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/*----------------------------------------------------------------------------
ADOL-C -- Automatic Differentiation by Overloading in C++
File: traceless_higher_order.cpp
Revision: $Id: traceless_higher_order.cpp ??? $
Contents: computation of partial derivatives
traceless forward mode for higher order derivatives
described in the manual
Copyright (c) Andrea Walther, Andreas Kowarz, Benjamin Jurgelucks
This file is part of ADOL-C. This software is provided as open source.
Any use, reproduction, or distribution of the software constitutes
recipient's acceptance of the terms of the accompanying license file.
---------------------------------------------------------------------------*/
/****************************************************************************/
/* INCLUDES */
#define ADOLC_TRACELESS_HIGHER_ORDER
//#include <adolc/adouble.h>
//typedef adhotl::adouble adouble;
#include <iostream>
#include <complex>
#include <adolc/adtl_hov.h>
typedef adtl_hov::adouble adouble;
using namespace std;
adouble poly (adouble* z){
adouble y;
y =exp(z[0])*log(pow(z[0],2.0));
return y;
}
double poly (double* z){
double y;
y = exp(z[0])*log(pow(z[0],2.0));
return y;
}
adouble higher_order(adouble* z)
{
double a=1.0;
adouble y;
y=z[0]*exp(a*z[0]);
return y;
}
double higher_order(double* z)
{
double a=1.0;
double y;
y=z[0]*exp(a*z[0]);
return y;
}
double higher_order_analytic(double* z, int n)
{
double a=1.0;
double y;
y=exp(a*z[0])*(n*pow(a,n-1)+pow(a,n)*z[0]);
return y;
}
int factorial(int n)
{
return (n == 1 || n == 0) ? 1 : factorial(n - 1) * n;
}
int main(){
int d=12, n=3;
cout << "Degree of derivative (precise up to degree 12): ";
cin >> d;
cout << endl;
double one[1];
one[0]=1;
//number of Taylor coefficients y_i
adtl_hov::setDegree(d);
adouble* z = new adouble[n];
adouble y;
double* dz = new double[n];
double dy;
//initialization of independent variables
for(int i=0; i<n; i++)
{
z[i]=2.0;
dz[i]=2.0;
}
//set Taylor coefficients x_i
z[0].setOneADValue(0,one);
double* ret;
if(d==2) // analytical derivative only for d=2 available
{
//function evaluation for case 1
y=poly(z);
dy= poly(dz);
ret=y.getOneADValue(d-1);
cout << "factorial(d): " << factorial(d) << endl;
cout << "ADOLC: Value of primal: "<< y.getValue() <<" Value of derivative: " << factorial(d)*ret[0] << endl;
cout << "DOUBLE: Value of primal: "<< dy <<" Value of derivative: " << (exp(dz[0]) *(-2 + 4*dz[0] + dz[0]*dz[0]*log(dz[0]*dz[0])))/ (dz[0]*dz[0]) << endl;
}
//function evaluation for case 2
y=higher_order(z);
dy=higher_order(dz);
ret=y.getOneADValue(d-1);
cout << "ADOLC: Value of primal: "<< y.getValue() <<" Value of derivative: " << factorial(d)*ret[0] << endl;
cout << "DOUBLE: Value of primal: "<< dy <<" Value of derivative: " << higher_order_analytic(dz,d) << endl;
delete []dz;
delete []z;
}
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