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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 .
ADFun Assignment: Example and Test
# include <cppad/cppad.hpp>
# include <limits>

bool fun_assign(void)
{   bool ok = true;
    using CppAD::AD;
    using CppAD::NearEqual;
    size_t i, j;

    // ten times machine percision
    double eps = 10. * CppAD::numeric_limits<double>::epsilon();

    // an empty ADFun<double> object
    CppAD::ADFun<double> g;

    // domain space vector
    size_t n  = 3;
    CPPAD_TESTVECTOR(AD<double>) x(n);
    for(j = 0; j < n; j++)
        x[j] = AD<double>(j + 2);

    // declare independent variables and start tape recording
    CppAD::Independent(x);

    // range space vector
    size_t m = 2;
    CPPAD_TESTVECTOR(AD<double>) y(m);
    y[0] = x[0] + x[0] * x[1];
    y[1] = x[1] * x[2] + x[2];

    // Store operation sequence, and order zero forward results, in f.
    // This assignment will use move semantics
    CppAD::ADFun<double> f;
    f = CppAD::ADFun<double>(x, y);

    // sparsity pattern for the identity matrix
    CPPAD_TESTVECTOR(std::set<size_t>) r(n);
    for(j = 0; j < n; j++)
        r[j].insert(j);

    // Store forward mode sparsity pattern in f
    f.ForSparseJac(n, r);

    // make a copy of f in g
    g = f;

    // check values that should be equal
    ok &= ( g.size_order() == f.size_order() );
    ok &= ( (g.size_forward_bool() > 0) == (f.size_forward_bool() > 0) );
    ok &= ( (g.size_forward_set() > 0)  == (f.size_forward_set() > 0) );

    // Use zero order Taylor coefficient from f for first order
    // calculation using g.
    CPPAD_TESTVECTOR(double) dx(n), dy(m);
    for(i = 0; i < n; i++)
        dx[i] = 0.;
    dx[1] = 1;
    dy    = g.Forward(1, dx);
    ok &= NearEqual(dy[0], x[0], eps, eps); // partial y[0] w.r.t x[1]
    ok &= NearEqual(dy[1], x[2], eps, eps); // partial y[1] w.r.t x[1]

    // Use forward Jacobian sparsity pattern from f to calculate
    // Hessian sparsity pattern using g.
    CPPAD_TESTVECTOR(std::set<size_t>) s(1), h(n);
    s[0].insert(0); // Compute sparsity pattern for Hessian of y[0]
    h =  f.RevSparseHes(n, s);

    // check sparsity pattern for Hessian of y[0] = x[0] + x[0] * x[1]
    ok  &= ( h[0].find(0) == h[0].end() ); // zero     w.r.t x[0], x[0]
    ok  &= ( h[0].find(1) != h[0].end() ); // non-zero w.r.t x[0], x[1]
    ok  &= ( h[0].find(2) == h[0].end() ); // zero     w.r.t x[0], x[2]

    ok  &= ( h[1].find(0) != h[1].end() ); // non-zero w.r.t x[1], x[0]
    ok  &= ( h[1].find(1) == h[1].end() ); // zero     w.r.t x[1], x[1]
    ok  &= ( h[1].find(2) == h[1].end() ); // zero     w.r.t x[1], x[2]

    ok  &= ( h[2].find(0) == h[2].end() ); // zero     w.r.t x[2], x[0]
    ok  &= ( h[2].find(1) == h[2].end() ); // zero     w.r.t x[2], x[1]
    ok  &= ( h[2].find(2) == h[2].end() ); // zero     w.r.t x[2], x[2]

    return ok;
}
Input File: example/general/fun_assign.cpp