Prev Next cppad_det_minor.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}} }@)@
CppAD Speed: Gradient of Determinant by Minor Expansion

Specifications
See link_det_minor .

Implementation
# include <cppad/cppad.hpp>
# include <cppad/speed/det_by_minor.hpp>
# include <cppad/speed/uniform_01.hpp>

// Note that CppAD uses global_option["memory"] at the main program level
# include <map>
extern std::map<std::string, bool> global_option;

bool link_det_minor(
     size_t                     size     ,
     size_t                     repeat   ,
     CppAD::vector<double>     &matrix   ,
     CppAD::vector<double>     &gradient )
{
     // --------------------------------------------------------------------
     // check global options
     const char* valid[] = { "memory", "onetape", "optimize"};
     size_t n_valid = sizeof(valid) / sizeof(valid[0]);
     typedef std::map<std::string, bool>::iterator iterator;
     //
     for(iterator itr=global_option.begin(); itr!=global_option.end(); ++itr)
     {     if( itr->second )
          {     bool ok = false;
               for(size_t i = 0; i < n_valid; i++)
                    ok |= itr->first == valid[i];
               if( ! ok )
                    return false;
          }
     }
     // --------------------------------------------------------------------

     // optimization options: no conditional skips or compare operators
     std::string options="no_compare_op";
     // -----------------------------------------------------
     // setup

     // object for computing determinant
     typedef CppAD::AD<double>       ADScalar;
     typedef CppAD::vector<ADScalar> ADVector;
     CppAD::det_by_minor<ADScalar>   Det(size);

     size_t i;               // temporary index
     size_t m = 1;           // number of dependent variables
     size_t n = size * size; // number of independent variables
     ADVector   A(n);        // AD domain space vector
     ADVector   detA(m);     // AD range space vector

     // vectors of reverse mode weights
     CppAD::vector<double> w(1);
     w[0] = 1.;

     // the AD function object
     CppAD::ADFun<double> f;

     // ---------------------------------------------------------------------
     if( ! global_option["onetape"] ) while(repeat--)
     {
          // choose a matrix
          CppAD::uniform_01(n, matrix);
          for( i = 0; i < size * size; i++)
               A[i] = matrix[i];

          // declare independent variables
          Independent(A);

          // AD computation of the determinant
          detA[0] = Det(A);

          // create function object f : A -> detA
          f.Dependent(A, detA);

          if( global_option["optimize"] )
               f.optimize(options);

          // skip comparison operators
          f.compare_change_count(0);

          // evaluate the determinant at the new matrix value
          f.Forward(0, matrix);

          // evaluate and return gradient using reverse mode
          gradient = f.Reverse(1, w);
     }
     else
     {
          // choose a matrix
          CppAD::uniform_01(n, matrix);
          for( i = 0; i < size * size; i++)
               A[i] = matrix[i];

          // declare independent variables
          Independent(A);

          // AD computation of the determinant
          detA[0] = Det(A);

          // create function object f : A -> detA
          f.Dependent(A, detA);

          if( global_option["optimize"] )
               f.optimize(options);

          // skip comparison operators
          f.compare_change_count(0);

          // ------------------------------------------------------
          while(repeat--)
          {     // get the next matrix
               CppAD::uniform_01(n, matrix);

               // evaluate the determinant at the new matrix value
               f.Forward(0, matrix);

               // evaluate and return gradient using reverse mode
               gradient = f.Reverse(1, w);
          }
     }
     return true;
}

Input File: speed/cppad/det_minor.cpp