Cppad Speed: Gradient of Ode Solution

cppad_ode.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 Ode Solution
Specifications
See link_ode .

Implementation

# include <cppad/cppad.hpp>
# include <cppad/speed/ode_evaluate.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <cassert>

// 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_ode(
    size_t                     size       ,
    size_t                     repeat     ,
    CppAD::vector<double>      &x         ,
    CppAD::vector<double>      &jacobian
)
{   global_cppad_thread_alloc_inuse = 0;

    // --------------------------------------------------------------------
    // check global options
    const char* valid[] = { "memory", "onetape", "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: no conditional skips or compare operators
    std::string optimize_options =
        "no_conditional_skip no_compare_op no_print_for_op";
    // --------------------------------------------------------------------
    // setup
    assert( x.size() == size );
    assert( jacobian.size() == size * size );

    typedef CppAD::AD<double>       ADScalar;
    typedef CppAD::vector<ADScalar> ADVector;

    size_t j;
    size_t p = 0;              // use ode to calculate function values
    size_t n = size;           // number of independent variables
    size_t m = n;              // number of dependent variables
    ADVector  X(n), Y(m);      // independent and dependent variables
    CppAD::ADFun<double>  f;   // AD function

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

    // -------------------------------------------------------------
    if( ! global_option["onetape"] ) while(repeat--)
    {   // choose next x value
        uniform_01(n, x);
        for(j = 0; j < n; j++)
            X[j] = x[j];

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

        // evaluate function
        CppAD::ode_evaluate(X, p, Y);

        // create function object f : X -> Y
        f.Dependent(X, Y);

        if( global_option["optimize"] )
            f.optimize(optimize_options);

        // skip comparison operators
        f.compare_change_count(0);

        jacobian = f.Jacobian(x);
    }
    else
    {   // an x value
        uniform_01(n, x);
        for(j = 0; j < n; j++)
            X[j] = x[j];

        // declare the independent variable vector
        Independent(X, abort_op_index, record_compare);

        // evaluate function
        CppAD::ode_evaluate(X, p, Y);

        // create function object f : X -> Y
        f.Dependent(X, Y);

        if( global_option["optimize"] )
            f.optimize(optimize_options);

        // skip comparison operators
        f.compare_change_count(0);

        while(repeat--)
        {   // get next argument value
            uniform_01(n, x);

            // evaluate jacobian
            jacobian = f.Jacobian(x);
        }
    }
    size_t thread                   = CppAD::thread_alloc::thread_num();
    global_cppad_thread_alloc_inuse = CppAD::thread_alloc::inuse(thread);
    return true;
}

Input File: speed/cppad/ode.cpp