optimize_forward_active.cpp¶

Optimize Forward Activity Analysis: Example and Test¶

# 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();

      // adding the constant zero does not take any operations
      scalar zero   = 0.0 + x[0];
      before.n_var += 0; before.n_op  += 0;
      after.n_var  += 0; after.n_op   += 0;

      // multiplication by the constant one does not take any operations
      scalar one    = 1.0 * x[1];
      before.n_var += 0; before.n_op  += 0;
      after.n_var  += 0; after.n_op   += 0;

      // multiplication by the constant zero does not take any operations
      // and results in the constant zero.
      scalar two    = 0.0 * x[0];

      // operations that only involve constants do not take any operations
      scalar three  = (1.0 + two) * 3.0;
      before.n_var += 0; before.n_op  += 0;
      after.n_var  += 0; after.n_op   += 0;

      // The optimizer will reconize that zero + one = one + zero
      // for all values of x.
      scalar four   = zero + one;
      scalar five   = one  + zero;
      before.n_var += 2; before.n_op  += 2;
      after.n_var  += 1; after.n_op   += 1;

      // The optimizer will reconize that sin(x[3]) = sin(x[3])
      // for all values of x. Note that, for computation of derivatives,
      // sin(x[3]) and cos(x[3]) are stored on the tape as a pair.
      scalar six    = sin(x[2]);
      scalar seven  = sin(x[2]);
      before.n_var += 4; before.n_op  += 2;
      after.n_var  += 2; after.n_op   += 1;

      // If we used addition here, five + seven = zero + one + seven
      // which would get converted to a cumulative summation operator.
      scalar eight = five * seven;
      before.n_var += 1; before.n_op  += 1;
      after.n_var  += 1; after.n_op   += 1;

      // Use two, three, four and six in order to avoid a compiler warning
      // Note that addition of two and three does not take any operations.
      // Also note that optimizer reconizes four * six == five * seven.
      scalar nine  = eight + four * six * (two + three);
      before.n_var += 3; before.n_op  += 3;
      after.n_var  += 2; after.n_op   += 2;

      // results for this operation sequence
      y[0] = nine;
      before.n_var += 0; before.n_op  += 0;
      after.n_var  += 0; after.n_op   += 0;
   }
}

bool forward_active(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  = 3;
   CPPAD_TESTVECTOR(AD<double>) ax(n);
   ax[0] = 0.5;
   ax[1] = 1.5;
   ax[2] = 2.0;

   // 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
   // Note that, for this case, all the optimization was done during
   // the recording and there is no benifit to the optimization.
   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 zero order forward with different argument value
   CPPAD_TESTVECTOR(double) x(n), y(m), check(m);
   for(size_t i = 0; i < n; i++)
      x[i] = double(i + 2);
   y    = f.Forward(0, x);
   fun(x, check, before, after);
   ok &= NearEqual(y[0], check[0], eps10, eps10);

   return ok;
}