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

code_gen_fun_sparse_jac_as_fun.cpp

View page source

Pass Sparse Jacobian as Code Gen Function: Example and Test

# include <cppad/example/code_gen_fun.hpp>

bool sparse_jac_as_fun(void)
{  bool ok = true;
   //
   typedef CppAD::cg::CG<double>     c_double;
   typedef CppAD::AD<c_double>      ac_double;
   //
   typedef CppAD::vector<size_t>     s_vector;
   typedef CppAD::vector<double>     d_vector;
   typedef CppAD::vector<ac_double> ac_vector;
   //
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

   // domain space vector
   size_t n  = 2;
   ac_vector ac_x(n);
   for(size_t j = 0; j < n; ++j)
      ac_x[j] = 1.0 / double(j + 1);

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

   // range space vector
   size_t m = 3;
   ac_vector ac_y(m);
   for(size_t i = 0; i < m; ++i)
      ac_y[i] = double(i + 1) * sin( ac_x[i % n] );

   // create f: x -> y and stop tape recording
   CppAD::ADFun<c_double> c_f(ac_x, ac_y);

   // create a version of f that evalutes using ac_double
   CppAD::ADFun<ac_double, c_double> ac_f = c_f.base2ad();

   // Independent varialbes while evaluating Jacobian
   CppAD::Independent(ac_x);

   // ----------------------------------------------------------------
   // Sparse Jacobian evaluation using any CppAD method
   // (there are lots of choices here)
   //
   // pattern_eye (pattern for identity matrix)
   CppAD::sparse_rc<s_vector> pattern_eye(n, n, n);
   for(size_t k = 0; k < n; ++k)
      pattern_eye.set(k, k, k);
   //
   // pattern_jac
   bool transpose     = false;
   bool dependency    = false;
   bool internal_bool = true;
   CppAD::sparse_rc<s_vector> pattern_jac;
   // note that c_f and ac_f have the same sparsity pattern
   c_f.for_jac_sparsity(
      pattern_eye, transpose, dependency, internal_bool, pattern_jac
   );
   //
   // ac_Jrcv
   CppAD::sparse_rcv<s_vector, ac_vector> ac_Jrcv( pattern_jac );
   CppAD::sparse_jac_work work;
   std::string coloring = "cppad";
   size_t group_max = n;
   ac_f.sparse_jac_for(
      group_max, ac_x, ac_Jrcv, pattern_jac, coloring, work
   );
   //
   // create g: x -> non-zero elements of Jacobian
   CppAD::ADFun<c_double> c_g(ac_x, ac_Jrcv.val());

   // create compiled version of c_g
   std::string file_name = "example_lib";
   code_gen_fun g(file_name, c_g);

   // evaluate the compiled jacobian
   d_vector x(n);
   for(size_t j = 0; j < n; ++j)
      x[j] = 1.0 / double(j + 2);
   d_vector val = g(x);

   // check Jaociban values
   size_t nnz = pattern_jac.nnz();
   const s_vector& row(pattern_jac.row());
   const s_vector& col(pattern_jac.col());
   s_vector row_major = pattern_jac.row_major();
   //
   size_t k = 0;
   ok &= val.size() == nnz;
   for(size_t i = 0; i < m; ++i)
   {  for(size_t j = 0; j < n; ++j)
      {  if( j == i % n )
         {  size_t ell = row_major[k];
            double check = double(i + 1) * cos( x[i % n] );
            ok &= i == row[ell];
            ok &= j == col[ell];
            ok &= CppAD::NearEqual(val[k], check, eps99, eps99);
            ++k;
         }
      }
   }
   ok &= k == nnz;
   return ok;
}