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

fadbad_poly.cpp

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Fadbad Speed: Second Derivative of a Polynomial

Specifications

See link_poly .

Implementation

# include <cppad/utility/vector.hpp>
# include <cppad/utility/poly.hpp>
# include <cppad/speed/uniform_01.hpp>
# include <FADBAD++/tadiff.h>

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

bool link_poly(
    size_t                     size     ,
    size_t                     repeat   ,
    CppAD::vector<double>     &a        ,  // coefficients of polynomial
    CppAD::vector<double>     &z        ,  // polynomial argument value
    CppAD::vector<double>     &ddp      )  // second derivative w.r.t z
{
    if( global_option["atomic"] )
        return false;
    if( global_option["memory"] || global_option["onetape"] || global_option["optimize"] )
        return false;
    // -----------------------------------------------------
    // setup
    size_t i;             // temporary index
    fadbad::T<double>  Z; // domain space AD value
    fadbad::T<double>  P; // range space AD value

    // choose the polynomial coefficients
    CppAD::uniform_01(size, a);

    // AD copy of the polynomial coefficients
    CppAD::vector< fadbad::T<double> > A(size);
    for(i = 0; i < size; i++)
        A[i] = a[i];

    // ------------------------------------------------------
    while(repeat--)
    {  // get the next argument value
        CppAD::uniform_01(1, z);

        // independent variable value
        Z    = z[0]; // argument value
        Z[1] = 1;    // argument first order Taylor coefficient

        // AD computation of the dependent variable
        P = CppAD::Poly(0, A, Z);

        // Taylor-expand P to degree one
        P.eval(2);

        // second derivative is twice second order Taylor coefficient
        ddp[0] = 2. * P[2];

        // Free DAG corresponding to P does not seem to improve speed.
        // Probably because it gets freed the next time P is assigned.
        // P.reset();
    }
    // ------------------------------------------------------
    return true;
}