\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)

sparse_jac_rev.cpp

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Computing Sparse Jacobian Using Reverse Mode: Example and Test

# include <cppad/cppad.hpp>
bool sparse_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;
   //
   // 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  ]
   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;
      }
   }
   //
   // m by m identity matrix sparsity
   sparse_rc<s_vector> pattern_in(m, m, m);
   for(size_t k = 0; k < m; k++)
      pattern_in.set(k, k, k);
   //
   // sparsity for J(x)
   bool transpose     = false;
   bool dependency    = false;
   bool internal_bool = true;
   sparse_rc<s_vector> pattern_jac;
   f.rev_jac_sparsity(
      pattern_in, transpose, dependency, internal_bool, pattern_jac
   );
   //
   // compute entire reverse mode Jacobian
   sparse_rcv<s_vector, d_vector> subset( pattern_jac );
   CppAD::sparse_jac_work work;
   std::string coloring = "cppad";
   size_t n_sweep = f.sparse_jac_rev(x, subset, pattern_jac, coloring, work);
   ok &= n_sweep == 2;
   //
   const s_vector row( subset.row() );
   const s_vector col( subset.col() );
   const d_vector val( subset.val() );
   s_vector row_major = subset.row_major();
   ok  &= subset.nnz() == nnz;
   for(size_t k = 0; k < nnz; k++)
   {  ok &= row[ row_major[k] ] == check_row[k];
      ok &= col[ row_major[k] ] == check_col[k];
      ok &= val[ row_major[k] ] == check_val[k];
   }
   //
   // test using work stored by previous sparse_jac_rev
   sparse_rc<s_vector> pattern_not_used;
   std::string         coloring_not_used;
   n_sweep = f.sparse_jac_rev(x, subset, pattern_jac, coloring, work);
   ok &= n_sweep == 2;
   for(size_t k = 0; k < nnz; k++)
   {  ok &= row[ row_major[k] ] == check_row[k];
      ok &= col[ row_major[k] ] == check_col[k];
      ok &= val[ row_major[k] ] == check_val[k];
   }
   //
   // compute non-zero in col 3 only, nr = m, nc = n, nnz = 2
   sparse_rc<s_vector> pattern_col3(m, n, 2);
   pattern_col3.set(0, 1, 3);    // row[0] = 1, col[0] = 3
   pattern_col3.set(1, 2, 3);    // row[1] = 2, col[1] = 3
   sparse_rcv<s_vector, d_vector> subset_col3( pattern_col3 );
   work.clear();
   n_sweep = f.sparse_jac_rev(x, subset_col3, pattern_jac, coloring, work);
   ok &= n_sweep == 2;
   //
   const s_vector row_col3( subset_col3.row() );
   const s_vector col_col3( subset_col3.col() );
   const d_vector val_col3( subset_col3.val() );
   ok &= subset_col3.nnz() == 2;
   //
   ok &= row_col3[0] == 1;
   ok &= col_col3[0] == 3;
   ok &= val_col3[0] == 1.0;
   //
   ok &= row_col3[1] == 2;
   ok &= col_col3[1] == 3;
   ok &= val_col3[1] == x[3];
   //
   return ok;
}