Prev Next adolc_poly.cpp

@(@\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }@)@
Adolc Speed: Second Derivative of a Polynomial

Specifications
See link_poly .

Implementation
// suppress conversion warnings before other includes
# include <cppad/wno_conversion.hpp>
//
# include <vector>
# include <adolc/adolc.h>

# include <cppad/speed/uniform_01.hpp>
# include <cppad/utility/poly.hpp>
# include <cppad/utility/vector.hpp>
# include <cppad/utility/thread_alloc.hpp>
# include "adolc_alloc_mat.hpp"

// list of possible options
# include <map>
extern std::map<std::string, bool> global_option;

bool link_poly(
     size_t                     size     ,
     size_t                     repeat   ,
     CppAD::vector<double>     &a        ,  // coefficients of polynomial
     CppAD::vector<double>     &z        ,  // polynomial argument value
     CppAD::vector<double>     &ddp      )  // second derivative w.r.t z
{
     if( global_option["atomic"] )
          return false;
     if( global_option["memory"] || global_option["optimize"] )
          return false;
     // -----------------------------------------------------
     // setup
     size_t i;
     int tag  = 0;  // tape identifier
     int keep = 0;  // do not keep forward mode results in buffer
     int m    = 1;  // number of dependent variables
     int n    = 1;  // number of independent variables
     int d    = 2;  // highest derivative degree
     double f;      // function value

     // set up for thread_alloc memory allocator (fast and checks for leaks)
     using CppAD::thread_alloc; // the allocator
     size_t capacity;           // capacity of an allocation

     // choose a vector of polynomial coefficients
     CppAD::uniform_01(size, a);

     // AD copy of the polynomial coefficients
     std::vector<adouble> A(size);
     for(i = 0; i < size; i++)
          A[i] = a[i];

     // domain and range space AD values
     adouble Z, P;

     // allocate arguments to hos_forward
     double* x0 = thread_alloc::create_array<double>(size_t(n), capacity);
     double* y0 = thread_alloc::create_array<double>(size_t(m), capacity);
     double** x = adolc_alloc_mat(size_t(n), size_t(d));
     double** y = adolc_alloc_mat(size_t(m), size_t(d));

     // Taylor coefficient for argument
     x[0][0] = 1.;  // first order
     x[0][1] = 0.;  // second order

     // ----------------------------------------------------------------------
     if( ! global_option["onetape"] ) while(repeat--)
     {     // choose an argument value
          CppAD::uniform_01(1, z);

          // declare independent variables
          trace_on(tag, keep);
          Z <<= z[0];

          // AD computation of the function value
          P = CppAD::Poly(0, A, Z);

          // create function object f : Z -> P
          P >>= f;
          trace_off();

          // set the argument value
          x0[0] = z[0];

          // evaluate the polynomial at the new argument value
          hos_forward(tag, m, n, d, keep, x0, x, y0, y);

          // second derivative is twice second order Taylor coef
          ddp[0] = 2. * y[0][1];
     }
     else
     {
          // choose an argument value
          CppAD::uniform_01(1, z);

          // declare independent variables
          trace_on(tag, keep);
          Z <<= z[0];

          // AD computation of the function value
          P = CppAD::Poly(0, A, Z);

          // create function object f : Z -> P
          P >>= f;
          trace_off();

          while(repeat--)
          {     // get the next argument value
               CppAD::uniform_01(1, z);
               x0[0] = z[0];

               // evaluate the polynomial at the new argument value
               hos_forward(tag, m, n, d, keep, x0, x, y0, y);

               // second derivative is twice second order Taylor coef
               ddp[0] = 2. * y[0][1];
          }
     }
     // ------------------------------------------------------
     // tear down
     adolc_free_mat(x);
     adolc_free_mat(y);
     thread_alloc::delete_array(x0);
     thread_alloc::delete_array(y0);

     return true;
}

Input File: speed/adolc/poly.cpp