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/*----------------------------------------------------------------------------
ADOL-C -- Automatic Differentiation by Overloading in C++
File: GantryCrane.cpp
Revision: $Id$
Contents: example for calculation of Lie derivatives
Copyright (c) Siquian Wang, Klaus Röbenack, Jan Winkler, Mirko Franke
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.
---------------------------------------------------------------------------*/
/** By the example of the gantry crane (as shown in Röbenack, Winkler and
* Wang. 'LIEDRIVERS - A Toolbox for the Efficient Computation of Lie
* Derivatives Based on the Object-Oriented Algorithmic Differentiation
* Package ADOL-C') the usage of the drivers of the Lie Toolbox is
* illustrated.
* Beside Lie derivatives of scalar fields and their gradients also Lie
* brackets are computed.
*/
/****************************************************************************/
/* INCLUDES */
#include <adolc/adolc.h>
#include <adolc/lie/drivers.h>
#include <iostream>
/****************************************************************************/
/* NAMESPACES AND DEFINES */
using namespace std;
#define TAPE_F 1
#define TAPE_G 2
#define TAPE_H 3
/****************************************************************************/
/* MAIN PROGRAM */
int main()
{
const int n = 4, m_H = 2;
double* x0 = myalloc(n);
double vf[n], vg[n], vh[n];
adouble aX[n], af[n], ag[n], ah[m_H];
const double mc = 1.0, ml = 1.0, l = 1.0, g = 9.81;
/****************************
* Trace for vector field f *
****************************/
trace_on(TAPE_F);
{
for (int i = 0; i < n; i++)
aX[i] <<= x0[i];
af[0] = aX[2];
af[1] = aX[3];
af[2] = (ml*l*pow(aX[3],2)*sin(aX[1]) + ml*g*sin(aX[1])*cos(aX[1]))/(ml*pow(sin(aX[1]),2)+mc);
af[3] = -(ml*l*pow(aX[3],2)*sin(aX[1])*cos(aX[1]) + (ml + mc)*g*sin(aX[1]))/(l*(ml*pow(sin(aX[1]),2)+mc));
for (int i = 0; i < n; i++)
af[i] >>= vf[i];
}
trace_off();
/****************************
* Trace for vector field g *
****************************/
trace_on(TAPE_G);
{
for (int i = 0; i < n; i++)
aX[i] <<= x0[i];
ag[0] = 0;
ag[1] = 0;
ag[2] = 1/(ml*pow(sin(aX[1]),2)+mc);
ag[3] = -cos(aX[1])/(l*(ml*pow(sin(aX[1]),2)+mc));
for (int i = 0; i < n; i++)
ag[i] >>= vg[i];
}
trace_off();
/**********************************
* Trace for scalar fields h1, h2 *
**********************************/
trace_on(TAPE_H);
{
for (int i = 0; i < n; i++)
aX[i] <<= x0[i];
ah[0] = aX[0] + l*sin(aX[1]);
ah[1] = l*cos(aX[1]);
for (int i = 0; i < m_H; i++)
ah[i] >>= vh[i];
}
trace_off();
const int d = 12;
x0[0] = 1.;
x0[1] = 0.2;
x0[2] = -0.5;
x0[3] = -0.4;
cout.precision(6); cout << scientific;
/***************************************************
* calculation of Lie derivatives of scalar fields *
***************************************************/
double** scalar = myalloc2(m_H, d+1);
cout << "Lie derivatives:" << endl << endl;
// calculate Lie derivatives using Lie drivers
lie_scalar(TAPE_F, TAPE_H, n, m_H, x0, d, scalar);
for (int i = 0; i <= d; i++)
{
for (int j = 0; j < m_H; j++)
cout << "Lfh_" << i << "_" << j << " =\t" << scalar[j][i] << endl;
cout << endl;
}
cout << endl;
myfree2(scalar);
/****************************************************************
* calculation of gradients of Lie derivatives of scalar fields *
****************************************************************/
double*** gradient = myalloc3(m_H, n, d+1);
cout << "gradients of Lie derivatives:" << endl << endl;
// calculate gradients of Lie derivatives using Lie drivers
lie_gradient(TAPE_F, TAPE_H, n, m_H, x0, d, gradient);
for (int i = 0; i <= d; i++)
{
for (int j = 0; j < m_H; j++)
cout << "dLfh_" << i << "_" << j << " =\t" << gradient[j][0][i] << "\t" << gradient[j][1][i] << "\t" << gradient[j][2][i] << "\t" << gradient[j][3][i] << endl;
cout << endl;
}
cout << endl;
myfree3(gradient);
/*******************************
* calculation of Lie brackets *
*******************************/
double** bracket = myalloc2(n, d+1);
cout << "Lie brackets:" << endl << endl;
// calculate Lie brackets using Lie drivers
lie_bracket(TAPE_F, TAPE_G, n, x0, d, bracket);
for (int i = 0; i <= d; i++)
{
for (int j = 0; j < n; j++)
cout << "adfg_" << i << "_" << j << " =\t" << bracket[j][i] << endl;
cout << endl;
}
myfree2(bracket);
myfree(x0);
cout << "Press RETURN to continue" << endl;
cin.get();
return 0;
}
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