for Jacobian of residual

[tmigot]

https://github.com/JuliaSmoothOptimizers/NLPModelsTest.jl/issues/101

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[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.