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<center><b><big><big>Adolc Speed: Second Derivative of a Polynomial</big></big></b></center>
<br/>
<b><big><a name="link_poly" id="link_poly">link_poly</a></big></b>
<code><font color='blue'><pre style='display:inline'>
# include <vector>
# include <cppad/speed/uniform_01.hpp>
# include <cppad/poly.hpp>
# include <cppad/vector.hpp>
# include <adolc/adouble.h>
# include <adolc/taping.h>
# include <adolc/interfaces.h>
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
{
// -----------------------------------------------------
// setup
int tag = 0; // tape identifier
int keep = 1; // keep forward mode results in buffer
int m = 1; // number of dependent variables
int n = 1; // number of independent variables
int d = 2; // order of the derivative
double f; // function value
int i; // temporary index
// choose a vector of polynomial coefficients
CppAD::uniform_01(size, a);
// AD copy of the polynomial coefficients
std::vector<adouble> A(size);
for(i = 0; i < int(size); i++)
A[i] = a[i];
// domain and range space AD values
adouble Z, P;
// allocate arguments to hos_forward
double *x0 = 0;
x0 = CPPAD_TRACK_NEW_VEC(n, x0);
double *y0 = 0;
y0 = CPPAD_TRACK_NEW_VEC(m, y0);
double **x = 0;
x = CPPAD_TRACK_NEW_VEC(n, x);
double **y = 0;
y = CPPAD_TRACK_NEW_VEC(m, y);
for(i = 0; i < n; i++)
{ x[i] = 0;
x[i] = CPPAD_TRACK_NEW_VEC(d, x[i]);
}
for(i = 0; i < m; i++)
{ y[i] = 0;
y[i] = CPPAD_TRACK_NEW_VEC(d, y[i]);
}
// Taylor coefficient for argument
x[0][0] = 1.; // first order
x[0][1] = 0.; // second order
extern bool global_retape;
if( global_retape ) while(repeat--)
{ // choose an argument value
CppAD::uniform_01(1, z);
// declare independent variables
trace_on(tag, keep);
Z <<= z[0];
// AD computation of the function value
P = CppAD::Poly(0, A, Z);
// create function object f : Z -> P
P >>= f;
trace_off();
// get the next argument value
CppAD::uniform_01(1, z);
x0[0] = z[0];
// evaluate the polynomial at the new argument value
hos_forward(tag, m, n, d, keep, x0, x, y0, y);
// second derivative is twice second order Taylor coef
ddp[0] = 2. * y[0][1];
}
else
{
// choose an argument value
CppAD::uniform_01(1, z);
// declare independent variables
trace_on(tag, keep);
Z <<= z[0];
// AD computation of the function value
P = CppAD::Poly(0, A, Z);
// create function object f : Z -> P
P >>= f;
trace_off();
while(repeat--)
{ // get the next argument value
CppAD::uniform_01(1, z);
x0[0] = z[0];
// evaluate the polynomial at the new argument value
hos_forward(tag, m, n, d, keep, x0, x, y0, y);
// second derivative is twice second order Taylor coef
ddp[0] = 2. * y[0][1];
}
}
// ------------------------------------------------------
// tear down
CPPAD_TRACK_DEL_VEC(x0);
CPPAD_TRACK_DEL_VEC(y0);
for(i = 0; i < n; i++)
CPPAD_TRACK_DEL_VEC(x[i]);
for(i = 0; i < m; i++)
CPPAD_TRACK_DEL_VEC(y[i]);
CPPAD_TRACK_DEL_VEC(x);
CPPAD_TRACK_DEL_VEC(y);
return true;
}
</pre></font></code>
<hr/>Input File: speed/adolc/poly.cpp
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