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

fadbad_det_lu.cpp

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Fadbad 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 <FADBAD++/badiff.h>
# include <cppad/speed/det_by_lu.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_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
    //
    // object for computing determinant
    typedef fadbad::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, (unsigned int) 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 true;
}