// 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 optimize_cumulative_sum.cpp}

Optimize Cumulative Sum Operations: Example and Test
####################################################

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

{xrst_end optimize_cumulative_sum.cpp}
*/
// BEGIN C++
# include <cppad/cppad.hpp>

namespace {
   struct tape_size { size_t n_var; size_t n_op; };

   template <class Vector> void fun(
      const Vector& x, Vector& y, tape_size& before, tape_size& after
   )
   {  typedef typename Vector::value_type scalar;

      // phantom variable with index 0 and independent variables
      // begin operator, independent variable operators and end operator
      before.n_var = 1 + x.size(); before.n_op  = 2 + x.size();
      after.n_var  = 1 + x.size(); after.n_op   = 2 + x.size();

      // operators that are identical, and that will be made part of the
      // cumulative summation. Make sure do not replace second variable
      // using the first and then remove the first as part of the
      // cumulative summation.
      scalar first  = x[0] + x[1];
      scalar second = x[0] + x[1];
      before.n_var += 2; before.n_op  += 2;
      after.n_var  += 0; after.n_op   += 0;

      // test that subtractions are also included in cumulative summations
      scalar third = x[1] - 2.0;
      before.n_var += 1; before.n_op  += 1;
      after.n_var  += 0; after.n_op   += 0;

      // the finial summation is converted to a cumulative summation
      // the other is removed.
      scalar csum = first + second + third;
      before.n_var += 2; before.n_op  += 2;
      after.n_var  += 1; after.n_op   += 1;

      // results for this operation sequence
      y[0] = csum;
      before.n_var += 0; before.n_op  += 0;
      after.n_var  += 0; after.n_op   += 0;
   }
}
bool cumulative_sum(void)
{  bool ok = true;
   using CppAD::AD;
   using CppAD::NearEqual;
   double eps10 = 10.0 * std::numeric_limits<double>::epsilon();

   // domain space vector
   size_t n  = 2;
   CPPAD_TESTVECTOR(AD<double>) ax(n);
   ax[0] = 0.5;
   ax[1] = 1.5;

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

   // range space vector
   size_t m = 1;
   CPPAD_TESTVECTOR(AD<double>) ay(m);
   tape_size before, after;
   fun(ax, ay, before, after);

   // create f: x -> y and stop tape recording
   CppAD::ADFun<double> f(ax, ay);
   ok &= f.size_order() == 1; // this constructor does 0 order forward
   ok &= f.size_var() == before.n_var;
   ok &= f.size_op()  == before.n_op;

   // Optimize the operation sequence
   f.optimize();
   ok &= f.size_order() == 0; // 0 order forward not present
   ok &= f.size_var() == after.n_var;
   ok &= f.size_op()  == after.n_op;

   // Check result for a zero order calculation for a different x,
   CPPAD_TESTVECTOR(double) x(n), y(m), check(m);
   x[0] = 0.75;
   x[1] = 2.25;
   y    = f.Forward(0, x);
   fun(x, check, before, after);
   ok  &= CppAD::NearEqual(y[0], check[0], eps10, eps10);

   return ok;
}
// END C++
