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/*----------------------------------------------------------------------------
ADOL-C -- Automatic Differentiation by Overloading in C++
File: fixpoint_exam.cpp
Revision: $Id$
Contents: example for differentiation of fixpoint iterations
Copyright (c) Andrea Walther
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.
---------------------------------------------------------------------------*/
#include <math.h>
#include <adolc/adolc.h>
#define imax 100
#define imax_deriv 100
// fixpoint iteration
// double version
int fixpoint_iter(double *x, double *u, double *y, int dim_x, int dim_u);
double norm(double *x, int dim_x);
// adouble version
int fixpoint_iter_act(adouble *x, adouble *u, adouble *y, int dim_x, int dim_u);
adouble norm(adouble *x, int dim_x);
int tag_full, tag_part, tag_fixpoint;
int main()
{
adouble x[1];
adouble u[1];
adouble y[1];
adouble diff[1];
double eps=1.0e-6;
double up[1];
double yp[1];
double grad[1];
int i;
tag_full = 1;
tag_part = 2;
tag_fixpoint = 3;
trace_on(tag_full);
i = 0;
u[0] <<= 0.5;
y[0] = 1.57079632679;
do
{
i++;
x[0] = y[0];
fixpoint_iter_act(x,u,y,1,1);
printf(" i = %3d y = %12.9f\n",i,y[0].value());
diff[0] = x[0]-y[0];
}
while((norm(diff,1)>eps) && (i<imax));
y[0] >>= yp[0];
trace_off(1);
up[0] = 0.5;
gradient(tag_full,1,up,grad);
printf("\n full taping:\n gradient = ( %f )\n",grad[0]);
printf("\n taping with fixpoint facility:\n\n");
trace_on(tag_part);
i = 0;
u[0] <<= 0.5;
x[0] = 1.57079632679;
fp_iteration(tag_fixpoint,fixpoint_iter,fixpoint_iter_act,norm,norm,eps,eps,imax,imax_deriv,x,u,y,1,1);
y[0] >>= yp[0];
trace_off(1);
up[0] = 0.5;
gradient(tag_part,1,up,grad);
printf("\n=> gradient = ( %f )\n",grad[0]);
return 0;
}
int fixpoint_iter(double *x, double *u, double *y, int dim_x, int dim_u)
{
y[0] = u[0]*(x[0]+cos(x[0]));
return 0;
}
double norm(double *x, int dim_x)
{
return fabs(x[0]);
}
int fixpoint_iter_act(adouble *x, adouble *u, adouble *y, int dim_x, int dim_u)
{
y[0] = u[0]*(x[0]+cos(x[0]));
return 0;
}
adouble norm(adouble *x, int dim_x)
{
return fabs(x[0]);
}
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