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/*----------------------------------------------------------------------------
ADOL-C -- Automatic Differentiation by Overloading in C++
File: sparse_hessian.cpp
Revision: $Id: sparse_hessian.cpp 299 2012-03-21 16:08:40Z kulshres $
Contents: example for computation of sparse hessians
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.
---------------------------------------------------------------------------*/
#include <math.h>
#include <cstdlib>
#include <cstdio>
#include <adolc/adolc.h>
#include <adolc/adolc_sparse.h>
#define tag 1
double feval(double *x);
adouble feval_ad(adouble *x);
void printmat(const char* kette, int n, int m, double** M);
int main() {
int n=6;
double f, x[6];
adouble fad, xad[6];
int i, j;
/****************************************************************************/
/******* function evaluation ***************/
/****************************************************************************/
for(i=0;i<n;i++)
x[i] = log(1.0+i);
/* Tracing of function f(x) */
trace_on(tag);
for(i=0;i<n;i++)
xad[i] <<= x[i];
fad = feval_ad(xad);
fad >>= f;
trace_off();
printf("\n f = %e\n\n\n",f);
/****************************************************************************/
/******** For comparisons: Full Hessian ********/
/****************************************************************************/
double **H;
H = myalloc2(n,n);
hessian(tag,n,x,H);
printmat(" H",n,n,H);
printf("\n");
/****************************************************************************/
/******* sparse Hessians, complete driver ***************/
/****************************************************************************/
/* coordinate format for Hessian */
unsigned int *rind = NULL;
unsigned int *cind = NULL;
double *values = NULL;
int nnz;
int options[2];
options[0] = 0; /* safe mode (default) */
options[1] = 0; /* indirect recovery (default) */
sparse_hess(tag, n, 0, x, &nnz, &rind, &cind, &values, options);
printf("In sparse format:\n");
for (i=0;i<nnz;i++)
printf("%2d %2d %10.6f\n\n",rind[i],cind[i],values[i]);
free(rind); rind = NULL;
free(cind); cind = NULL;
free(values); values = NULL;
options[0] = 0; /* safe mode (default) */
options[1] = 1; /* direct recovery */
sparse_hess(tag, n, 0, x, &nnz, &rind, &cind, &values, options);
printf("In sparse format:\n");
for (i=0;i<nnz;i++)
printf("%2d %2d %10.6f\n\n",rind[i],cind[i],values[i]);
free(rind); rind=NULL;
free(cind); cind=NULL;
free(values); values=NULL;
/*--------------------------------------------------------------------------*/
/* change value of x, but not the sparsity pattern */
/*--------------------------------------------------------------------------*/
for(i=0;i<n;i++)
x[i] = 2.0*i;
/* For comparisons: Full Hessian: */
hessian(tag,n,x,H);
printmat(" H",n,n,H);
printf("\n");
/* repeated call of sparse_hess with same sparsity pattern => repeat = 1 */
sparse_hess(tag, n, 0, x, &nnz, &rind, &cind, &values, options);
printf("In sparse format:\n");
for (i=0;i<nnz;i++)
printf("%2d %2d %10.6f\n\n",rind[i],cind[i],values[i]);
free(rind); rind=NULL;
free(cind); cind=NULL;
free(values); values=NULL;
/****************************************************************************/
/******* sparse Hessians, separate drivers ***************/
/****************************************************************************/
/*--------------------------------------------------------------------------*/
/* sparsity pattern Hessian */
/*--------------------------------------------------------------------------*/
unsigned int **HP=NULL; /* compressed block row storage */
int ctrl;
HP = (unsigned int **) malloc(n*sizeof(unsigned int*));
ctrl = 0;
hess_pat(tag, n, x, HP, ctrl);
printf("\n");
printf("Sparsity pattern of Hessian: \n");
for (i=0;i<n;i++) {
printf(" %d: ",i);
for (j=1;j<= (int) HP[i][0];j++)
printf(" %d ",HP[i][j]);
printf("\n");
}
printf("\n");
/*--------------------------------------------------------------------------*/
/* seed matrix */
/*--------------------------------------------------------------------------*/
double **Seed;
int p;
int option = 1;
/* option = 0 indirect recovery (default),
option = 1 direct recovery */
generate_seed_hess(n, HP, &Seed, &p, option);
printmat(" Seed matrix",n,p,Seed);
printf("\n");
/*--------------------------------------------------------------------------*/
/* compressed Hessian */
/*--------------------------------------------------------------------------*/
double **Hcomp;
Hcomp = myalloc2(n,p);
hess_mat(tag, n, p, x, Seed, Hcomp);
printmat("compressed H:",n,p,Hcomp);
printf("\n");
/*--------------------------------------------------------------------------*/
/* change value of x, but not the sparsity pattern */
/*--------------------------------------------------------------------------*/
for(i=0;i<n;i++)
x[i] = 2.0*i;
/* For comparisons: Full Hessian */
hessian(tag,n,x,H);
printmat(" H",n,n,H);
printf("\n");
hess_mat(tag, n, p, x, Seed, Hcomp);
printmat("compressed H:",n,p,Hcomp);
printf("\n");
for(i=0;i<n;i++)
free(HP[i]);
free(HP);
myfree2(H);
myfree2(Hcomp);
for (i = 0; i < n; i++)
delete[] Seed[i];
delete[] Seed;
}
/***************************************************************************/
double feval(double *x) {
double res;
res = 0.5*(x[0] - 1)*(x[0] -1) + 0.8*(x[1] - 2)*(x[1] -2) + 0.9*(x[2] - 3)*(x[2] -3);
res += 5*x[0]*x[1];
res += cos(x[3]);
res += sin(x[4])*x[1]*x[1];
res += exp(x[5])*x[2];
res += sin(x[4]*x[5]);
return res;
}
/***************************************************************************/
adouble feval_ad(adouble *x) {
adouble res;
res = 0.5*(x[0] - 1)*(x[0] -1) + 0.8*(x[1] - 2)*(x[1] -2) + 0.9*(x[2] - 2)*(x[2] -2);
res += 5*x[0]*x[1];
res += cos(x[3]);
res += sin(x[4])*x[1]*x[1];
res += exp(x[5])*x[2];
res += sin(x[4]*x[5]);
return res;
}
/***************************************************************************/
void printmat(const char* name, int m, int n, double** M) {
int i,j;
printf("%s \n",name);
for(i=0; i<m ;i++) {
printf("\n %d: ",i);
for(j=0;j<n ;j++)
printf(" %10.4f ", M[i][j]);
}
printf("\n");
}
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