Subgraph Dependency Sparsity Patterns: Example and Test

subgraph_sparsity.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 . Subgraph Dependency Sparsity Patterns: Example and Test

# include <cppad/cppad.hpp>

bool subgraph_sparsity(void)
{   bool ok = true;
    using CppAD::AD;
    typedef CPPAD_TESTVECTOR(size_t)     SizeVector;
    typedef CppAD::sparse_rc<SizeVector> sparsity;
    //
    // domain space vector
    size_t n = 2;
    CPPAD_TESTVECTOR(AD<double>) ax(n);
    ax[0] = 0.;
    ax[1] = 1.;

    // declare independent variables and start recording
    CppAD::Independent(ax);

    // range space vector
    size_t m = 3;
    CPPAD_TESTVECTOR(AD<double>) ay(m);
    ay[0] = ax[0];
    ay[1] = ax[0] * ax[1];
    ay[2] = ax[1];

    // create f: x -> y and stop tape recording
    CppAD::ADFun<double> f(ax, ay);
    ok &= f.size_random() == 0;

    // compute sparsite pattern for F'(x)
    CPPAD_TESTVECTOR(bool) 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;
    bool transpose       = false;
    sparsity pattern_out;
    f.subgraph_sparsity(select_domain, select_range, transpose, pattern_out);

    // check sparsity pattern
    size_t nnz = pattern_out.nnz();
    ok        &= nnz == 4;
    ok        &= pattern_out.nr() == m;
    ok        &= pattern_out.nc() == n;
    {   // check results
        const SizeVector& row( pattern_out.row() );
        const SizeVector& col( pattern_out.col() );
        SizeVector col_major = pattern_out.col_major();
        //
        ok &= row[ col_major[0] ] ==  0  && col[ col_major[0] ] ==  0;
        ok &= row[ col_major[1] ] ==  1  && col[ col_major[1] ] ==  0;
        ok &= row[ col_major[2] ] ==  1  && col[ col_major[2] ] ==  1;
        ok &= row[ col_major[3] ] ==  2  && col[ col_major[3] ] ==  1;
    }
    // note that the transpose of the identity is the identity
    transpose     = true;
    f.subgraph_sparsity(select_domain, select_range, transpose, pattern_out);
    //
    nnz  = pattern_out.nnz();
    ok  &= nnz == 4;
    ok  &= pattern_out.nr() == n;
    ok  &= pattern_out.nc() == m;
    {   // check results
        const SizeVector& row( pattern_out.row() );
        const SizeVector& col( pattern_out.col() );
        SizeVector row_major = pattern_out.row_major();
        //
        ok &= col[ row_major[0] ] ==  0  && row[ row_major[0] ] ==  0;
        ok &= col[ row_major[1] ] ==  1  && row[ row_major[1] ] ==  0;
        ok &= col[ row_major[2] ] ==  1  && row[ row_major[2] ] ==  1;
        ok &= col[ row_major[3] ] ==  2  && row[ row_major[3] ] ==  1;
    }
    ok &= f.size_random() > 0;
    f.clear_subgraph();
    ok &= f.size_random() == 0;
    return ok;
}

Input File: example/sparse/subgraph_sparsity.cpp