3 #include <barvinok/util.h>
4 #include <barvinok/options.h>
7 #ifndef HAVE_ENUMERATE4
8 #define Polyhedron_Enumerate(a,b,c,d) Polyhedron_Enumerate(a,b,c)
11 #define ALLOC(type) (type*)malloc(sizeof(type))
12 #define ALLOCN(type,n) (type*)malloc((n) * sizeof(type))
15 #define NALLOC(p,n) p = (typeof(p))malloc((n) * sizeof(*p))
17 #define NALLOC(p,n) p = (void *)malloc((n) * sizeof(*p))
20 #ifndef HAVE_ENUMERATION_FREE
21 #define Enumeration_Free(en) /* just leak some memory */
24 void manual_count(Polyhedron
*P
, Value
* result
)
26 Polyhedron
*U
= Universe_Polyhedron(0);
27 Enumeration
*en
= Polyhedron_Enumerate(P
,U
,1024,NULL
);
28 Value
*v
= compute_poly(en
,NULL
);
29 value_assign(*result
, *v
);
36 #ifndef HAVE_ENUMERATION_FREE
37 #undef Enumeration_Free
40 #include <barvinok/evalue.h>
41 #include <barvinok/util.h>
42 #include <barvinok/barvinok.h>
44 /* Return random value between 0 and max-1 inclusive
46 int random_int(int max
) {
47 return (int) (((double)(max
))*rand()/(RAND_MAX
+1.0));
50 Polyhedron
*Polyhedron_Read(unsigned MaxRays
)
53 unsigned NbRows
, NbColumns
;
58 while (fgets(s
, sizeof(s
), stdin
)) {
61 if (strncasecmp(s
, "vertices", sizeof("vertices")-1) == 0)
63 if (sscanf(s
, "%u %u", &NbRows
, &NbColumns
) == 2)
68 M
= Matrix_Alloc(NbRows
,NbColumns
);
71 P
= Rays2Polyhedron(M
, MaxRays
);
73 P
= Constraints2Polyhedron(M
, MaxRays
);
78 /* Inplace polarization
80 void Polyhedron_Polarize(Polyhedron
*P
)
82 unsigned NbRows
= P
->NbConstraints
+ P
->NbRays
;
86 q
= (Value
**)malloc(NbRows
* sizeof(Value
*));
88 for (i
= 0; i
< P
->NbRays
; ++i
)
90 for (; i
< NbRows
; ++i
)
91 q
[i
] = P
->Constraint
[i
-P
->NbRays
];
92 P
->NbConstraints
= NbRows
- P
->NbConstraints
;
93 P
->NbRays
= NbRows
- P
->NbRays
;
96 P
->Ray
= q
+ P
->NbConstraints
;
100 * Rather general polar
101 * We can optimize it significantly if we assume that
104 * Also, we calculate the polar as defined in Schrijver
105 * The opposite should probably work as well and would
106 * eliminate the need for multiplying by -1
108 Polyhedron
* Polyhedron_Polar(Polyhedron
*P
, unsigned NbMaxRays
)
112 unsigned dim
= P
->Dimension
+ 2;
113 Matrix
*M
= Matrix_Alloc(P
->NbRays
, dim
);
117 value_set_si(mone
, -1);
118 for (i
= 0; i
< P
->NbRays
; ++i
) {
119 Vector_Scale(P
->Ray
[i
], M
->p
[i
], mone
, dim
);
120 value_multiply(M
->p
[i
][0], M
->p
[i
][0], mone
);
121 value_multiply(M
->p
[i
][dim
-1], M
->p
[i
][dim
-1], mone
);
123 P
= Constraints2Polyhedron(M
, NbMaxRays
);
131 * Returns the supporting cone of P at the vertex with index v
133 Polyhedron
* supporting_cone(Polyhedron
*P
, int v
)
138 unsigned char *supporting
= (unsigned char *)malloc(P
->NbConstraints
);
139 unsigned dim
= P
->Dimension
+ 2;
141 assert(v
>=0 && v
< P
->NbRays
);
142 assert(value_pos_p(P
->Ray
[v
][dim
-1]));
146 for (i
= 0, n
= 0; i
< P
->NbConstraints
; ++i
) {
147 Inner_Product(P
->Constraint
[i
] + 1, P
->Ray
[v
] + 1, dim
- 1, &tmp
);
148 if ((supporting
[i
] = value_zero_p(tmp
)))
151 assert(n
>= dim
- 2);
153 M
= Matrix_Alloc(n
, dim
);
155 for (i
= 0, j
= 0; i
< P
->NbConstraints
; ++i
)
157 value_set_si(M
->p
[j
][dim
-1], 0);
158 Vector_Copy(P
->Constraint
[i
], M
->p
[j
++], dim
-1);
161 P
= Constraints2Polyhedron(M
, P
->NbRays
+1);
167 void value_lcm(const Value i
, const Value j
, Value
* lcm
)
171 value_multiply(aux
,i
,j
);
173 value_division(*lcm
,aux
,*lcm
);
177 unsigned char *supporting_constraints(Polyhedron
*P
, Param_Vertices
*v
, int *n
)
179 Value lcm
, tmp
, tmp2
;
180 unsigned dim
= P
->Dimension
+ 2;
181 unsigned nparam
= v
->Vertex
->NbColumns
- 2;
182 unsigned nvar
= dim
- nparam
- 2;
183 unsigned char *supporting
= (unsigned char *)malloc(P
->NbConstraints
);
188 row
= Vector_Alloc(nparam
+1);
193 value_set_si(lcm
, 1);
194 for (i
= 0, *n
= 0; i
< P
->NbConstraints
; ++i
) {
195 Vector_Set(row
->p
, 0, nparam
+1);
196 for (j
= 0 ; j
< nvar
; ++j
) {
197 value_set_si(tmp
, 1);
198 value_assign(tmp2
, P
->Constraint
[i
][j
+1]);
199 if (value_ne(lcm
, v
->Vertex
->p
[j
][nparam
+1])) {
200 value_assign(tmp
, lcm
);
201 value_lcm(lcm
, v
->Vertex
->p
[j
][nparam
+1], &lcm
);
202 value_division(tmp
, lcm
, tmp
);
203 value_multiply(tmp2
, tmp2
, lcm
);
204 value_division(tmp2
, tmp2
, v
->Vertex
->p
[j
][nparam
+1]);
206 Vector_Combine(row
->p
, v
->Vertex
->p
[j
], row
->p
,
207 tmp
, tmp2
, nparam
+1);
209 value_set_si(tmp
, 1);
210 Vector_Combine(row
->p
, P
->Constraint
[i
]+1+nvar
, row
->p
, tmp
, lcm
, nparam
+1);
211 for (j
= 0; j
< nparam
+1; ++j
)
212 if (value_notzero_p(row
->p
[j
]))
214 if ((supporting
[i
] = (j
== nparam
+ 1)))
226 Polyhedron
* supporting_cone_p(Polyhedron
*P
, Param_Vertices
*v
)
229 unsigned dim
= P
->Dimension
+ 2;
230 unsigned nparam
= v
->Vertex
->NbColumns
- 2;
231 unsigned nvar
= dim
- nparam
- 2;
233 unsigned char *supporting
;
235 supporting
= supporting_constraints(P
, v
, &n
);
236 M
= Matrix_Alloc(n
, nvar
+2);
238 for (i
= 0, j
= 0; i
< P
->NbConstraints
; ++i
)
240 value_set_si(M
->p
[j
][nvar
+1], 0);
241 Vector_Copy(P
->Constraint
[i
], M
->p
[j
++], nvar
+1);
244 P
= Constraints2Polyhedron(M
, P
->NbRays
+1);
250 Polyhedron
* triangulate_cone(Polyhedron
*P
, unsigned NbMaxCons
)
252 struct barvinok_options
*options
= barvinok_options_new_with_defaults();
253 options
->MaxRays
= NbMaxCons
;
254 P
= triangulate_cone_with_options(P
, options
);
255 barvinok_options_free(options
);
259 Polyhedron
* triangulate_cone_with_options(Polyhedron
*P
,
260 struct barvinok_options
*options
)
262 const static int MAX_TRY
=10;
265 unsigned dim
= P
->Dimension
;
266 Matrix
*M
= Matrix_Alloc(P
->NbRays
+1, dim
+3);
268 Polyhedron
*L
, *R
, *T
;
269 assert(P
->NbEq
== 0);
275 Vector_Set(M
->p
[0]+1, 0, dim
+1);
276 value_set_si(M
->p
[0][0], 1);
277 value_set_si(M
->p
[0][dim
+2], 1);
278 Vector_Set(M
->p
[P
->NbRays
]+1, 0, dim
+2);
279 value_set_si(M
->p
[P
->NbRays
][0], 1);
280 value_set_si(M
->p
[P
->NbRays
][dim
+1], 1);
282 for (i
= 0, r
= 1; i
< P
->NbRays
; ++i
) {
283 if (value_notzero_p(P
->Ray
[i
][dim
+1]))
285 Vector_Copy(P
->Ray
[i
], M
->p
[r
], dim
+1);
286 value_set_si(M
->p
[r
][dim
+2], 0);
290 M2
= Matrix_Alloc(dim
+1, dim
+2);
293 if (options
->try_Delaunay_triangulation
) {
294 /* Delaunay triangulation */
295 for (r
= 1; r
< P
->NbRays
; ++r
) {
296 Inner_Product(M
->p
[r
]+1, M
->p
[r
]+1, dim
, &tmp
);
297 value_assign(M
->p
[r
][dim
+1], tmp
);
300 L
= Rays2Polyhedron(M3
, options
->MaxRays
);
305 /* Usually R should still be 0 */
308 for (r
= 1; r
< P
->NbRays
; ++r
) {
309 value_set_si(M
->p
[r
][dim
+1], random_int((t
+1)*dim
*P
->NbRays
)+1);
312 L
= Rays2Polyhedron(M3
, options
->MaxRays
);
316 assert(t
<= MAX_TRY
);
321 POL_ENSURE_FACETS(L
);
322 for (i
= 0; i
< L
->NbConstraints
; ++i
) {
323 /* Ignore perpendicular facets, i.e., facets with 0 z-coordinate */
324 if (value_negz_p(L
->Constraint
[i
][dim
+1]))
326 if (value_notzero_p(L
->Constraint
[i
][dim
+2]))
328 for (j
= 1, r
= 1; j
< M
->NbRows
; ++j
) {
329 Inner_Product(M
->p
[j
]+1, L
->Constraint
[i
]+1, dim
+1, &tmp
);
330 if (value_notzero_p(tmp
))
334 Vector_Copy(M
->p
[j
]+1, M2
->p
[r
]+1, dim
);
335 value_set_si(M2
->p
[r
][0], 1);
336 value_set_si(M2
->p
[r
][dim
+1], 0);
340 Vector_Set(M2
->p
[0]+1, 0, dim
);
341 value_set_si(M2
->p
[0][0], 1);
342 value_set_si(M2
->p
[0][dim
+1], 1);
343 T
= Rays2Polyhedron(M2
, P
->NbConstraints
+1);
357 void check_triangulization(Polyhedron
*P
, Polyhedron
*T
)
359 Polyhedron
*C
, *D
, *E
, *F
, *G
, *U
;
360 for (C
= T
; C
; C
= C
->next
) {
364 U
= DomainConvex(DomainUnion(U
, C
, 100), 100);
365 for (D
= C
->next
; D
; D
= D
->next
) {
370 E
= DomainIntersection(C
, D
, 600);
371 assert(E
->NbRays
== 0 || E
->NbEq
>= 1);
377 assert(PolyhedronIncludes(U
, P
));
378 assert(PolyhedronIncludes(P
, U
));
381 /* Computes x, y and g such that g = gcd(a,b) and a*x+b*y = g */
382 void Extended_Euclid(Value a
, Value b
, Value
*x
, Value
*y
, Value
*g
)
384 Value c
, d
, e
, f
, tmp
;
391 value_absolute(c
, a
);
392 value_absolute(d
, b
);
395 while(value_pos_p(d
)) {
396 value_division(tmp
, c
, d
);
397 value_multiply(tmp
, tmp
, f
);
398 value_subtract(e
, e
, tmp
);
399 value_division(tmp
, c
, d
);
400 value_multiply(tmp
, tmp
, d
);
401 value_subtract(c
, c
, tmp
);
408 else if (value_pos_p(a
))
410 else value_oppose(*x
, e
);
414 value_multiply(tmp
, a
, *x
);
415 value_subtract(tmp
, c
, tmp
);
416 value_division(*y
, tmp
, b
);
425 static int unimodular_complete_1(Matrix
*m
)
427 Value g
, b
, c
, old
, tmp
;
436 value_assign(g
, m
->p
[0][0]);
437 for (i
= 1; value_zero_p(g
) && i
< m
->NbColumns
; ++i
) {
438 for (j
= 0; j
< m
->NbColumns
; ++j
) {
440 value_set_si(m
->p
[i
][j
], 1);
442 value_set_si(m
->p
[i
][j
], 0);
444 value_assign(g
, m
->p
[0][i
]);
446 for (; i
< m
->NbColumns
; ++i
) {
447 value_assign(old
, g
);
448 Extended_Euclid(old
, m
->p
[0][i
], &c
, &b
, &g
);
450 for (j
= 0; j
< m
->NbColumns
; ++j
) {
452 value_multiply(tmp
, m
->p
[0][j
], b
);
453 value_division(m
->p
[i
][j
], tmp
, old
);
455 value_assign(m
->p
[i
][j
], c
);
457 value_set_si(m
->p
[i
][j
], 0);
469 int unimodular_complete(Matrix
*M
, int row
)
476 return unimodular_complete_1(M
);
478 left_hermite(M
, &H
, &Q
, &U
);
480 for (r
= 0; ok
&& r
< row
; ++r
)
481 if (value_notone_p(H
->p
[r
][r
]))
484 for (r
= row
; r
< M
->NbRows
; ++r
)
485 Vector_Copy(Q
->p
[r
], M
->p
[r
], M
->NbColumns
);
491 * Returns a full-dimensional polyhedron with the same number
492 * of integer points as P
494 Polyhedron
*remove_equalities(Polyhedron
*P
, unsigned MaxRays
)
496 Polyhedron
*Q
= Polyhedron_Copy(P
);
497 unsigned dim
= P
->Dimension
;
504 Q
= DomainConstraintSimplify(Q
, MaxRays
);
508 m1
= Matrix_Alloc(dim
, dim
);
509 for (i
= 0; i
< Q
->NbEq
; ++i
)
510 Vector_Copy(P
->Constraint
[i
]+1, m1
->p
[i
], dim
);
512 /* m1 may not be unimodular, but we won't be throwing anything away */
513 unimodular_complete(m1
, Q
->NbEq
);
515 m2
= Matrix_Alloc(dim
+1-Q
->NbEq
, dim
+1);
516 for (i
= Q
->NbEq
; i
< dim
; ++i
)
517 Vector_Copy(m1
->p
[i
], m2
->p
[i
-Q
->NbEq
], dim
);
518 value_set_si(m2
->p
[dim
-Q
->NbEq
][dim
], 1);
521 P
= Polyhedron_Image(Q
, m2
, MaxRays
);
529 * Returns a full-dimensional polyhedron with the same number
530 * of integer points as P
531 * nvar specifies the number of variables
532 * The remaining dimensions are assumed to be parameters
534 * factor is NbEq x (nparam+2) matrix, containing stride constraints
535 * on the parameters; column nparam is the constant;
536 * column nparam+1 is the stride
538 * if factor is NULL, only remove equalities that don't affect
539 * the number of points
541 Polyhedron
*remove_equalities_p(Polyhedron
*P
, unsigned nvar
, Matrix
**factor
,
546 unsigned dim
= P
->Dimension
;
553 m1
= Matrix_Alloc(nvar
, nvar
);
554 P
= DomainConstraintSimplify(P
, MaxRays
);
556 f
= Matrix_Alloc(P
->NbEq
, dim
-nvar
+2);
560 for (i
= 0, j
= 0; i
< P
->NbEq
; ++i
) {
561 if (First_Non_Zero(P
->Constraint
[i
]+1, nvar
) == -1)
564 Vector_Gcd(P
->Constraint
[i
]+1, nvar
, &g
);
565 if (!factor
&& value_notone_p(g
))
569 Vector_Copy(P
->Constraint
[i
]+1+nvar
, f
->p
[j
], dim
-nvar
+1);
570 value_assign(f
->p
[j
][dim
-nvar
+1], g
);
573 Vector_Copy(P
->Constraint
[i
]+1, m1
->p
[j
], nvar
);
579 unimodular_complete(m1
, j
);
581 m2
= Matrix_Alloc(dim
+1-j
, dim
+1);
582 for (i
= 0; i
< nvar
-j
; ++i
)
583 Vector_Copy(m1
->p
[i
+j
], m2
->p
[i
], nvar
);
585 for (i
= nvar
-j
; i
<= dim
-j
; ++i
)
586 value_set_si(m2
->p
[i
][i
+j
], 1);
588 Q
= Polyhedron_Image(P
, m2
, MaxRays
);
595 void Line_Length(Polyhedron
*P
, Value
*len
)
601 assert(P
->Dimension
== 1);
607 for (i
= 0; i
< P
->NbConstraints
; ++i
) {
608 value_oppose(tmp
, P
->Constraint
[i
][2]);
609 if (value_pos_p(P
->Constraint
[i
][1])) {
610 mpz_cdiv_q(tmp
, tmp
, P
->Constraint
[i
][1]);
611 if (!p
|| value_gt(tmp
, pos
))
612 value_assign(pos
, tmp
);
615 mpz_fdiv_q(tmp
, tmp
, P
->Constraint
[i
][1]);
616 if (!n
|| value_lt(tmp
, neg
))
617 value_assign(neg
, tmp
);
621 value_subtract(tmp
, neg
, pos
);
622 value_increment(*len
, tmp
);
624 value_set_si(*len
, -1);
633 * Factors the polyhedron P into polyhedra Q_i such that
634 * the number of integer points in P is equal to the product
635 * of the number of integer points in the individual Q_i
637 * If no factors can be found, NULL is returned.
638 * Otherwise, a linked list of the factors is returned.
640 * If there are factors and if T is not NULL, then a matrix will be
641 * returned through T expressing the old variables in terms of the
642 * new variables as they appear in the sequence of factors.
644 * The algorithm works by first computing the Hermite normal form
645 * and then grouping columns linked by one or more constraints together,
646 * where a constraints "links" two or more columns if the constraint
647 * has nonzero coefficients in the columns.
649 Polyhedron
* Polyhedron_Factor(Polyhedron
*P
, unsigned nparam
, Matrix
**T
,
653 Matrix
*M
, *H
, *Q
, *U
;
654 int *pos
; /* for each column: row position of pivot */
655 int *group
; /* group to which a column belongs */
656 int *cnt
; /* number of columns in the group */
657 int *rowgroup
; /* group to which a constraint belongs */
658 int nvar
= P
->Dimension
- nparam
;
659 Polyhedron
*F
= NULL
;
667 NALLOC(rowgroup
, P
->NbConstraints
);
669 M
= Matrix_Alloc(P
->NbConstraints
, nvar
);
670 for (i
= 0; i
< P
->NbConstraints
; ++i
)
671 Vector_Copy(P
->Constraint
[i
]+1, M
->p
[i
], nvar
);
672 left_hermite(M
, &H
, &Q
, &U
);
676 for (i
= 0; i
< P
->NbConstraints
; ++i
)
678 for (i
= 0, j
= 0; i
< H
->NbColumns
; ++i
) {
679 for ( ; j
< H
->NbRows
; ++j
)
680 if (value_notzero_p(H
->p
[j
][i
]))
682 assert (j
< H
->NbRows
);
685 for (i
= 0; i
< nvar
; ++i
) {
689 for (i
= 0; i
< H
->NbColumns
&& cnt
[0] < nvar
; ++i
) {
690 if (rowgroup
[pos
[i
]] == -1)
691 rowgroup
[pos
[i
]] = i
;
692 for (j
= pos
[i
]+1; j
< H
->NbRows
; ++j
) {
693 if (value_zero_p(H
->p
[j
][i
]))
695 if (rowgroup
[j
] != -1)
697 rowgroup
[j
] = group
[i
];
698 for (k
= i
+1; k
< H
->NbColumns
&& j
>= pos
[k
]; ++k
) {
703 if (group
[k
] != group
[i
] && value_notzero_p(H
->p
[j
][k
])) {
704 assert(cnt
[group
[k
]] != 0);
705 assert(cnt
[group
[i
]] != 0);
706 if (group
[i
] < group
[k
]) {
707 cnt
[group
[i
]] += cnt
[group
[k
]];
711 cnt
[group
[k
]] += cnt
[group
[i
]];
720 if (cnt
[0] != nvar
) {
721 /* Extract out pure context constraints separately */
722 Polyhedron
**next
= &F
;
725 *T
= Matrix_Alloc(nvar
, nvar
);
726 for (i
= nparam
? -1 : 0; i
< nvar
; ++i
) {
730 for (j
= 0, k
= 0; j
< P
->NbConstraints
; ++j
)
731 if (rowgroup
[j
] == -1) {
732 if (First_Non_Zero(P
->Constraint
[j
]+1+nvar
,
745 for (j
= 0, k
= 0; j
< P
->NbConstraints
; ++j
)
746 if (rowgroup
[j
] >= 0 && group
[rowgroup
[j
]] == i
) {
753 for (j
= 0; j
< nvar
; ++j
) {
755 for (l
= 0, m
= 0; m
< d
; ++l
) {
758 value_assign((*T
)->p
[j
][tot_d
+m
++], U
->p
[j
][l
]);
762 M
= Matrix_Alloc(k
, d
+nparam
+2);
763 for (j
= 0, k
= 0; j
< P
->NbConstraints
; ++j
) {
765 if (rowgroup
[j
] != i
)
767 value_assign(M
->p
[k
][0], P
->Constraint
[j
][0]);
768 for (l
= 0, m
= 0; m
< d
; ++l
) {
771 value_assign(M
->p
[k
][1+m
++], H
->p
[j
][l
]);
773 Vector_Copy(P
->Constraint
[j
]+1+nvar
, M
->p
[k
]+1+m
, nparam
+1);
776 *next
= Constraints2Polyhedron(M
, NbMaxRays
);
777 next
= &(*next
)->next
;
792 * Project on final dim dimensions
794 Polyhedron
* Polyhedron_Project(Polyhedron
*P
, int dim
)
797 int remove
= P
->Dimension
- dim
;
801 if (P
->Dimension
== dim
)
802 return Polyhedron_Copy(P
);
804 T
= Matrix_Alloc(dim
+1, P
->Dimension
+1);
805 for (i
= 0; i
< dim
+1; ++i
)
806 value_set_si(T
->p
[i
][i
+remove
], 1);
807 I
= Polyhedron_Image(P
, T
, P
->NbConstraints
);
812 /* Constructs a new constraint that ensures that
813 * the first constraint is (strictly) smaller than
816 static void smaller_constraint(Value
*a
, Value
*b
, Value
*c
, int pos
, int shift
,
817 int len
, int strict
, Value
*tmp
)
819 value_oppose(*tmp
, b
[pos
+1]);
820 value_set_si(c
[0], 1);
821 Vector_Combine(a
+1+shift
, b
+1+shift
, c
+1, *tmp
, a
[pos
+1], len
-shift
-1);
823 value_decrement(c
[len
-shift
-1], c
[len
-shift
-1]);
824 ConstraintSimplify(c
, c
, len
-shift
, tmp
);
827 struct section
{ Polyhedron
* D
; evalue E
; };
829 evalue
* ParamLine_Length_mod(Polyhedron
*P
, Polyhedron
*C
, int MaxRays
)
831 unsigned dim
= P
->Dimension
;
832 unsigned nvar
= dim
- C
->Dimension
;
847 NALLOC(pos
, P
->NbConstraints
);
850 evalue_set_si(&mone
, -1, 1);
852 for (i
= 0, z
= 0; i
< P
->NbConstraints
; ++i
)
853 if (value_zero_p(P
->Constraint
[i
][1]))
855 /* put those with positive coefficients first; number: p */
856 for (i
= 0, p
= 0, n
= P
->NbConstraints
-z
-1; i
< P
->NbConstraints
; ++i
)
857 if (value_pos_p(P
->Constraint
[i
][1]))
859 else if (value_neg_p(P
->Constraint
[i
][1]))
861 n
= P
->NbConstraints
-z
-p
;
862 assert (p
>= 1 && n
>= 1);
863 s
= (struct section
*) malloc(p
* n
* sizeof(struct section
));
864 M
= Matrix_Alloc((p
-1) + (n
-1), dim
-nvar
+2);
865 for (k
= 0; k
< p
; ++k
) {
866 for (k2
= 0; k2
< p
; ++k2
) {
871 P
->Constraint
[pos
[k
]],
872 P
->Constraint
[pos
[k2
]],
873 M
->p
[q
], 0, nvar
, dim
+2, k2
> k
, &g
);
875 for (l
= p
; l
< p
+n
; ++l
) {
876 for (l2
= p
; l2
< p
+n
; ++l2
) {
881 P
->Constraint
[pos
[l2
]],
882 P
->Constraint
[pos
[l
]],
883 M
->p
[q
], 0, nvar
, dim
+2, l2
> l
, &g
);
886 T
= Constraints2Polyhedron(M2
, P
->NbRays
);
888 s
[nd
].D
= DomainIntersection(T
, C
, MaxRays
);
890 POL_ENSURE_VERTICES(s
[nd
].D
);
891 if (emptyQ(s
[nd
].D
)) {
892 Polyhedron_Free(s
[nd
].D
);
895 L
= bv_ceil3(P
->Constraint
[pos
[k
]]+1+nvar
,
897 P
->Constraint
[pos
[k
]][0+1], s
[nd
].D
);
898 U
= bv_ceil3(P
->Constraint
[pos
[l
]]+1+nvar
,
900 P
->Constraint
[pos
[l
]][0+1], s
[nd
].D
);
916 value_set_si(F
->d
, 0);
917 F
->x
.p
= new_enode(partition
, 2*nd
, dim
-nvar
);
918 for (k
= 0; k
< nd
; ++k
) {
919 EVALUE_SET_DOMAIN(F
->x
.p
->arr
[2*k
], s
[k
].D
);
920 value_clear(F
->x
.p
->arr
[2*k
+1].d
);
921 F
->x
.p
->arr
[2*k
+1] = s
[k
].E
;
925 free_evalue_refs(&mone
);
932 evalue
* ParamLine_Length(Polyhedron
*P
, Polyhedron
*C
,
933 struct barvinok_options
*options
)
936 tmp
= ParamLine_Length_mod(P
, C
, options
->MaxRays
);
937 if (options
->lookup_table
) {
938 evalue_mod2table(tmp
, C
->Dimension
);
944 Bool
isIdentity(Matrix
*M
)
947 if (M
->NbRows
!= M
->NbColumns
)
950 for (i
= 0;i
< M
->NbRows
; i
++)
951 for (j
= 0; j
< M
->NbColumns
; j
++)
953 if(value_notone_p(M
->p
[i
][j
]))
956 if(value_notzero_p(M
->p
[i
][j
]))
962 void Param_Polyhedron_Print(FILE* DST
, Param_Polyhedron
*PP
, char **param_names
)
967 for(P
=PP
->D
;P
;P
=P
->next
) {
969 /* prints current val. dom. */
970 fprintf(DST
, "---------------------------------------\n");
971 fprintf(DST
, "Domain :\n");
972 Print_Domain(DST
, P
->Domain
, param_names
);
974 /* scan the vertices */
975 fprintf(DST
, "Vertices :\n");
976 FORALL_PVertex_in_ParamPolyhedron(V
,P
,PP
) {
978 /* prints each vertex */
979 Print_Vertex(DST
, V
->Vertex
, param_names
);
982 END_FORALL_PVertex_in_ParamPolyhedron
;
986 void Enumeration_Print(FILE *Dst
, Enumeration
*en
, char **params
)
988 for (; en
; en
= en
->next
) {
989 Print_Domain(Dst
, en
->ValidityDomain
, params
);
990 print_evalue(Dst
, &en
->EP
, params
);
994 void Enumeration_Free(Enumeration
*en
)
1000 free_evalue_refs( &(en
->EP
) );
1001 Domain_Free( en
->ValidityDomain
);
1008 void Enumeration_mod2table(Enumeration
*en
, unsigned nparam
)
1010 for (; en
; en
= en
->next
) {
1011 evalue_mod2table(&en
->EP
, nparam
);
1012 reduce_evalue(&en
->EP
);
1016 size_t Enumeration_size(Enumeration
*en
)
1020 for (; en
; en
= en
->next
) {
1021 s
+= domain_size(en
->ValidityDomain
);
1022 s
+= evalue_size(&en
->EP
);
1027 void Free_ParamNames(char **params
, int m
)
1034 /* Check whether every set in D2 is included in some set of D1 */
1035 int DomainIncludes(Polyhedron
*D1
, Polyhedron
*D2
)
1037 for ( ; D2
; D2
= D2
->next
) {
1039 for (P1
= D1
; P1
; P1
= P1
->next
)
1040 if (PolyhedronIncludes(P1
, D2
))
1048 int line_minmax(Polyhedron
*I
, Value
*min
, Value
*max
)
1053 value_oppose(I
->Constraint
[0][2], I
->Constraint
[0][2]);
1054 /* There should never be a remainder here */
1055 if (value_pos_p(I
->Constraint
[0][1]))
1056 mpz_fdiv_q(*min
, I
->Constraint
[0][2], I
->Constraint
[0][1]);
1058 mpz_fdiv_q(*min
, I
->Constraint
[0][2], I
->Constraint
[0][1]);
1059 value_assign(*max
, *min
);
1060 } else for (i
= 0; i
< I
->NbConstraints
; ++i
) {
1061 if (value_zero_p(I
->Constraint
[i
][1])) {
1066 value_oppose(I
->Constraint
[i
][2], I
->Constraint
[i
][2]);
1067 if (value_pos_p(I
->Constraint
[i
][1]))
1068 mpz_cdiv_q(*min
, I
->Constraint
[i
][2], I
->Constraint
[i
][1]);
1070 mpz_fdiv_q(*max
, I
->Constraint
[i
][2], I
->Constraint
[i
][1]);
1078 PROCEDURES TO COMPUTE ENUMERATION. recursive procedure, recurse for
1081 @param pos index position of current loop index (1..hdim-1)
1082 @param P loop domain
1083 @param context context values for fixed indices
1084 @param exist number of existential variables
1085 @return the number of integer points in this
1089 void count_points_e (int pos
, Polyhedron
*P
, int exist
, int nparam
,
1090 Value
*context
, Value
*res
)
1095 value_set_si(*res
, 0);
1099 value_init(LB
); value_init(UB
); value_init(k
);
1103 if (lower_upper_bounds(pos
,P
,context
,&LB
,&UB
) !=0) {
1104 /* Problem if UB or LB is INFINITY */
1105 value_clear(LB
); value_clear(UB
); value_clear(k
);
1106 if (pos
> P
->Dimension
- nparam
- exist
)
1107 value_set_si(*res
, 1);
1109 value_set_si(*res
, -1);
1116 for (value_assign(k
,LB
); value_le(k
,UB
); value_increment(k
,k
)) {
1117 fprintf(stderr
, "(");
1118 for (i
=1; i
<pos
; i
++) {
1119 value_print(stderr
,P_VALUE_FMT
,context
[i
]);
1120 fprintf(stderr
,",");
1122 value_print(stderr
,P_VALUE_FMT
,k
);
1123 fprintf(stderr
,")\n");
1128 value_set_si(context
[pos
],0);
1129 if (value_lt(UB
,LB
)) {
1130 value_clear(LB
); value_clear(UB
); value_clear(k
);
1131 value_set_si(*res
, 0);
1136 value_set_si(*res
, 1);
1138 value_subtract(k
,UB
,LB
);
1139 value_add_int(k
,k
,1);
1140 value_assign(*res
, k
);
1142 value_clear(LB
); value_clear(UB
); value_clear(k
);
1146 /*-----------------------------------------------------------------*/
1147 /* Optimization idea */
1148 /* If inner loops are not a function of k (the current index) */
1149 /* i.e. if P->Constraint[i][pos]==0 for all P following this and */
1151 /* Then CNT = (UB-LB+1)*count_points(pos+1, P->next, context) */
1152 /* (skip the for loop) */
1153 /*-----------------------------------------------------------------*/
1156 value_set_si(*res
, 0);
1157 for (value_assign(k
,LB
);value_le(k
,UB
);value_increment(k
,k
)) {
1158 /* Insert k in context */
1159 value_assign(context
[pos
],k
);
1160 count_points_e(pos
+1, P
->next
, exist
, nparam
, context
, &c
);
1161 if(value_notmone_p(c
))
1162 value_addto(*res
, *res
, c
);
1164 value_set_si(*res
, -1);
1167 if (pos
> P
->Dimension
- nparam
- exist
&&
1174 fprintf(stderr
,"%d\n",CNT
);
1178 value_set_si(context
[pos
],0);
1179 value_clear(LB
); value_clear(UB
); value_clear(k
);
1181 } /* count_points_e */
1183 int DomainContains(Polyhedron
*P
, Value
*list_args
, int len
,
1184 unsigned MaxRays
, int set
)
1189 if (P
->Dimension
== len
)
1190 return in_domain(P
, list_args
);
1192 assert(set
); // assume list_args is large enough
1193 assert((P
->Dimension
- len
) % 2 == 0);
1195 for (i
= 0; i
< P
->Dimension
- len
; i
+= 2) {
1197 for (j
= 0 ; j
< P
->NbEq
; ++j
)
1198 if (value_notzero_p(P
->Constraint
[j
][1+len
+i
]))
1200 assert(j
< P
->NbEq
);
1201 value_absolute(m
, P
->Constraint
[j
][1+len
+i
]);
1202 k
= First_Non_Zero(P
->Constraint
[j
]+1, len
);
1204 assert(First_Non_Zero(P
->Constraint
[j
]+1+k
+1, len
- k
- 1) == -1);
1205 mpz_fdiv_q(list_args
[len
+i
], list_args
[k
], m
);
1206 mpz_fdiv_r(list_args
[len
+i
+1], list_args
[k
], m
);
1210 return in_domain(P
, list_args
);
1213 Polyhedron
*DomainConcat(Polyhedron
*head
, Polyhedron
*tail
)
1218 for (S
= head
; S
->next
; S
= S
->next
)
1224 #ifndef HAVE_LEXSMALLER
1226 evalue
*barvinok_lexsmaller_ev(Polyhedron
*P
, Polyhedron
*D
, unsigned dim
,
1227 Polyhedron
*C
, unsigned MaxRays
)
1233 #include <polylib/ranking.h>
1235 evalue
*barvinok_lexsmaller_ev(Polyhedron
*P
, Polyhedron
*D
, unsigned dim
,
1236 Polyhedron
*C
, unsigned MaxRays
)
1239 Polyhedron
*RC
, *RD
, *Q
;
1240 unsigned nparam
= dim
+ C
->Dimension
;
1244 RC
= LexSmaller(P
, D
, dim
, C
, MaxRays
);
1248 exist
= RD
->Dimension
- nparam
- dim
;
1249 CA
= align_context(RC
, RD
->Dimension
, MaxRays
);
1250 Q
= DomainIntersection(RD
, CA
, MaxRays
);
1251 Polyhedron_Free(CA
);
1253 Polyhedron_Free(RC
);
1256 for (Q
= RD
; Q
; Q
= Q
->next
) {
1258 Polyhedron
*next
= Q
->next
;
1261 t
= barvinok_enumerate_e(Q
, exist
, nparam
, MaxRays
);
1267 free_evalue_refs(t
);
1279 Enumeration
*barvinok_lexsmaller(Polyhedron
*P
, Polyhedron
*D
, unsigned dim
,
1280 Polyhedron
*C
, unsigned MaxRays
)
1282 evalue
*EP
= barvinok_lexsmaller_ev(P
, D
, dim
, C
, MaxRays
);
1284 return partition2enumeration(EP
);
1288 /* "align" matrix to have nrows by inserting
1289 * the necessary number of rows and an equal number of columns in front
1291 Matrix
*align_matrix(Matrix
*M
, int nrows
)
1294 int newrows
= nrows
- M
->NbRows
;
1295 Matrix
*M2
= Matrix_Alloc(nrows
, newrows
+ M
->NbColumns
);
1296 for (i
= 0; i
< newrows
; ++i
)
1297 value_set_si(M2
->p
[i
][i
], 1);
1298 for (i
= 0; i
< M
->NbRows
; ++i
)
1299 Vector_Copy(M
->p
[i
], M2
->p
[newrows
+i
]+newrows
, M
->NbColumns
);
1303 static void print_varlist(FILE *out
, int n
, char **names
)
1307 for (i
= 0; i
< n
; ++i
) {
1310 fprintf(out
, "%s", names
[i
]);
1315 static void print_term(FILE *out
, Value v
, int pos
, int dim
, int nparam
,
1316 char **iter_names
, char **param_names
, int *first
)
1318 if (value_zero_p(v
)) {
1319 if (first
&& *first
&& pos
>= dim
+ nparam
)
1325 if (!*first
&& value_pos_p(v
))
1329 if (pos
< dim
+ nparam
) {
1330 if (value_mone_p(v
))
1332 else if (!value_one_p(v
))
1333 value_print(out
, VALUE_FMT
, v
);
1335 fprintf(out
, "%s", iter_names
[pos
]);
1337 fprintf(out
, "%s", param_names
[pos
-dim
]);
1339 value_print(out
, VALUE_FMT
, v
);
1342 char **util_generate_names(int n
, char *prefix
)
1345 int len
= (prefix
? strlen(prefix
) : 0) + 10;
1346 char **names
= ALLOCN(char*, n
);
1348 fprintf(stderr
, "ERROR: memory overflow.\n");
1351 for (i
= 0; i
< n
; ++i
) {
1352 names
[i
] = ALLOCN(char, len
);
1354 fprintf(stderr
, "ERROR: memory overflow.\n");
1358 snprintf(names
[i
], len
, "%d", i
);
1360 snprintf(names
[i
], len
, "%s%d", prefix
, i
);
1366 void util_free_names(int n
, char **names
)
1369 for (i
= 0; i
< n
; ++i
)
1374 void Polyhedron_pprint(FILE *out
, Polyhedron
*P
, int dim
, int nparam
,
1375 char **iter_names
, char **param_names
)
1380 assert(dim
+ nparam
== P
->Dimension
);
1386 print_varlist(out
, nparam
, param_names
);
1387 fprintf(out
, " -> ");
1389 print_varlist(out
, dim
, iter_names
);
1390 fprintf(out
, " : ");
1393 fprintf(out
, "FALSE");
1394 else for (i
= 0; i
< P
->NbConstraints
; ++i
) {
1396 int v
= First_Non_Zero(P
->Constraint
[i
]+1, P
->Dimension
);
1397 if (v
== -1 && value_pos_p(P
->Constraint
[i
][0]))
1400 fprintf(out
, " && ");
1401 if (v
== -1 && value_notzero_p(P
->Constraint
[i
][1+P
->Dimension
]))
1402 fprintf(out
, "FALSE");
1403 else if (value_pos_p(P
->Constraint
[i
][v
+1])) {
1404 print_term(out
, P
->Constraint
[i
][v
+1], v
, dim
, nparam
,
1405 iter_names
, param_names
, NULL
);
1406 if (value_zero_p(P
->Constraint
[i
][0]))
1407 fprintf(out
, " = ");
1409 fprintf(out
, " >= ");
1410 for (j
= v
+1; j
<= dim
+nparam
; ++j
) {
1411 value_oppose(tmp
, P
->Constraint
[i
][1+j
]);
1412 print_term(out
, tmp
, j
, dim
, nparam
,
1413 iter_names
, param_names
, &first
);
1416 value_oppose(tmp
, P
->Constraint
[i
][1+v
]);
1417 print_term(out
, tmp
, v
, dim
, nparam
,
1418 iter_names
, param_names
, NULL
);
1419 fprintf(out
, " <= ");
1420 for (j
= v
+1; j
<= dim
+nparam
; ++j
)
1421 print_term(out
, P
->Constraint
[i
][1+j
], j
, dim
, nparam
,
1422 iter_names
, param_names
, &first
);
1426 fprintf(out
, " }\n");
1431 /* Construct a cone over P with P placed at x_d = 1, with
1432 * x_d the coordinate of an extra dimension
1434 * It's probably a mistake to depend so much on the internal
1435 * representation. We should probably simply compute the
1436 * vertices/facets first.
1438 Polyhedron
*Cone_over_Polyhedron(Polyhedron
*P
)
1440 unsigned NbConstraints
= 0;
1441 unsigned NbRays
= 0;
1445 if (POL_HAS(P
, POL_INEQUALITIES
))
1446 NbConstraints
= P
->NbConstraints
+ 1;
1447 if (POL_HAS(P
, POL_POINTS
))
1448 NbRays
= P
->NbRays
+ 1;
1450 C
= Polyhedron_Alloc(P
->Dimension
+1, NbConstraints
, NbRays
);
1451 if (POL_HAS(P
, POL_INEQUALITIES
)) {
1453 for (i
= 0; i
< P
->NbConstraints
; ++i
)
1454 Vector_Copy(P
->Constraint
[i
], C
->Constraint
[i
], P
->Dimension
+2);
1456 value_set_si(C
->Constraint
[P
->NbConstraints
][0], 1);
1457 value_set_si(C
->Constraint
[P
->NbConstraints
][1+P
->Dimension
], 1);
1459 if (POL_HAS(P
, POL_POINTS
)) {
1460 C
->NbBid
= P
->NbBid
;
1461 for (i
= 0; i
< P
->NbRays
; ++i
)
1462 Vector_Copy(P
->Ray
[i
], C
->Ray
[i
], P
->Dimension
+2);
1464 value_set_si(C
->Ray
[P
->NbRays
][0], 1);
1465 value_set_si(C
->Ray
[P
->NbRays
][1+C
->Dimension
], 1);
1467 POL_SET(C
, POL_VALID
);
1468 if (POL_HAS(P
, POL_INEQUALITIES
))
1469 POL_SET(C
, POL_INEQUALITIES
);
1470 if (POL_HAS(P
, POL_POINTS
))
1471 POL_SET(C
, POL_POINTS
);
1472 if (POL_HAS(P
, POL_VERTICES
))
1473 POL_SET(C
, POL_VERTICES
);
1477 /* Returns a (dim+nparam+1)x((dim-n)+nparam+1) matrix
1478 * mapping the transformed subspace back to the original space.
1479 * n is the number of equalities involving the variables
1480 * (i.e., not purely the parameters).
1481 * The remaining n coordinates in the transformed space would
1482 * have constant (parametric) values and are therefore not
1483 * included in the variables of the new space.
1485 Matrix
*compress_variables(Matrix
*Equalities
, unsigned nparam
)
1487 unsigned dim
= (Equalities
->NbColumns
-2) - nparam
;
1488 Matrix
*M
, *H
, *Q
, *U
, *C
, *ratH
, *invH
, *Ul
, *T1
, *T2
, *T
;
1493 for (n
= 0; n
< Equalities
->NbRows
; ++n
)
1494 if (First_Non_Zero(Equalities
->p
[n
]+1, dim
) == -1)
1497 return Identity(dim
+nparam
+1);
1499 value_set_si(mone
, -1);
1500 M
= Matrix_Alloc(n
, dim
);
1501 C
= Matrix_Alloc(n
+1, nparam
+1);
1502 for (i
= 0; i
< n
; ++i
) {
1503 Vector_Copy(Equalities
->p
[i
]+1, M
->p
[i
], dim
);
1504 Vector_Scale(Equalities
->p
[i
]+1+dim
, C
->p
[i
], mone
, nparam
+1);
1506 value_set_si(C
->p
[n
][nparam
], 1);
1507 left_hermite(M
, &H
, &Q
, &U
);
1512 ratH
= Matrix_Alloc(n
+1, n
+1);
1513 invH
= Matrix_Alloc(n
+1, n
+1);
1514 for (i
= 0; i
< n
; ++i
)
1515 Vector_Copy(H
->p
[i
], ratH
->p
[i
], n
);
1516 value_set_si(ratH
->p
[n
][n
], 1);
1517 ok
= Matrix_Inverse(ratH
, invH
);
1521 T1
= Matrix_Alloc(n
+1, nparam
+1);
1522 Matrix_Product(invH
, C
, T1
);
1525 if (value_notone_p(T1
->p
[n
][nparam
])) {
1526 for (i
= 0; i
< n
; ++i
) {
1527 if (!mpz_divisible_p(T1
->p
[i
][nparam
], T1
->p
[n
][nparam
])) {
1532 /* compress_params should have taken care of this */
1533 for (j
= 0; j
< nparam
; ++j
)
1534 assert(mpz_divisible_p(T1
->p
[i
][j
], T1
->p
[n
][nparam
]));
1535 Vector_AntiScale(T1
->p
[i
], T1
->p
[i
], T1
->p
[n
][nparam
], nparam
+1);
1537 value_set_si(T1
->p
[n
][nparam
], 1);
1539 Ul
= Matrix_Alloc(dim
+1, n
+1);
1540 for (i
= 0; i
< dim
; ++i
)
1541 Vector_Copy(U
->p
[i
], Ul
->p
[i
], n
);
1542 value_set_si(Ul
->p
[dim
][n
], 1);
1543 T2
= Matrix_Alloc(dim
+1, nparam
+1);
1544 Matrix_Product(Ul
, T1
, T2
);
1548 T
= Matrix_Alloc(dim
+nparam
+1, (dim
-n
)+nparam
+1);
1549 for (i
= 0; i
< dim
; ++i
) {
1550 Vector_Copy(U
->p
[i
]+n
, T
->p
[i
], dim
-n
);
1551 Vector_Copy(T2
->p
[i
], T
->p
[i
]+dim
-n
, nparam
+1);
1553 for (i
= 0; i
< nparam
+1; ++i
)
1554 value_set_si(T
->p
[dim
+i
][(dim
-n
)+i
], 1);
1555 assert(value_one_p(T2
->p
[dim
][nparam
]));
1562 /* Computes the left inverse of an affine embedding M and, if Eq is not NULL,
1563 * the equalities that define the affine subspace onto which M maps
1566 Matrix
*left_inverse(Matrix
*M
, Matrix
**Eq
)
1569 Matrix
*L
, *H
, *Q
, *U
, *ratH
, *invH
, *Ut
, *inv
;
1572 if (M
->NbColumns
== 1) {
1573 inv
= Matrix_Alloc(1, M
->NbRows
);
1574 value_set_si(inv
->p
[0][M
->NbRows
-1], 1);
1576 *Eq
= Matrix_Alloc(M
->NbRows
-1, 1+(M
->NbRows
-1)+1);
1577 for (i
= 0; i
< M
->NbRows
-1; ++i
) {
1578 value_oppose((*Eq
)->p
[i
][1+i
], M
->p
[M
->NbRows
-1][0]);
1579 value_assign((*Eq
)->p
[i
][1+(M
->NbRows
-1)], M
->p
[i
][0]);
1586 L
= Matrix_Alloc(M
->NbRows
-1, M
->NbColumns
-1);
1587 for (i
= 0; i
< L
->NbRows
; ++i
)
1588 Vector_Copy(M
->p
[i
], L
->p
[i
], L
->NbColumns
);
1589 right_hermite(L
, &H
, &U
, &Q
);
1592 t
= Vector_Alloc(U
->NbColumns
);
1593 for (i
= 0; i
< U
->NbColumns
; ++i
)
1594 value_oppose(t
->p
[i
], M
->p
[i
][M
->NbColumns
-1]);
1596 *Eq
= Matrix_Alloc(H
->NbRows
- H
->NbColumns
, 2 + U
->NbColumns
);
1597 for (i
= 0; i
< H
->NbRows
- H
->NbColumns
; ++i
) {
1598 Vector_Copy(U
->p
[H
->NbColumns
+i
], (*Eq
)->p
[i
]+1, U
->NbColumns
);
1599 Inner_Product(U
->p
[H
->NbColumns
+i
], t
->p
, U
->NbColumns
,
1600 (*Eq
)->p
[i
]+1+U
->NbColumns
);
1603 ratH
= Matrix_Alloc(H
->NbColumns
+1, H
->NbColumns
+1);
1604 invH
= Matrix_Alloc(H
->NbColumns
+1, H
->NbColumns
+1);
1605 for (i
= 0; i
< H
->NbColumns
; ++i
)
1606 Vector_Copy(H
->p
[i
], ratH
->p
[i
], H
->NbColumns
);
1607 value_set_si(ratH
->p
[ratH
->NbRows
-1][ratH
->NbColumns
-1], 1);
1609 ok
= Matrix_Inverse(ratH
, invH
);
1612 Ut
= Matrix_Alloc(invH
->NbRows
, U
->NbColumns
+1);
1613 for (i
= 0; i
< Ut
->NbRows
-1; ++i
) {
1614 Vector_Copy(U
->p
[i
], Ut
->p
[i
], U
->NbColumns
);
1615 Inner_Product(U
->p
[i
], t
->p
, U
->NbColumns
, &Ut
->p
[i
][Ut
->NbColumns
-1]);
1619 value_set_si(Ut
->p
[Ut
->NbRows
-1][Ut
->NbColumns
-1], 1);
1620 inv
= Matrix_Alloc(invH
->NbRows
, Ut
->NbColumns
);
1621 Matrix_Product(invH
, Ut
, inv
);
1627 /* Check whether all rays are revlex positive in the parameters
1629 int Polyhedron_has_revlex_positive_rays(Polyhedron
*P
, unsigned nparam
)
1632 for (r
= 0; r
< P
->NbRays
; ++r
) {
1634 if (value_notzero_p(P
->Ray
[r
][P
->Dimension
+1]))
1636 for (i
= P
->Dimension
-1; i
>= P
->Dimension
-nparam
; --i
) {
1637 if (value_neg_p(P
->Ray
[r
][i
+1]))
1639 if (value_pos_p(P
->Ray
[r
][i
+1]))
1642 /* A ray independent of the parameters */
1643 if (i
< P
->Dimension
-nparam
)
1649 static Polyhedron
*Recession_Cone(Polyhedron
*P
, unsigned nparam
, unsigned MaxRays
)
1652 unsigned nvar
= P
->Dimension
- nparam
;
1653 Matrix
*M
= Matrix_Alloc(P
->NbConstraints
, 1 + nvar
+ 1);
1655 for (i
= 0; i
< P
->NbConstraints
; ++i
)
1656 Vector_Copy(P
->Constraint
[i
], M
->p
[i
], 1+nvar
);
1657 R
= Constraints2Polyhedron(M
, MaxRays
);
1662 int Polyhedron_is_unbounded(Polyhedron
*P
, unsigned nparam
, unsigned MaxRays
)
1666 Polyhedron
*R
= Recession_Cone(P
, nparam
, MaxRays
);
1667 POL_ENSURE_VERTICES(R
);
1669 for (i
= 0; i
< R
->NbRays
; ++i
)
1670 if (value_zero_p(R
->Ray
[i
][1+R
->Dimension
]))
1672 is_unbounded
= R
->NbBid
> 0 || i
< R
->NbRays
;
1674 return is_unbounded
;
1677 void Vector_Oppose(Value
*p1
, Value
*p2
, unsigned len
)
1681 for (i
= 0; i
< len
; ++i
)
1682 value_oppose(p2
[i
], p1
[i
]);
1685 /* perform transposition inline; assumes M is a square matrix */
1686 void Matrix_Transposition(Matrix
*M
)
1690 assert(M
->NbRows
== M
->NbColumns
);
1691 for (i
= 0; i
< M
->NbRows
; ++i
)
1692 for (j
= i
+1; j
< M
->NbColumns
; ++j
)
1693 value_swap(M
->p
[i
][j
], M
->p
[j
][i
]);