multi_atomic_two_user¶

Defines a atomic_two Operation that Computes Square Root¶

Syntax¶

atomic_user a_square_root

a_square_root ( au , ay )

Purpose¶

This atomic function operation computes a square root using Newton’s method. It is meant to be very inefficient in order to demonstrate timing results.

au¶

This argument has prototype

const ADvector & au

where ADvector is a simple vector class with elements of type AD<double> . The size of au is three.

num_itr¶

We use the notation

num_itr = size_t ( Integer ( au [0] ) )

for the number of Newton iterations in the computation of the square root function. The component au [0] must be a Parameter .

y_initial¶

We use the notation

y_initial = au [1]

for the initial value of the Newton iterate.

y_squared¶

We use the notation

y_squared = au [2]

for the value we are taking the square root of.

ay¶

This argument has prototype

ADvector & ay

The size of ay is one and ay [0] is the square root of y_squared .

Limitations¶

Only zero order forward mode is implements for the atomic_user class.

Source¶

// includes used by all source code in multi_atomic_two.cpp file
# include <cppad/cppad.hpp>
# include "multi_atomic_two.hpp"
# include "team_thread.hpp"
//
namespace {
using CppAD::thread_alloc; // fast multi-threading memory allocator
using CppAD::vector;       // uses thread_alloc

class atomic_user : public CppAD::atomic_base<double> {
public:
   // ctor
   atomic_user(void)
   : CppAD::atomic_base<double>("atomic_square_root")
   { }
private:
   // forward mode routine called by CppAD
   bool forward(
      size_t                   p   ,
      size_t                   q   ,
      const vector<bool>&      vu  ,
      vector<bool>&            vy  ,
      const vector<double>&    tu  ,
      vector<double>&          ty  ) override
   {
# ifndef NDEBUG
      size_t n = tu.size() / (q + 1);
      size_t m = ty.size() / (q + 1);
      assert( n == 3 );
      assert( m == 1 );
# endif
      // only implementing zero order forward for this example
      if( q != 0 )
         return false;

      // extract components of argument vector
      size_t num_itr    = size_t( tu[0] );
      double y_initial  = tu[1];
      double y_squared  = tu[2];

      // check for setting variable information
      if( vu.size() > 0 )
      {  if( vu[0] )
            return false;
         vy[0] = vu[1] || vu[2];
      }

      // Use Newton's method to solve f(y) = y^2 = y_squared
      double y_itr = y_initial;
      for(size_t itr = 0; itr < num_itr; itr++)
      {  // solve (y - y_itr) * f'(y_itr) = y_squared - y_itr^2
         double fp_itr = 2.0 * y_itr;
         y_itr         = y_itr + (y_squared - y_itr * y_itr) / fp_itr;
      }

      // return the Newton approximation for f(y) = y_squared
      ty[0] = y_itr;
      return true;
   }
};
}