what do we use fvar<fvar<double>> for?

[Charles Margossian]

I'm learning how to implement unit tests. When looking at existing tests for forward mode, I found functions were expected to handle variables of the type fvar<fvar<double>> (see round_test and sin_test for example). What do we use this variable type for?

I'm guessing for second derivatives, since with x of type fvar<fvar<...>> the tangent of x is itself an AD variable for which we can compute the derivative. But then again, it's just a guest.

[Bob Carpenter]

I don't think we ever use that in Stan right now, but
it would be used to compute second derivatives with respect
to a single pair of variables. So calling the density with
that argument N times would be the most efficient way to
compute the diagonal of a Hessian as we might use in RHMC.

We'd usually use fvar<var> to compute Hessians and
fvar<fvar<var> > to compute third order derivatives
(as required by the SoftAbs version of RHMC).

- Bob

> On Aug 23, 2016, at 4:44 PM, Charles Margossian <charles.ma...@gmail.com> wrote:
>
> I'm learning how to implement unit tests. When looking at existing tests for forward mode, I found functions were expected to handle variables of the type fvar<fvar<double>> (see round_test and sin_test for example). What do we use this variable type for?
>
> I'm guessing for second derivatives, since with x of type fvar<fvar<...>> the tangent of x is itself an AD variable for which we can compute the derivative. But then again, it's just a guest.
>

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