static enum order_sign interval_minmax(Polyhedron *I) { int i; int min = 1; int max = -1; assert(I->Dimension == 1); POL_ENSURE_VERTICES(I); for (i = 0; i < I->NbRays; ++i) { if (value_pos_p(I->Ray[i][1])) max = 1; else if (value_neg_p(I->Ray[i][1])) min = -1; else { if (max < 0) max = 0; if (min > 0) min = 0; } } if (min > 0) return order_gt; if (max < 0) return order_lt; if (min == max) return order_eq; if (max == 0) return order_le; if (min == 0) return order_ge; return order_unknown; }
/*---------------------------------------------------------------------*/ static int exist_points(int pos,Polyhedron *Pol,Value *context) { Value LB, UB, k,tmp; value_init(LB); value_init(UB); value_init(k); value_init(tmp); value_set_si(LB,0); value_set_si(UB,0); /* Problem if UB or LB is INFINITY */ if (lower_upper_bounds(pos,Pol,context,&LB,&UB) !=0) { errormsg1("exist_points", "infdom", "infinite domain"); value_clear(LB); value_clear(UB); value_clear(k); value_clear(tmp); return -1; } value_set_si(context[pos],0); if(value_lt(UB,LB)) { value_clear(LB); value_clear(UB); value_clear(k); value_clear(tmp); return 0; } if (!Pol->next) { value_subtract(tmp,UB,LB); value_increment(tmp,tmp); value_clear(UB); value_clear(LB); value_clear(k); return (value_pos_p(tmp)); } for (value_assign(k,LB);value_le(k,UB);value_increment(k,k)) { /* insert k in context */ value_assign(context[pos],k); if (exist_points(pos+1,Pol->next,context) > 0 ) { value_clear(LB); value_clear(UB); value_clear(k); value_clear(tmp); return 1; } } /* Reset context */ value_set_si(context[pos],0); value_clear(UB); value_clear(LB); value_clear(k); value_clear(tmp); return 0; }
enum lp_result PL_polyhedron_opt(Polyhedron *P, Value *obj, Value denom, enum lp_dir dir, Value *opt) { int i; int first = 1; Value val, d; enum lp_result res = lp_empty; POL_ENSURE_VERTICES(P); if (emptyQ(P)) return res; value_init(val); value_init(d); for (i = 0; i < P->NbRays; ++ i) { Inner_Product(P->Ray[i]+1, obj, P->Dimension+1, &val); if (value_zero_p(P->Ray[i][0]) && value_notzero_p(val)) { res = lp_unbounded; break; } if (value_zero_p(P->Ray[i][1+P->Dimension])) { if ((dir == lp_min && value_neg_p(val)) || (dir == lp_max && value_pos_p(val))) { res = lp_unbounded; break; } } else { res = lp_ok; value_multiply(d, denom, P->Ray[i][1+P->Dimension]); if (dir == lp_min) mpz_cdiv_q(val, val, d); else mpz_fdiv_q(val, val, d); if (first || (dir == lp_min ? value_lt(val, *opt) : value_gt(val, *opt))) value_assign(*opt, val); first = 0; } } value_clear(d); value_clear(val); return res; }
/* INDEX = 1 .... Dimension */ int PolyhedronLTQ (Polyhedron *Pol1,Polyhedron *Pol2,int INDEX, int PDIM, int NbMaxConstrs) { int res, dim, i, j, k; Polyhedron *Q1, *Q2, *Q3, *Q4, *Q; Matrix *Mat; if (Pol1->next || Pol2->next) { errormsg1("PolyhedronLTQ", "compoly", "Can only compare polyhedra"); return 0; } if (Pol1->Dimension != Pol2->Dimension) { errormsg1("PolyhedronLTQ","diffdim","Polyhedra are not same dimension"); return 0; } dim = Pol1->Dimension+2; POL_ENSURE_FACETS(Pol1); POL_ENSURE_VERTICES(Pol1); POL_ENSURE_FACETS(Pol2); POL_ENSURE_VERTICES(Pol2); #ifdef DEBUG fprintf(stdout, "P1\n"); Polyhedron_Print(stdout,P_VALUE_FMT,Pol1); fprintf(stdout, "P2\n"); Polyhedron_Print(stdout,P_VALUE_FMT,Pol2); #endif /* Create the Line to add */ k = Pol1->Dimension-INDEX+1-PDIM; Mat = Matrix_Alloc(k,dim); Vector_Set(Mat->p_Init,0,dim*k); for(j=0,i=INDEX;j<k;i++,j++) value_set_si(Mat->p[j][i],1); Q1 = AddRays(Mat->p[0],k,Pol1,NbMaxConstrs); Q2 = AddRays(Mat->p[0],k,Pol2,NbMaxConstrs); #ifdef DEBUG fprintf(stdout, "Q1\n"); Polyhedron_Print(stdout,P_VALUE_FMT,Q1); fprintf(stdout, "Q2\n"); Polyhedron_Print(stdout,P_VALUE_FMT,Q2); #endif Matrix_Free(Mat); Q = DomainIntersection(Q1,Q2,NbMaxConstrs); #ifdef DEBUG fprintf(stdout, "Q\n"); Polyhedron_Print(stdout,P_VALUE_FMT,Q); #endif Domain_Free(Q1); Domain_Free(Q2); if (emptyQ(Q)) res = 0; /* not comparable */ else { Q1 = DomainIntersection(Pol1,Q,NbMaxConstrs); Q2 = DomainIntersection(Pol2,Q,NbMaxConstrs); #ifdef DEBUG fprintf(stdout, "Q1\n"); Polyhedron_Print(stdout,P_VALUE_FMT,Q1); fprintf(stdout, "Q2\n"); Polyhedron_Print(stdout,P_VALUE_FMT,Q2); #endif k = Q1->NbConstraints + Q2->NbConstraints; Mat = Matrix_Alloc(k, dim); Vector_Set(Mat->p_Init,0,k*dim); /* First compute surrounding polyhedron */ j=0; for (i=0; i<Q1->NbConstraints; i++) { if ((value_one_p(Q1->Constraint[i][0])) && (value_pos_p(Q1->Constraint[i][INDEX]))) { /* keep Q1's lower bounds */ for (k=0; k<dim; k++) value_assign(Mat->p[j][k],Q1->Constraint[i][k]); j++; } } for (i=0; i<Q2->NbConstraints; i++) { if ((value_one_p(Q2->Constraint[i][0])) && (value_neg_p(Q2->Constraint[i][INDEX]))) { /* and keep Q2's upper bounds */ for (k=0; k<dim; k++) value_assign(Mat->p[j][k],Q2->Constraint[i][k]); j++; } } Q4 = AddConstraints(Mat->p[0], j, Q, NbMaxConstrs); Matrix_Free(Mat); #ifdef debug fprintf(stderr, "Q4 surrounding polyhedron\n"); Polyhderon_Print(stderr,P_VALUE_FMT, Q4); #endif /* if surrounding polyhedron is empty, D1>D2 */ if (emptyQ(Q4)) { res = 1; #ifdef debug fprintf(stderr, "Surrounding polyhedron is empty\n"); #endif goto LTQdone2; } /* Test if Q1 < Q2 */ /* Build a constraint array for >= Q1 and <= Q2 */ Mat = Matrix_Alloc(2,dim); Vector_Set(Mat->p_Init,0,2*dim); /* Choose a contraint from Q1 */ for (i=0; i<Q1->NbConstraints; i++) { if (value_zero_p(Q1->Constraint[i][0])) { /* Equality */ if (value_zero_p(Q1->Constraint[i][INDEX])) { /* Ignore side constraint (they are in Q) */ continue; } else if (value_neg_p(Q1->Constraint[i][INDEX])) { /* copy -constraint to Mat */ value_set_si(Mat->p[0][0],1); for (k=1; k<dim; k++) value_oppose(Mat->p[0][k],Q1->Constraint[i][k]); } else { /* Copy constraint to Mat */ value_set_si(Mat->p[0][0],1); for (k=1; k<dim; k++) value_assign(Mat->p[0][k],Q1->Constraint[i][k]); } } else if(value_neg_p(Q1->Constraint[i][INDEX])) { /* Upper bound -- make a lower bound from it */ value_set_si(Mat->p[0][0],1); for (k=1; k<dim; k++) value_oppose(Mat->p[0][k],Q1->Constraint[i][k]); } else { /* Lower or side bound -- ignore it */ continue; } /* Choose a constraint from Q2 */ for (j=0; j<Q2->NbConstraints; j++) { if (value_zero_p(Q2->Constraint[j][0])) { /* equality */ if (value_zero_p(Q2->Constraint[j][INDEX])) { /* Ignore side constraint (they are in Q) */ continue; } else if (value_pos_p(Q2->Constraint[j][INDEX])) { /* Copy -constraint to Mat */ value_set_si(Mat->p[1][0],1); for (k=1; k<dim; k++) value_oppose(Mat->p[1][k],Q2->Constraint[j][k]); } else { /* Copy constraint to Mat */ value_set_si(Mat->p[1][0],1); for (k=1; k<dim; k++) value_assign(Mat->p[1][k],Q2->Constraint[j][k]); }; } else if (value_pos_p(Q2->Constraint[j][INDEX])) { /* Lower bound -- make an upper bound from it */ value_set_si(Mat->p[1][0],1); for(k=1;k<dim;k++) value_oppose(Mat->p[1][k],Q2->Constraint[j][k]); } else { /* Upper or side bound -- ignore it */ continue; }; #ifdef DEBUG fprintf(stdout, "i=%d j=%d M=\n", i+1, j+1); Matrix_Print(stdout,P_VALUE_FMT,Mat); #endif /* Add Mat to Q and see if anything is made */ Q3 = AddConstraints(Mat->p[0],2,Q,NbMaxConstrs); #ifdef DEBUG fprintf(stdout, "Q3\n"); Polyhedron_Print(stdout,P_VALUE_FMT,Q3); #endif if (!emptyQ(Q3)) { Domain_Free(Q3); #ifdef DEBUG fprintf(stdout, "not empty\n"); #endif res = -1; goto LTQdone; } #ifdef DEBUG fprintf(stdout,"empty\n"); #endif Domain_Free(Q3); } /* end for j */ } /* end for i */ res = 1; LTQdone: Matrix_Free(Mat); LTQdone2: Domain_Free(Q4); Domain_Free(Q1); Domain_Free(Q2); } Domain_Free(Q); #ifdef DEBUG fprintf(stdout, "res = %d\n", res); #endif return res; } /* PolyhedronLTQ */