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hes =
f.Hessian(
x,
i)
F : B^n \rightarrow B^m
to denote the
AD function
corresponding to f.
The syntax above sets hes to the
Hessian of F_i evaluated at x; i.e.,
\[
hes = F^{(2)} (x)
\]
ADFun<
Base>
f
Note that the ADFun
object f is not const
(see Hessian Uses Forward
below).
const
Vector &
x
(see Vector
below)
and its size
must be equal to n, the dimension of the
domain
space for f.
It specifies
that point at which to evaluate the Hessian.
size_t
i
and is less than m, the dimension of the
range
space for f.
It specifies the component of F
for which we are evaluating the Hessian.
Vector
hes
(see Vector
below)
and its size is
n * n
.
For
j = 0 , \ldots , n - 1
and
\ell = 0 , \ldots , n - 1
\[
hes [ j * n + \ell ] = \DD{ F_i }{ x_j }{ x_\ell } ( x )
\]
Hessian
,
the previous calls to Forward
are undefined.
Hessian
.
They return true
, if they succeed and false
otherwise.