# include <cppad/cppad.hpp>

bool rev_jac_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);

     // sparsity pattern for the identity matrix
     size_t nr     = m;
     size_t nc     = m;
     size_t nnz_in = m;
     sparsity pattern_in(nr, nc, nnz_in);
     for(size_t k = 0; k < nnz_in; k++)
     {     size_t r = k;
          size_t c = k;
          pattern_in.set(k, r, c);
     }
     // compute sparsite pattern for J(x) = F'(x)
     bool transpose       = false;
     bool dependency      = false;
     bool internal_bool   = false;
     sparsity pattern_out;
     f.rev_jac_sparsity(
          pattern_in, transpose, dependency, internal_bool, pattern_out
     );
     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;
     internal_bool = true;
     f.rev_jac_sparsity(
          pattern_in, transpose, dependency, internal_bool, 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;
     }
     return ok;
}