atomic_three_get_started.cpp¶

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Getting Started with Atomic Functions: Example and Test¶

Purpose¶

This example demonstrates the minimal amount of information necessary for a atomic_three function.

Start Class Definition¶

# include <cppad/cppad.hpp>  // CppAD include file
namespace {                  // start empty namespace
using CppAD::vector;         // abbreviate CppAD::vector using vector
// start definition of atomic derived class using atomic_three interface
class atomic_get_started : public CppAD::atomic_three<double> {

Constructor¶

public:
   // can use const char* name when calling this constructor
   atomic_get_started(const std::string& name) : // can have more arguments
   CppAD::atomic_three<double>(name)             // inform base class of name
   { }

private:

for_type¶

   // calculate type_y
   bool for_type(
      const vector<double>&               parameter_x ,
      const vector<CppAD::ad_type_enum>&  type_x      ,
      vector<CppAD::ad_type_enum>&        type_y      ) override
   {  assert( parameter_x.size() == type_x.size() );
      bool ok = type_x.size() == 1; // n
      ok     &= type_y.size() == 1; // m
      if( ! ok )
         return false;
      type_y[0] = type_x[0];
      return true;
   }

forward¶

   // forward mode routine called by CppAD
   bool forward(
      const vector<double>&               parameter_x  ,
      const vector<CppAD::ad_type_enum>&  type_x       ,
      size_t                              need_y       ,
      size_t                              order_low    ,
      size_t                              order_up     ,
      const vector<double>&               taylor_x     ,
      vector<double>&                     taylor_y     ) override
   {
# ifndef NDEBUG
      size_t n = taylor_x.size() / (order_up + 1);
      size_t m = taylor_y.size() / (order_up + 1);
# endif
      assert( n == 1 );
      assert( m == 1 );
      assert( order_low <= order_up );

      // return flag
      bool ok = order_up == 0;
      if( ! ok )
         return ok;

      // Order zero forward mode.
      // This case must always be implemented
      // y^0 = g( x^0 ) = 1 / x^0
      taylor_y[0] = 1. / taylor_x[0];
      //
      return ok;
   }

End Class Definition¶

}; // End of atomic_get_started class
}  // End empty namespace

Use Atomic Function¶

bool get_started(void)
{  bool ok = true;
   using CppAD::AD;
   using CppAD::NearEqual;
   double eps = 10. * CppAD::numeric_limits<double>::epsilon();

Constructor¶

   // Create the atomic get_started object corresponding to g(x)
   atomic_get_started afun("atomic_get_started");

Recording¶

   // Create the function f(x) which is eqaul to g(x) for this example.
   //
   // domain space vector
   size_t  n  = 1;
   double  x0 = 0.5;
   CPPAD_TESTVECTOR( AD<double> ) ax(n);
   ax[0]     = x0;

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

   // range space vector
   size_t m = 1;
   CPPAD_TESTVECTOR( AD<double> ) ay(m);

   // call atomic function and store result in au[0]
   // u = 1 / x
   CPPAD_TESTVECTOR( AD<double> ) au(m);
   afun(ax, au);

   // now use AD division to invert to invert the operation
   ay[0] = 1.0 / au[0]; // y = 1 / u = x

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

forward¶

   // check function value
   double check = x0;
   ok &= NearEqual( Value(ay[0]) , check,  eps, eps);

   // check zero order forward mode
   size_t q;
   CPPAD_TESTVECTOR( double ) x_q(n), y_q(m);
   q      = 0;
   x_q[0] = x0;
   y_q    = f.Forward(q, x_q);
   ok    &= NearEqual(y_q[0] , check,  eps, eps);

Return Test Result¶

   return ok;
}