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

fadbad_det_minor.cpp

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Fadbad Speed: Gradient of Determinant by Minor Expansion

Specifications

See link_det_minor .

Implementation

// suppress conversion warnings before other includes
# include <cppad/wno_conversion.hpp>
//
# include <FADBAD++/badiff.h>
# include <cppad/speed/det_by_minor.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/utility/vector.hpp>

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

bool link_det_minor(
    const std::string&         job      ,
    size_t                     size     ,
    size_t                     repeat   ,
    CppAD::vector<double>     &matrix   ,
    CppAD::vector<double>     &gradient )
{
    // --------------------------------------------------------------------
    // check not global options
    typedef std::map<std::string, bool>::iterator iterator;
    for(iterator itr=global_option.begin(); itr!=global_option.end(); ++itr)
    {  if( itr->second )
            return false;
    }
    // -----------------------------------------------------

    // AD types
    typedef fadbad::B<double>       b_double;
    typedef CppAD::vector<b_double> b_vector;

    // object that computes the determinant
    CppAD::det_by_minor<b_double>   b_det(size);

    // number of dependent variables
    unsigned int m = 1;

    // number of independent variables
    size_t n = size * size;

    // independent variable vector
    b_vector   b_A(n);

    // AD value of the determinant
    b_double  b_detA;

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

        // set independent variable values
        for(size_t j = 0; j < n; j++)
            b_A[j] = matrix[j];

        // compute the determinant
        b_detA = b_det(b_A);

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

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