Computing Sparse Jacobian Using Reverse Mode: Example and Test

subgraph_jac_rev.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 . Computing Sparse Jacobian Using Reverse Mode: Example and Test

# include <cppad/cppad.hpp>
bool subgraph_jac_rev(void)
{   bool ok = true;
    //
    using CppAD::AD;
    using CppAD::NearEqual;
    using CppAD::sparse_rc;
    using CppAD::sparse_rcv;
    //
    typedef CPPAD_TESTVECTOR(AD<double>) a_vector;
    typedef CPPAD_TESTVECTOR(double)     d_vector;
    typedef CPPAD_TESTVECTOR(size_t)     s_vector;
    typedef CPPAD_TESTVECTOR(bool)       b_vector;
    //
    // 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);
    ok &= f.size_random() == 0;
    //
    // 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  ]
    J(x) = [ 0 0 1 1  ]
           [ 1 1 1 x_3]
    */
    //
    // row-major order values of J(x)
    size_t nnz = 8;
    s_vector check_row(nnz), check_col(nnz);
    d_vector check_val(nnz);
    for(size_t k = 0; k < nnz; k++)
    {   // check_val
        if( k < 7 )
            check_val[k] = 1.0;
        else
            check_val[k] = x[3];
        //
        // check_row and check_col
        check_col[k] = k;
        if( k < 2 )
            check_row[k] = 0;
        else if( k < 4 )
            check_row[k] = 1;
        else
        {   check_row[k] = 2;
            check_col[k] = k - 4;
        }
    }
    //
    // select all range components of domain and range
    b_vector select_domain(n), select_range(m);
    for(size_t j = 0; j < n; ++j)
        select_domain[j] = true;
    for(size_t i = 0; i < m; ++i)
        select_range[i] = true;
    // -----------------------------------------------------------------------
    // Compute Jacobian using f.subgraph_jac_rev(x, subset)
    // -----------------------------------------------------------------------
    //
    // get sparsity pattern
    bool transpose     = false;
    sparse_rc<s_vector> pattern_jac;
    f.subgraph_sparsity(
        select_domain, select_range, transpose, pattern_jac
    );
    // f.subgraph_jac_rev(x, subset)
    sparse_rcv<s_vector, d_vector> subset( pattern_jac );
    f.subgraph_jac_rev(x, subset);
    //
    // check result
    ok  &= subset.nnz() == nnz;
    s_vector row_major = subset.row_major();
    for(size_t k = 0; k < nnz; k++)
    {   ok &= subset.row()[ row_major[k] ] == check_row[k];
        ok &= subset.col()[ row_major[k] ] == check_col[k];
        ok &= subset.val()[ row_major[k] ] == check_val[k];
    }
    // -----------------------------------------------------------------------
    // f.subgraph_jac_rev(select_domain, select_range, x, matrix_out)
    // -----------------------------------------------------------------------
    sparse_rcv<s_vector, d_vector>  matrix_out;
    f.subgraph_jac_rev(select_domain, select_range, x, matrix_out);
    //
    // check result
    ok  &= matrix_out.nnz() == nnz;
    row_major = matrix_out.row_major();
    for(size_t k = 0; k < nnz; k++)
    {   ok &= matrix_out.row()[ row_major[k] ] == check_row[k];
        ok &= matrix_out.col()[ row_major[k] ] == check_col[k];
        ok &= matrix_out.val()[ row_major[k] ] == check_val[k];
    }
    //
    ok &= f.size_random() > 0;
    f.clear_subgraph();
    ok &= f.size_random() == 0;
    return ok;
}

Input File: example/sparse/subgraph_jac_rev.cpp