\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)

adolc_det_lu.cpp

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Adolc Speed: Gradient of Determinant Using Lu Factorization

Specifications

See link_det_lu .

Implementation

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

# include <cppad/speed/det_by_lu.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/utility/track_new_del.hpp>

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

bool link_det_lu(
   size_t                     size     ,
   size_t                     repeat   ,
   CppAD::vector<double>     &matrix   ,
   CppAD::vector<double>     &gradient )
{
   // speed test global option values
   if( global_option["onetape"] || global_option["atomic"] )
      return false;
   if( global_option["memory"] || global_option["optimize"] )
      return false;
   // -----------------------------------------------------
   // setup
   int tag  = 0;         // tape identifier
   int keep = 1;         // keep forward mode results in buffer
   int m    = 1;         // number of dependent variables
   int n    = size*size; // number of independent variables
   double f;             // function value
   int j;                // temporary index

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

   // object for computing determinant
   typedef adouble            ADScalar;
   typedef ADScalar*          ADVector;
   CppAD::det_by_lu<ADScalar> Det(size);

   // AD value of determinant
   ADScalar   detA;

   // AD version of matrix
   size_min    = n;
   ADVector A  = thread_alloc::create_array<ADScalar>(size_min, size_out);

   // vectors of reverse mode weights
   size_min    = m;
   double* u   = thread_alloc::create_array<double>(size_min, size_out);
   u[0] = 1.;

   // vector with matrix value
   size_min     = n;
   double* mat  = thread_alloc::create_array<double>(size_min, size_out);

   // vector to receive gradient result
   size_min     = n;
   double* grad = thread_alloc::create_array<double>(size_min, size_out);
   // ------------------------------------------------------
   while(repeat--)
   {  // get the next matrix
      CppAD::uniform_01(n, mat);

      // declare independent variables
      trace_on(tag, keep);
      for(j = 0; j < n; j++)
         A[j] <<= mat[j];

      // AD computation of the determinant
      detA = Det(A);

      // create function object f : A -> detA
      detA >>= f;
      trace_off();

      // evaluate and return gradient using reverse mode
      fos_reverse(tag, m, n, u, grad);
   }
   // ------------------------------------------------------

   // return matrix and gradient
   for(j = 0; j < n; j++)
   {  matrix[j] = mat[j];
      gradient[j] = grad[j];
   }
   // tear down
   thread_alloc::delete_array(grad);
   thread_alloc::delete_array(mat);
   thread_alloc::delete_array(u);
   thread_alloc::delete_array(A);

   return true;
}