Derivative of a function of derivatives about forwarddiff.jl HOT 7 OPEN

The obvious thing here is ForwardDiff.gradient(x -> det(ForwardDiff.hessian(g, x)), x). Does this fail?

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That might work; I didn't know you could do that. Just to be clear, though, my determinant is not the full determinant of the hessian (which would be a 3x3), so I'm still not sure how to construct it. I will experiment with the ForwardDiff.hessian function, see how its output is formatted, and see if I can select the first two rows and columns via an inline method.

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I am new enough to Julia that I am not entirely sure which "x"s in your formula should be replaced with my input and which should be left alone (since my function is defined as g(x::Vector)=...). However, it was easy to select the first two rows and columns via an inline method, so I'm sure this will work, as soon as I figure it out.

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Final question: is the partial derivative in row 2, column 1 of my formula in the corresponding location in the hessian?

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Well, the code runs and appears to function, but the answer is very different from what I obtained by hand-coding a finite difference, so I think I screwed something up.

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is this related to criticality conditions?

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I found an example in a journal article, coded the example, and managed to replicate it, so perhaps the code is OK and my hand-coded version is wrong. I still have issues, but they seem to be chemistry issues, not numerical methods issues, so: thank you very much, your solution worked like a charm!

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