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dy =
f.ForOne(
x,
j)
F : B^n \rightarrow B^m
to denote the
AD function
corresponding to f.
The syntax above sets dy to the
partial of
F
with respect to
x_j
; i.e.,
\[
dy
= \D{F}{ x_j } (x)
= \left[
\D{ F_0 }{ x_j } (x) , \cdots , \D{ F_{m-1} }{ x_j } (x)
\right]
\]
ADFun<
Base>
f
Note that the ADFun
object f is not const
(see ForOne 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 partial derivative.
size_t
j
an is less than n,
domain
space for f.
It specifies the component of F
for which we are computing the partial derivative.
Vector
dy
(see Vector
below)
and its size is
m
, the dimension of the
range
space for f.
The value of dy is the partial of
F
with respect to
x_j
evaluated at x; i.e.,
for
i = 0 , \ldots , m - 1
\[.
dy[i] = \D{ F_i }{ x_j } ( x )
\]
ForOne
,
the previous calls to Forward
are undefined.
true
, if it succeeds and false
otherwise.