// SPDX-License-Identifier: EPL-2.0 OR GPL-2.0-or-later
// SPDX-FileCopyrightText: Bradley M. Bell <bradbell@seanet.com>
// SPDX-FileContributor: 2003-22 Bradley M. Bell
// ----------------------------------------------------------------------------

/*
Sparse Hessian Using Subgraphs and Jacobian: Example and Test
*/
# include <cppad/cppad.hpp>
bool subgraph_hes2jac(void)
{  bool ok = true;
   using CppAD::NearEqual;
   typedef CppAD::AD<double>                      a1double;
   typedef CppAD::AD<a1double>                    a2double;
   typedef CPPAD_TESTVECTOR(double)               d_vector;
   typedef CPPAD_TESTVECTOR(a1double)             a1vector;
   typedef CPPAD_TESTVECTOR(a2double)             a2vector;
   typedef CPPAD_TESTVECTOR(size_t)               s_vector;
   typedef CPPAD_TESTVECTOR(bool)                 b_vector;
   typedef CppAD::sparse_rcv<s_vector, d_vector>  sparse_matrix;
   //
   double eps = 10. * CppAD::numeric_limits<double>::epsilon();
   //
   // double version of x
   size_t n = 12;
   d_vector x(n);
   for(size_t j = 0; j < n; j++)
      x[j] = double(j + 2);
   //
   // a1double version of x
   a1vector a1x(n);
   for(size_t j = 0; j < n; j++)
      a1x[j] = x[j];
   //
   // a2double version of x
   a2vector a2x(n);
   for(size_t j = 0; j < n; j++)
      a2x[j] = a1x[j];
   //
   // declare independent variables and starting recording
   CppAD::Independent(a2x);
   //
   // a2double version of y = f(x) = 5 * x0 * x1 + sum_j xj^3
   size_t m = 1;
   a2vector a2y(m);
   a2y[0] = 5.0 * a2x[0] * a2x[1];
   for(size_t j = 0; j < n; j++)
      a2y[0] += a2x[j] * a2x[j] * a2x[j];
   //
   // create a1double version of f: x -> y and stop tape recording
   // (without executing zero order forward calculation)
   CppAD::ADFun<a1double> a1f;
   a1f.Dependent(a2x, a2y);
   //
   // Optimize this function to reduce future computations.
   // Perhaps only one optimization at the end would be faster.
   a1f.optimize();
   //
   // declare independent variables and start recording g(x) = f'(x)
   Independent(a1x);
   //
   // Use one reverse mode pass to compute z = f'(x)
   a1vector a1w(m), a1z(n);
   a1w[0] = 1.0;
   a1f.Forward(0, a1x);
   a1z = a1f.Reverse(1, a1w);
   //
   // create double version of g : x -> f'(x)
   CppAD::ADFun<double> g;
   g.Dependent(a1x, a1z);
   ok &= g.size_random() == 0;
   //
   // Optimize this function to reduce future computations.
   // Perhaps no optimization would be faster.
   g.optimize();
   //
   // compute f''(x) = g'(x)
   b_vector select_domain(n), select_range(n);
   for(size_t j = 0; j < n; ++j)
   {  select_domain[j] = true;
      select_range[j]  = true;
   }
   sparse_matrix hessian;
   g.subgraph_jac_rev(select_domain, select_range, x, hessian);
   // -------------------------------------------------------------------
   // check number of non-zeros in the Hessian
   // (only x0 * x1 generates off diagonal terms)
   ok &= hessian.nnz() == n + 2;
   //
   for(size_t k = 0; k < hessian.nnz(); ++k)
   {  size_t r = hessian.row()[k];
      size_t c = hessian.col()[k];
      double v = hessian.val()[k];
      //
      if( r == c )
      {  // a diagonal element
         double check = 6.0 * x[r];
         ok          &= NearEqual(v, check, eps, eps);
      }
      else
      {  // off diagonal element
         ok   &= (r == 0 && c == 1) || (r == 1 && c == 0);
         double check = 5.0;
         ok          &= NearEqual(v, check, eps, eps);
      }
   }
   ok &= g.size_random() > 0;
   g.clear_subgraph();
   ok &= g.size_random() == 0;
   return ok;
}
