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

sacado_poly.cpp

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Sacado Speed: Second Derivative of a Polynomial

Specifications

See link_poly .

Implementation

// suppress conversion warnings before other includes
# include <cppad/wno_conversion.hpp>
//
# include <Sacado.hpp>
# include <cppad/utility/vector.hpp>
# include <cppad/utility/poly.hpp>
# include <cppad/speed/uniform_01.hpp>

// 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
    typedef Sacado::Tay::Taylor<double>  ADScalar;
    CppAD::vector<ADScalar>              A(size);

    size_t i;               // temporary index
    ADScalar   Z;           // domain space AD value
    ADScalar   P;           // range space AD value
    int order = 2;          // order of Taylor coefficients
    Z.resize(order+1, false);
    P.resize(order+1, false);

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

    // AD copy of the polynomial coefficients
    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.fastAccessCoeff(0)   = z[0]; // argument value
        Z.fastAccessCoeff(1)   = 1.;   // first order coefficient
        Z.fastAccessCoeff(2)   = 0.;   // second order coefficient

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

        // second derivative is twice second order Taylor coefficient
        ddp[0] = 2. * P.fastAccessCoeff(2);
    }
    // ------------------------------------------------------
    return true;
}