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/*----------------------------------------------------------------------------
ADOL-C -- Automatic Differentiation by Overloading in C++
File: detexam.cpp
Revision: $Id: detexam.cpp 527 2014-07-15 14:09:31Z kulshres $
Contents: modified computation of determinants
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 "../clock/myclock.h"
/****************************************************************************/
/* DOUBLE ROUTINE */
int n,it;
double** PA;
double pdet( int k, int m ) {
if (m == 0)
return 1.0 ;
else {
double* pt = PA[k-1];
double t = 0;
int p = 1;
int s;
if (k%2)
s = 1;
else
s = -1;
for (int i=0; i<n; i++) {
int p1 = 2*p;
if (m%p1 >= p) {
if (m == p) {
if (s>0)
t += *pt;
else
t -= *pt;
} else {
if (s>0)
t += *pt*pdet(k-1, m-p);
else
t -= *pt*pdet(k-1, m-p);
}
s = -s;
}
++pt;
p = p1;
}
return t;
}
}
/****************************************************************************/
/* ADOUBLE ROUTINE */
adouble** A;
adouble zero = 0;
adouble det( int k, int m ) {
if (m == 0)
return 1.0;
else {
adouble* pt = A[k-1];
adouble t = zero;
int p = 1;
int s;
if (k%2)
s = 1;
else
s = -1;
for (int i=0; i<n; i++) {
int p1 = 2*p;
if (m%p1 >= p) {
if (m == p) {
if (s>0)
t += *pt;
else
t -= *pt;
} else {
if (s>0)
t += *pt*det(k-1, m-p);
else
t -= *pt*det(k-1, m-p);
}
s = -s;
}
++pt;
p = p1;
}
return t;
}
}
/****************************************************************************/
/* MAIN PROGRAM */
int main() {
int i, j;
int tag = 1;
fprintf(stdout,"COMPUTATION OF DETERMINANTS Type 1 (ADOL-C Example)\n\n");
fprintf(stdout,"order of matrix = ? \n");
scanf("%d",&n);
A = new adouble*[n];
PA = new double*[n];
int n2 = n*n;
double* a = new double[n2];
/*--------------------------------------------------------------------------*/
/* Preparation */
double diag = 0;
int m = 1;
double* pa = a;
for (i=0; i<n; i++) {
m *= 2;
PA[i] = new double[n];
double* ppt = PA[i];
for (j=0; j<n; j++) {
*ppt++ = j/(1.0+i);
*pa++ = j/(1.0+i);
}
diag += PA[i][i]; // val corrected to value 2/23/91
PA[i][i] += 1.0;
a[i*n+i] += 1.0;
}
diag += 1;
/*--------------------------------------------------------------------------*/
double t00 = myclock(); /* 0. time (taping) */
trace_on(tag);
for (i=0; i<n; i++) {
A[i] = new adouble[n];
adouble* pt = A[i];
double* ppt = PA[i];
for (j=0; j<n; j++)
*pt++ <<= *ppt++;
}
adouble deter;
deter = det(n,m-1);
double detout = 0.0;
deter >>= detout;
trace_off();
double t01 = myclock();
fprintf(stdout,"\n %f =? %f should be the same \n",detout,diag);
/*--------------------------------------------------------------------------*/
size_t tape_stats[STAT_SIZE];
tapestats(tag,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]);
/*--------------------------------------------------------------------------*/
int itu = 8-n;
itu = itu*itu*itu*itu;
itu = itu > 0 ? itu : 1;
double raus;
/*--------------------------------------------------------------------------*/
double t10 = myclock(); /* 1. time (original) */
for (it = 0; it < itu; it++)
raus = pdet(n,m-1);
double t11 = myclock();
double rtu = itu/(t11-t10);
double* B = new double[n2];
double* detaut = new double[1];
/*--------------------------------------------------------------------------*/
double t40 = myclock(); /* 4. time (forward no keep) */
for (it = 0; it < itu; it++)
forward(tag,1,n2,0,a,detaut);
double t41 = myclock();
/*--------------------------------------------------------------------------*/
double t20 = myclock(); /* 2. time (forward+keep) */
for(it = 0; it < itu; it++)
forward(tag,1,n2,1,a,detaut);
double t21 = myclock();
// fprintf(stdout,"\n %f =? %f should be the same \n",detout,*detaut);
double u[1];
u[0] = 1.0;
/*--------------------------------------------------------------------------*/
double t30 = myclock(); /* 3. time (reverse) */
for (it = 0; it < itu; it++)
reverse(tag,1,n2,0,u,B);
double t31 = myclock();
/*--------------------------------------------------------------------------*/
/* output of results */
// optional generation of tape_doc.tex
// tape_doc(tag,1,n2,a,detaut);
fprintf(stdout,"\n first base? : \n");
for (i=0; i<n; i++) {
adouble sum = 0;
adouble* pt;
pt = A[i];
for (j=0; j<n; j++)
sum += (*pt++)*B[j];
fprintf(stdout,"%E ",sum.value());
}
fprintf(stdout,"\n\n times for ");
fprintf(stdout,"\n tracing : \t%E",(t01-t00)*rtu);
fprintf(stdout," units \t%E seconds",(t01-t00));
fprintf(stdout,"\n forward (no keep): \t%E",(t41-t40)*rtu/itu);
fprintf(stdout," units \t%E seconds",(t41-t40)/itu);
fprintf(stdout,"\n forward + keep : \t%E",(t21-t20)*rtu/itu);
fprintf(stdout," units \t%E seconds",(t21-t20)/itu);
fprintf(stdout,"\n reverse : \t%E",(t31-t30)*rtu/itu);
fprintf(stdout," units \t%E seconds\n",(t31-t30)/itu);
return 1;
}
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