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Up-> CppAD Install cmake colpack_prefix colpack_hessian.cpp

colpack_hessian.cpp

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# include <cppad/cppad.hpp>
bool colpack_hessian(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 = 5;
    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);

    // colpack example case where hessian is a spear head
    // i.e, H(i, j) non zero implies i = 0, j = 0, or i = j
    AD<double> sum = 0.0;
    // partial_0 partial_j = x[j]
    // partial_j partial_j = x[0]
    for(j = 1; j < n; j++)
        sum += a_x[0] * a_x[j] * a_x[j] / 2.0;
    //
    // partial_i partial_i = 2 * x[i]
    for(i = 0; i < n; i++)
        sum += a_x[i] * a_x[i] * a_x[i] / 3.0;

    // declare dependent variables
    size_t m = 1;
    a_vector  a_y(m);
    a_y[0] = sum;

    // 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);

    /*
          [ 2  2  3  4  5 ]
    hes = [ 2  5  0  0  0 ]
          [ 3  0  7  0  0 ]
          [ 4  0  0  9  0 ]
          [ 5  0  0  0 11 ]
    */
    d_vector check(n * n);
    for(i = 0; i < n; i++)
    {   for(j = 0; j < n; j++)
        {   size_t index = i * n + j;
            check[index] = 0.0;
            if( i == 0 && 1 <= j )
                check[index] += x[j];
            if( 1 <= i && j == 0 )
                check[index] += x[i];
            if( i == j )
            {   check[index] += 2.0 * x[i];
                if( i != 0 )
                    check[index] += x[0];
            }
        }
    }
    // Normally one would use f.RevSparseHes to compute
    // sparsity pattern, but for this example we extract it from check.
    std::vector< std::set<size_t> >  p(n);
    i_vector row, col;
    for(i = 0; i < n; i++)
    {   for(j = 0; j < n; j++)
        {   ell = i * n + j;
            if( check[ell] != 0. )
            {   // insert this non-zero entry in sparsity pattern
                p[i].insert(j);

                // the Hessian is symmetric, so only lower triangle
                if( j <= i )
                {   row.push_back(i);
                    col.push_back(j);
                }
            }
        }
    }
    size_t K = row.size();
    d_vector hes(K);

    // default coloring method is cppad.symmetric
    CppAD::sparse_hessian_work work;
    ok &= work.color_method == "cppad.symmetric";

    // contrast and check results for both CppAD and Colpack
    for(size_t i_method = 0; i_method < 4; i_method++)
    {   // empty work structure
        switch(i_method)
        {   case 0:
            work.color_method = "cppad.symmetric";
            break;

            case 1:
            work.color_method = "cppad.general";
            break;

            case 2:
            work.color_method = "colpack.symmetric";
            break;

            case 3:
            work.color_method = "colpack.general";
            break;
        }

        // compute Hessian
        d_vector w(m);
        w[0] = 1.0;
        size_t n_sweep = f.SparseHessian(x, w, p, row, col, hes, work);
        //
        // check result
        for(k = 0; k < K; k++)
        {   ell = row[k] * n + col[k];
            ok &= NearEqual(check[ell], hes[k], eps, eps);
        }
        if(
            work.color_method == "cppad.symmetric"
        ||  work.color_method == "colpack.symmetric"
        )
            ok &= n_sweep == 2;
        else
            ok &= n_sweep == 5;
        //
        // check that clear resets color_method to cppad.symmetric
        work.clear();
        ok &= work.color_method == "cppad.symmetric";
    }

    return ok;
}