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@(@\newcommand{\B}[1]{ {\bf #1} } \newcommand{\R}[1]{ {\rm #1} }@)@
Declare Independent Variables and Start Recording

Syntax
ax = module_ref independent(x)

module_ref
This is the module reference for the particular language.

x
This argument has prototype
     const vec_double& 
x
Its specifies the number of independent variables and their values during the recording. We use the notation n = x.size() to denote the number of independent variables.

ax
The result has prototype
     vec_a_double& 
ax
This is the vector of independent variables. It has size n and for i = 0 to n-1
     
ax[i].value() == x[i]

Purpose
This starts a recording of the a_double operation. This recording is terminated, and the information is stored, by calling the a_fun constructor . It is terminated, and the information is lost, by calling abort_recording .

Example
All of the a_fun examples use this function.
Input File: lib/a_fun.cpp