// 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 forward_dir.cpp}

Forward Mode: Example and Test of Multiple Directions
#####################################################

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

{xrst_end forward_dir.cpp}
*/
// BEGIN C++
# include <limits>
# include <cppad/cppad.hpp>
bool forward_dir(void)
{  bool ok = true;
   using CppAD::AD;
   using CppAD::NearEqual;
   double eps = 10. * std::numeric_limits<double>::epsilon();
   size_t j;

   // domain space vector
   size_t n = 3;
   CPPAD_TESTVECTOR(AD<double>) ax(n);
   ax[0] = 0.;
   ax[1] = 1.;
   ax[2] = 2.;

   // declare independent variables and starting recording
   CppAD::Independent(ax);

   // range space vector
   size_t m = 1;
   CPPAD_TESTVECTOR(AD<double>) ay(m);
   ay[0] = ax[0] * ax[1] * ax[2];

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

   // initially, the variable values during taping are stored in f
   ok &= f.size_order() == 1;

   // zero order Taylor coefficients
   CPPAD_TESTVECTOR(double) x0(n), y0;
   for(j = 0; j < n; j++)
      x0[j] = double(j+1);
   y0          = f.Forward(0, x0);
   ok         &= size_t( y0.size() ) == m;
   double y_0  = 1.*2.*3.;
   ok         &= NearEqual(y0[0], y_0, eps, eps);

   // first order Taylor coefficients
   size_t r = 2, ell;
   CPPAD_TESTVECTOR(double) x1(r*n), y1;
   for(ell = 0; ell < r; ell++)
   {  for(j = 0; j < n; j++)
         x1[ r * j + ell ] = double(j + 1 + ell);
   }
   y1  = f.Forward(1, r, x1);
   ok &= size_t( y1.size() ) == r*m;

   // secondorder Taylor coefficients
   CPPAD_TESTVECTOR(double) x2(r*n), y2;
   for(ell = 0; ell < r; ell++)
   {  for(j = 0; j < n; j++)
         x2[ r * j + ell ] = 0.0;
   }
   y2  = f.Forward(2, r, x2);
   ok &= size_t( y2.size() ) == r*m;
   //
   // Y_0 (t)     = F[X_0(t)]
   //             =  (1 + 1t)(2 + 2t)(3 + 3t)
   double y_1_0   = 1.*2.*3. + 2.*1.*3. + 3.*1.*2.;
   double y_2_0   = 1.*2.*3. + 2.*1.*3. + 3.*1.*2.;
   //
   // Y_1 (t)     = F[X_1(t)]
   //             =  (1 + 2t)(2 + 3t)(3 + 4t)
   double y_1_1   = 2.*2.*3. + 3.*1.*3. + 4.*1.*2.;
   double y_2_1   = 1.*3.*4. + 2.*2.*4. + 3.*2.*3.;
   //
   ok  &= NearEqual(y1[0] , y_1_0, eps, eps);
   ok  &= NearEqual(y1[1] , y_1_1, eps, eps);
   ok  &= NearEqual(y2[0] , y_2_0, eps, eps);
   ok  &= NearEqual(y2[1] , y_2_1, eps, eps);
   //
   // check number of orders
   ok   &= f.size_order() == 3;
   //
   // check number of directions
   ok   &= f.size_direction() == 2;
   //
   return ok;
}
// END C++
