# ifndef CPPAD_CPPAD_IPOPT_EXAMPLE_ODE_FAST_HPP
# define CPPAD_CPPAD_IPOPT_EXAMPLE_ODE_FAST_HPP
// 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
// ----------------------------------------------------------------------------
/*
{xrst_begin ipopt_nlp_ode_fast.hpp dev}

ODE Fitting Using Fast Representation
#####################################

{xrst_literal
   // BEGIN C++
   // END C++
}

{xrst_end ipopt_nlp_ode_fast.hpp}
*/

// BEGIN C++
# include "ode_problem.hpp"

namespace {
   using namespace cppad_ipopt;

   class FG_fast : public cppad_ipopt_fg_info
   {
   private:
      bool       retape_;
      SizeVector N_;
      SizeVector S_;
   public:
      // derived class part of constructor
      FG_fast(bool retape_in, const SizeVector& N)
      : retape_ (retape_in), N_(N)
      {  assert( N_[0] == 0 );
         S_.resize( N_.size() );
         S_[0] = 0;
         for(size_t i = 1; i < N_.size(); i++)
            S_[i] = S_[i-1] + N_[i];
      }
      // r^k for k = 0, 1, ..., Nz-1 used for measurements
      // r^k for k = Nz              use for initial condition
      // r^k for k = Nz+1, ..., 2*Nz used for trapezoidal approx
      size_t number_functions(void)
      {  return Nz + 1 + Nz; }
      ADVector eval_r(size_t k, const ADVector &u)
      {  count_eval_r();

         size_t j;
         ADVector y(Ny), a(Na);
         // objective function --------------------------------
         if( k < Nz )
         {  // used for measurement with index k+1
            ADVector r(1); // return value is a scalar
            // u is [y( s[k+1] ) , a]
            for(j = 0; j < Ny; j++)
               y[j] = u[j];
            for(j = 0; j < Na; j++)
               a[j] = u[Ny + j];
            r[0] = eval_H<ADNumber>(k+1, y, a);
            return r;
         }
         // initial condition ---------------------------------
         if( k == Nz )
         {  ADVector r(Ny), F(Ny);
            // u is [y(t), a] at t = 0
            for(j = 0; j < Ny; j++)
               y[j] = u[j];
            for(j = 0; j < Na; j++)
               a[j] = u[Ny + j];
            F    = eval_F(a);
            for(j = 0; j < Ny; j++)
               r[j]   = y[j] - F[j];
            return  r;
         }
         // trapezoidal approximation -------------------------
         ADVector ym(Ny), G(Ny), Gm(Ny), r(Ny);
         // r^k for k = Nz+1, ... , 2*Nz
         // interval between data samples
         Number T = s[k-Nz] - s[k-Nz-1];
         // integration step size
         Number dt = T / Number( N_[k-Nz] );
         // u = [ y(t[i-1], a) , y(t[i], a), a )
         for(j = 0; j < Ny; j++)
         {  ym[j] = u[j];
            y[j]  = u[Ny + j];
         }
         for(j = 0; j < Na; j++)
            a[j] = u[2 * Ny + j];
         Gm  = eval_G(ym, a);
         G   = eval_G(y,  a);
         for(j = 0; j < Ny; j++)
            r[j] = y[j] - ym[j] - (G[j] + Gm[j]) * dt / 2.;
         return r;
      }
      // The operations sequence for r_eval does not depend on u,
      // hence retape = false should work and be faster.
      bool retape(size_t k)
      {  return retape_; }
      // size of the vector u in eval_r
      size_t domain_size(size_t k)
      {  if( k < Nz )
            return Ny + Na;   // objective function
         if( k == Nz )
            return Ny + Na;  // initial value constraint
         return 2 * Ny + Na;      // trapezodial constraints
      }
      // size of the return value from eval_r
      size_t range_size(size_t k)
      {  if( k < Nz )
            return 1;
         return Ny;
      }
      // number of terms that use this value of k
      size_t number_terms(size_t k)
      {  if( k <= Nz )
            return 1;  // r^k used once for k <= Nz
         // r^k used N_[k-Nz] times for k > Nz
         return N_[k-Nz];
      }
      void index(size_t k, size_t ell, SizeVector& I, SizeVector& J)
      {  size_t i, j;
         // # of components of x corresponding to values for y
         size_t ny_inx = (S_[Nz] + 1) * Ny;
         // objective function -------------------------------
         if( k < Nz )
         {  // index in fg corresponding to objective
            I[0] = 0;
            // u = [ y(t, a) , a ]
            // The first Ny components of u is y(t) at
            //    t = s[k+1] = t[S_[k+1]]
            // x indices corresponding to this value of y
            for(j = 0; j < Ny; j++)
               J[j] = S_[k + 1] * Ny + j;
            // components of x corresponding to a
            for(j = 0; j < Na; j++)
               J[Ny + j] = ny_inx + j;
            return;
         }
         // initial conditions --------------------------------
         if( k == Nz )
         {  // index in fg for inidial condition constraint
            for(j = 0; j < Ny; j++)
               I[j] = 1 + j;
            // u = [ y(t, a) , a ] where t = 0
            // x indices corresponding to this value of y
            for(j = 0; j < Ny; j++)
               J[j] = j;
            // following that, u contains the vector a
            for(j = 0; j < Na; j++)
               J[Ny + j] = ny_inx + j;
            return;
         }
         // trapoziodal approximation -------------------------
         // index of first grid point in this approximation
         i = S_[k - Nz - 1]  + ell;
         // There are Ny difference equations for each time
         // point.  Add one for the objective function, and Ny
         // for the initial value constraints.
         for(j = 0; j < Ny; j++)
            I[j] = 1 + Ny + i * Ny + j;
         // u = [ y(t, a) , y(t+dt, a) , a ] at t = t[i]
         for(j = 0; j < Ny; j++)
         {  J[j]      = i * Ny  + j; // y^i indices
            J[Ny + j] = J[j] + Ny;   // y^{i+1} indices
         }
         for(j = 0; j < Na; j++)
            J[2 * Ny + j] = ny_inx + j; // a indices
      }
   };

}
// END C++
# endif
