Exemple #1
0
SPMAT	*comp_AAT(SPMAT *A)
#endif
{
	SPMAT	*AAT;
	SPROW	*r, *r2;
	row_elt	*elts, *elts2;
	int	i, idx, idx2, j, m, minim, n, num_scan, tmp1;
	Real	ip;

	if ( ! A )
		error(E_NULL,"comp_AAT");
	m = A->m;	n = A->n;

	/* set up column access paths */
	if ( ! A->flag_col )
		sp_col_access(A);

	AAT = sp_get(m,m,10);

	for ( i = 0; i < m; i++ )
	{
		/* initialisation */
		r = &(A->row[i]);
		elts = r->elt;

		/* set up scan lists for this row */
		if ( r->len > scan_len )
		    set_scan(r->len);
		for ( j = 0; j < r->len; j++ )
		{
		    col_list[j] = elts[j].col;
		    scan_row[j] = elts[j].nxt_row;
		    scan_idx[j] = elts[j].nxt_idx;
		}
		num_scan = r->len;

		/* scan down the rows for next non-zero not
			associated with a diagonal entry */
		for ( ; ; )
		{
		    minim = m;
		    for ( idx = 0; idx < num_scan; idx++ )
		    {
			tmp1 = scan_row[idx];
			minim = ( tmp1 >= 0 && tmp1 < minim ) ? tmp1 : minim;
		    }
		    if ( minim >= m )
		 	break;
		    r2 = &(A->row[minim]);
		    if ( minim > i )
		    {
			ip = sprow_ip(r,r2,n);
		        sp_set_val(AAT,minim,i,ip);
		        sp_set_val(AAT,i,minim,ip);
		    }
		    /* update scan entries */
		    elts2 = r2->elt;
		    for ( idx = 0; idx < num_scan; idx++ )
		    {
			if ( scan_row[idx] != minim || scan_idx[idx] < 0 )
			    continue;
			idx2 = scan_idx[idx];
			scan_row[idx] = elts2[idx2].nxt_row;
			scan_idx[idx] = elts2[idx2].nxt_idx;
		    }
		}

		/* set the diagonal entry */
		sp_set_val(AAT,i,i,sprow_sqr(r,n));
	}

	return AAT;
}
Exemple #2
0
SPMAT	*spCHsymb(SPMAT *A)
#endif
{
	register 	int	i;
	int	idx, k, m, minim, n, num_scan, diag_idx, tmp1;
	SPROW	*r_piv, *r_op;
	row_elt	*elt_piv, *elt_op, *old_elt;

	if ( A == SMNULL )
		error(E_NULL,"spCHsymb");
	if ( A->m != A->n )
		error(E_SQUARE,"spCHsymb");

	/* set up access paths if not already done so */
	if ( ! A->flag_col )
		sp_col_access(A);
	if ( ! A->flag_diag )
		sp_diag_access(A);

	/* printf("spCHsymb() -- checkpoint 1\n"); */
	m = A->m;	n = A->n;
	for ( k = 0; k < m; k++ )
	{
		r_piv = &(A->row[k]);
		if ( r_piv->len > scan_len )
			set_scan(r_piv->len);
		elt_piv = r_piv->elt;
		diag_idx = sprow_idx2(r_piv,k,r_piv->diag);
		if ( diag_idx < 0 )
			error(E_POSDEF,"spCHsymb");
		old_elt = &(elt_piv[diag_idx]);
		for ( i = 0; i < r_piv->len; i++ )
		{
			if ( elt_piv[i].col > k )
				break;
			col_list[i] = elt_piv[i].col;
			scan_row[i] = elt_piv[i].nxt_row;
			scan_idx[i] = elt_piv[i].nxt_idx;
		}
		/* printf("spCHsymb() -- checkpoint 2\n"); */
		num_scan = i;	/* number of actual entries in scan_row etc. */
		/* printf("num_scan = %d\n",num_scan); */

		/* now set the k-th column of the Cholesky factors */
		/* printf("k = %d\n",k); */
		for ( ; ; )	/* forever do... */
		{
		    /* printf("spCHsymb() -- checkpoint 3\n"); */
		    /* find next row where something (non-trivial) happens
			i.e. find min(scan_row) */
		    minim = n;
		    for ( i = 0; i < num_scan; i++ )
		    {
			tmp1 = scan_row[i];
			/* printf("%d ",tmp1); */
			minim = ( tmp1 >= 0 && tmp1 < minim ) ? tmp1 : minim;
		    }

		    if ( minim >= n )
			break;	/* nothing more to do for this column */
		    r_op = &(A->row[minim]);
		    elt_op = r_op->elt;

		    /* set next entry in column k of Cholesky factors */
		    idx = sprow_idx2(r_op,k,scan_idx[num_scan-1]);
		    if ( idx < 0 )
		    {	/* fill-in */
			sp_set_val(A,minim,k,0.0);
			/* in case a realloc() has occurred... */
			elt_op = r_op->elt;
			/* now set up column access path again */
			idx = sprow_idx2(r_op,k,-(idx+2));
			tmp1 = old_elt->nxt_row;
			old_elt->nxt_row = minim;
			r_op->elt[idx].nxt_row = tmp1;
			tmp1 = old_elt->nxt_idx;
			old_elt->nxt_idx = idx;
			r_op->elt[idx].nxt_idx = tmp1;
		    }

		    /* printf("spCHsymb() -- checkpoint 4\n"); */

		    /* remember current element in column k for column chain */
		    idx = sprow_idx2(r_op,k,idx);
		    old_elt = &(r_op->elt[idx]);

		    /* update scan_row */
		    /* printf("spCHsymb() -- checkpoint 5\n"); */
		    /* printf("minim = %d\n",minim); */
		    for ( i = 0; i < num_scan; i++ )
		    {
			if ( scan_row[i] != minim )
				continue;
			idx = sprow_idx2(r_op,col_list[i],scan_idx[i]);
			if ( idx < 0 )
			{	scan_row[i] = -1;	continue;	}
			scan_row[i] = elt_op[idx].nxt_row;
			scan_idx[i] = elt_op[idx].nxt_idx;
			/* printf("scan_row[%d] = %d\n",i,scan_row[i]); */
			/* printf("scan_idx[%d] = %d\n",i,scan_idx[i]); */
		    }
			
		}
	    /* printf("spCHsymb() -- checkpoint 6\n"); */
	}

	return A;
}
Exemple #3
0
//--------------------------------------------------------------------------
void Hqp_IpRedSpBKP::init(const Hqp_Program *qp)
{
  IVEC *degree, *neigh_start, *neighs;
  SPMAT *QCTC;
  SPROW *r1, *r2;
  int i, j;
  int len, dim;
  Real sum;

  _n = qp->c->dim;
  _me = qp->b->dim;
  _m = qp->d->dim;
  dim = _n + _me;

  // reallocations

  _pivot = px_resize(_pivot, dim);
  _blocks = px_resize(_blocks, dim);
  _zw = v_resize(_zw, _m);
  _scale = v_resize(_scale, _n);
  _r12 = v_resize(_r12, dim);
  _xy = v_resize(_xy, dim);

  // store C' for further computations
  // analyze structure of C'*C

  _CT = sp_transp(qp->C, _CT);
  sp_ones(_CT);
  v_ones(_zw);
  QCTC = sp_get(_n, _n, 10);
  r1 = _CT->row;
  for (i=0; i<_n; i++, r1++) {
    r2 = r1;
    for (j=i; j<_n; j++, r2++) {
      sum = sprow_inprod(r1, _zw, r2);
      if (sum != 0.0) {
	sp_set_val(QCTC, i, j, sum);
	if (i != j)
	  sp_set_val(QCTC, j, i, sum);
      }
    }
  }
  _CTC_degree = iv_resize(_CTC_degree, _n);
  _CTC_neigh_start = iv_resize(_CTC_neigh_start, _n + 1);
  _CTC_neighs = sp_rcm_scan(QCTC, SMNULL, SMNULL,
			    _CTC_degree, _CTC_neigh_start, _CTC_neighs);

  // initialize structure of reduced qp

  QCTC = sp_add(qp->Q, QCTC, QCTC);

  // determine RCM ordering

  degree = iv_get(dim);
  neigh_start = iv_get(dim + 1);
  neighs = sp_rcm_scan(QCTC, qp->A, SMNULL, degree, neigh_start, IVNULL);

  _QP2J = sp_rcm_order(degree, neigh_start, neighs, _QP2J);
  _sbw = sp_rcm_sbw(neigh_start, neighs, _QP2J);
  _J2QP = px_inv(_QP2J, _J2QP);

  iv_free(degree);
  iv_free(neigh_start);
  iv_free(neighs);

  len = 1 + (int)(log((double)dim) / log(2.0));
  sp_free(_J);
  sp_free(_J_raw);
  _J_raw = sp_get(dim, dim, len);
  _J = SMNULL;

  // fill up data (to allocate _J_raw)
  sp_into_symsp(QCTC, -1.0, _J_raw, _QP2J, 0, 0);
  spT_into_symsp(qp->A, 1.0, _J_raw, _QP2J, 0, _n);
  sp_into_symsp(qp->A, 1.0, _J_raw, _QP2J, _n, 0);

  sp_free(QCTC);

  // prepare iterations

  update(qp);
}
Exemple #4
0
SPMAT	*spLUfactor(SPMAT *A, PERM *px, double alpha)
#endif
{
	int	i, best_i, k, idx, len, best_len, m, n;
	SPROW	*r, *r_piv, tmp_row;
	STATIC	SPROW	*merge = (SPROW *)NULL;
	Real	max_val, tmp;
	STATIC VEC	*col_vals=VNULL;

	if ( ! A || ! px )
		error(E_NULL,"spLUfctr");
	if ( alpha <= 0.0 || alpha > 1.0 )
		error(E_RANGE,"alpha in spLUfctr");
	if ( px->size <= A->m )
		px = px_resize(px,A->m);
	px_ident(px);
	col_vals = v_resize(col_vals,A->m);
	MEM_STAT_REG(col_vals,TYPE_VEC);

	m = A->m;	n = A->n;
	if ( ! A->flag_col )
		sp_col_access(A);
	if ( ! A->flag_diag )
		sp_diag_access(A);
	A->flag_col = A->flag_diag = FALSE;
	if ( ! merge ) {
	   merge = sprow_get(20);
	   MEM_STAT_REG(merge,TYPE_SPROW);
	}

	for ( k = 0; k < n; k++ )
	{
	    /* find pivot row/element for partial pivoting */

	    /* get first row with a non-zero entry in the k-th column */
	    max_val = 0.0;
	    for ( i = k; i < m; i++ )
	    {
		r = &(A->row[i]);
		idx = sprow_idx(r,k);
		if ( idx < 0 )
		    tmp = 0.0;
		else
		    tmp = r->elt[idx].val;
		if ( fabs(tmp) > max_val )
		    max_val = fabs(tmp);
		col_vals->ve[i] = tmp;
	    }

	    if ( max_val == 0.0 )
		continue;

	    best_len = n+1;	/* only if no possibilities */
	    best_i = -1;
	    for ( i = k; i < m; i++ )
	    {
		tmp = fabs(col_vals->ve[i]);
		if ( tmp == 0.0 )
		    continue;
		if ( tmp >= alpha*max_val )
		{
		    r = &(A->row[i]);
		    idx = sprow_idx(r,k);
		    len = (r->len) - idx;
		    if ( len < best_len )
		    {
			best_len = len;
			best_i = i;
		    }
		}
	    }

	    /* swap row #best_i with row #k */
	    MEM_COPY(&(A->row[best_i]),&tmp_row,sizeof(SPROW));
	    MEM_COPY(&(A->row[k]),&(A->row[best_i]),sizeof(SPROW));
	    MEM_COPY(&tmp_row,&(A->row[k]),sizeof(SPROW));
	    /* swap col_vals entries */
	    tmp = col_vals->ve[best_i];
	    col_vals->ve[best_i] = col_vals->ve[k];
	    col_vals->ve[k] = tmp;
	    px_transp(px,k,best_i);

	    r_piv = &(A->row[k]);
	    for ( i = k+1; i < n; i++ )
	    {
		/* compute and set multiplier */
		tmp = col_vals->ve[i]/col_vals->ve[k];
		if ( tmp != 0.0 )
		    sp_set_val(A,i,k,tmp);
		else
		    continue;

		/* perform row operations */
		merge->len = 0;
		r = &(A->row[i]);
		sprow_mltadd(r,r_piv,-tmp,k+1,merge,TYPE_SPROW);
		idx = sprow_idx(r,k+1);
		if ( idx < 0 )
		    idx = -(idx+2);
		/* see if r needs expanding */
		if ( r->maxlen < idx + merge->len )
		    sprow_xpd(r,idx+merge->len,TYPE_SPMAT);
		r->len = idx+merge->len;
		MEM_COPY((char *)(merge->elt),(char *)&(r->elt[idx]),
			merge->len*sizeof(row_elt));
	    }
	}
#ifdef	THREADSAFE
	sprow_free(merge);	V_FREE(col_vals);
#endif

	return A;
}
Exemple #5
0
/*
 * n_vars is the number of variables to be considered,
 * d is the data array of variables d[0],...,d[n_vars-1],
 * pred determines which estimate is required: BLUE, BLUP, or BLP
 */
void gls(DATA **d /* pointer to DATA array */,
		int n_vars, /* length of DATA array (to consider) */
		enum GLS_WHAT pred, /* what type of prediction is requested */
		DPOINT *where, /* prediction location */
		double *est /* output: array that holds the predicted values and variances */)
{
	GLM *glm = NULL; /* to be copied to/from d */
	static MAT *X0 = MNULL, *C0 = MNULL, *MSPE = MNULL, *CinvC0 = MNULL,
		*Tmp1 = MNULL, *Tmp2 = MNULL, *Tmp3, *R = MNULL;
	static VEC *blup = VNULL, *tmpa = VNULL, *tmpb = VNULL;
	volatile unsigned int i, rows_C;
	unsigned int j, k, l = 0, row, col, start_i, start_j, start_X, global;
	VARIOGRAM *v = NULL;
	static enum GLS_WHAT last_pred = GLS_INIT; /* the initial value */
	double c_value, *X_ori;

	if (d == NULL) { /* clean up */
		if (X0 != MNULL) M_FREE(X0); 
		if (C0 != MNULL) M_FREE(C0);
		if (MSPE != MNULL) M_FREE(MSPE);
		if (CinvC0 != MNULL) M_FREE(CinvC0);
		if (Tmp1 != MNULL) M_FREE(Tmp1);
		if (Tmp2 != MNULL) M_FREE(Tmp2);
		if (Tmp3 != MNULL) M_FREE(Tmp3);
		if (R != MNULL) M_FREE(R);
		if (blup != VNULL) V_FREE(blup);
		if (tmpa != VNULL) V_FREE(tmpa);
		if (tmpb != VNULL) V_FREE(tmpb);
		last_pred = GLS_INIT;
		return;
	}
#ifndef HAVE_SPARSE
	if (gl_sparse) {
		pr_warning("sparse matrices not supported: compile with --with-sparse");
		gl_sparse = 0;
	}
#endif

	if (DEBUG_COV) {
		printlog("we're at %s X: %g Y: %g Z: %g\n",
			IS_BLOCK(where) ? "block" : "point",
			where->x, where->y, where->z);
	}

	if (pred != UPDATE) /* it right away: */
		last_pred = pred;

	assert(last_pred != GLS_INIT);

	if (d[0]->glm == NULL) { /* allocate and initialize: */
		glm = new_glm();
		d[0]->glm = (void *) glm;
	} else
		glm = (GLM *) d[0]->glm;

	glm->mu0 = v_resize(glm->mu0, n_vars);
	MSPE = m_resize(MSPE, n_vars, n_vars);
	if (pred == GLS_BLP || UPDATE_BLP) {
		X_ori = where->X;
		for (i = 0; i < n_vars; i++) { /* mu(0) */
			glm->mu0->ve[i] = calc_mu(d[i], where);
			blup = v_copy(glm->mu0, v_resize(blup, glm->mu0->dim));
			where->X += d[i]->n_X; /* shift to next x0 entry */
		}
		where->X = X_ori; /* ... and set back */
		for (i = 0; i < n_vars; i++) { /* Cij(0,0): */
			for (j = 0; j <= i; j++) {
				v = get_vgm(LTI(d[i]->id,d[j]->id));
				MSPE->me[i][j] = MSPE->me[j][i] = COVARIANCE0(v, where, where, d[j]->pp_norm2);
			}
		}
		fill_est(NULL, blup, MSPE, n_vars, est); /* in case of empty neighbourhood */
	}
	/* xxx */
	/*
	logprint_variogram(v, 1);
	*/

/* 
 * selection dependent problem dimensions: 
 */
	for (i = rows_C = 0; i < n_vars; i++)
		rows_C += d[i]->n_sel;

	if (rows_C == 0) { /* empty selection list(s) */
		if (pred == GLS_BLP || UPDATE_BLP)
			debug_result(blup, MSPE, pred);
		return;
	}

	for (i = 0, global = 1; i < n_vars && global; i++)
		global = (d[i]->sel == d[i]->list && d[i]->n_list == d[i]->n_original);

/*
 * global things: enter whenever (a) first time, (b) local selections or
 * (c) the size of the problem grew since the last call (e.g. simulation)
 */
	if ((glm->C == NULL && glm->spC == NULL) || !global || rows_C > glm->C->m) {
/* 
 * fill y: 
 */
		glm->y = get_y(d, glm->y, n_vars);

		if (pred != UPDATE) {
			if (! gl_sparse) {
				glm->C = m_resize(glm->C, rows_C, rows_C);
				m_zero(glm->C);
			} 
#ifdef HAVE_SPARSE
			else {
				if (glm->C == NULL) {
					glm->spC = sp_get(rows_C, rows_C, gl_sparse);
					/* d->spLLT = spLLT = sp_get(rows_C, rows_C, gl_sparse); */
				} else {
					glm->spC = sp_resize(glm->spC, rows_C, rows_C);
					/* d->spLLT = spLLT = sp_resize(spLLT, rows_C, rows_C); */
				}
				sp_zero(glm->spC);
			} 
#endif
			glm->X = get_X(d, glm->X, n_vars);
			M_DEBUG(glm->X, "X");
			glm->CinvX = m_resize(glm->CinvX, rows_C, glm->X->n);
			glm->XCinvX = m_resize(glm->XCinvX, glm->X->n, glm->X->n);
			glm->beta = v_resize(glm->beta, glm->X->n);
			for (i = start_X = start_i = 0; i < n_vars; i++) { /* row var */
				/* fill C, mu: */
				for (j = start_j = 0; j <= i; j++) { /* col var */
					v = get_vgm(LTI(d[i]->id,d[j]->id));
					for (k = 0; k < d[i]->n_sel; k++) { /* rows */
						row = start_i + k;
						for (l = 0, col = start_j; col <= row && l < d[j]->n_sel; l++, col++) {
							if (pred == GLS_BLUP)
								c_value = GCV(v, d[i]->sel[k], d[j]->sel[l]);
							else
								c_value = COVARIANCE(v, d[i]->sel[k], d[j]->sel[l]);
							/* on the diagonal, if necessary, add measurement error variance */
							if (d[i]->colnvariance && i == j && k == l)
								c_value += d[i]->sel[k]->variance;
							if (! gl_sparse)
								glm->C->me[row][col] = c_value;
#ifdef HAVE_SPARSE
							else {
								if (c_value != 0.0)
									sp_set_val(glm->spC, row, col, c_value);
							} 
#endif
						} /* for l */
					} /* for k */
					start_j += d[j]->n_sel;
				} /* for j */
				start_i += d[i]->n_sel;
				if (d[i]->n_sel > 0)
					start_X += d[i]->n_X - d[i]->n_merge;
			} /* for i */

			/*
			if (d[0]->colnvmu)
				glm->C = convert_vmuC(glm->C, d[0]);
			*/
			if (d[0]->variance_fn) {
				glm->mu = get_mu(glm->mu, glm->y, d, n_vars);
				convert_C(glm->C, glm->mu, d[0]->variance_fn);
			}

			if (DEBUG_COV && pred == GLS_BLUP)
				printlog("[using generalized covariances: max_val - semivariance()]");
			if (! gl_sparse) {
				M_DEBUG(glm->C, "Covariances (x_i, x_j) matrix C (lower triangle only)");
			}
#ifdef HAVE_SPARSE
			else {
				SM_DEBUG(glm->spC, "Covariances (x_i, x_j) sparse matrix C (lower triangle only)")
			}
#endif
/* check for singular C: */
			if (! gl_sparse && gl_cn_max > 0.0) {
				for (i = 0; i < rows_C; i++) /* row */ 
					for (j = i+1; j < rows_C; j++) /* col > row */
						glm->C->me[i][j] = glm->C->me[j][i]; /* fill symmetric */
				if (is_singular(glm->C, gl_cn_max)) {
					pr_warning("Covariance matrix (nearly) singular at location [%g,%g,%g]: skipping...",
						where->x, where->y, where->z);
					m_free(glm->C); glm->C = MNULL; /* assure re-entrance if global */
					return;
				}
			}
/* 
 * factorize C: 
 */
			if (! gl_sparse)
				LDLfactor(glm->C);
#ifdef HAVE_SPARSE
			else {
				sp_compact(glm->spC, 0.0);
				spCHfactor(glm->spC);
			}
#endif
		} /* if (pred != UPDATE) */
		if (pred != GLS_BLP && !UPDATE_BLP) { /* C-1 X and X'C-1 X, beta */
/* 
 * calculate CinvX: 
 */
    		tmpa = v_resize(tmpa, rows_C);
    		for (i = 0; i < glm->X->n; i++) {
				tmpa = get_col(glm->X, i, tmpa);
				if (! gl_sparse)
					tmpb = LDLsolve(glm->C, tmpa, tmpb);
#ifdef HAVE_SPARSE
				else
					tmpb = spCHsolve(glm->spC, tmpa, tmpb);
#endif
				set_col(glm->CinvX, i, tmpb);
			}
/* 
 * calculate X'C-1 X: 
 */
			glm->XCinvX = mtrm_mlt(glm->X, glm->CinvX, glm->XCinvX); /* X'C-1 X */
			M_DEBUG(glm->XCinvX, "X'C-1 X");
			if (gl_cn_max > 0.0 && is_singular(glm->XCinvX, gl_cn_max)) {
				pr_warning("X'C-1 X matrix (nearly) singular at location [%g,%g,%g]: skipping...",
					where->x, where->y, where->z);
				m_free(glm->C); glm->C = MNULL; /* assure re-entrance if global */
				return;
			}
			m_inverse(glm->XCinvX, glm->XCinvX);
/* 
 * calculate beta: 
 */
			tmpa = vm_mlt(glm->CinvX, glm->y, tmpa); /* X'C-1 y */
			glm->beta = vm_mlt(glm->XCinvX, tmpa, glm->beta); /* (X'C-1 X)-1 X'C-1 y */
			V_DEBUG(glm->beta, "beta");
			M_DEBUG(glm->XCinvX, "Cov(beta), (X'C-1 X)-1");
			M_DEBUG(R = get_corr_mat(glm->XCinvX, R), "Corr(beta)");
		} /* if pred != GLS_BLP */
	} /* if redo the heavy part */
Exemple #6
0
//-------------------------------------------------------------------------
void Prg_ASCEND::setup()
{
  int n, me, m;
  int i, j, row_idx, idx;
  SPMAT *J;
  int nincidences;
  const struct var_variable **incidences;

  // obtain ASCEND system
  // todo: should check that system can be solved with HQP (e.g. no integers)
  _nvars = slv_get_num_solvers_vars(_slv_system);
  _vars = slv_get_solvers_var_list(_slv_system);
  _nrels = slv_get_num_solvers_rels(_slv_system);
  _rels = slv_get_solvers_rel_list(_slv_system);
  _obj = slv_get_obj_relation(_slv_system);

  // count number of optimization variables and bounds
  _var_lb = v_resize(_var_lb, _nvars);
  _var_ub = v_resize(_var_ub, _nvars);
  _var_asc2hqp = iv_resize(_var_asc2hqp, _nvars);
  _derivatives = v_resize(_derivatives, _nvars);
  _var_master_idxs = iv_resize(_var_master_idxs, _nvars);
  _var_solver_idxs = iv_resize(_var_solver_idxs, _nvars);
  n = 0;
  me = 0;
  m = 0;
  for (i = 0; i < _nvars; i++) {
    _var_lb[i] = var_lower_bound(_vars[i]); 
    _var_ub[i] = var_upper_bound(_vars[i]);
    /*
    var_write_name(_slv_system, _vars[i], stderr);
    fprintf(stderr, ":\t%i,\t%g,\t%g\n", var_fixed(_vars[i]),
            _var_lb[i], _var_ub[i]);
    */
    if (var_fixed(_vars[i])) {
      _var_asc2hqp[i] = -1;
    }
    else {
      _var_asc2hqp[i] = n++;
      if (_var_lb[i] == _var_ub[i])
	++me;
      else {
	if (_var_lb[i] > -_Inf)
	  ++m;
	if (_var_ub[i] < _Inf)
	  ++m;
      }
    }
  }

  // consider bounds as linear constraints (i.e. no Jacobian update)
  _me_bounds = me;
  _m_bounds = m;

  // count number of HQP constraints
  for (i = 0; i < _nrels; i++) {
    if (rel_equal(_rels[i]))
      ++me;	// equality constraint
    else
      ++m;	// inequality constraint
  }

  // allocate QP approximation and optimization variables vector
  _qp->resize(n, me, m);
  _x = v_resize(_x, n);

  // allocate sparse structure for bounds
  // (write constant elements in Jacobians)
  me = m = 0;
  for (i = 0; i < _nvars; i++) {
    idx = _var_asc2hqp[i];
    if (idx < 0)
      continue;
    if (_var_lb[i] == _var_ub[i]) {
      row_idx = me++;
      sp_set_val(_qp->A, row_idx, idx, 1.0);
    }
    else {
      if (_var_lb[i] > -_Inf) {
	row_idx = m++;
	sp_set_val(_qp->C, row_idx, idx, 1.0);
      }
      if (_var_ub[i] < _Inf) {
	row_idx = m++;
	sp_set_val(_qp->C, row_idx, idx, -1.0);
      }
    }
  }
  
  // allocate sparse structure for general constraints
  // (just insert dummy values; actual values are set in update method)
  for (i = 0; i < _nrels; i++) {
    if (rel_equal(_rels[i])) {
      row_idx = me++;
      J = _qp->A;
    }
    else {
      row_idx = m++;
      J = _qp->C;
    }
    nincidences = rel_n_incidences(_rels[i]);
    incidences = rel_incidence_list(_rels[i]);
    for (j = 0; j < nincidences; j++) {
      idx = _var_asc2hqp[var_sindex(incidences[j])];
      if (idx >= 0)
	sp_set_val(J, row_idx, idx, 1.0);
    }      
  }

  // todo: setup sparse structure of Hessian
  // for now initialize something resulting in dense BFGS update
  for (j = 0; j < n-1; j++) {
    sp_set_val(_qp->Q, j, j, 0.0);
    sp_set_val(_qp->Q, j, j+1, 0.0);
  }
  sp_set_val(_qp->Q, j, j, 0.0);
}