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Fadbad Speed: Gradient of Determinant Using Lu Factorization

Operation Sequence
Note that the Lu factorization operation sequence depends on the matrix being factored. Hence we use a different DAG for each matrix.

compute_det_lu
Routine that computes the gradient of determinant using Fadbad:
# include <FADBAD++/badiff.h>
# include <cppad/speed/det_by_lu.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/vector.hpp>

void compute_det_lu(
     size_t                     size     , 
     size_t                     repeat   , 
     CppAD::vector<double>      &matrix   ,
     CppAD::vector<double>      &gradient )
{
     // -----------------------------------------------------
     // setup

     // object for computing determinant
     typedef B<double>             ADScalar; 
     typedef CppAD::vector<ADScalar> ADVector; 
     CppAD::det_by_lu<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
     ADScalar   detA;         // AD value of the determinant
     ADVector   A(n);         // AD version of matrix 
     
     // ------------------------------------------------------
     while(repeat--)
       {  // get the next matrix
          CppAD::uniform_01(n, matrix);

          // set independent variable values
          for(i = 0; i < n; i++)
               A[i] = matrix[i];

          // compute the determinant
          detA = Det(A);

          // create function object f : A -> detA
          detA.diff(0, m);  // index 0 of m dependent variables

          // evaluate and return gradient using reverse mode
          for(i =0; i < n; i++)
               gradient[i] = A[i].d(0); // partial detA w.r.t A[i]
     }
     // ---------------------------------------------------------
     return;
}

Input File: speed/fadbad/det_lu.cpp