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/*----------------------------------------------------------------------------
ADOL-C -- Automatic Differentiation by Overloading in C++
File: paramexam.cpp
Revision: $Id$
Contents: example for parameter dependent functions
Copyright (c) Kshitij Kulshreshtha
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 <adolc/adolc.h>
#include <cmath>
#include "myclock.h"
using namespace std;
/****************************************************************************/
/* CONSTANTS & VARIABLES */
const double TE = 0.01; /* originally 0.0 */
const double R = sqrt(2.0);
/****************************************************************************/
/* HELMHOLTZ ENERGY */
adouble energy( int n, adouble x[], double bv[] ) {
adouble he, xax, bx, tem;
int i,j;
xax = 0;
bx = 0;
he = 0;
for (i=0; i<n; i++) {
he += x[i]*log(x[i]);
bx += bv[i]*x[i];
tem = (2.0/(1.0+i+i))*x[i];
for (j=0; j<i; j++)
tem += (1.0/(1.0+i+j))*x[j];
xax += x[i]*tem;
}
xax *= 0.5;
he = 1.3625E-3*(he-TE*log(1.0-bx));
he = he - log((1+bx*(1+R))/(1+bx*(1-R)))*xax/bx;
return he;
}
/* Now with parameters */
adouble energy_p( int n, adouble x[], double bv[] ) {
adouble he, xax, bx, tem;
int i,j;
xax = 0;
bx = 0;
he = 0;
for (i=0; i<n; i++) {
he += x[i]*log(x[i]);
bx += mkparam(bv[i])*x[i];
tem = (2.0/(1.0+i+i))*x[i];
for (j=0; j<i; j++)
tem += (1.0/(1.0+i+j))*x[j];
xax += x[i]*tem;
}
xax *= 0.5;
he = 1.3625E-3*(he-TE*log(1.0-bx));
he = he - log((1+bx*(1+R))/(1+bx*(1-R)))*xax/bx;
return he;
}
/* now with more independents */
adouble energy_a( int n, adouble x[], adouble b[] ) {
adouble he, xax, bx, tem;
int i,j;
xax = 0;
bx = 0;
he = 0;
for (i=0; i<n; i++) {
he += x[i]*log(x[i]);
bx += b[i]*x[i];
tem = (2.0/(1.0+i+i))*x[i];
for (j=0; j<i; j++)
tem += (1.0/(1.0+i+j))*x[j];
xax += x[i]*tem;
}
xax *= 0.5;
he = 1.3625E-3*(he-TE*log(1.0-bx));
he = he - log((1+bx*(1+R))/(1+bx*(1-R)))*xax/bx;
return he;
}
/****************************************************************************/
/* MAIN */
/* This program computes first order directional derivatives
for the helmholtz energy function */
int main() {
int nf, n, j, l;
fprintf(stdout,"HELM-AUTO-EXAM (ADOL-C Example)\n\n");
fprintf(stdout," # of independents/10 =? \n ");
scanf("%d",&nf);
/*--------------------------------------------------------------------------*/
double result = 0.0, result_p = 0.0, result_a; /* Initilizations */
double tt1s, tt1e, tt2s, tt2e, trt1s, trt1e, tpxs, tpxe,
tt3s, tt3e, tixs, tixe;
n = 10 * nf;
double* bv = new double[n];
double* grad = new double[n];
double* grad_p = new double[n];
double* px = new double[n];
double* lpx = new double[2*n];
double* grad_a = new double[2*n];
double** hess = myalloc2(n,n);
double** hess_p = myalloc2(n,n);
double** hess_a = myalloc2(2*n,2*n);
adouble* x = new adouble[n];
adouble* b = new adouble[n];
adouble he;
double r = 1.0/n;
for (j=0; j<n; j++)
bv[j]= 0.02*(1.0+fabs(sin(double(j))));
/*--------------------------------------------------------------------------*/
int imd_rev = 1; /* Tracing with keep */
tt1s = myclock();
trace_on(1,imd_rev);
for (j=0; j<n; j++)
x[j] <<= (px[j] = r*sqrt(1.0+j));
he = energy(n,x,bv);
he >>= result;
trace_off();
reverse(1,1,n,0,1.0,grad); /* reverse computation of gradient */
hessian2(1,n,px,hess);
tt1e = myclock();
/*--------------------------------------------------------------------------*/
imd_rev = 1; /* Tracing with keep */
tt2s = myclock();
trace_on(2,imd_rev);
for (j=0; j<n; j++)
x[j] <<= px[j];
he = energy_p(n,x,bv);
he >>= result_p;
trace_off();
reverse(2,1,n,0,1.0,grad_p); /* reverse computation of gradient */
hessian2(2,n,px,hess_p);
tt2e = myclock();
/*--------------------------------------------------------------------------*/
for (j=0; j<n; j++) {
lpx[j] = px[j];
lpx[n+j] = bv[j];
}
imd_rev = 1; /* Tracing with keep */
tt3s = myclock();
trace_on(3,imd_rev);
for (j=0; j<n; j++)
x[j] <<= px[j];
for (j=0; j<n; j++)
b[j] <<= bv[j];
he = energy_a(n,x,b);
he >>= result_a;
trace_off();
reverse(3,1,2*n,0,1.0,grad_a); /* reverse computation of gradient */
hessian2(3,2*n,lpx,hess_a);
tt3e = myclock();
/*--------------------------------------------------------------------------*/
printTapeStats(stdout,1);
printTapeStats(stdout,2);
printTapeStats(stdout,3);
fprintf(stdout, "%14.6E -- energy\n",result);
fprintf(stdout, "%14.6E -- energy\n",result_p);
fprintf(stdout, "%14.6E -- energy\n",result_a);
/*--------------------------------------------------------------------------*/
for (l=0; l<n; l++) /* results */
fprintf(stdout,"%3d: 2*%14.6E - %14.6E - %14.6E = %14.6E ( = 0 )\n",l,grad[l],grad_p[l],grad_a[l],2*grad[l]-grad_p[l]-grad_a[l]);
/*--------------------------------------------------------------------------*/
/* change constant parameters */
fprintf(stdout, "changed constant parameters\n");
for (j=0; j<n; j++)
bv[j]= 0.01*(1.0+fabs(sin(double(j))));
/* parameter tape */
tpxs = myclock();
set_param_vec(2,n,bv);
zos_forward(2,1,n,1,px,&result_p);
reverse(2,1,n,0,1.0,grad_p);
hessian2(2,n,px,hess_p);
tpxe = myclock();
/* double independents tape */
for (j=0; j<n; j++) {
lpx[j] = px[j];
lpx[n+j] = bv[j];
}
tixs = myclock();
zos_forward(3,1,2*n,1,lpx,&result_a);
reverse(3,1,2*n,0,1.0,grad_a);
hessian2(3,2*n,lpx,hess_a);
tixe = myclock();
/*--------------------------------------------------------------------------*/
/* with retaping on tape 1 */
trt1s = myclock();
trace_on(1,imd_rev);
for (j=0; j<n; j++)
x[j] <<= px[j];
he = energy(n,x,bv);
he >>= result;
trace_off();
reverse(1,1,n,0,1.0,grad); /* reverse computation of gradient */
hessian2(1,n,px,hess);
trt1e = myclock();
fprintf(stdout, "%14.6E -- energy\n",result);
fprintf(stdout, "%14.6E -- energy\n",result_p);
fprintf(stdout, "%14.6E -- energy\n",result_a);
for (l=0; l<n; l++) /* results */
fprintf(stdout,"%3d: 2*%14.6E - %14.6E - %14.6E = %14.6E ( = 0 )\n",l,grad[l],grad_p[l],grad_a[l],2*grad[l]-grad_p[l]-grad_a[l]);
fprintf(stdout, "\n\n Times for ");
fprintf(stdout, "\n Tracing + Reverse + Hess2 1: \t%E", tt1e-tt1s);
fprintf(stdout, "\n Tracing + Reverse + Hess2 2: \t%E", tt2e-tt2s);
fprintf(stdout, "\n Tracing + Reverse + Hess2 3: \t%E", tt3e-tt3s);
fprintf(stdout, "\n Retracing Reverse + Hess2 1: \t%E", trt1e-trt1s);
fprintf(stdout, "\n Point change grad + Hess2 2: \t%E", tpxe-tpxs);
fprintf(stdout, "\n Point change grad + Hess2 3: \t%E", tixe-tixs);
myfree2(hess);
myfree2(hess_p);
myfree2(hess_a);
delete[] bv;
delete[] px;
delete[] grad;
delete[] grad_p;
delete[] lpx;
delete[] grad_a;
delete[] x;
return 0;
}
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