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 Matrix
* unimodular_complete(Vector
*row
)
427 Value g
, b
, c
, old
, tmp
;
436 m
= Matrix_Alloc(row
->Size
, row
->Size
);
437 for (j
= 0; j
< row
->Size
; ++j
) {
438 value_assign(m
->p
[0][j
], row
->p
[j
]);
440 value_assign(g
, row
->p
[0]);
441 for (i
= 1; value_zero_p(g
) && i
< row
->Size
; ++i
) {
442 for (j
= 0; j
< row
->Size
; ++j
) {
444 value_set_si(m
->p
[i
][j
], 1);
446 value_set_si(m
->p
[i
][j
], 0);
448 value_assign(g
, row
->p
[i
]);
450 for (; i
< row
->Size
; ++i
) {
451 value_assign(old
, g
);
452 Extended_Euclid(old
, row
->p
[i
], &c
, &b
, &g
);
454 for (j
= 0; j
< row
->Size
; ++j
) {
456 value_multiply(tmp
, row
->p
[j
], b
);
457 value_division(m
->p
[i
][j
], tmp
, old
);
459 value_assign(m
->p
[i
][j
], c
);
461 value_set_si(m
->p
[i
][j
], 0);
473 * Returns a full-dimensional polyhedron with the same number
474 * of integer points as P
476 Polyhedron
*remove_equalities(Polyhedron
*P
)
480 Polyhedron
*p
= Polyhedron_Copy(P
), *q
;
481 unsigned dim
= p
->Dimension
;
486 while (!emptyQ2(p
) && p
->NbEq
> 0) {
488 Vector_Gcd(p
->Constraint
[0]+1, dim
+1, &g
);
489 Vector_AntiScale(p
->Constraint
[0]+1, p
->Constraint
[0]+1, g
, dim
+1);
490 Vector_Gcd(p
->Constraint
[0]+1, dim
, &g
);
491 if (value_notone_p(g
) && value_notmone_p(g
)) {
493 p
= Empty_Polyhedron(0);
496 v
= Vector_Alloc(dim
);
497 Vector_Copy(p
->Constraint
[0]+1, v
->p
, dim
);
498 m1
= unimodular_complete(v
);
499 m2
= Matrix_Alloc(dim
, dim
+1);
500 for (i
= 0; i
< dim
-1 ; ++i
) {
501 Vector_Copy(m1
->p
[i
+1], m2
->p
[i
], dim
);
502 value_set_si(m2
->p
[i
][dim
], 0);
504 Vector_Set(m2
->p
[dim
-1], 0, dim
);
505 value_set_si(m2
->p
[dim
-1][dim
], 1);
506 q
= Polyhedron_Image(p
, m2
, p
->NbConstraints
+1+p
->NbRays
);
519 * Returns a full-dimensional polyhedron with the same number
520 * of integer points as P
521 * nvar specifies the number of variables
522 * The remaining dimensions are assumed to be parameters
524 * factor is NbEq x (nparam+2) matrix, containing stride constraints
525 * on the parameters; column nparam is the constant;
526 * column nparam+1 is the stride
528 * if factor is NULL, only remove equalities that don't affect
529 * the number of points
531 Polyhedron
*remove_equalities_p(Polyhedron
*P
, unsigned nvar
, Matrix
**factor
)
535 Polyhedron
*p
= P
, *q
;
536 unsigned dim
= p
->Dimension
;
542 f
= Matrix_Alloc(p
->NbEq
, dim
-nvar
+2);
547 while (nvar
> 0 && p
->NbEq
- skip
> 0) {
550 while (skip
< p
->NbEq
&&
551 First_Non_Zero(p
->Constraint
[skip
]+1, nvar
) == -1)
556 Vector_Gcd(p
->Constraint
[skip
]+1, dim
+1, &g
);
557 Vector_AntiScale(p
->Constraint
[skip
]+1, p
->Constraint
[skip
]+1, g
, dim
+1);
558 Vector_Gcd(p
->Constraint
[skip
]+1, nvar
, &g
);
559 if (!factor
&& value_notone_p(g
) && value_notmone_p(g
)) {
564 Vector_Copy(p
->Constraint
[skip
]+1+nvar
, f
->p
[j
], dim
-nvar
+1);
565 value_assign(f
->p
[j
][dim
-nvar
+1], g
);
567 v
= Vector_Alloc(dim
);
568 Vector_AntiScale(p
->Constraint
[skip
]+1, v
->p
, g
, nvar
);
569 Vector_Set(v
->p
+nvar
, 0, dim
-nvar
);
570 m1
= unimodular_complete(v
);
571 m2
= Matrix_Alloc(dim
, dim
+1);
572 for (i
= 0; i
< dim
-1 ; ++i
) {
573 Vector_Copy(m1
->p
[i
+1], m2
->p
[i
], dim
);
574 value_set_si(m2
->p
[i
][dim
], 0);
576 Vector_Set(m2
->p
[dim
-1], 0, dim
);
577 value_set_si(m2
->p
[dim
-1][dim
], 1);
578 q
= Polyhedron_Image(p
, m2
, p
->NbConstraints
+1+p
->NbRays
);
592 void Line_Length(Polyhedron
*P
, Value
*len
)
598 assert(P
->Dimension
== 1);
604 for (i
= 0; i
< P
->NbConstraints
; ++i
) {
605 value_oppose(tmp
, P
->Constraint
[i
][2]);
606 if (value_pos_p(P
->Constraint
[i
][1])) {
607 mpz_cdiv_q(tmp
, tmp
, P
->Constraint
[i
][1]);
608 if (!p
|| value_gt(tmp
, pos
))
609 value_assign(pos
, tmp
);
612 mpz_fdiv_q(tmp
, tmp
, P
->Constraint
[i
][1]);
613 if (!n
|| value_lt(tmp
, neg
))
614 value_assign(neg
, tmp
);
618 value_subtract(tmp
, neg
, pos
);
619 value_increment(*len
, tmp
);
621 value_set_si(*len
, -1);
630 * Factors the polyhedron P into polyhedra Q_i such that
631 * the number of integer points in P is equal to the product
632 * of the number of integer points in the individual Q_i
634 * If no factors can be found, NULL is returned.
635 * Otherwise, a linked list of the factors is returned.
637 * If there are factors and if T is not NULL, then a matrix will be
638 * returned through T expressing the old variables in terms of the
639 * new variables as they appear in the sequence of factors.
641 * The algorithm works by first computing the Hermite normal form
642 * and then grouping columns linked by one or more constraints together,
643 * where a constraints "links" two or more columns if the constraint
644 * has nonzero coefficients in the columns.
646 Polyhedron
* Polyhedron_Factor(Polyhedron
*P
, unsigned nparam
, Matrix
**T
,
650 Matrix
*M
, *H
, *Q
, *U
;
651 int *pos
; /* for each column: row position of pivot */
652 int *group
; /* group to which a column belongs */
653 int *cnt
; /* number of columns in the group */
654 int *rowgroup
; /* group to which a constraint belongs */
655 int nvar
= P
->Dimension
- nparam
;
656 Polyhedron
*F
= NULL
;
664 NALLOC(rowgroup
, P
->NbConstraints
);
666 M
= Matrix_Alloc(P
->NbConstraints
, nvar
);
667 for (i
= 0; i
< P
->NbConstraints
; ++i
)
668 Vector_Copy(P
->Constraint
[i
]+1, M
->p
[i
], nvar
);
669 left_hermite(M
, &H
, &Q
, &U
);
673 for (i
= 0; i
< P
->NbConstraints
; ++i
)
675 for (i
= 0, j
= 0; i
< H
->NbColumns
; ++i
) {
676 for ( ; j
< H
->NbRows
; ++j
)
677 if (value_notzero_p(H
->p
[j
][i
]))
679 assert (j
< H
->NbRows
);
682 for (i
= 0; i
< nvar
; ++i
) {
686 for (i
= 0; i
< H
->NbColumns
&& cnt
[0] < nvar
; ++i
) {
687 if (rowgroup
[pos
[i
]] == -1)
688 rowgroup
[pos
[i
]] = i
;
689 for (j
= pos
[i
]+1; j
< H
->NbRows
; ++j
) {
690 if (value_zero_p(H
->p
[j
][i
]))
692 if (rowgroup
[j
] != -1)
694 rowgroup
[j
] = group
[i
];
695 for (k
= i
+1; k
< H
->NbColumns
&& j
>= pos
[k
]; ++k
) {
700 if (group
[k
] != group
[i
] && value_notzero_p(H
->p
[j
][k
])) {
701 assert(cnt
[group
[k
]] != 0);
702 assert(cnt
[group
[i
]] != 0);
703 if (group
[i
] < group
[k
]) {
704 cnt
[group
[i
]] += cnt
[group
[k
]];
708 cnt
[group
[k
]] += cnt
[group
[i
]];
717 if (cnt
[0] != nvar
) {
718 /* Extract out pure context constraints separately */
719 Polyhedron
**next
= &F
;
722 *T
= Matrix_Alloc(nvar
, nvar
);
723 for (i
= nparam
? -1 : 0; i
< nvar
; ++i
) {
727 for (j
= 0, k
= 0; j
< P
->NbConstraints
; ++j
)
728 if (rowgroup
[j
] == -1) {
729 if (First_Non_Zero(P
->Constraint
[j
]+1+nvar
,
742 for (j
= 0, k
= 0; j
< P
->NbConstraints
; ++j
)
743 if (rowgroup
[j
] >= 0 && group
[rowgroup
[j
]] == i
) {
750 for (j
= 0; j
< nvar
; ++j
) {
752 for (l
= 0, m
= 0; m
< d
; ++l
) {
755 value_assign((*T
)->p
[j
][tot_d
+m
++], U
->p
[j
][l
]);
759 M
= Matrix_Alloc(k
, d
+nparam
+2);
760 for (j
= 0, k
= 0; j
< P
->NbConstraints
; ++j
) {
762 if (rowgroup
[j
] != i
)
764 value_assign(M
->p
[k
][0], P
->Constraint
[j
][0]);
765 for (l
= 0, m
= 0; m
< d
; ++l
) {
768 value_assign(M
->p
[k
][1+m
++], H
->p
[j
][l
]);
770 Vector_Copy(P
->Constraint
[j
]+1+nvar
, M
->p
[k
]+1+m
, nparam
+1);
773 *next
= Constraints2Polyhedron(M
, NbMaxRays
);
774 next
= &(*next
)->next
;
789 * Project on final dim dimensions
791 Polyhedron
* Polyhedron_Project(Polyhedron
*P
, int dim
)
794 int remove
= P
->Dimension
- dim
;
798 if (P
->Dimension
== dim
)
799 return Polyhedron_Copy(P
);
801 T
= Matrix_Alloc(dim
+1, P
->Dimension
+1);
802 for (i
= 0; i
< dim
+1; ++i
)
803 value_set_si(T
->p
[i
][i
+remove
], 1);
804 I
= Polyhedron_Image(P
, T
, P
->NbConstraints
);
809 /* Constructs a new constraint that ensures that
810 * the first constraint is (strictly) smaller than
813 static void smaller_constraint(Value
*a
, Value
*b
, Value
*c
, int pos
, int shift
,
814 int len
, int strict
, Value
*tmp
)
816 value_oppose(*tmp
, b
[pos
+1]);
817 value_set_si(c
[0], 1);
818 Vector_Combine(a
+1+shift
, b
+1+shift
, c
+1, *tmp
, a
[pos
+1], len
-shift
-1);
820 value_decrement(c
[len
-shift
-1], c
[len
-shift
-1]);
821 ConstraintSimplify(c
, c
, len
-shift
, tmp
);
824 struct section
{ Polyhedron
* D
; evalue E
; };
826 evalue
* ParamLine_Length_mod(Polyhedron
*P
, Polyhedron
*C
, int MaxRays
)
828 unsigned dim
= P
->Dimension
;
829 unsigned nvar
= dim
- C
->Dimension
;
844 NALLOC(pos
, P
->NbConstraints
);
847 evalue_set_si(&mone
, -1, 1);
849 for (i
= 0, z
= 0; i
< P
->NbConstraints
; ++i
)
850 if (value_zero_p(P
->Constraint
[i
][1]))
852 /* put those with positive coefficients first; number: p */
853 for (i
= 0, p
= 0, n
= P
->NbConstraints
-z
-1; i
< P
->NbConstraints
; ++i
)
854 if (value_pos_p(P
->Constraint
[i
][1]))
856 else if (value_neg_p(P
->Constraint
[i
][1]))
858 n
= P
->NbConstraints
-z
-p
;
859 assert (p
>= 1 && n
>= 1);
860 s
= (struct section
*) malloc(p
* n
* sizeof(struct section
));
861 M
= Matrix_Alloc((p
-1) + (n
-1), dim
-nvar
+2);
862 for (k
= 0; k
< p
; ++k
) {
863 for (k2
= 0; k2
< p
; ++k2
) {
868 P
->Constraint
[pos
[k
]],
869 P
->Constraint
[pos
[k2
]],
870 M
->p
[q
], 0, nvar
, dim
+2, k2
> k
, &g
);
872 for (l
= p
; l
< p
+n
; ++l
) {
873 for (l2
= p
; l2
< p
+n
; ++l2
) {
878 P
->Constraint
[pos
[l2
]],
879 P
->Constraint
[pos
[l
]],
880 M
->p
[q
], 0, nvar
, dim
+2, l2
> l
, &g
);
883 T
= Constraints2Polyhedron(M2
, P
->NbRays
);
885 s
[nd
].D
= DomainIntersection(T
, C
, MaxRays
);
887 POL_ENSURE_VERTICES(s
[nd
].D
);
888 if (emptyQ(s
[nd
].D
)) {
889 Polyhedron_Free(s
[nd
].D
);
892 L
= bv_ceil3(P
->Constraint
[pos
[k
]]+1+nvar
,
894 P
->Constraint
[pos
[k
]][0+1], s
[nd
].D
);
895 U
= bv_ceil3(P
->Constraint
[pos
[l
]]+1+nvar
,
897 P
->Constraint
[pos
[l
]][0+1], s
[nd
].D
);
913 value_set_si(F
->d
, 0);
914 F
->x
.p
= new_enode(partition
, 2*nd
, dim
-nvar
);
915 for (k
= 0; k
< nd
; ++k
) {
916 EVALUE_SET_DOMAIN(F
->x
.p
->arr
[2*k
], s
[k
].D
);
917 value_clear(F
->x
.p
->arr
[2*k
+1].d
);
918 F
->x
.p
->arr
[2*k
+1] = s
[k
].E
;
922 free_evalue_refs(&mone
);
929 evalue
* ParamLine_Length(Polyhedron
*P
, Polyhedron
*C
,
930 struct barvinok_options
*options
)
933 tmp
= ParamLine_Length_mod(P
, C
, options
->MaxRays
);
934 if (options
->lookup_table
) {
935 evalue_mod2table(tmp
, C
->Dimension
);
941 Bool
isIdentity(Matrix
*M
)
944 if (M
->NbRows
!= M
->NbColumns
)
947 for (i
= 0;i
< M
->NbRows
; i
++)
948 for (j
= 0; j
< M
->NbColumns
; j
++)
950 if(value_notone_p(M
->p
[i
][j
]))
953 if(value_notzero_p(M
->p
[i
][j
]))
959 void Param_Polyhedron_Print(FILE* DST
, Param_Polyhedron
*PP
, char **param_names
)
964 for(P
=PP
->D
;P
;P
=P
->next
) {
966 /* prints current val. dom. */
967 fprintf(DST
, "---------------------------------------\n");
968 fprintf(DST
, "Domain :\n");
969 Print_Domain(DST
, P
->Domain
, param_names
);
971 /* scan the vertices */
972 fprintf(DST
, "Vertices :\n");
973 FORALL_PVertex_in_ParamPolyhedron(V
,P
,PP
) {
975 /* prints each vertex */
976 Print_Vertex(DST
, V
->Vertex
, param_names
);
979 END_FORALL_PVertex_in_ParamPolyhedron
;
983 void Enumeration_Print(FILE *Dst
, Enumeration
*en
, char **params
)
985 for (; en
; en
= en
->next
) {
986 Print_Domain(Dst
, en
->ValidityDomain
, params
);
987 print_evalue(Dst
, &en
->EP
, params
);
991 void Enumeration_Free(Enumeration
*en
)
997 free_evalue_refs( &(en
->EP
) );
998 Domain_Free( en
->ValidityDomain
);
1005 void Enumeration_mod2table(Enumeration
*en
, unsigned nparam
)
1007 for (; en
; en
= en
->next
) {
1008 evalue_mod2table(&en
->EP
, nparam
);
1009 reduce_evalue(&en
->EP
);
1013 size_t Enumeration_size(Enumeration
*en
)
1017 for (; en
; en
= en
->next
) {
1018 s
+= domain_size(en
->ValidityDomain
);
1019 s
+= evalue_size(&en
->EP
);
1024 void Free_ParamNames(char **params
, int m
)
1031 /* Check whether every set in D2 is included in some set of D1 */
1032 int DomainIncludes(Polyhedron
*D1
, Polyhedron
*D2
)
1034 for ( ; D2
; D2
= D2
->next
) {
1036 for (P1
= D1
; P1
; P1
= P1
->next
)
1037 if (PolyhedronIncludes(P1
, D2
))
1045 int line_minmax(Polyhedron
*I
, Value
*min
, Value
*max
)
1050 value_oppose(I
->Constraint
[0][2], I
->Constraint
[0][2]);
1051 /* There should never be a remainder here */
1052 if (value_pos_p(I
->Constraint
[0][1]))
1053 mpz_fdiv_q(*min
, I
->Constraint
[0][2], I
->Constraint
[0][1]);
1055 mpz_fdiv_q(*min
, I
->Constraint
[0][2], I
->Constraint
[0][1]);
1056 value_assign(*max
, *min
);
1057 } else for (i
= 0; i
< I
->NbConstraints
; ++i
) {
1058 if (value_zero_p(I
->Constraint
[i
][1])) {
1063 value_oppose(I
->Constraint
[i
][2], I
->Constraint
[i
][2]);
1064 if (value_pos_p(I
->Constraint
[i
][1]))
1065 mpz_cdiv_q(*min
, I
->Constraint
[i
][2], I
->Constraint
[i
][1]);
1067 mpz_fdiv_q(*max
, I
->Constraint
[i
][2], I
->Constraint
[i
][1]);
1075 PROCEDURES TO COMPUTE ENUMERATION. recursive procedure, recurse for
1078 @param pos index position of current loop index (1..hdim-1)
1079 @param P loop domain
1080 @param context context values for fixed indices
1081 @param exist number of existential variables
1082 @return the number of integer points in this
1086 void count_points_e (int pos
, Polyhedron
*P
, int exist
, int nparam
,
1087 Value
*context
, Value
*res
)
1092 value_set_si(*res
, 0);
1096 value_init(LB
); value_init(UB
); value_init(k
);
1100 if (lower_upper_bounds(pos
,P
,context
,&LB
,&UB
) !=0) {
1101 /* Problem if UB or LB is INFINITY */
1102 value_clear(LB
); value_clear(UB
); value_clear(k
);
1103 if (pos
> P
->Dimension
- nparam
- exist
)
1104 value_set_si(*res
, 1);
1106 value_set_si(*res
, -1);
1113 for (value_assign(k
,LB
); value_le(k
,UB
); value_increment(k
,k
)) {
1114 fprintf(stderr
, "(");
1115 for (i
=1; i
<pos
; i
++) {
1116 value_print(stderr
,P_VALUE_FMT
,context
[i
]);
1117 fprintf(stderr
,",");
1119 value_print(stderr
,P_VALUE_FMT
,k
);
1120 fprintf(stderr
,")\n");
1125 value_set_si(context
[pos
],0);
1126 if (value_lt(UB
,LB
)) {
1127 value_clear(LB
); value_clear(UB
); value_clear(k
);
1128 value_set_si(*res
, 0);
1133 value_set_si(*res
, 1);
1135 value_subtract(k
,UB
,LB
);
1136 value_add_int(k
,k
,1);
1137 value_assign(*res
, k
);
1139 value_clear(LB
); value_clear(UB
); value_clear(k
);
1143 /*-----------------------------------------------------------------*/
1144 /* Optimization idea */
1145 /* If inner loops are not a function of k (the current index) */
1146 /* i.e. if P->Constraint[i][pos]==0 for all P following this and */
1148 /* Then CNT = (UB-LB+1)*count_points(pos+1, P->next, context) */
1149 /* (skip the for loop) */
1150 /*-----------------------------------------------------------------*/
1153 value_set_si(*res
, 0);
1154 for (value_assign(k
,LB
);value_le(k
,UB
);value_increment(k
,k
)) {
1155 /* Insert k in context */
1156 value_assign(context
[pos
],k
);
1157 count_points_e(pos
+1, P
->next
, exist
, nparam
, context
, &c
);
1158 if(value_notmone_p(c
))
1159 value_addto(*res
, *res
, c
);
1161 value_set_si(*res
, -1);
1164 if (pos
> P
->Dimension
- nparam
- exist
&&
1171 fprintf(stderr
,"%d\n",CNT
);
1175 value_set_si(context
[pos
],0);
1176 value_clear(LB
); value_clear(UB
); value_clear(k
);
1178 } /* count_points_e */
1180 int DomainContains(Polyhedron
*P
, Value
*list_args
, int len
,
1181 unsigned MaxRays
, int set
)
1186 if (P
->Dimension
== len
)
1187 return in_domain(P
, list_args
);
1189 assert(set
); // assume list_args is large enough
1190 assert((P
->Dimension
- len
) % 2 == 0);
1192 for (i
= 0; i
< P
->Dimension
- len
; i
+= 2) {
1194 for (j
= 0 ; j
< P
->NbEq
; ++j
)
1195 if (value_notzero_p(P
->Constraint
[j
][1+len
+i
]))
1197 assert(j
< P
->NbEq
);
1198 value_absolute(m
, P
->Constraint
[j
][1+len
+i
]);
1199 k
= First_Non_Zero(P
->Constraint
[j
]+1, len
);
1201 assert(First_Non_Zero(P
->Constraint
[j
]+1+k
+1, len
- k
- 1) == -1);
1202 mpz_fdiv_q(list_args
[len
+i
], list_args
[k
], m
);
1203 mpz_fdiv_r(list_args
[len
+i
+1], list_args
[k
], m
);
1207 return in_domain(P
, list_args
);
1210 Polyhedron
*DomainConcat(Polyhedron
*head
, Polyhedron
*tail
)
1215 for (S
= head
; S
->next
; S
= S
->next
)
1221 #ifndef HAVE_LEXSMALLER
1223 evalue
*barvinok_lexsmaller_ev(Polyhedron
*P
, Polyhedron
*D
, unsigned dim
,
1224 Polyhedron
*C
, unsigned MaxRays
)
1230 #include <polylib/ranking.h>
1232 evalue
*barvinok_lexsmaller_ev(Polyhedron
*P
, Polyhedron
*D
, unsigned dim
,
1233 Polyhedron
*C
, unsigned MaxRays
)
1236 Polyhedron
*RC
, *RD
, *Q
;
1237 unsigned nparam
= dim
+ C
->Dimension
;
1241 RC
= LexSmaller(P
, D
, dim
, C
, MaxRays
);
1245 exist
= RD
->Dimension
- nparam
- dim
;
1246 CA
= align_context(RC
, RD
->Dimension
, MaxRays
);
1247 Q
= DomainIntersection(RD
, CA
, MaxRays
);
1248 Polyhedron_Free(CA
);
1250 Polyhedron_Free(RC
);
1253 for (Q
= RD
; Q
; Q
= Q
->next
) {
1255 Polyhedron
*next
= Q
->next
;
1258 t
= barvinok_enumerate_e(Q
, exist
, nparam
, MaxRays
);
1264 free_evalue_refs(t
);
1276 Enumeration
*barvinok_lexsmaller(Polyhedron
*P
, Polyhedron
*D
, unsigned dim
,
1277 Polyhedron
*C
, unsigned MaxRays
)
1279 evalue
*EP
= barvinok_lexsmaller_ev(P
, D
, dim
, C
, MaxRays
);
1281 return partition2enumeration(EP
);
1285 /* "align" matrix to have nrows by inserting
1286 * the necessary number of rows and an equal number of columns in front
1288 Matrix
*align_matrix(Matrix
*M
, int nrows
)
1291 int newrows
= nrows
- M
->NbRows
;
1292 Matrix
*M2
= Matrix_Alloc(nrows
, newrows
+ M
->NbColumns
);
1293 for (i
= 0; i
< newrows
; ++i
)
1294 value_set_si(M2
->p
[i
][i
], 1);
1295 for (i
= 0; i
< M
->NbRows
; ++i
)
1296 Vector_Copy(M
->p
[i
], M2
->p
[newrows
+i
]+newrows
, M
->NbColumns
);
1300 static void print_varlist(FILE *out
, int n
, char **names
)
1304 for (i
= 0; i
< n
; ++i
) {
1307 fprintf(out
, "%s", names
[i
]);
1312 static void print_term(FILE *out
, Value v
, int pos
, int dim
, int nparam
,
1313 char **iter_names
, char **param_names
, int *first
)
1315 if (value_zero_p(v
)) {
1316 if (first
&& *first
&& pos
>= dim
+ nparam
)
1322 if (!*first
&& value_pos_p(v
))
1326 if (pos
< dim
+ nparam
) {
1327 if (value_mone_p(v
))
1329 else if (!value_one_p(v
))
1330 value_print(out
, VALUE_FMT
, v
);
1332 fprintf(out
, "%s", iter_names
[pos
]);
1334 fprintf(out
, "%s", param_names
[pos
-dim
]);
1336 value_print(out
, VALUE_FMT
, v
);
1339 char **util_generate_names(int n
, char *prefix
)
1342 int len
= (prefix
? strlen(prefix
) : 0) + 10;
1343 char **names
= ALLOCN(char*, n
);
1345 fprintf(stderr
, "ERROR: memory overflow.\n");
1348 for (i
= 0; i
< n
; ++i
) {
1349 names
[i
] = ALLOCN(char, len
);
1351 fprintf(stderr
, "ERROR: memory overflow.\n");
1355 snprintf(names
[i
], len
, "%d", i
);
1357 snprintf(names
[i
], len
, "%s%d", prefix
, i
);
1363 void util_free_names(int n
, char **names
)
1366 for (i
= 0; i
< n
; ++i
)
1371 void Polyhedron_pprint(FILE *out
, Polyhedron
*P
, int dim
, int nparam
,
1372 char **iter_names
, char **param_names
)
1377 assert(dim
+ nparam
== P
->Dimension
);
1383 print_varlist(out
, nparam
, param_names
);
1384 fprintf(out
, " -> ");
1386 print_varlist(out
, dim
, iter_names
);
1387 fprintf(out
, " : ");
1390 fprintf(out
, "FALSE");
1391 else for (i
= 0; i
< P
->NbConstraints
; ++i
) {
1393 int v
= First_Non_Zero(P
->Constraint
[i
]+1, P
->Dimension
);
1394 if (v
== -1 && value_pos_p(P
->Constraint
[i
][0]))
1397 fprintf(out
, " && ");
1398 if (v
== -1 && value_notzero_p(P
->Constraint
[i
][1+P
->Dimension
]))
1399 fprintf(out
, "FALSE");
1400 else if (value_pos_p(P
->Constraint
[i
][v
+1])) {
1401 print_term(out
, P
->Constraint
[i
][v
+1], v
, dim
, nparam
,
1402 iter_names
, param_names
, NULL
);
1403 if (value_zero_p(P
->Constraint
[i
][0]))
1404 fprintf(out
, " = ");
1406 fprintf(out
, " >= ");
1407 for (j
= v
+1; j
<= dim
+nparam
; ++j
) {
1408 value_oppose(tmp
, P
->Constraint
[i
][1+j
]);
1409 print_term(out
, tmp
, j
, dim
, nparam
,
1410 iter_names
, param_names
, &first
);
1413 value_oppose(tmp
, P
->Constraint
[i
][1+v
]);
1414 print_term(out
, tmp
, v
, dim
, nparam
,
1415 iter_names
, param_names
, NULL
);
1416 fprintf(out
, " <= ");
1417 for (j
= v
+1; j
<= dim
+nparam
; ++j
)
1418 print_term(out
, P
->Constraint
[i
][1+j
], j
, dim
, nparam
,
1419 iter_names
, param_names
, &first
);
1423 fprintf(out
, " }\n");
1428 /* Construct a cone over P with P placed at x_d = 1, with
1429 * x_d the coordinate of an extra dimension
1431 * It's probably a mistake to depend so much on the internal
1432 * representation. We should probably simply compute the
1433 * vertices/facets first.
1435 Polyhedron
*Cone_over_Polyhedron(Polyhedron
*P
)
1437 unsigned NbConstraints
= 0;
1438 unsigned NbRays
= 0;
1442 if (POL_HAS(P
, POL_INEQUALITIES
))
1443 NbConstraints
= P
->NbConstraints
+ 1;
1444 if (POL_HAS(P
, POL_POINTS
))
1445 NbRays
= P
->NbRays
+ 1;
1447 C
= Polyhedron_Alloc(P
->Dimension
+1, NbConstraints
, NbRays
);
1448 if (POL_HAS(P
, POL_INEQUALITIES
)) {
1450 for (i
= 0; i
< P
->NbConstraints
; ++i
)
1451 Vector_Copy(P
->Constraint
[i
], C
->Constraint
[i
], P
->Dimension
+2);
1453 value_set_si(C
->Constraint
[P
->NbConstraints
][0], 1);
1454 value_set_si(C
->Constraint
[P
->NbConstraints
][1+P
->Dimension
], 1);
1456 if (POL_HAS(P
, POL_POINTS
)) {
1457 C
->NbBid
= P
->NbBid
;
1458 for (i
= 0; i
< P
->NbRays
; ++i
)
1459 Vector_Copy(P
->Ray
[i
], C
->Ray
[i
], P
->Dimension
+2);
1461 value_set_si(C
->Ray
[P
->NbRays
][0], 1);
1462 value_set_si(C
->Ray
[P
->NbRays
][1+C
->Dimension
], 1);
1464 POL_SET(C
, POL_VALID
);
1465 if (POL_HAS(P
, POL_INEQUALITIES
))
1466 POL_SET(C
, POL_INEQUALITIES
);
1467 if (POL_HAS(P
, POL_POINTS
))
1468 POL_SET(C
, POL_POINTS
);
1469 if (POL_HAS(P
, POL_VERTICES
))
1470 POL_SET(C
, POL_VERTICES
);
1474 /* Returns a (dim+nparam+1)x((dim-n)+nparam+1) matrix
1475 * mapping the transformed subspace back to the original space.
1476 * n is the number of equalities involving the variables
1477 * (i.e., not purely the parameters).
1478 * The remaining n coordinates in the transformed space would
1479 * have constant (parametric) values and are therefore not
1480 * included in the variables of the new space.
1482 Matrix
*compress_variables(Matrix
*Equalities
, unsigned nparam
)
1484 unsigned dim
= (Equalities
->NbColumns
-2) - nparam
;
1485 Matrix
*M
, *H
, *Q
, *U
, *C
, *ratH
, *invH
, *Ul
, *T1
, *T2
, *T
;
1490 for (n
= 0; n
< Equalities
->NbRows
; ++n
)
1491 if (First_Non_Zero(Equalities
->p
[n
]+1, dim
) == -1)
1494 return Identity(dim
+nparam
+1);
1496 value_set_si(mone
, -1);
1497 M
= Matrix_Alloc(n
, dim
);
1498 C
= Matrix_Alloc(n
+1, nparam
+1);
1499 for (i
= 0; i
< n
; ++i
) {
1500 Vector_Copy(Equalities
->p
[i
]+1, M
->p
[i
], dim
);
1501 Vector_Scale(Equalities
->p
[i
]+1+dim
, C
->p
[i
], mone
, nparam
+1);
1503 value_set_si(C
->p
[n
][nparam
], 1);
1504 left_hermite(M
, &H
, &Q
, &U
);
1509 ratH
= Matrix_Alloc(n
+1, n
+1);
1510 invH
= Matrix_Alloc(n
+1, n
+1);
1511 for (i
= 0; i
< n
; ++i
)
1512 Vector_Copy(H
->p
[i
], ratH
->p
[i
], n
);
1513 value_set_si(ratH
->p
[n
][n
], 1);
1514 ok
= Matrix_Inverse(ratH
, invH
);
1518 T1
= Matrix_Alloc(n
+1, nparam
+1);
1519 Matrix_Product(invH
, C
, T1
);
1522 if (value_notone_p(T1
->p
[n
][nparam
])) {
1523 for (i
= 0; i
< n
; ++i
) {
1524 if (!mpz_divisible_p(T1
->p
[i
][nparam
], T1
->p
[n
][nparam
])) {
1529 /* compress_params should have taken care of this */
1530 for (j
= 0; j
< nparam
; ++j
)
1531 assert(mpz_divisible_p(T1
->p
[i
][j
], T1
->p
[n
][nparam
]));
1532 Vector_AntiScale(T1
->p
[i
], T1
->p
[i
], T1
->p
[n
][nparam
], nparam
+1);
1534 value_set_si(T1
->p
[n
][nparam
], 1);
1536 Ul
= Matrix_Alloc(dim
+1, n
+1);
1537 for (i
= 0; i
< dim
; ++i
)
1538 Vector_Copy(U
->p
[i
], Ul
->p
[i
], n
);
1539 value_set_si(Ul
->p
[dim
][n
], 1);
1540 T2
= Matrix_Alloc(dim
+1, nparam
+1);
1541 Matrix_Product(Ul
, T1
, T2
);
1545 T
= Matrix_Alloc(dim
+nparam
+1, (dim
-n
)+nparam
+1);
1546 for (i
= 0; i
< dim
; ++i
) {
1547 Vector_Copy(U
->p
[i
]+n
, T
->p
[i
], dim
-n
);
1548 Vector_Copy(T2
->p
[i
], T
->p
[i
]+dim
-n
, nparam
+1);
1550 for (i
= 0; i
< nparam
+1; ++i
)
1551 value_set_si(T
->p
[dim
+i
][(dim
-n
)+i
], 1);
1552 assert(value_one_p(T2
->p
[dim
][nparam
]));
1559 Matrix
*left_inverse(Matrix
*M
, Matrix
**Eq
)
1562 Matrix
*L
, *H
, *Q
, *U
, *ratH
, *invH
, *Ut
, *inv
;
1565 if (M
->NbColumns
== 1) {
1566 inv
= Matrix_Alloc(1, M
->NbRows
);
1567 value_set_si(inv
->p
[0][M
->NbRows
-1], 1);
1569 *Eq
= Matrix_Alloc(M
->NbRows
-1, 1+(M
->NbRows
-1)+1);
1570 for (i
= 0; i
< M
->NbRows
-1; ++i
) {
1571 value_oppose((*Eq
)->p
[i
][1+i
], M
->p
[M
->NbRows
-1][0]);
1572 value_assign((*Eq
)->p
[i
][1+(M
->NbRows
-1)], M
->p
[i
][0]);
1579 L
= Matrix_Alloc(M
->NbRows
-1, M
->NbColumns
-1);
1580 for (i
= 0; i
< L
->NbRows
; ++i
)
1581 Vector_Copy(M
->p
[i
], L
->p
[i
], L
->NbColumns
);
1582 right_hermite(L
, &H
, &U
, &Q
);
1585 t
= Vector_Alloc(U
->NbColumns
);
1586 for (i
= 0; i
< U
->NbColumns
; ++i
)
1587 value_oppose(t
->p
[i
], M
->p
[i
][M
->NbColumns
-1]);
1589 *Eq
= Matrix_Alloc(H
->NbRows
- H
->NbColumns
, 2 + U
->NbColumns
);
1590 for (i
= 0; i
< H
->NbRows
- H
->NbColumns
; ++i
) {
1591 Vector_Copy(U
->p
[H
->NbColumns
+i
], (*Eq
)->p
[i
]+1, U
->NbColumns
);
1592 Inner_Product(U
->p
[H
->NbColumns
+i
], t
->p
, U
->NbColumns
,
1593 (*Eq
)->p
[i
]+1+U
->NbColumns
);
1596 ratH
= Matrix_Alloc(H
->NbColumns
+1, H
->NbColumns
+1);
1597 invH
= Matrix_Alloc(H
->NbColumns
+1, H
->NbColumns
+1);
1598 for (i
= 0; i
< H
->NbColumns
; ++i
)
1599 Vector_Copy(H
->p
[i
], ratH
->p
[i
], H
->NbColumns
);
1600 value_set_si(ratH
->p
[ratH
->NbRows
-1][ratH
->NbColumns
-1], 1);
1602 ok
= Matrix_Inverse(ratH
, invH
);
1605 Ut
= Matrix_Alloc(invH
->NbRows
, U
->NbColumns
+1);
1606 for (i
= 0; i
< Ut
->NbRows
-1; ++i
) {
1607 Vector_Copy(U
->p
[i
], Ut
->p
[i
], U
->NbColumns
);
1608 Inner_Product(U
->p
[i
], t
->p
, U
->NbColumns
, &Ut
->p
[i
][Ut
->NbColumns
-1]);
1612 value_set_si(Ut
->p
[Ut
->NbRows
-1][Ut
->NbColumns
-1], 1);
1613 inv
= Matrix_Alloc(invH
->NbRows
, Ut
->NbColumns
);
1614 Matrix_Product(invH
, Ut
, inv
);
1620 /* Check whether all rays are revlex positive in the parameters
1622 int Polyhedron_has_revlex_positive_rays(Polyhedron
*P
, unsigned nparam
)
1625 for (r
= 0; r
< P
->NbRays
; ++r
) {
1627 if (value_notzero_p(P
->Ray
[r
][P
->Dimension
+1]))
1629 for (i
= P
->Dimension
-1; i
>= P
->Dimension
-nparam
; --i
) {
1630 if (value_neg_p(P
->Ray
[r
][i
+1]))
1632 if (value_pos_p(P
->Ray
[r
][i
+1]))
1635 /* A ray independent of the parameters */
1636 if (i
< P
->Dimension
-nparam
)
1642 static Polyhedron
*Recession_Cone(Polyhedron
*P
, unsigned nparam
, unsigned MaxRays
)
1645 unsigned nvar
= P
->Dimension
- nparam
;
1646 Matrix
*M
= Matrix_Alloc(P
->NbConstraints
, 1 + nvar
+ 1);
1648 for (i
= 0; i
< P
->NbConstraints
; ++i
)
1649 Vector_Copy(P
->Constraint
[i
], M
->p
[i
], 1+nvar
);
1650 R
= Constraints2Polyhedron(M
, MaxRays
);
1655 int Polyhedron_is_unbounded(Polyhedron
*P
, unsigned nparam
, unsigned MaxRays
)
1659 Polyhedron
*R
= Recession_Cone(P
, nparam
, MaxRays
);
1660 POL_ENSURE_VERTICES(R
);
1662 for (i
= 0; i
< R
->NbRays
; ++i
)
1663 if (value_zero_p(R
->Ray
[i
][1+R
->Dimension
]))
1665 is_unbounded
= R
->NbBid
> 0 || i
< R
->NbRays
;
1667 return is_unbounded
;