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/*----------------------------------------------------------------------------
ADOL-C -- Automatic Differentiation by Overloading in C++
File: LUsolve.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+size; // # of indeps
const int depen = size; // # of deps
double A[size][size], a1[size], a2[size], // passive variables
b[size], x[size];
adouble **AA, *AAp, *Abx; // active variables
double *args = myalloc1(indep); // arguments
double **jac = myalloc2(depen,indep); // the Jacobian
double *laghessvec = myalloc1(indep); // Hessian-vector product
int i,j;
/*------------------------------------------------------------------------*/
/* Info */
fprintf(stdout,"LINEAR SYSTEM SOLVING by "
"LU-DECOMPOSITION (ADOL-C Example)\n\n");
/*------------------------------------------------------------------------*/
/* Allocation 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;
}
Abx = new adouble[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;
b[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]);
for(i=0; i<size; i++)
Abx[i] <<= (args[size*size+i] = b[i]);
/* LU-factorization and computation of solution */
LUfact(size,AA);
LUsolve(size,AA,Abx);
/* marking deps */
for (i=0; i<size; i++)
Abx[i] >>= x[i];
trace_off();
fprintf(stdout," x[0] (original): %16.4E\n",x[0]);
/*------------------------------------------------------------------------*/
/* Recomputation */
function(tag,depen,indep,args,x);
fprintf(stdout," x[0] (from tape): %16.4E\n",x[0]);
/*------------------------------------------------------------------------*/
/* Computation of Jacobian */
jacobian(tag,depen,indep,args,jac);
fprintf(stdout," Jacobian:\n");
for (i=0; i<depen; i++) {
for (j=0; j<indep; j++)
fprintf(stdout," %14.6E",jac[i][j]);
fprintf(stdout,"\n");
}
/*------------------------------------------------------------------------*/
/* Computation of Lagrange-Hessian-vector product */
lagra_hess_vec(tag,depen,indep,args,args,x,laghessvec);
fprintf(stdout," Part of Lagrange-Hessian-vector product:\n");
for (i=0; i<size; i++) {
for (j=0; j<size; j++)
fprintf(stdout," %14.6E",laghessvec[i*size+j]);
fprintf(stdout,"\n");
}
/*------------------------------------------------------------------------*/
/* Tape-documentation */
tape_doc(tag,depen,indep,args,x);
/*------------------------------------------------------------------------*/
/* 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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