Computing Hessian of the Langrangian efficiently with DI.jl

[gdalle]

@franckgaga

Well, clearly prep2 will be wrong since sparsity detection is done with typical_μ2 = spzeros(10) effectively saying “μ will be systematically always zeros”. But sparsity detection in prep1 is done with typical_μ1 = zeros(10), so also zeros but not structured zeros, so it seems to work here.

Yes it does work here, but if you had a slightly more sneaky function, like

f(x, mu) = sum(iszero(mui) ? 0 : xi for (xi, mui) in zip(x, mu))

then the zeros in your preparation vector typical_mu would deceive sparsity detection.

@franckgaga

Are you saying that I should do e.g.: typical_μ1 = ones(10) to guarantee no false-negatives in the pattern ?

Ideally SCT would trace through every Constant context provided, but for arbitrarily complex objects that is not possible. So instead we keep these constants fixed during sparsity detection. This means that, as a rule, you should probably choose a typical_mu that is rather generic, like rand(n), instead of very specific like zeros(n).

That’s probably something I should stress in the DI docs