f
This is either a
d_fun
or
a_fun
function object.
Upon return, the zero order
Taylor coefficients
in
f
correspond to the value of
x
.
The other Taylor coefficients in
f
are unspecified.
f(x)
We use the notation @(@
f: \B{R}^n \rightarrow \B{R}^m
@)@
for the function corresponding to
f
.
Note that
n
is the size of ax
and
m
is the size of ay
in to the constructor for
f
.
g(x)
We use the notation @(@
g: \B{R}^n \rightarrow \B{R}
@)@
for the function defined by
@[@
g(x) = \sum_{i=0}^{n-1} w_i f_i (x)
@]@
x
If
f
is a d_fun or a_fun,
this argument has prototype
const vec_double& x
const vec_a_double& x
and its size must be
n
.
It specifies the argument value at we are computing the Hessian
@(@
g^{(2)}(x)
@)@.
w
If
f
is a d_fun or a_fun,
this argument has prototype
const vec_double& w
const vec_a_double& w
and its size must be
m
.
It specifies the vector
w
in the definition of @(@
g(x)
@)@ above.
H
If
f
is a d_fun or a_fun,
the result has prototype
vec_double H
vec_a_double H
and its size is
n*n
.
For
i
between zero and
n-1
and
j
between zero and
n-1
,
@[@
H [ i * n + j ] = \frac{ \partial^2 g }{ \partial x_i \partial x_j } (x)
@]@
