ColPack: Sparse Jacobian Example and Test

colpack_jacobian.cpp

Headings

@(@\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 . ColPack: Sparse Jacobian Example and Test


# include <cppad/cppad.hpp>
bool colpack_jacobian(void)
{   bool ok = true;
    using CppAD::AD;
    using CppAD::NearEqual;
    typedef CPPAD_TESTVECTOR(AD<double>) a_vector;
    typedef CPPAD_TESTVECTOR(double)     d_vector;
    typedef CppAD::vector<size_t>        i_vector;
    size_t i, j, k, ell;
    double eps = 10. * CppAD::numeric_limits<double>::epsilon();

    // domain space vector
    size_t n = 4;
    a_vector  a_x(n);
    for(j = 0; j < n; j++)
        a_x[j] = AD<double> (0);

    // declare independent variables and starting recording
    CppAD::Independent(a_x);

    size_t m = 3;
    a_vector  a_y(m);
    a_y[0] = a_x[0] + a_x[1];
    a_y[1] = a_x[2] + a_x[3];
    a_y[2] = a_x[0] + a_x[1] + a_x[2] + a_x[3] * a_x[3] / 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(j = 0; j < n; j++)
        x[j] = double(j);

    /*
          [ 1 1 0 0  ]
    jac = [ 0 0 1 1  ]
          [ 1 1 1 x_3]
    */
    d_vector check(m * n);
    check[0] = 1.; check[1] = 1.; check[2]  = 0.; check[3]  = 0.;
    check[4] = 0.; check[5] = 0.; check[6]  = 1.; check[7]  = 1.;
    check[8] = 1.; check[9] = 1.; check[10] = 1.; check[11] = x[3];

    // Normally one would use f.ForSparseJac or f.RevSparseJac to compute
    // sparsity pattern, but for this example we extract it from check.
    std::vector< std::set<size_t> >  p(m);

    // using row and column indices to compute non-zero in rows 1 and 2
    i_vector row, col;
    for(i = 0; i < m; i++)
    {   for(j = 0; j < n; j++)
        {   ell = i * n + j;
            if( check[ell] != 0. )
            {   row.push_back(i);
                col.push_back(j);
                p[i].insert(j);
            }
        }
    }
    size_t K = row.size();
    d_vector jac(K);

    // empty work structure
    CppAD::sparse_jacobian_work work;
    ok &= work.color_method == "cppad";

    // choose to use ColPack
    work.color_method = "colpack";

    // forward mode
    size_t n_sweep = f.SparseJacobianForward(x, p, row, col, jac, work);
    for(k = 0; k < K; k++)
    {   ell = row[k] * n + col[k];
        ok &= NearEqual(check[ell], jac[k], eps, eps);
    }
    ok &= n_sweep == 4;

    // reverse mode
    work.clear();
    work.color_method = "colpack";
    n_sweep = f.SparseJacobianReverse(x, p, row, col, jac, work);
    for(k = 0; k < K; k++)
    {   ell = row[k] * n + col[k];
        ok &= NearEqual(check[ell], jac[k], eps, eps);
    }
    ok &= n_sweep == 2;

    return ok;
}

Input File: example/sparse/colpack_jacobian.cpp