Cppad Speed: Gradient of Determinant Using Lu Factorization

cppad_det_lu.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}} }@)@This is cppad-20221105 documentation. Here is a link to its current documentation . Cppad Speed: Gradient of Determinant Using Lu Factorization
Specifications
See link_det_lu .

Implementation

# include <cppad/speed/det_by_lu.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/cppad.hpp>

// Note that CppAD uses global_option["memory"] at the main program level
# include <map>
extern std::map<std::string, bool> global_option;
// see comments in main program for this external
extern size_t global_cppad_thread_alloc_inuse;

bool link_det_lu(
    size_t                           size     ,
    size_t                           repeat   ,
    CppAD::vector<double>           &matrix   ,
    CppAD::vector<double>           &gradient )
{   global_cppad_thread_alloc_inuse = 0;

    // --------------------------------------------------------------------
    // check global options
    const char* valid[] = { "memory", "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:
    std::string optimize_options =
        "no_conditional_skip no_compare_op no_print_for_op";
    // -----------------------------------------------------
    // setup
    typedef CppAD::AD<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
    ADVector   A(n);        // AD domain space vector
    ADVector   detA(m);     // AD range space vector
    CppAD::ADFun<double> f; // AD function object

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

    // do not even record comparison operators
    size_t abort_op_index = 0;
    bool record_compare   = false;

    // ------------------------------------------------------
    while(repeat--)
    {   // get the next matrix
        CppAD::uniform_01(n, matrix);
        for( i = 0; i < n; i++)
            A[i] = matrix[i];

        // declare independent variables
        Independent(A, abort_op_index, record_compare);

        // 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(optimize_options);

        // evaluate and return gradient using reverse mode
        f.Forward(0, matrix);
        gradient = f.Reverse(1, w);
    }
    size_t thread                   = CppAD::thread_alloc::thread_num();
    global_cppad_thread_alloc_inuse = CppAD::thread_alloc::inuse(thread);
    return true;
}

Input File: speed/cppad/det_lu.cpp