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

eigen_array.cpp

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Using Eigen Arrays: Example and Test

# include <cppad/cppad.hpp>
# include <cppad/example/cppad_eigen.hpp>

bool eigen_array(void)
{   bool ok = true;
    using CppAD::AD;
    using CppAD::NearEqual;
    //
    typedef CppAD::eigen_vector< AD<double> > a_vector;
    //
    // domain and range space vectors
    size_t n  = 10, m = n;
    a_vector a_x(n), a_y(m);

    // set and declare independent variables and start tape recording
    for(size_t j = 0; j < n; j++)
        a_x[j] = double(1 + j);
    CppAD::Independent(a_x);

    // evaluate a component wise function
    for(size_t j = 0; j < n; j++)
        a_y[j] = a_x[j] + sin( a_x[j] );

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

    // compute the derivative of y w.r.t x using CppAD
    CPPAD_TESTVECTOR(double) x(n);
    for(size_t j = 0; j < n; j++)
        x[j] = double(j) + 1.0 / double(j+1);
    CPPAD_TESTVECTOR(double) jac = f.Jacobian(x);

    // check Jacobian
    double eps = 100. * CppAD::numeric_limits<double>::epsilon();
    for(size_t i = 0; i < m; i++)
    {   for(size_t j = 0; j < n; j++)
        {   double check = 1.0 + cos(x[i]);
            if( i != j )
                check = 0.0;
            ok &= NearEqual(jac[i * n + j], check, eps, eps);
        }
    }

    return ok;
}