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/*----------------------------------------------------------------------------
ADOL-C -- Automatic Differentiation by Overloading in C++
File: LUdet.cpp
Revision: $Id$
Contents: example for
* Computation of the determinant of a matrix
by LU-decomposition of the system matrix without pivoting
* application of tapedoc to observe taping of
the new op_codes for the elementary operations
y += x1 * x2;
y -= x1 * x2;
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 "LU.h"
/****************************************************************************/
/* MAIN PROGRAM */
int main() { /*------------------------------------------------------------------------*/
/* variables */
const int tag = 1; // tape tag
const int size = 5; // system size
const int indep = size*size; // # of indeps
const int depen = 1; // # of deps
double A[size][size], a1[size], a2[size], det; // passive variables
adouble **AA, *AAp, Adet; // active variables
double *args = myalloc1(indep); // arguments
double *grad = myalloc1(indep); // the gradient
double **hess = myalloc2(indep,indep); // the hessian
int i,j;
/*------------------------------------------------------------------------*/
/* Info */
fprintf(stdout,"DETERMINANT by LU-DECOMPOSITION (ADOL-C Example)\n\n");
/*------------------------------------------------------------------------*/
/* Allcoation und initialization of the system matrix */
AA = new adouble*[size];
AAp = new adouble[size*size];
for (i=0; i<size; i++) {
AA[i] = AAp;
AAp += size;
}
for(i=0; i<size; i++) {
a1[i] = i*0.25;
a2[i] = i*0.33;
}
for(i=0; i<size; i++) {
for(j=0; j<size; j++)
A[i][j] = a1[i]*a2[j];
A[i][i] += i+1;
}
/*------------------------------------------------------------------------*/
/* Taping the computation of the determinant */
trace_on(tag);
/* marking indeps */
for(i=0; i<size; i++)
for(j=0; j<size; j++)
AA[i][j] <<= (args[i*size+j] = A[i][j]); // indep. vars
/* LU-factorization and computation of determinant */
LUfact(size,AA);
Adet = AA[0][0];
for (i=1; i<size; i++)
Adet *= AA[i][i];
/* marking deps */
Adet >>= det;
trace_off();
fprintf(stdout," Determinant (original): %16.4E\n",det);
/*------------------------------------------------------------------------*/
/* Recomputation of determinant */
function(tag,depen,indep,args,&det);
fprintf(stdout," Determinant (from tape): %16.4E\n",det);
/*------------------------------------------------------------------------*/
/* Computation of gradient */
gradient(tag,indep,args,grad);
fprintf(stdout," Gradient:\n");
for (i=0; i<size; i++) {
for (j=0; j<size; j++)
fprintf(stdout," %14.6E",grad[i*size+j]);
fprintf(stdout,"\n");
}
/*------------------------------------------------------------------------*/
/* Computation of hessian */
hessian(tag,indep,args,hess);
fprintf(stdout," Part of Hessian:\n");
for (i=0; i<size; i++) {
for (j=0; j<size; j++)
fprintf(stdout," %14.6E",hess[0][i*size+j]);
fprintf(stdout,"\n");
}
/*------------------------------------------------------------------------*/
/* Tape-documentation */
tape_doc(tag,depen,indep,args,&det);
/*------------------------------------------------------------------------*/
/* Tape statistics */
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]);
/*------------------------------------------------------------------------*/
/* That's it */
return 1;
}
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