lines 8-127 of file: cpp/include/cmpad/gradient.hpp

{xrst_begin cpp_gradient}
{xrst_spell
   typedef
}

C++ Abstract Class For Calculating Gradient
###########################################

Syntax
******
| |tab| ``# include <cmpad/gradient.hpp>``
| |tab| ``template< template<class`` *ADVector* ``> class`` *Algo* ``> class``
| |tab| *Grad* ``: public cmpad::gradient`` {
| |tab| |tab| *...*
| |tab| };



Source Code
***********
{xrst_literal
   // BEGIN C++
   // END C++
}

ADVector
********
This is a :ref:`cpp_fun_obj@Vector` type chosen by the package.
The type *ADVector*\ ``::value_type`` is the scalar type used by the package
to record the operations in the algorithm.

Algo
****
The *Algo* class is derived from the :ref:`cpp_fun_obj-name` class
(we use *algo* for a corresponding object).
The gradient is for the last component of the range space of the algorithm.
Hence, *algo*\ ``.range()`` can be greater than one.

setup
=====
An *Algo* object is initialized using its
:ref:`cpp_fun_obj@setup` member function.

Grad
****
This is a :ref:`cpp_fun_obj-name` interface to the
gradient of the function corresponding to *Algo*
(we use *grad* for a corresponding object).
The object *grad* calculates the gradient of the last component of the vector
returned by *algo*.

setup
=====
The object *grad* is initialized using its ``setup`` member function
(which in turn initializes *algo* using its ``setup`` member function).
The ``setup`` functions should do calculations that do not depend on *x*
(to make the evaluation of the gradient faster).

vector_type
***********
The type of the vectors *x* and *g* is

| |tab| ``typedef cmpad::vector<double>`` *Grad* :: ``vector_type``

This is different from *Algo* :: ``vector_type`` which usually is
an AD vector type for a particular package..

scalar_type
***********
The type of the elements of *x* and *g* is

| |tab| ``typedef double`` *Grad* :: ``scalar_type``

This is different from *Algo* :: ``scalar_type`` which usually is
an AD scalar type for a particular package.


domain
******
This returns the dimension of the
:ref:`cpp_fun_obj@domain` space dimension for the function and gradient.

range
*****
This returns the dimension of the
:ref:`cpp_fun_obj@range` space dimension for the gradient.
The dimension of the range space for the gradient is equal
to the dimension of the domain space for the gradient and function.
Hence ``range`` is implemented by this interface and not virtual.

x
*
This vector has size equal to the dimension of the domain space.
It is the point at which the gradient,
of the function represented by *algo* , is evaluated.

g
*
This result is has equal to the dimension of the range space for the gradient,
which is equal to the size of *x* .
It is the gradient evaluated at the point *x* .

Example and Derived Classes
***************************
{xrst_comment BEGIN_SORT_THIS_LINE_PLUS_3}
{xrst_toc_table
   cpp/xam/gradient/gradient.xrst
   cpp/include/cmpad/adept/gradient.hpp
   cpp/include/cmpad/adolc/gradient.hpp
   cpp/include/cmpad/autodiff/gradient.hpp
   cpp/include/cmpad/codi/gradient.hpp
   cpp/include/cmpad/cppad/gradient.hpp
   cpp/include/cmpad/cppad_jit/gradient.hpp
   cpp/include/cmpad/cppadcg/gradient.hpp
   cpp/include/cmpad/sacado/gradient.hpp
   cpp/include/cmpad/xad/gradient.hpp
}
{xrst_comment END_SORT_THIS_LINE_MINUS_2}

{xrst_end cpp_gradient}