Prev

Next

Index-> contents reference index search external

Up-> cppad_swig library a_fun a_fun_hessian

cppad_swig-> testing swig_xam.i library whats_new_2018

library-> module a_double vector a_fun sparse error xam.m4

a_fun-> independent abort_recording a_fun_ctor a_fun_jacobian a_fun_hessian a_fun_forward a_fun_reverse a_fun_optimize a_fun_property

a_fun_hessian-> a_fun_hessian_xam.cpp a_fun_hessian_xam.m a_fun_hessian_xam.pm a_fun_hessian_xam.py

Headings-> Syntax af f(x) g(x) x w H Example

@(@\newcommand{\B}[1]{ {\bf #1} } \newcommand{\R}[1]{ {\rm #1} }@)@ Hessian of an AD Function
Syntax
H = af.hessian(x, w)

af
This object has prototype
     a_fun af
Note that its state is changed by this operation. The zero order Taylor coefficients in af correspond to the value of x . The other Taylor coefficients in af are unspecified.

f(x)
We use the notation @(@ f: \B{R}^n \rightarrow \B{R}^m @)@ for the function corresponding to af . Note that n is the size of ax and m is the size of ay in to the constructor for af .

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
This argument has prototype
     const vec_double& x
and its size must be n . It specifies the argument value at we are computing the Hessian @(@ g^{(2)}(x) @)@.

w
This argument has prototype
     const vec_double& w
and its size must be m . It specifies the vector w in the definition of @(@ g(x) @)@ above.

H
The result has prototype
     vec_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) @]@

Example
C++ , Octave , Perl , Python .

---

Input File: lib/a_fun.cpp