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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 .
Computing Sparse Jacobian Using Forward Mode: Example and Test
# include <cppad/cppad.hpp>
bool sparse_jac_for(void)
{   bool ok = true;
    //
    using CppAD::AD;
    using CppAD::NearEqual;
    using CppAD::sparse_rc;
    using CppAD::sparse_rcv;
    //
    typedef CPPAD_TESTVECTOR(AD<double>) a_vector;
    typedef CPPAD_TESTVECTOR(double)     d_vector;
    typedef CPPAD_TESTVECTOR(size_t)     s_vector;
    //
    // domain space vector
    size_t n = 3;
    a_vector  a_x(n);
    for(size_t j = 0; j < n; j++)
        a_x[j] = AD<double> (0);
    //
    // declare independent variables and starting recording
    CppAD::Independent(a_x);
    //
    size_t m = 4;
    a_vector  a_y(m);
    a_y[0] = a_x[0] + a_x[2];
    a_y[1] = a_x[0] + a_x[2];
    a_y[2] = a_x[1] + a_x[2];
    a_y[3] = a_x[1] + a_x[2] * a_x[2] / 2.;
    //
    // create f: x -> y and stop tape recording
    CppAD::ADFun<double> f(a_x, a_y);
    //
    // new value for the independent variable vector
    d_vector x(n);
    for(size_t j = 0; j < n; j++)
        x[j] = double(j);
    /*
           [ 1 0 1   ]
    J(x) = [ 1 0 1   ]
           [ 0 1 1   ]
           [ 0 1 x_2 ]
    */
    d_vector check(m * n);
    //
    // column-major order values of J(x)
    size_t nnz = 8;
    s_vector check_row(nnz), check_col(nnz);
    d_vector check_val(nnz);
    for(size_t k = 0; k < nnz; k++)
    {   // check_val
        if( k < 7 )
            check_val[k] = 1.0;
        else
            check_val[k] = x[2];
        //
        // check_row and check_col
        check_row[k] = k;
        if( k < 2 )
            check_col[k] = 0;
        else if( k < 4 )
            check_col[k] = 1;
        else
        {   check_col[k] = 2;
            check_row[k] = k - 4;
        }
    }
    //
    // n by n identity matrix sparsity
    sparse_rc<s_vector> pattern_in;
    pattern_in.resize(n, n, n);
    for(size_t k = 0; k < n; k++)
        pattern_in.set(k, k, k);
    //
    // sparsity for J(x)
    bool transpose     = false;
    bool dependency    = false;
    bool internal_bool = true;
    sparse_rc<s_vector> pattern_jac;
    f.for_jac_sparsity(
        pattern_in, transpose, dependency, internal_bool, pattern_jac
    );
    //
    // compute entire forward mode Jacobian
    sparse_rcv<s_vector, d_vector> subset( pattern_jac );
    CppAD::sparse_jac_work work;
    std::string coloring = "cppad";
    size_t group_max = 10;
    size_t n_color = f.sparse_jac_for(
        group_max, x, subset, pattern_jac, coloring, work
    );
    ok &= n_color == 2;
    //
    const s_vector row( subset.row() );
    const s_vector col( subset.col() );
    const d_vector val( subset.val() );
    s_vector col_major = subset.col_major();
    ok  &= subset.nnz() == nnz;
    for(size_t k = 0; k < nnz; k++)
    {   ok &= row[ col_major[k] ] == check_row[k];
        ok &= col[ col_major[k] ] == check_col[k];
        ok &= val[ col_major[k] ] == check_val[k];
    }
    // compute non-zero in row 3 only
    sparse_rc<s_vector> pattern_row3;
    pattern_row3.resize(m, n, 2); // nr = m, nc = n, nnz = 2
    pattern_row3.set(0, 3, 1);    // row[0] = 3, col[0] = 1
    pattern_row3.set(1, 3, 2);    // row[1] = 3, col[1] = 2
    sparse_rcv<s_vector, d_vector> subset_row3( pattern_row3 );
    work.clear();
    n_color = f.sparse_jac_for(
        group_max, x, subset_row3, pattern_jac, coloring, work
    );
    ok &= n_color == 2;
    //
    const s_vector row_row3( subset_row3.row() );
    const s_vector col_row3( subset_row3.col() );
    const d_vector val_row3( subset_row3.val() );
    ok &= subset_row3.nnz() == 2;
    //
    ok &= row_row3[0] == 3;
    ok &= col_row3[0] == 1;
    ok &= val_row3[0] == 1.0;
    //
    ok &= row_row3[1] == 3;
    ok &= col_row3[1] == 2;
    ok &= val_row3[1] == x[2];
    //
    return ok;
}
Input File: example/sparse/sparse_jac_for.cpp