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

sacado_det_minor.cpp

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Sacado 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 <Sacado.hpp>
# 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 none of the global options is true
    typedef std::map<std::string, bool>::iterator iterator;
    for(iterator itr=global_option.begin(); itr!=global_option.end(); ++itr)
    {  if( itr->second )
            return false;
    }
    // -----------------------------------------------------
    // not using job
    // -----------------------------------------------------

    // AD types
    typedef Sacado::Rad::ADvar<double>    r_double;
    typedef CppAD::vector<r_double>       r_vector;

    // object for computing deterinant
    CppAD::det_by_minor<r_double>         r_det(size);

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

    // independent variable vector
    r_vector   r_A(n);

    // AD value of the determinant
    r_double   r_detA;

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

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

        // compute the determinant
        r_detA = r_det(r_A);

        // reverse mode compute gradient of last computed value; i.e., detA
        r_double::Gradcomp();

        // return gradient
        for(size_t j =0; j < n; ++j)
            gradient[j] = r_A[j].adj(); // partial detA w.r.t A[j]
    }
    // ---------------------------------------------------------
    return true;
}