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hes =
f.Hessian(
x,
w)
hes =
f.Hessian(
x,
l)
F : B^n \rightarrow B^m
to denote the
AD function
corresponding to f.
The syntax above sets hes to the Hessian
The syntax above sets h to the Hessian
\[
hes = \dpow{2}{x} \sum_{i=1}^m w_i F_i (x)
\]
The routine sparse_hessian
may be faster in the case
where the Hessian is sparse.
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
l
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.
To be specific, in the case where the argument l is present,
\[
w_i = \left\{ \begin{array}{ll}
1 & i = l \\
0 & {\rm otherwise}
\end{array} \right.
\]
const
Vector &
w
and size
m
.
It specifies the value of
w_i
in the expression
for h.
Vector
hes
(see Vector
below)
and its size is
n * n
.
For
j = 0 , \ldots , n - 1
and
\ell = 0 , \ldots , n - 1
\[
hes [ j * n + \ell ] = \DD{ w^{\rm T} F }{ x_j }{ x_\ell } ( x )
\]
Hessian
,
the previous calls to Forward
are undefined.
Hessian
.
They return true
, if they succeed and false
otherwise.