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

subgraph_jac_rev.cpp

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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;
}