\(\newcommand{\W}[1]{ \; #1 \; }\) \(\newcommand{\R}[1]{ {\rm #1} }\) \(\newcommand{\B}[1]{ {\bf #1} }\) \(\newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} }\) \(\newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} }\) \(\newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} }\) \(\newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }\)
fadbad_poly.cpp¶
View page sourceFadbad 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;
}