lines 14-102 of file: lib/cplusplus/fun.cpp

{xrst_begin cpp_independent}
{xrst_spell
   nd
   nx
}


Declare Independent Variables and Start Recording
#################################################

Syntax
******

| *ax* =  ``cppad_py::independent`` ( *x* )
| *a_both* =  ``cppad_py::independent`` ( *x* , *dynamic* )

Purpose
*******
This starts recording :ref:`a_double-name` operations.
This recording is terminated, and the information is stored,
by calling the :ref:`d_fun_constructor<cpp_fun_ctor-name>`.
It can be terminated, and the information is lost,
by calling :ref:`abort_recording<cpp_abort_recording-name>`.

x
*
This argument has prototype

| |tab| ``const vec_double&`` *x*

Its specifies the number of independent variables
and their values during the recording.
We use the notation *nx* = *x*\ ``.size`` ()
to denote the number of independent variables.

dynamic
*******
This argument has prototype

| |tab| ``const vec_double&`` *dynamic*

Its specifies the number of independent dynamic parameters
and their values during the recording.
We use the notation *nd* = *dynamic*\ ``.size`` ()
to denote the number of independent variables.

ax
**
This result has prototype

| |tab| ``vec_a_double&`` *ax*

and is the vector of independent variables.
It has size *nx* and for
*i* = 0 to *n* -1

| |tab| *ax* [ *i* ] == *x* [ *i* ]

a_both
******
this result has prototype

| |tab| ``vec_a_double&`` *a_both*

and is the vector of both the independent variables
and independent dynamic parameters.
It has size *nx* + *nd* .
For *i* = 0 to *nx* -1

| |tab| *a_both* [ *i* ] == *x* [ *i* ]

is the *i*-th independent variable.
For *i* = 0 to *nd* -1

| |tab| *a_both* [ *nx* + *i* ] == *dynamic* [ *i* ]

is the *i*-th independent dynamic parameter.

{xrst_toc_hidden
   example/cplusplus/fun_dynamic_xam.cpp
}
Example
*******
Most of the c++ ``d_fun`` examples use the *ax*
return syntax.
The :ref:`fun_dynamic_xam.cpp-name` example uses the *a_both*
return syntax.

{xrst_end cpp_independent}