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/*----------------------------------------------------------------------------
ADOL-C -- Automatic Differentiation by Overloading in C++
File: cubic.cpp
Revision: $Id$
Contents: example for cubic lighthouse example of Griewank's Book
using Cardan's formula with two tapes
Copyright (c) Andrea Walther, Andreas Griewank, Andreas Kowarz,
Hristo Mitev, Sebastian Schlenkrich, Jean Utke, Olaf Vogel
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 */
#include <adolc/adolc.h>
#include <math.h>
#define PI 3.1415926536
/****************************************************************************/
/* ADOUBLE ROUTINE */
adouble activeCubicLighthouse1( adouble t ) {
adouble p, q, d, r, u, u1,u2, v, c;
/*---------------------*/
p = tan(t);
q = p - 0.2;
p /= 3.0;
d = q*q;
d -= p*p*p;
/* 1. branch ----------*/
r = sqrt(d);
u = q + r;
u1 = pow(fabs(u),1.0/3.0);
u2 = -u1;
condassign(u,u,u1,u2);
v = q - r;
u1 = pow(fabs(v),1.0/3.0);
u2 = -u1;
condassign(v,v,u1,u2);
c = u + v;
/*---------------------*/
c += 2.0;
return c;
}
/****************************************************************************/
/* ADOUBLE ROUTINE */
adouble activeCubicLighthouse2( adouble t ) {
adouble p, q, d, r, u, v, c, a, z, b;
/*---------------------*/
p = tan(t);
q = p - 0.2;
p /= 3.0;
d = q*q;
d -= p*p*p;
/* 2. branch ----------*/
p = fabs(p);
p = sqrt(p);
q /= p*p*p;
a = acos(q);
a /= 3.0;
z = cos(a);
b = a + PI/3.0;
b = -cos(b);
z = fmin(z,b);
b = a - PI/3.0;
b = -cos(b);
z = fmin(z,b);
z = 2.0*z*p;
/*---------------------*/
z += 2.0;
return z;
}
/****************************************************************************/
/* MAIN PROGRAM */
int main() {
int i, vc;
int tag1 = 1, tag2 = 2;
double z, z1, z2, t, tmin, tmax, tdist, dz;
/*--------------------------------------------------------------------------*/
/* Preparation */
fprintf(stdout,"CUBIC LIGHTHOUSE Using CARDAN (ADOL-C Example)\n\n");
tmin = 0.15;
tmax = 0.24;
fprintf(stdout,"How many values = ? \n");
scanf("%d",&vc);
/*--------------------------------------------------------------------------*/
t = 0.1;
adouble az,at;
trace_on(tag1);
at <<= t;
az = activeCubicLighthouse1(at);
az >>= z;
trace_off();
trace_on(tag2);
at <<= t;
az = activeCubicLighthouse2(at);
az >>= z;
trace_off();
/*--------------------------------------------------------------------------*/
size_t tape_stats[STAT_SIZE];
tapestats(tag1,tape_stats);
fprintf(stdout,"\n independents %zu\n",tape_stats[NUM_INDEPENDENTS]);
fprintf(stdout," dependents %zu\n",tape_stats[NUM_DEPENDENTS]);
fprintf(stdout," operations %zu\n",tape_stats[NUM_OPERATIONS]);
fprintf(stdout," operations buffer size %zu\n",tape_stats[OP_BUFFER_SIZE]);
fprintf(stdout," locations buffer size %zu\n",tape_stats[LOC_BUFFER_SIZE]);
fprintf(stdout," constants buffer size %zu\n",tape_stats[VAL_BUFFER_SIZE]);
fprintf(stdout," maxlive %zu\n",tape_stats[NUM_MAX_LIVES]);
fprintf(stdout," valstack size %zu\n\n",tape_stats[TAY_STACK_SIZE]);
tapestats(tag2,tape_stats);
fprintf(stdout,"\n independents %zu\n",tape_stats[NUM_INDEPENDENTS]);
fprintf(stdout," dependents %zu\n",tape_stats[NUM_DEPENDENTS]);
fprintf(stdout," operations %zu\n",tape_stats[NUM_OPERATIONS]);
fprintf(stdout," operations buffer size %zu\n",tape_stats[OP_BUFFER_SIZE]);
fprintf(stdout," locations buffer size %zu\n",tape_stats[LOC_BUFFER_SIZE]);
fprintf(stdout," constants buffer size %zu\n",tape_stats[VAL_BUFFER_SIZE]);
fprintf(stdout," maxlive %zu\n",tape_stats[NUM_MAX_LIVES]);
fprintf(stdout," valstack size %zu\n\n",tape_stats[TAY_STACK_SIZE]);
/*--------------------------------------------------------------------------*/
tdist = (tmax-tmin)/((double) (vc-1));
t = tmin;
for (i=0; i<vc; i++) {
function(tag1,1,1,&t,&z1);
function(tag2,1,1,&t,&z2);
if (!(z1==z1)) // check for NaN
{ gradient(tag2,1,&t,&dz);
fprintf(stdout,"%e %e %e\n",t,z2,dz);
} else {
gradient(tag1,1,&t,&dz);
fprintf(stdout,"%e %e %e\n",t,z1,dz);
}
t += tdist;
}
/*--------------------------------------------------------------------------*/
return 1;
}
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