ColPack: Sparse Jacobian Example and Test

colpack_jac.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_jac(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;
    typedef CppAD::sparse_rc<i_vector>              sparsity;
    typedef CppAD::sparse_rcv<i_vector, d_vector>   sparse_matrix;

    // domain space vector
    size_t n = 4;
    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 = 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(size_t j = 0; j < n; j++)
        x[j] = double(j);

    /*
          [ 1 1 0 0  ]
    jac = [ 0 0 1 1  ]
          [ 1 1 1 x_3]
    */
    // Normally one would use CppAD to compute sparsity pattern, but for this
    // example we set it directly
    size_t nr  = m;
    size_t nc  = n;
    size_t nnz = 8;
    sparsity pattern(nr, nc, nnz);
    d_vector check(nnz);
    for(size_t k = 0; k < nnz; k++)
    {   size_t r, c;
        if( k < 2 )
        {   r = 0;
            c = k;
        }
        else if( k < 4 )
        {   r = 1;
            c = k;
        }
        else
        {   r = 2;
            c = k - 4;
        }
        pattern.set(k, r, c);
        if( k == nnz - 1 )
            check[k] = x[3];
        else
            check[k] = 1.0;
    }

    // using row and column indices to compute non-zero in rows 1 and 2
    sparse_matrix subset( pattern );

    // check results for both CppAD and Colpack
    for(size_t i_method = 0; i_method < 4; i_method++)
    {   // coloring method
        std::string coloring;
        if( i_method % 2 == 0 )
            coloring = "cppad";
        else
            coloring = "colpack";
        //
        CppAD::sparse_jac_work work;
        size_t group_max = 1;
        if( i_method / 2 == 0 )
        {   size_t n_sweep = f.sparse_jac_for(
                group_max, x, subset, pattern, coloring, work
            );
            ok &= n_sweep == 4;
        }
        else
        {   size_t n_sweep = f.sparse_jac_rev(
                x, subset, pattern, coloring, work
            );
            ok &= n_sweep == 2;
        }
        const d_vector& hes( subset.val() );
        for(size_t k = 0; k < nnz; k++)
            ok &= check[k] == hes[k];
    }
    return ok;
}

Input File: example/sparse/colpack_jac.cpp