\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)

sparse_jac_fun.cpp

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sparse_jac_fun: Example and test

# include <cppad/speed/sparse_jac_fun.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/cppad.hpp>

bool sparse_jac_fun(void)
{   using CppAD::NearEqual;
    using CppAD::AD;

    bool ok = true;

    size_t j, k;
    double eps = CppAD::numeric_limits<double>::epsilon();
    size_t n   = 3;
    size_t m   = 4;
    size_t K   = 5;
    CppAD::vector<size_t>       row(K), col(K);
    CppAD::vector<double>       x(n),   yp(K);
    CppAD::vector< AD<double> > a_x(n), a_y(m);

    // choose x
    for(j = 0; j < n; j++)
        a_x[j] = x[j] = double(j + 1);

    // choose row, col
    for(k = 0; k < K; k++)
    {   row[k] = k % m;
        col[k] = (K - k) % n;
    }

    // declare independent variables
    Independent(a_x);

    // evaluate function
    size_t order = 0;
    CppAD::sparse_jac_fun< AD<double> >(m, n, a_x, row, col, order, a_y);

    // evaluate derivative
    order = 1;
    CppAD::sparse_jac_fun<double>(m, n, x, row, col, order, yp);

    // use AD to evaluate derivative
    CppAD::ADFun<double>   f(a_x, a_y);
    CppAD::vector<double>  jac(m * n);
    jac = f.Jacobian(x);

    for(k = 0; k < K; k++)
    {   size_t index = row[k] * n + col[k];
        ok &= NearEqual(jac[index], yp[k] , eps, eps);
    }
    return ok;
}