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// SPDX-License-Identifier: EPL-2.0 OR GPL-2.0-or-later
// SPDX-FileCopyrightText: Bradley M. Bell <bradbell@seanet.com>
// SPDX-FileContributor: 2003-22 Bradley M. Bell
// ----------------------------------------------------------------------------
/*
{xrst_begin fadbad_poly.cpp}
Fadbad Speed: Second Derivative of a Polynomial
###############################################
Specifications
**************
See :ref:`link_poly-name` .
Implementation
**************
{xrst_spell_off}
{xrst_code cpp} */
# 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;
}
/* {xrst_code}
{xrst_spell_on}
{xrst_end fadbad_poly.cpp}
*/
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