// 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
// ----------------------------------------------------------------------------

/*
Old DivEq example now used just for valiadation testing
*/
# include <cppad/cppad.hpp>

namespace { // BEGIN empty namespace

bool DivEqTestOne(void)
{  bool ok = true;

   using namespace CppAD;
   using CppAD::NearEqual;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

   // independent variable vector, indices, values, and declaration
   CPPAD_TESTVECTOR(AD<double>) U(2);
   size_t s = 0;
   size_t t = 1;
   U[s]     = 3.;
   U[t]     = 2.;
   Independent(U);

   // dependent variable vector and indices
   CPPAD_TESTVECTOR(AD<double>) Z(2);
   size_t x = 0;
   size_t y = 1;

   // some constants
   AD<double> zero = 0.;
   AD<double> one  = 1.;

   // dependent variable values
   Z[x] = U[s];
   Z[y] = U[t];
   Z[x] /= U[t]; // AD<double> *= AD<double>
   Z[y] /= 5.;   // AD<double> *= double
   zero /= Z[y]; // divide into a parameter equal to zero
   Z[y] /= one;  // divide by a parameter equal to one
   Z[y] /= 1.;   // divide by a double equal to one

   // check that zero is still a parameter
   // (must do this before creating f because it erases the tape)
   ok &= Parameter(zero);

   // create f : U -> Z and vectors for derivative calculations
   ADFun<double> f(U, Z);
   CPPAD_TESTVECTOR(double) v( f.Domain() );
   CPPAD_TESTVECTOR(double) w( f.Range() );

   // check that none of the components of f are parameters
   size_t i;
   for(i = 0; i < f.Range(); i++)
      ok &= ! f.Parameter(i);

   // check function values
   ok &= NearEqual(Z[x] , 3. / 2. , eps99, eps99);
   ok &= NearEqual(Z[y] , 2. / 5. , eps99, eps99);

   // forward computation of partials w.r.t. t
   v[s] = 0.;
   v[t] = 1.;
   w    = f.Forward(1, v);
   ok &= NearEqual(w[x] , -1.*U[s]/(U[t]*U[t]) , eps99, eps99); // dx/dt
   ok &= NearEqual(w[y] , 1. / 5.              , eps99, eps99); // dy/dt

   // reverse computation of second partials of x
   CPPAD_TESTVECTOR(double) r( f.Domain() * 2 );
   w[x] = 1.;
   w[y] = 0.;
   r    = f.Reverse(2, w);
   ok &= NearEqual(r[2 * s + 1]                 // d^2 x / (dt ds)
         , - 1. / (U[t] * U[t])     , eps99 , eps99 );
   ok &= NearEqual(r[2 * t + 1]                 // d^2 x / (dt dt)
      , 2. * U[s] / (U[t] * U[t] * U[t])  , eps99 , eps99 );

   return ok;
}

bool DivEqTestTwo(void)
{  bool ok = true;

   using namespace CppAD;
   using CppAD::NearEqual;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

   // independent variable vector
   double u0 = .5;
   CPPAD_TESTVECTOR(AD<double>) U(1);
   U[0]      = u0;
   Independent(U);

   // dependent variable vector
   CPPAD_TESTVECTOR(AD<double>) Z(1);
   Z[0] = U[0] * U[0]; // initial value
   Z[0] /= 2;          // AD<double> /= int
   Z[0] /= 4.;         // AD<double> /= double
   Z[0] /= U[0];       // AD<double> /= AD<double>

   // create f: U -> Z and vectors used for derivative calculations
   ADFun<double> f(U, Z);
   CPPAD_TESTVECTOR(double) v(1);
   CPPAD_TESTVECTOR(double) w(1);

   // check value
   ok &= NearEqual(Z[0] , u0*u0/(2*4*u0), eps99, eps99);

   // forward computation of partials w.r.t. u
   size_t j;
   size_t p     = 5;
   double jfac  = 1.;
   double value = 1./8.;
   v[0]         = 1.;
   for(j = 1; j < p; j++)
   {  jfac *= double(j);
      w     = f.Forward(j, v);
      ok &= NearEqual(w[0], value/jfac, eps99, eps99); // d^jz/du^j
      v[0]  = 0.;
      value = 0.;
   }

   // reverse computation of partials of Taylor coefficients
   CPPAD_TESTVECTOR(double) r(p);
   w[0]  = 1.;
   r     = f.Reverse(p, w);
   jfac  = 1.;
   value = 1./8.;
   for(j = 0; j < p; j++)
   {  ok &= NearEqual(r[j], value/jfac, eps99, eps99); // d^jz/du^j
      jfac *= double(j + 1);
      value = 0.;
   }

   return ok;
}

} // END empty namespace

bool DivEq(void)
{  bool ok = true;
   ok &= DivEqTestOne();
   ok &= DivEqTestTwo();
   return ok;
}
