# include <cppad/cppad.hpp>

// To print the comparision, change the 0 to 1 on the next line.
# define CPPAD_ODE_STIFF_PRINT 0

namespace {
     // --------------------------------------------------------------
     class Fun {
     private:
          CPPAD_TESTVECTOR(double) a;
     public:
          // constructor
          Fun(const CPPAD_TESTVECTOR(double)& a_) : a(a_)
          { }
          // compute f(t, x)
          void Ode(
               const double                    &t,
               const CPPAD_TESTVECTOR(double) &x,
               CPPAD_TESTVECTOR(double)       &f)
          {     f[0]  = - a[0] * x[0];
               f[1]  = + a[0] * x[0] - a[1] * x[1];
          }
          // compute partial of f(t, x) w.r.t. t
          void Ode_ind(
               const double                    &t,
               const CPPAD_TESTVECTOR(double) &x,
               CPPAD_TESTVECTOR(double)       &f_t)
          {     f_t[0] = 0.;
               f_t[1] = 0.;
          }
          // compute partial of f(t, x) w.r.t. x
          void Ode_dep(
               const double                    &t,
               const CPPAD_TESTVECTOR(double) &x,
               CPPAD_TESTVECTOR(double)       &f_x)
          {     f_x[0] = -a[0];
               f_x[1] = 0.;
               f_x[2] = +a[0];
               f_x[3] = -a[1];
          }
     };
     // --------------------------------------------------------------
     class RungeMethod {
     private:
          Fun F;
     public:
          // constructor
          RungeMethod(const CPPAD_TESTVECTOR(double) &a_) : F(a_)
          { }
          void step(
               double                     ta ,
               double                     tb ,
               CPPAD_TESTVECTOR(double) &xa ,
               CPPAD_TESTVECTOR(double) &xb ,
               CPPAD_TESTVECTOR(double) &eb )
          {     xb = CppAD::Runge45(F, 1, ta, tb, xa, eb);
          }
          size_t order(void)
          {     return 5; }
     };
     class RosenMethod {
     private:
          Fun F;
     public:
          // constructor
          RosenMethod(const CPPAD_TESTVECTOR(double) &a_) : F(a_)
          { }
          void step(
               double                     ta ,
               double                     tb ,
               CPPAD_TESTVECTOR(double) &xa ,
               CPPAD_TESTVECTOR(double) &xb ,
               CPPAD_TESTVECTOR(double) &eb )
          {     xb = CppAD::Rosen34(F, 1, ta, tb, xa, eb);
          }
          size_t order(void)
          {     return 4; }
     };
}

bool OdeStiff(void)
{     bool ok = true;     // initial return value

     CPPAD_TESTVECTOR(double) a(2);
     a[0] = 1e3;
     a[1] = 1.;
     RosenMethod rosen(a);
     RungeMethod runge(a);
     Fun          gear(a);

     CPPAD_TESTVECTOR(double) xi(2);
     xi[0] = 1.;
     xi[1] = 0.;

     CPPAD_TESTVECTOR(double) eabs(2);
     eabs[0] = 1e-6;
     eabs[1] = 1e-6;

     CPPAD_TESTVECTOR(double) ef(2);
     CPPAD_TESTVECTOR(double) xf(2);
     CPPAD_TESTVECTOR(double) maxabs(2);
     size_t                nstep;

     size_t k;
     for(k = 0; k < 3; k++)
     {
          size_t M    = 5;
          double ti   = 0.;
          double tf   = 1.;
          double smin = 1e-7;
          double sini = 1e-7;
          double smax = 1.;
          double scur = .5;
          double erel = 0.;

          if( k == 0 )
          {     xf = CppAD::OdeErrControl(rosen, ti, tf,
               xi, smin, smax, scur, eabs, erel, ef, maxabs, nstep);
          }
          else if( k == 1 )
          {     xf = CppAD::OdeErrControl(runge, ti, tf,
               xi, smin, smax, scur, eabs, erel, ef, maxabs, nstep);
          }
          else if( k == 2 )
          {     xf = CppAD::OdeGearControl(gear, M, ti, tf,
               xi, smin, smax, sini, eabs, erel, ef, maxabs, nstep);
          }
          double x0 = exp(-a[0]*tf);
          ok &= CppAD::NearEqual(x0, xf[0], 0., eabs[0]);
          ok &= CppAD::NearEqual(0., ef[0], 0., eabs[0]);

          double x1 = a[0] *
               (exp(-a[1]*tf) - exp(-a[0]*tf))/(a[0] - a[1]);
          ok &= CppAD::NearEqual(x1, xf[1], 0., eabs[1]);
          ok &= CppAD::NearEqual(0., ef[1], 0., eabs[0]);
# if CPPAD_ODE_STIFF_PRINT
          const char* method[]={ "Rosen34", "Runge45", "Gear5" };
          std::cout << std::endl;
          std::cout << "method     = " << method[k] << std::endl;
          std::cout << "nstep      = " << nstep  << std::endl;
          std::cout << "x0         = " << x0 << std::endl;
          std::cout << "xf[0]      = " << xf[0] << std::endl;
          std::cout << "x0 - xf[0] = " << x0 - xf[0] << std::endl;
          std::cout << "ef[0]      = " << ef[0] << std::endl;
          std::cout << "x1         = " << x1 << std::endl;
          std::cout << "xf[1]      = " << xf[1] << std::endl;
          std::cout << "x1 - xf[1] = " << x1 - xf[1] << std::endl;
          std::cout << "ef[1]      = " << ef[1] << std::endl;
# endif
     }

     return ok;
}