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af = module_ref a_fun(ax, ay)
     const vec_a_double& ax
independent.
To be specific, it must be the original independent variables.
We use the notation 
n = ax.size()
to denote the number of independent variables.
     const vec_a_double& ax
m = ax.size()
to denote the number of dependent variables.
     a_fun af
a_fun examples use an a_fun constructor.