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@(@\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }@)@ This is cppad-20221105 documentation. Here is a link to its current documentation .
Dynamic Parameters: Example and Test
# include <limits>
# include <cppad/cppad.hpp>

bool new_dynamic(void)
{   bool ok = true;
    using CppAD::AD;
    using CppAD::NearEqual;
    double eps = 10. * std::numeric_limits<double>::epsilon();

    // independent dynamic parameter vector
    size_t nd = 3;
    CPPAD_TESTVECTOR(AD<double>) adynamic(nd);
    adynamic[0] = 1.0;
    adynamic[1] = 1.0;
    adynamic[2] = 1.0;

    // domain space vector
    size_t nx = 2;
    CPPAD_TESTVECTOR(AD<double>) ax(nx);
    ax[0] = 0.;
    ax[1] = 1.;

    // declare independent variables, dynamic parammeters, starting recording
    CppAD::Independent(ax, adynamic);

    // create a dependent dynamic parameter
    AD<double> adependent_dyn = adynamic[0] + 2.0;

    // check that elements of adynamic are currently dynamic parameters
    for(size_t j = 0; j < nd; ++j)
        ok &= Dynamic( adynamic[j] );
    ok &= Dynamic( adependent_dyn );

    // range space vector
    size_t ny = 1;
    CPPAD_TESTVECTOR(AD<double>) ay(ny);
    ay[0]  = adependent_dyn  + ax[0];
    ay[0] *= adynamic[1]     + ax[0];
    ay[0] *= adynamic[2]     + ax[1];

    // create f: x -> y and stop tape recording
    CppAD::ADFun<double> f(ax, ay);

    // check the number of independent dynamic parameters in f
    ok &= f.size_dyn_ind() == nd;

    // total number of dynamic parameters in f
    ok &= f.size_dyn_par() == nd + 1;

    // check that these are no longer dynamic parameters
    for(size_t j = 0; j < nd; ++j)
        ok &= ! Dynamic( adynamic[j] );
    ok &= ! Dynamic( adependent_dyn );

    // zero order forward mode
    CPPAD_TESTVECTOR(double) x(nx), y(ny);
    x[0] = 3.;
    x[1] = 4.;
    y    = f.Forward(0, x);
    ok  &= f.size_order() == 1;
    double check;
    check  = Value( adynamic[0] ) + 2.0 + x[0];
    check *= Value( adynamic[1] ) + x[0];
    check *= Value( adynamic[2] ) + x[1];
    ok  &= NearEqual(y[0] , check, eps, eps);

    // change the dynamic parameter values
    CPPAD_TESTVECTOR(double) dynamic(nd);
    dynamic[0] = 2.0;
    dynamic[1] = 3.0;
    dynamic[2] = 4.0;
    f.new_dynamic(dynamic);
    ok  &= f.size_order() == 0;
    //
    y    = f.Forward(0, x);
    ok  &= f.size_order() == 1;
    check  = dynamic[0] + 2.0 + x[0];
    check *= dynamic[1] + x[0];
    check *= dynamic[2] + x[1];
    ok  &= NearEqual(y[0] , check, eps, eps);

    // use first order foward mode to compute partial of f w.r.t x[0]
    CPPAD_TESTVECTOR(double) dx(nx), dy(ny);
    dx[0] = 1.0;
    dx[1] = 0.0;
    dy    = f.Forward(1, dx);
    ok   &= f.size_order() == 2;
    check = (dynamic[2] + x[1])*(dynamic[0] + 2.0 + x[0] + dynamic[1] + x[0]);
    ok  &= NearEqual(dy[0] , check, eps, eps);
    //
    return ok;
}
Input File: example/general/new_dynamic.cpp