Document use of conditionals for sparsity detection

[gdalle]

With the new TracerSparsityDetector from SparseConnectivityTracer, if blocks are not supported if they involve an input variable. They must be replaced with ifelse statements, which are compatible with operator overloading.

In your objective functions or constraints, do not write

y = if x[1] > 0
    x[2]
else
    x[3]
end

but instead write

y = ifelse(x[1] > 0, x[2], x[3])

Related:

• Sparsity detection breaks the norm function on 0.8 #247 (comment)

[timholy]

Can one turn off sparsity detection? (Or better, turn off sparsity altogether.) I have a problem where the Hessian is not very sparse and the objective function uses PDMats.jl, which involves representing matrices via their Cholesky factorization. I get errors like

julia> solveconstr(<my args>)
ERROR: TypeError: non-boolean (SparseConnectivityTracer.GradientTracer{SparseConnectivityTracer.IndexSetGradientPattern{Int64, BitSet}}) used in boolean context
Stacktrace:
  [1] ishermitian(A::SMatrix{2, 2, SparseConnectivityTracer.GradientTracer{…}, 4})
    @ LinearAlgebra ~/.julia/juliaup/julia-1.10.5+0.x64.linux.gnu/share/julia/stdlib/v1.10/LinearAlgebra/src/generic.jl:1257
  [2] #cholesky#549
    @ ~/.julia/packages/StaticArrays/MSJcA/src/cholesky.jl:4 [inlined]
  [3] cholesky
    @ ~/.julia/packages/StaticArrays/MSJcA/src/cholesky.jl:3 [inlined]
  [4] PDMat(mat::SMatrix{2, 2, SparseConnectivityTracer.GradientTracer{…}, 4})
    @ PDMats ~/.julia/dev/PDMats/src/pdmat.jl:19
 ...

[tmigot]

Hi @timholy !
Yes, you can pass another backend for the Hessian like this:

f(x) = 100 * (x[2] - x[1]^2)^2 + (x[1] - 1)^2
x0 = [-1.2; 1.0]
nlp = ADNLPModel(f, x0, hessian_backend = ADNLPModels.ForwardDiffADHessian)

I think the documentation for this is here https://jso.dev/ADNLPModels.jl/dev/backend/ but can be improved.

If you don't use the Hessian, then this works as well:

nlp = ADNLPModel(f, x0, hessian_backend = ADNLPModels.EmptyADbackend)
nlp = ADNLPModel(f, x0, matrix_free = true) # is an alternative that skip Hessian and Jacobian computation