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Using Adolc with Multiple Levels of Taping: Example and Test

Purpose
In this example, we use AD< adouble> > (level two taping), the compute values of the function f : R n R where f ( x ) = 1 2 (x 0 2 + + x n -1 2 ) We then use Adolc's adouble (level one taping) to compute the directional derivative f ( 1 ) ( x ) * v = x 0 v 0 + + x n -1 v n -1 . where v R n . We then use double (no taping) to compute d dx [f ( 1 ) ( x ) * v ] = v This is only meant as an example of multiple levels of taping. The example hes_times_dir.cpp computes the same value more efficiently by using the identity: d dx [f ( 1 ) ( x ) * v ] = f ( 2 ) ( x ) * v The example mul_level.cpp computes the same values using AD< AD<double> > and AD<double>.

Memory Management
Adolc uses raw memory arrays that depend on the number of dependent and independent variables. The memory management utility thread_alloc is used to manage this memory allocation.

Configuration Requirement
This example will be compiled and tested provided that the value adolc_prefix is specified on the cmake command line.

Source

// suppress conversion warnings before other includes
# include <cppad/wno_conversion.hpp>
//

# include <adolc/adouble.h>
# include <adolc/taping.h>
# include <adolc/interfaces.h>

// adouble definitions not in Adolc distribution and
// required in order to use CppAD::AD<adouble>
# include <cppad/example/base_adolc.hpp>

# include <cppad/cppad.hpp>

namespace {
     // f(x) = |x|^2 / 2 = .5 * ( x[0]^2 + ... + x[n-1]^2 )
     template <class Type>
     Type f(const CPPAD_TESTVECTOR(Type)& x)
     {     Type sum;

          sum  = 0.;
          size_t i = size_t(x.size());
          for(i = 0; i < size_t(x.size()); i++)
               sum += x[i] * x[i];

          return .5 * sum;
     }
}

bool mul_level_adolc(void)
{     bool ok = true;                // initialize test result
     using CppAD::thread_alloc;        // The CppAD memory allocator

     typedef adouble           a1type;  // for first level of taping
     typedef CppAD::AD<a1type> a2type; // for second level of taping
     size_t n = 5;                          // number independent variables
     size_t j;

     // 10 times machine epsilon
     double eps = 10. * std::numeric_limits<double>::epsilon();

     CPPAD_TESTVECTOR(double) x(n);
     CPPAD_TESTVECTOR(a1type) a1x(n);
     CPPAD_TESTVECTOR(a2type) a2x(n);

     // Values for the independent variables while taping the function f(x)
     for(j = 0; j < n; j++)
          a2x[j] = double(j);
     // Declare the independent variable for taping f(x)
     CppAD::Independent(a2x);

     // Use AD<adouble> to tape the evaluation of f(x)
     CPPAD_TESTVECTOR(a2type) a2y(1);
     a2y[0] = f(a2x);

     // Declare a1f as the corresponding ADFun<adouble> function f(x)
     // (make sure we do not run zero order forward during constructor)
     CppAD::ADFun<a1type> a1f;
     a1f.Dependent(a2x, a2y);

     // Value of the independent variables whitle taping f'(x) * v
     int tag = 0;
     int keep = 1;
     trace_on(tag, keep);
     for(j = 0; j < n; j++)
          a1x[j] <<= double(j);

     // set the argument value x for computing f'(x) * v
     a1f.Forward(0, a1x);

     // compute f'(x) * v
     CPPAD_TESTVECTOR(a1type) a1v(n);
     CPPAD_TESTVECTOR(a1type) a1df(1);
     for(j = 0; j < n; j++)
          a1v[j] = double(n - j);
     a1df = a1f.Forward(1, a1v);

     // declare Adolc function corresponding to f'(x) * v
     double df;
     a1df[0] >>= df;
     trace_off();

     // compute the d/dx of f'(x) * v = f''(x) * v
     size_t m      = 1;                     // # dependent in f'(x) * v

     // w = new double[capacity] where capacity >= m
     size_t capacity;
     double* w  = thread_alloc::create_array<double>(m, capacity);

     // dw = new double[capacity] where capacity >= n
     double* dw = thread_alloc::create_array<double>(n, capacity);

     w[0]  = 1.;
     fos_reverse(tag, int(m), int(n), w, dw);

     for(j = 0; j < n; j++)
     {     double vj = a1v[j].value();
          ok &= CppAD::NearEqual(dw[j], vj, eps, eps);
     }

     // make memory avaialble for other use by this thread
     thread_alloc::delete_array(w);
     thread_alloc::delete_array(dw);
     return ok;
}

Input File: example/general/mul_level_adolc.cpp