// 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
// ----------------------------------------------------------------------------
/*
Atomic function
g( x ) = [ x_2, x_0 * x_1 ]
\] $$
*/
# include <cppad/cppad.hpp>
namespace {   // isolate items below to this file
using   CppAD::vector;                          // vector
typedef vector< std::set<size_t> > set_vector;  // atomic_sparsity
//
// a utility to compute the union of two sets.
using CppAD::set_union;
//
class atomic_set_sparsity : public CppAD::atomic_base<double> {
public:
   // constructor
   atomic_set_sparsity(const std::string& name) :
   // this exampel only uses set sparsity patterns
   CppAD::atomic_base<double>(name, set_sparsity_enum )
   { }
private:
   // forward
   virtual bool forward(
      size_t                    p ,
      size_t                    q ,
      const vector<bool>&      vx ,
      vector<bool>&            vy ,
      const vector<double>&    tx ,
      vector<double>&          ty
   )
   {
      size_t n = tx.size() / (q + 1);
# ifndef NDEBUG
      size_t m = ty.size() / (q + 1);
# endif
      assert( n == 3 );
      assert( m == 2 );

      // only order zero
      bool ok = q == 0;
      if( ! ok )
         return ok;

      // check for defining variable information
      if( vx.size() > 0 )
      {  ok   &= vx.size() == n;
         vy[0] = vx[2];
         vy[1] = vx[0] || vx[1];
      }

      // Order zero forward mode.
      // y[0] = x[2], y[1] = x[0] * x[1]
      if( p <= 0 )
      {  ty[0] = tx[2];
         ty[1] = tx[0] * tx[1];
      }
      return ok;
   }
   // for_sparse_jac
   virtual bool for_sparse_jac(
      size_t                          p ,
      const set_vector&               r ,
      set_vector&                     s ,
      const vector<double>&           x )
   {  // This function needed if using f.ForSparseJac
# ifndef NDEBUG
      size_t n = r.size();
      size_t m = s.size();
# endif
      assert( n == x.size() );
      assert( n == 3 );
      assert( m == 2 );

      // sparsity for S(x) = f'(x) * R  = [ 0,   0, 1 ] * R
      s[0] = r[2];
      // s[1] = union(r[0], r[1])
      s[1] = set_union(r[0], r[1]);
      //
      return true;
   }
   virtual bool rev_sparse_jac(
      size_t                                p  ,
      const set_vector&                     rt ,
      set_vector&                           st ,
      const vector<double>&                 x  )
   {  // This function needed if using RevSparseJac or optimize
# ifndef NDEBUG
      size_t n = st.size();
      size_t m = rt.size();
# endif
      assert( n == x.size() );
      assert( n == 3 );
      assert( m == 2 );

      //                                       [ 0, x1 ]
      // sparsity for S(x)^T = f'(x)^T * R^T = [ 0, x0 ] * R^T
      //                                       [ 1, 0  ]
      st[0] = rt[1];
      st[1] = rt[1];
      st[2] = rt[0];
      return true;
   }
   virtual bool for_sparse_hes(
      const vector<bool>&                   vx,
      const vector<bool>&                   r ,
      const vector<bool>&                   s ,
      set_vector&                           h ,
      const vector<double>&                 x )
   {
      size_t n = r.size();
# ifndef NDEBUG
      size_t m = s.size();
# endif
      assert( x.size() == n );
      assert( h.size() == n );
      assert( n == 3 );
      assert( m == 2 );

      // initialize h as empty
      for(size_t i = 0; i < n; i++)
         h[i].clear();

      // only f_1 has a non-zero hessian
      if( ! s[1] )
         return true;

      // only the cross term between x[0] and x[1] is non-zero
      if( ! ( r[0] & r[1] ) )
         return true;

      // set the possibly non-zero terms in the hessian
      h[0].insert(1);
      h[1].insert(0);

      return true;
   }
   virtual bool rev_sparse_hes(
      const vector<bool>&                   vx,
      const vector<bool>&                   s ,
      vector<bool>&                         t ,
      size_t                                p ,
      const set_vector&                     r ,
      const set_vector&                     u ,
      set_vector&                           v ,
      const vector<double>&                 x )
   {  // This function needed if using RevSparseHes
# ifndef NDEBUG
      size_t m = s.size();
      size_t n = t.size();
# endif
      assert( x.size() == n );
      assert( r.size() == n );
      assert( u.size() == m );
      assert( v.size() == n );
      assert( n == 3 );
      assert( m == 2 );

      // sparsity for T(x) = S(x) * f'(x) = S(x) * [  0,  0,  1 ]
      //                                           [ x1, x0,  0 ]
      t[0] = s[1];
      t[1] = s[1];
      t[2] = s[0];

      // V(x) = f'(x)^T * g''(y) * f'(x) * R  +  g'(y) * f''(x) * R
      // U(x) = g''(y) * f'(x) * R
      // S(x) = g'(y)

      //                                      [ 0, x1 ]
      // sparsity for W(x) = f'(x)^T * U(x) = [ 0, x0 ] * U(x)
      //                                      [ 1, 0  ]
      v[0] = u[1];
      v[1] = u[1];
      v[2] = u[0];
      //
      //                                      [ 0, 1, 0 ]
      // sparsity for V(x) = W(x) + S_1 (x) * [ 1, 0, 0 ] * R
      //                                      [ 0, 0, 0 ]
      if( s[1] )
      {  // v[0] = union( v[0], r[1] )
         v[0] = set_union(v[0], r[1]);
         // v[1] = union( v[1], r[0] )
         v[1] = set_union(v[1], r[0]);
      }
      return true;
   }
}; // End of atomic_set_sparsity class


// f(u) = g( u_0 + u_1 , u_0 + u_1 , u_2 )
//      = [ u_2 , (u_0 + u_1)^2 ]
bool test_one(void)
{  bool ok = true;
   using CppAD::AD;
   using CppAD::NearEqual;
   double eps = 10. * std::numeric_limits<double>::epsilon();
   // Create the atomic get_started object
   atomic_set_sparsity afun("atomic_set_sparsity");
   size_t n = 3;
   size_t m = 2;
   vector< AD<double> > au(n), ay(m);
   for(size_t j = 0; j < n; j++)
      au[j] = double(j + 1);

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

   // ax
   vector< AD<double> > ax(n);
   ax[0] = au[0] + au[1];
   ax[1] = au[0] + au[1];
   ax[2] = au[2];

   // call atomic function
   afun(ax, ay);

   // create f: u -> y and stop tape recording
   CppAD::ADFun<double> f(au, ay);

   // check function value
   ok &= NearEqual(ay[0] , au[2],  eps, eps);
   ok &= NearEqual(ay[1] , (au[0] + au[1]) * (au[0] + au[1]),  eps, eps);

   // correct Jacobian result
   set_vector check_s(m);
   check_s[0].insert(2);
   check_s[1].insert(0);
   check_s[1].insert(1);
   // compute and test forward mode
   {  set_vector r(n), s(m);
      for(size_t i = 0; i < n; i++)
         r[i].insert(i);
      s = f.ForSparseJac(n, r);
      for(size_t i = 0; i < m; i++)
         ok &= s[i] == check_s[i];
   }
   // compute and test reverse mode
   {  set_vector r(m), s(m);
      for(size_t i = 0; i < m; i++)
         r[i].insert(i);
      s = f.RevSparseJac(m, r);
      for(size_t i = 0; i < m; i++)
         ok &= s[i] == check_s[i];
   }
   // correct Hessian result for w_0 * f_0 (u) + w_1 * f_1(u)
   set_vector check_h(n);
   check_h[0].insert(0);
   check_h[0].insert(1);
   check_h[1].insert(0);
   check_h[1].insert(1);
   // compute and test forward mode
   {  set_vector r(1), s(1), h(n);
      for(size_t i = 0; i < m; i++)
         s[0].insert(i);
      for(size_t j = 0; j < n; j++)
         r[0].insert(j);
      h = f.ForSparseHes(r, s);
      for(size_t i = 0; i < n; i++)
         ok &= h[i] == check_h[i];
   }
   // compute and test reverse mode
   {  set_vector s(1), h(n);
      for(size_t i = 0; i < m; i++)
         s[0].insert(i);
      h = f.RevSparseHes(n, s);
      for(size_t i = 0; i < n; i++)
         ok &= h[i] == check_h[i];
   }
   return ok;
}

// f(u) = g( u_0 + u_1 , u_1 + u_2 , u_2 + u_0 )
//      = [ u_2 + u_0 , (u_0 + u_1)*(u_1 + u_2) ]
bool test_two(void)
{  bool ok = true;
   using CppAD::AD;
   using CppAD::NearEqual;
   double eps = 10. * std::numeric_limits<double>::epsilon();
   // Create the atomic get_started object
   atomic_set_sparsity afun("atomic_set_sparsity");
   size_t n = 3;
   size_t m = 2;
   vector< AD<double> > au(n), ay(m);
   for(size_t j = 0; j < n; j++)
      au[j] = double(j + 1);

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

   // ax
   vector< AD<double> > ax(n);
   ax[0] = au[0] + au[1];
   ax[1] = au[1] + au[2];
   ax[2] = au[2] + au[0];

   // call atomic function
   afun(ax, ay);

   // create f: u -> y and stop tape recording
   CppAD::ADFun<double> f(au, ay);

   // check function value
   ok &= NearEqual(ay[0] , au[2] + au[0],  eps, eps);
   ok &= NearEqual(ay[1] , (au[0] + au[1]) * (au[1] + au[2]),  eps, eps);

   // correct Jacobian result
   set_vector check_s(m);
   check_s[0].insert(2);
   check_s[0].insert(0);
   check_s[1].insert(0);
   check_s[1].insert(1);
   check_s[1].insert(2);
   // compute and test forward mode
   {  set_vector r(n), s(m);
      for(size_t i = 0; i < n; i++)
         r[i].insert(i);
      s = f.ForSparseJac(n, r);
      for(size_t i = 0; i < m; i++)
         ok &= s[i] == check_s[i];
   }
   // compute and test reverse mode
   {  set_vector r(m), s(m);
      for(size_t i = 0; i < m; i++)
         r[i].insert(i);
      s = f.RevSparseJac(m, r);
      for(size_t i = 0; i < m; i++)
         ok &= s[i] == check_s[i];
   }
   // ----------------------------------------------------------------------
   // correct Hessian result for f_0 (u)
   set_vector check_h(n), s(1);
   s[0].insert(0);
   // compute and test forward mode
   {  set_vector r(1), h(n);
      for(size_t j = 0; j < n; j++)
         r[0].insert(j);
      h = f.ForSparseHes(r, s);
      for(size_t i = 0; i < n; i++)
         ok &= h[i] == check_h[i];
   }
   // compute and test reverse mode
   {  set_vector h(n);
      h = f.RevSparseHes(n, s);
      for(size_t i = 0; i < n; i++)
         ok &= h[i] == check_h[i];
   }
   // ----------------------------------------------------------------------
   // correct Hessian result for f_1 (u)
   s[0].clear();
   s[0].insert(1);
   check_h[0].insert(1);
   check_h[0].insert(2);
   check_h[1].insert(0);
   check_h[1].insert(1);
   check_h[1].insert(2);
   check_h[2].insert(0);
   check_h[2].insert(1);
   // compute and test forward mode
   {  set_vector r(1), h(n);
      for(size_t j = 0; j < n; j++)
         r[0].insert(j);
      h = f.ForSparseHes(r, s);
      for(size_t i = 0; i < n; i++)
         ok &= h[i] == check_h[i];
   }
   // compute and test reverse mode
   {  set_vector h(n);
      h = f.RevSparseHes(n, s);
      for(size_t i = 0; i < n; i++)
         ok &= h[i] == check_h[i];
   }
   return ok;
}

}  // End empty namespace

bool atomic_sparsity(void)
{  bool ok = true;
   ok     &= test_one();
   ok     &= test_two();
   return ok;
}
