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/*
--------------------------------------------------------------
File scalexam.C of ADOL-C version 1.8.0 as of Dec/01/98
--------------------------------------------------------------
This program can be used to verify the consistency and
correctness of derivatives computed by ADOL-C in its forward
and reverse mode.
The use is required to selct one integer input id.
For positive n = id the monomial x^n is evaluated recursively
at x=0.5 and all its nonzero Taylor coeffcients at this point
are evaluated in the forward and reverse mode.
A negative choice of id >= -9 leads to one of nine
identities, whose derivatives should be trivial. These identities
may be used to check the correctness of particular code segments
in the ADOL-C sources uni5_.c and *o_rev.c. No timings are
performed in this example program.
Last changes:
981201 olvo: new headers
980821 olvo: this is the old version 1.7
--------------------------------------------------------------
*/
/****************************************************************************/
/* INCLUDES */
#include "adouble.h" // These includes provide the compiler with
#include "interfaces.h" // definitions and utilities for `adoubles'.
#include <math.h>
/****************************************************************************/
/* POWER */
/* The monomial evaluation routine which has been obtained from
the original version by retyping all `doubles' as `adoubles' */
adouble power( adouble x, int n )
{ adouble z = 1;
if (n > 0)
{ int nh =n/2;
z = power(x,nh);
z *= z;
if (2*nh != n)
z *= x;
return z;
}
else
if (n == 0)
return z;
else
return 1.0/power(x,-n);
}
/****************************************************************************/
/* MAIN */
int main()
{ int n, i, id;
int tag = 0;
/*--------------------------------------------------------------------------*/
fprintf(stdout,"SCALEXAM (ADOL-C Example)\n\n");
fprintf(stdout,"problem number(-1 .. -10) / degree of monomial =? \n");
scanf("%d",&id);
n = id >0 ? id : 3;
double *xp,*yp;
xp = new double[n+4];
yp = new double[n+4];
yp[0] = 0;
xp[0] = 0.5;
xp[1] = 1.0;
/*--------------------------------------------------------------------------*/
int dum = 1;
trace_on(tag,dum); // Begin taping all calculations with 'adoubles'
adouble y,x;
x <<= xp[0];
if (id >= 0)
{ fprintf(stdout,"Evaluate and differentiate recursive power routine \n");
y = power(x,n);
}
else
{ fprintf(stdout,
"Check Operations and Functions by Algebraic Identities \n");
double pi = 2*asin(1.0);
switch (id) {
case -1 :
fprintf(stdout,
"Addition/Subtraction: y = x + x - (2.0/3)*x - x/3 \n");
y = x + x - (2.0/3)*x - x/3 ;
break;
case -2 :
fprintf(stdout,"Multiplication/divison: y = x*x/x \n");
y = x*x/x;
break;
case -3 :
fprintf(stdout,"Square root and power: y = sqrt(pow(x,2)) \n");
y = sqrt(pow(x,2));
break;
case -4 :
fprintf(stdout,"Exponential and log: y = exp(log(log(exp(x)))) \n");
y = exp(log(log(exp(x))));
break;
case -5 :
fprintf(stdout,"Trig identity: y = x + sin(2*x)-2*cos(x)*sin(x) \n");
y = x + sin(2.0*x)-2.0*cos(x)*sin(x);
break;
case -6 :
fprintf(stdout,"Check out quadrature macro \n");
y = exp(myquad(myquad(exp(x))));
break;
case -7 :
fprintf(stdout,"Arcsin: y = sin(asin(acos(cos(x)))) \n");
y = sin(asin(acos(cos(x))));
break;
case -8 :
fprintf(stdout,
"Hyperbolic tangent: y = x + tanh(x)-sinh(x)/cosh(x) \n");
y = x + tanh(x)-sinh(x)/cosh(x) ;
break;
case -9 :
fprintf(stdout,"Absolute value: y = x + fabs(x) - fabs(-x) \n");
y = x + fabs(-x) - fabs(x);
break;
case -10 :
fprintf(stdout,"atan2: y = atan2(sin(x-0.5+pi),cos(x-0.5+pi)) \n");
y = atan2(sin(x),cos(x));
break;
default : fprintf(stdout," Please select problem number >= -10 \n");
exit(-1);
}
}
y >>= yp[0];
trace_off(); // The (partial) execution trace is completed.
/*--------------------------------------------------------------------------*/
if( id < 0 )
fprintf(stdout,"Round-off error: %14.6le\n",value(y-x));
/*--------------------------------------------------------------------------*/
int tape_stats[11];
tapestats(tag,tape_stats); /* Reading of tape statistics */
fprintf(stdout,"\n independents %d\n",tape_stats[0]);
fprintf(stdout," dependents %d\n",tape_stats[1]);
fprintf(stdout," operations %d\n",tape_stats[5]);
fprintf(stdout," buffer size %d\n",tape_stats[4]);
fprintf(stdout," maxlive %d\n",tape_stats[2]);
fprintf(stdout," valstack size %d\n\n",tape_stats[3]);
/*--------------------------------------------------------------------------*/
double *res;
res = new double[n+2];
double u[1];
u[0] = 1;
fprintf(stdout,
"\nThe two Taylor coefficients in each row should agree\n\n");
double ***V = (double***)new double**[1];
V[0] = new double*[1];
V[0][0] = new double[n+2];
double **U = new double*[1];
U[0] = new double[1];
U[0][0] = 1;
double** xpoint = &xp;
double** ypoint = &yp;
double** respoint = &res;
// tape_doc(tag,depen,indep,*xpoint,*respoint);
fprintf(stdout," \n \t forward \t reverse \n");
for (i=0; i < n+2; i++)
{ xp[i+2]=0;
forward(tag,1,1,i,i+1,xpoint,respoint);
fprintf(stdout,"%d\t%14.6le\t\t%14.6le\n",i,res[i],yp[i]);
reverse(tag,1,1,i,u,ypoint); // call higher order scalar reverse
reverse(tag,1,1,i,1,U,V);
yp[i+1] = yp[i]/(i+1);
if (V[0][0][i] != yp[i])
fprintf(stdout,"%d-th component in error %14.6le\n",i,V[0][0][i]-yp[i]);
}
cout << "\nWhen n<0 all rows except the first two should vanish \n";
return 1;
}
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