3 #include <barvinok/util.h>
4 #include <barvinok/options.h>
5 #include <polylib/ranking.h>
8 #define ALLOC(type) (type*)malloc(sizeof(type))
9 #define ALLOCN(type,n) (type*)malloc((n) * sizeof(type))
12 #define NALLOC(p,n) p = (typeof(p))malloc((n) * sizeof(*p))
14 #define NALLOC(p,n) p = (void *)malloc((n) * sizeof(*p))
17 void manual_count(Polyhedron
*P
, Value
* result
)
19 Polyhedron
*U
= Universe_Polyhedron(0);
20 Enumeration
*en
= Polyhedron_Enumerate(P
,U
,1024,NULL
);
21 Value
*v
= compute_poly(en
,NULL
);
22 value_assign(*result
, *v
);
29 #include <barvinok/evalue.h>
30 #include <barvinok/util.h>
31 #include <barvinok/barvinok.h>
33 /* Return random value between 0 and max-1 inclusive
35 int random_int(int max
) {
36 return (int) (((double)(max
))*rand()/(RAND_MAX
+1.0));
39 Polyhedron
*Polyhedron_Read(unsigned MaxRays
)
42 unsigned NbRows
, NbColumns
;
47 while (fgets(s
, sizeof(s
), stdin
)) {
50 if (strncasecmp(s
, "vertices", sizeof("vertices")-1) == 0)
52 if (sscanf(s
, "%u %u", &NbRows
, &NbColumns
) == 2)
57 M
= Matrix_Alloc(NbRows
,NbColumns
);
60 P
= Rays2Polyhedron(M
, MaxRays
);
62 P
= Constraints2Polyhedron(M
, MaxRays
);
67 /* Inplace polarization
69 void Polyhedron_Polarize(Polyhedron
*P
)
71 unsigned NbRows
= P
->NbConstraints
+ P
->NbRays
;
75 q
= (Value
**)malloc(NbRows
* sizeof(Value
*));
77 for (i
= 0; i
< P
->NbRays
; ++i
)
79 for (; i
< NbRows
; ++i
)
80 q
[i
] = P
->Constraint
[i
-P
->NbRays
];
81 P
->NbConstraints
= NbRows
- P
->NbConstraints
;
82 P
->NbRays
= NbRows
- P
->NbRays
;
85 P
->Ray
= q
+ P
->NbConstraints
;
89 * Rather general polar
90 * We can optimize it significantly if we assume that
93 * Also, we calculate the polar as defined in Schrijver
94 * The opposite should probably work as well and would
95 * eliminate the need for multiplying by -1
97 Polyhedron
* Polyhedron_Polar(Polyhedron
*P
, unsigned NbMaxRays
)
101 unsigned dim
= P
->Dimension
+ 2;
102 Matrix
*M
= Matrix_Alloc(P
->NbRays
, dim
);
106 value_set_si(mone
, -1);
107 for (i
= 0; i
< P
->NbRays
; ++i
) {
108 Vector_Scale(P
->Ray
[i
], M
->p
[i
], mone
, dim
);
109 value_multiply(M
->p
[i
][0], M
->p
[i
][0], mone
);
110 value_multiply(M
->p
[i
][dim
-1], M
->p
[i
][dim
-1], mone
);
112 P
= Constraints2Polyhedron(M
, NbMaxRays
);
120 * Returns the supporting cone of P at the vertex with index v
122 Polyhedron
* supporting_cone(Polyhedron
*P
, int v
)
127 unsigned char *supporting
= (unsigned char *)malloc(P
->NbConstraints
);
128 unsigned dim
= P
->Dimension
+ 2;
130 assert(v
>=0 && v
< P
->NbRays
);
131 assert(value_pos_p(P
->Ray
[v
][dim
-1]));
135 for (i
= 0, n
= 0; i
< P
->NbConstraints
; ++i
) {
136 Inner_Product(P
->Constraint
[i
] + 1, P
->Ray
[v
] + 1, dim
- 1, &tmp
);
137 if ((supporting
[i
] = value_zero_p(tmp
)))
140 assert(n
>= dim
- 2);
142 M
= Matrix_Alloc(n
, dim
);
144 for (i
= 0, j
= 0; i
< P
->NbConstraints
; ++i
)
146 value_set_si(M
->p
[j
][dim
-1], 0);
147 Vector_Copy(P
->Constraint
[i
], M
->p
[j
++], dim
-1);
150 P
= Constraints2Polyhedron(M
, P
->NbRays
+1);
156 #define INT_BITS (sizeof(unsigned) * 8)
158 unsigned *supporting_constraints(Matrix
*Constraints
, Param_Vertices
*v
, int *n
)
160 Value lcm
, tmp
, tmp2
;
161 unsigned dim
= Constraints
->NbColumns
;
162 unsigned nparam
= v
->Vertex
->NbColumns
- 2;
163 unsigned nvar
= dim
- nparam
- 2;
164 int len
= (Constraints
->NbRows
+INT_BITS
-1)/INT_BITS
;
165 unsigned *supporting
= (unsigned *)calloc(len
, sizeof(unsigned));
172 row
= Vector_Alloc(nparam
+1);
177 value_set_si(lcm
, 1);
178 for (i
= 0, *n
= 0, ix
= 0, bx
= MSB
; i
< Constraints
->NbRows
; ++i
) {
179 Vector_Set(row
->p
, 0, nparam
+1);
180 for (j
= 0 ; j
< nvar
; ++j
) {
181 value_set_si(tmp
, 1);
182 value_assign(tmp2
, Constraints
->p
[i
][j
+1]);
183 if (value_ne(lcm
, v
->Vertex
->p
[j
][nparam
+1])) {
184 value_assign(tmp
, lcm
);
185 value_lcm(lcm
, lcm
, v
->Vertex
->p
[j
][nparam
+1]);
186 value_division(tmp
, lcm
, tmp
);
187 value_multiply(tmp2
, tmp2
, lcm
);
188 value_division(tmp2
, tmp2
, v
->Vertex
->p
[j
][nparam
+1]);
190 Vector_Combine(row
->p
, v
->Vertex
->p
[j
], row
->p
,
191 tmp
, tmp2
, nparam
+1);
193 value_set_si(tmp
, 1);
194 Vector_Combine(row
->p
, Constraints
->p
[i
]+1+nvar
, row
->p
, tmp
, lcm
, nparam
+1);
195 for (j
= 0; j
< nparam
+1; ++j
)
196 if (value_notzero_p(row
->p
[j
]))
198 if (j
== nparam
+ 1) {
199 supporting
[ix
] |= bx
;
213 Polyhedron
* supporting_cone_p(Polyhedron
*P
, Param_Vertices
*v
)
216 unsigned dim
= P
->Dimension
+ 2;
217 unsigned nparam
= v
->Vertex
->NbColumns
- 2;
218 unsigned nvar
= dim
- nparam
- 2;
222 unsigned *supporting
;
225 Polyhedron_Matrix_View(P
, &View
, P
->NbConstraints
);
226 supporting
= supporting_constraints(&View
, v
, &n
);
227 M
= Matrix_Alloc(n
, nvar
+2);
229 for (i
= 0, j
= 0, ix
= 0, bx
= MSB
; i
< P
->NbConstraints
; ++i
) {
230 if (supporting
[ix
] & bx
) {
231 value_set_si(M
->p
[j
][nvar
+1], 0);
232 Vector_Copy(P
->Constraint
[i
], M
->p
[j
++], nvar
+1);
237 P
= Constraints2Polyhedron(M
, P
->NbRays
+1);
243 Polyhedron
* triangulate_cone(Polyhedron
*P
, unsigned NbMaxCons
)
245 struct barvinok_options
*options
= barvinok_options_new_with_defaults();
246 options
->MaxRays
= NbMaxCons
;
247 P
= triangulate_cone_with_options(P
, options
);
248 barvinok_options_free(options
);
252 Polyhedron
* triangulate_cone_with_options(Polyhedron
*P
,
253 struct barvinok_options
*options
)
255 const static int MAX_TRY
=10;
258 unsigned dim
= P
->Dimension
;
259 Matrix
*M
= Matrix_Alloc(P
->NbRays
+1, dim
+3);
261 Polyhedron
*L
, *R
, *T
;
262 assert(P
->NbEq
== 0);
268 Vector_Set(M
->p
[0]+1, 0, dim
+1);
269 value_set_si(M
->p
[0][0], 1);
270 value_set_si(M
->p
[0][dim
+2], 1);
271 Vector_Set(M
->p
[P
->NbRays
]+1, 0, dim
+2);
272 value_set_si(M
->p
[P
->NbRays
][0], 1);
273 value_set_si(M
->p
[P
->NbRays
][dim
+1], 1);
275 for (i
= 0, r
= 1; i
< P
->NbRays
; ++i
) {
276 if (value_notzero_p(P
->Ray
[i
][dim
+1]))
278 Vector_Copy(P
->Ray
[i
], M
->p
[r
], dim
+1);
279 value_set_si(M
->p
[r
][dim
+2], 0);
283 M2
= Matrix_Alloc(dim
+1, dim
+2);
286 if (options
->try_Delaunay_triangulation
) {
287 /* Delaunay triangulation */
288 for (r
= 1; r
< P
->NbRays
; ++r
) {
289 Inner_Product(M
->p
[r
]+1, M
->p
[r
]+1, dim
, &tmp
);
290 value_assign(M
->p
[r
][dim
+1], tmp
);
293 L
= Rays2Polyhedron(M3
, options
->MaxRays
);
298 /* Usually R should still be 0 */
301 for (r
= 1; r
< P
->NbRays
; ++r
) {
302 value_set_si(M
->p
[r
][dim
+1], random_int((t
+1)*dim
*P
->NbRays
)+1);
305 L
= Rays2Polyhedron(M3
, options
->MaxRays
);
309 assert(t
<= MAX_TRY
);
314 POL_ENSURE_FACETS(L
);
315 for (i
= 0; i
< L
->NbConstraints
; ++i
) {
316 /* Ignore perpendicular facets, i.e., facets with 0 z-coordinate */
317 if (value_negz_p(L
->Constraint
[i
][dim
+1]))
319 if (value_notzero_p(L
->Constraint
[i
][dim
+2]))
321 for (j
= 1, r
= 1; j
< M
->NbRows
; ++j
) {
322 Inner_Product(M
->p
[j
]+1, L
->Constraint
[i
]+1, dim
+1, &tmp
);
323 if (value_notzero_p(tmp
))
327 Vector_Copy(M
->p
[j
]+1, M2
->p
[r
]+1, dim
);
328 value_set_si(M2
->p
[r
][0], 1);
329 value_set_si(M2
->p
[r
][dim
+1], 0);
333 Vector_Set(M2
->p
[0]+1, 0, dim
);
334 value_set_si(M2
->p
[0][0], 1);
335 value_set_si(M2
->p
[0][dim
+1], 1);
336 T
= Rays2Polyhedron(M2
, P
->NbConstraints
+1);
350 void check_triangulization(Polyhedron
*P
, Polyhedron
*T
)
352 Polyhedron
*C
, *D
, *E
, *F
, *G
, *U
;
353 for (C
= T
; C
; C
= C
->next
) {
357 U
= DomainConvex(DomainUnion(U
, C
, 100), 100);
358 for (D
= C
->next
; D
; D
= D
->next
) {
363 E
= DomainIntersection(C
, D
, 600);
364 assert(E
->NbRays
== 0 || E
->NbEq
>= 1);
370 assert(PolyhedronIncludes(U
, P
));
371 assert(PolyhedronIncludes(P
, U
));
374 /* Computes x, y and g such that g = gcd(a,b) and a*x+b*y = g */
375 void Extended_Euclid(Value a
, Value b
, Value
*x
, Value
*y
, Value
*g
)
377 Value c
, d
, e
, f
, tmp
;
384 value_absolute(c
, a
);
385 value_absolute(d
, b
);
388 while(value_pos_p(d
)) {
389 value_division(tmp
, c
, d
);
390 value_multiply(tmp
, tmp
, f
);
391 value_subtract(e
, e
, tmp
);
392 value_division(tmp
, c
, d
);
393 value_multiply(tmp
, tmp
, d
);
394 value_subtract(c
, c
, tmp
);
401 else if (value_pos_p(a
))
403 else value_oppose(*x
, e
);
407 value_multiply(tmp
, a
, *x
);
408 value_subtract(tmp
, c
, tmp
);
409 value_division(*y
, tmp
, b
);
418 static int unimodular_complete_1(Matrix
*m
)
420 Value g
, b
, c
, old
, tmp
;
429 value_assign(g
, m
->p
[0][0]);
430 for (i
= 1; value_zero_p(g
) && i
< m
->NbColumns
; ++i
) {
431 for (j
= 0; j
< m
->NbColumns
; ++j
) {
433 value_set_si(m
->p
[i
][j
], 1);
435 value_set_si(m
->p
[i
][j
], 0);
437 value_assign(g
, m
->p
[0][i
]);
439 for (; i
< m
->NbColumns
; ++i
) {
440 value_assign(old
, g
);
441 Extended_Euclid(old
, m
->p
[0][i
], &c
, &b
, &g
);
443 for (j
= 0; j
< m
->NbColumns
; ++j
) {
445 value_multiply(tmp
, m
->p
[0][j
], b
);
446 value_division(m
->p
[i
][j
], tmp
, old
);
448 value_assign(m
->p
[i
][j
], c
);
450 value_set_si(m
->p
[i
][j
], 0);
462 int unimodular_complete(Matrix
*M
, int row
)
469 return unimodular_complete_1(M
);
471 left_hermite(M
, &H
, &Q
, &U
);
473 for (r
= 0; ok
&& r
< row
; ++r
)
474 if (value_notone_p(H
->p
[r
][r
]))
477 for (r
= row
; r
< M
->NbRows
; ++r
)
478 Vector_Copy(Q
->p
[r
], M
->p
[r
], M
->NbColumns
);
484 * Returns a full-dimensional polyhedron with the same number
485 * of integer points as P
487 Polyhedron
*remove_equalities(Polyhedron
*P
, unsigned MaxRays
)
489 Polyhedron
*Q
= Polyhedron_Copy(P
);
490 unsigned dim
= P
->Dimension
;
497 Q
= DomainConstraintSimplify(Q
, MaxRays
);
501 m1
= Matrix_Alloc(dim
, dim
);
502 for (i
= 0; i
< Q
->NbEq
; ++i
)
503 Vector_Copy(Q
->Constraint
[i
]+1, m1
->p
[i
], dim
);
505 /* m1 may not be unimodular, but we won't be throwing anything away */
506 unimodular_complete(m1
, Q
->NbEq
);
508 m2
= Matrix_Alloc(dim
+1-Q
->NbEq
, dim
+1);
509 for (i
= Q
->NbEq
; i
< dim
; ++i
)
510 Vector_Copy(m1
->p
[i
], m2
->p
[i
-Q
->NbEq
], dim
);
511 value_set_si(m2
->p
[dim
-Q
->NbEq
][dim
], 1);
514 P
= Polyhedron_Image(Q
, m2
, MaxRays
);
522 * Returns a full-dimensional polyhedron with the same number
523 * of integer points as P
524 * nvar specifies the number of variables
525 * The remaining dimensions are assumed to be parameters
527 * factor is NbEq x (nparam+2) matrix, containing stride constraints
528 * on the parameters; column nparam is the constant;
529 * column nparam+1 is the stride
531 * if factor is NULL, only remove equalities that don't affect
532 * the number of points
534 Polyhedron
*remove_equalities_p(Polyhedron
*P
, unsigned nvar
, Matrix
**factor
,
539 unsigned dim
= P
->Dimension
;
546 m1
= Matrix_Alloc(nvar
, nvar
);
547 P
= DomainConstraintSimplify(P
, MaxRays
);
549 f
= Matrix_Alloc(P
->NbEq
, dim
-nvar
+2);
553 for (i
= 0, j
= 0; i
< P
->NbEq
; ++i
) {
554 if (First_Non_Zero(P
->Constraint
[i
]+1, nvar
) == -1)
557 Vector_Gcd(P
->Constraint
[i
]+1, nvar
, &g
);
558 if (!factor
&& value_notone_p(g
))
562 Vector_Copy(P
->Constraint
[i
]+1+nvar
, f
->p
[j
], dim
-nvar
+1);
563 value_assign(f
->p
[j
][dim
-nvar
+1], g
);
566 Vector_Copy(P
->Constraint
[i
]+1, m1
->p
[j
], nvar
);
572 unimodular_complete(m1
, j
);
574 m2
= Matrix_Alloc(dim
+1-j
, dim
+1);
575 for (i
= 0; i
< nvar
-j
; ++i
)
576 Vector_Copy(m1
->p
[i
+j
], m2
->p
[i
], nvar
);
578 for (i
= nvar
-j
; i
<= dim
-j
; ++i
)
579 value_set_si(m2
->p
[i
][i
+j
], 1);
581 Q
= Polyhedron_Image(P
, m2
, MaxRays
);
588 void Line_Length(Polyhedron
*P
, Value
*len
)
594 assert(P
->Dimension
== 1);
600 for (i
= 0; i
< P
->NbConstraints
; ++i
) {
601 value_oppose(tmp
, P
->Constraint
[i
][2]);
602 if (value_pos_p(P
->Constraint
[i
][1])) {
603 mpz_cdiv_q(tmp
, tmp
, P
->Constraint
[i
][1]);
604 if (!p
|| value_gt(tmp
, pos
))
605 value_assign(pos
, tmp
);
607 } else if (value_neg_p(P
->Constraint
[i
][1])) {
608 mpz_fdiv_q(tmp
, tmp
, P
->Constraint
[i
][1]);
609 if (!n
|| value_lt(tmp
, neg
))
610 value_assign(neg
, tmp
);
614 value_subtract(tmp
, neg
, pos
);
615 value_increment(*len
, tmp
);
617 value_set_si(*len
, -1);
626 * Factors the polyhedron P into polyhedra Q_i such that
627 * the number of integer points in P is equal to the product
628 * of the number of integer points in the individual Q_i
630 * If no factors can be found, NULL is returned.
631 * Otherwise, a linked list of the factors is returned.
633 * If there are factors and if T is not NULL, then a matrix will be
634 * returned through T expressing the old variables in terms of the
635 * new variables as they appear in the sequence of factors.
637 * The algorithm works by first computing the Hermite normal form
638 * and then grouping columns linked by one or more constraints together,
639 * where a constraints "links" two or more columns if the constraint
640 * has nonzero coefficients in the columns.
642 Polyhedron
* Polyhedron_Factor(Polyhedron
*P
, unsigned nparam
, Matrix
**T
,
646 Matrix
*M
, *H
, *Q
, *U
;
647 int *pos
; /* for each column: row position of pivot */
648 int *group
; /* group to which a column belongs */
649 int *cnt
; /* number of columns in the group */
650 int *rowgroup
; /* group to which a constraint belongs */
651 int nvar
= P
->Dimension
- nparam
;
652 Polyhedron
*F
= NULL
;
660 NALLOC(rowgroup
, P
->NbConstraints
);
662 M
= Matrix_Alloc(P
->NbConstraints
, nvar
);
663 for (i
= 0; i
< P
->NbConstraints
; ++i
)
664 Vector_Copy(P
->Constraint
[i
]+1, M
->p
[i
], nvar
);
665 left_hermite(M
, &H
, &Q
, &U
);
669 for (i
= 0; i
< P
->NbConstraints
; ++i
)
671 for (i
= 0, j
= 0; i
< H
->NbColumns
; ++i
) {
672 for ( ; j
< H
->NbRows
; ++j
)
673 if (value_notzero_p(H
->p
[j
][i
]))
675 assert (j
< H
->NbRows
);
678 for (i
= 0; i
< nvar
; ++i
) {
682 for (i
= 0; i
< H
->NbColumns
&& cnt
[0] < nvar
; ++i
) {
683 if (rowgroup
[pos
[i
]] == -1)
684 rowgroup
[pos
[i
]] = i
;
685 for (j
= pos
[i
]+1; j
< H
->NbRows
; ++j
) {
686 if (value_zero_p(H
->p
[j
][i
]))
688 if (rowgroup
[j
] != -1)
690 rowgroup
[j
] = group
[i
];
691 for (k
= i
+1; k
< H
->NbColumns
&& j
>= pos
[k
]; ++k
) {
696 if (group
[k
] != group
[i
] && value_notzero_p(H
->p
[j
][k
])) {
697 assert(cnt
[group
[k
]] != 0);
698 assert(cnt
[group
[i
]] != 0);
699 if (group
[i
] < group
[k
]) {
700 cnt
[group
[i
]] += cnt
[group
[k
]];
704 cnt
[group
[k
]] += cnt
[group
[i
]];
713 if (cnt
[0] != nvar
) {
714 /* Extract out pure context constraints separately */
715 Polyhedron
**next
= &F
;
718 *T
= Matrix_Alloc(nvar
, nvar
);
719 for (i
= nparam
? -1 : 0; i
< nvar
; ++i
) {
723 for (j
= 0, k
= 0; j
< P
->NbConstraints
; ++j
)
724 if (rowgroup
[j
] == -1) {
725 if (First_Non_Zero(P
->Constraint
[j
]+1+nvar
,
738 for (j
= 0, k
= 0; j
< P
->NbConstraints
; ++j
)
739 if (rowgroup
[j
] >= 0 && group
[rowgroup
[j
]] == i
) {
746 for (j
= 0; j
< nvar
; ++j
) {
748 for (l
= 0, m
= 0; m
< d
; ++l
) {
751 value_assign((*T
)->p
[j
][tot_d
+m
++], U
->p
[j
][l
]);
755 M
= Matrix_Alloc(k
, d
+nparam
+2);
756 for (j
= 0, k
= 0; j
< P
->NbConstraints
; ++j
) {
758 if (rowgroup
[j
] != i
)
760 value_assign(M
->p
[k
][0], P
->Constraint
[j
][0]);
761 for (l
= 0, m
= 0; m
< d
; ++l
) {
764 value_assign(M
->p
[k
][1+m
++], H
->p
[j
][l
]);
766 Vector_Copy(P
->Constraint
[j
]+1+nvar
, M
->p
[k
]+1+m
, nparam
+1);
769 *next
= Constraints2Polyhedron(M
, NbMaxRays
);
770 next
= &(*next
)->next
;
785 * Project on final dim dimensions
787 Polyhedron
* Polyhedron_Project(Polyhedron
*P
, int dim
)
790 int remove
= P
->Dimension
- dim
;
794 if (P
->Dimension
== dim
)
795 return Polyhedron_Copy(P
);
797 T
= Matrix_Alloc(dim
+1, P
->Dimension
+1);
798 for (i
= 0; i
< dim
+1; ++i
)
799 value_set_si(T
->p
[i
][i
+remove
], 1);
800 I
= Polyhedron_Image(P
, T
, P
->NbConstraints
);
805 /* Constructs a new constraint that ensures that
806 * the first constraint is (strictly) smaller than
809 static void smaller_constraint(Value
*a
, Value
*b
, Value
*c
, int pos
, int shift
,
810 int len
, int strict
, Value
*tmp
)
812 value_oppose(*tmp
, b
[pos
+1]);
813 value_set_si(c
[0], 1);
814 Vector_Combine(a
+1+shift
, b
+1+shift
, c
+1, *tmp
, a
[pos
+1], len
-shift
-1);
816 value_decrement(c
[len
-shift
-1], c
[len
-shift
-1]);
817 ConstraintSimplify(c
, c
, len
-shift
, tmp
);
821 /* For each pair of lower and upper bounds on the first variable,
822 * calls fn with the set of constraints on the remaining variables
823 * where these bounds are active, i.e., (stricly) larger/smaller than
824 * the other lower/upper bounds, the lower and upper bound and the
827 * If the first variable is equal to an affine combination of the
828 * other variables then fn is called with both lower and upper
829 * pointing to the corresponding equality.
831 void for_each_lower_upper_bound(Polyhedron
*P
, for_each_lower_upper_bound_fn fn
,
834 unsigned dim
= P
->Dimension
;
841 if (value_zero_p(P
->Constraint
[0][0]) &&
842 value_notzero_p(P
->Constraint
[0][1])) {
843 M
= Matrix_Alloc(P
->NbConstraints
-1, dim
-1+2);
844 for (i
= 1; i
< P
->NbConstraints
; ++i
) {
845 value_assign(M
->p
[i
-1][0], P
->Constraint
[i
][0]);
846 Vector_Copy(P
->Constraint
[i
]+2, M
->p
[i
-1]+1, dim
);
848 fn(M
, P
->Constraint
[0], P
->Constraint
[0], cb_data
);
854 pos
= ALLOCN(int, P
->NbConstraints
);
856 for (i
= 0, z
= 0; i
< P
->NbConstraints
; ++i
)
857 if (value_zero_p(P
->Constraint
[i
][1]))
858 pos
[P
->NbConstraints
-1 - z
++] = i
;
859 /* put those with positive coefficients first; number: p */
860 for (i
= 0, p
= 0, n
= P
->NbConstraints
-z
-1; i
< P
->NbConstraints
; ++i
)
861 if (value_pos_p(P
->Constraint
[i
][1]))
863 else if (value_neg_p(P
->Constraint
[i
][1]))
865 n
= P
->NbConstraints
-z
-p
;
866 assert (p
>= 1 && n
>= 1);
868 M
= Matrix_Alloc((p
-1) + (n
-1) + z
+ 1, dim
-1+2);
869 for (i
= 0; i
< z
; ++i
) {
870 value_assign(M
->p
[i
][0], P
->Constraint
[pos
[P
->NbConstraints
-1 - i
]][0]);
871 Vector_Copy(P
->Constraint
[pos
[P
->NbConstraints
-1 - i
]]+2,
874 for (k
= 0; k
< p
; ++k
) {
875 for (k2
= 0; k2
< p
; ++k2
) {
878 q
= 1 + z
+ k2
- (k2
> k
);
880 P
->Constraint
[pos
[k
]],
881 P
->Constraint
[pos
[k2
]],
882 M
->p
[q
], 0, 1, dim
+2, k2
> k
, &g
);
884 for (l
= p
; l
< p
+n
; ++l
) {
885 for (l2
= p
; l2
< p
+n
; ++l2
) {
888 q
= 1 + z
+ l2
-1 - (l2
> l
);
890 P
->Constraint
[pos
[l2
]],
891 P
->Constraint
[pos
[l
]],
892 M
->p
[q
], 0, 1, dim
+2, l2
> l
, &g
);
894 smaller_constraint(P
->Constraint
[pos
[k
]],
895 P
->Constraint
[pos
[l
]],
896 M
->p
[z
], 0, 1, dim
+2, 0, &g
);
897 fn(M
, P
->Constraint
[pos
[k
]], P
->Constraint
[pos
[l
]], cb_data
);
906 struct section
{ Polyhedron
* D
; evalue E
; };
916 static void PLL_cb(Matrix
*M
, Value
*lower
, Value
*upper
, void *cb_data
)
918 struct PLL_data
*data
= (struct PLL_data
*)cb_data
;
919 unsigned dim
= M
->NbColumns
-1;
925 T
= Constraints2Polyhedron(M2
, data
->MaxRays
);
927 data
->s
[data
->nd
].D
= DomainIntersection(T
, data
->C
, data
->MaxRays
);
930 POL_ENSURE_VERTICES(data
->s
[data
->nd
].D
);
931 if (emptyQ(data
->s
[data
->nd
].D
)) {
932 Polyhedron_Free(data
->s
[data
->nd
].D
);
935 L
= bv_ceil3(lower
+1+1, dim
-1+1, lower
[0+1], data
->s
[data
->nd
].D
);
936 U
= bv_ceil3(upper
+1+1, dim
-1+1, upper
[0+1], data
->s
[data
->nd
].D
);
938 eadd(&data
->mone
, U
);
939 emul(&data
->mone
, U
);
940 data
->s
[data
->nd
].E
= *U
;
946 static evalue
*ParamLine_Length_mod(Polyhedron
*P
, Polyhedron
*C
, unsigned MaxRays
)
948 unsigned dim
= P
->Dimension
;
949 unsigned nvar
= dim
- C
->Dimension
;
950 int ssize
= (P
->NbConstraints
+1) * (P
->NbConstraints
+1) / 4;
951 struct PLL_data data
;
957 value_init(data
.mone
.d
);
958 evalue_set_si(&data
.mone
, -1, 1);
960 data
.s
= ALLOCN(struct section
, ssize
);
962 data
.MaxRays
= MaxRays
;
964 for_each_lower_upper_bound(P
, PLL_cb
, &data
);
968 value_set_si(F
->d
, 0);
969 F
->x
.p
= new_enode(partition
, 2*data
.nd
, dim
-nvar
);
970 for (k
= 0; k
< data
.nd
; ++k
) {
971 EVALUE_SET_DOMAIN(F
->x
.p
->arr
[2*k
], data
.s
[k
].D
);
972 value_clear(F
->x
.p
->arr
[2*k
+1].d
);
973 F
->x
.p
->arr
[2*k
+1] = data
.s
[k
].E
;
977 free_evalue_refs(&data
.mone
);
982 evalue
* ParamLine_Length(Polyhedron
*P
, Polyhedron
*C
,
983 struct barvinok_options
*options
)
986 tmp
= ParamLine_Length_mod(P
, C
, options
->MaxRays
);
987 if (options
->lookup_table
) {
988 evalue_mod2table(tmp
, C
->Dimension
);
994 Bool
isIdentity(Matrix
*M
)
997 if (M
->NbRows
!= M
->NbColumns
)
1000 for (i
= 0;i
< M
->NbRows
; i
++)
1001 for (j
= 0; j
< M
->NbColumns
; j
++)
1003 if(value_notone_p(M
->p
[i
][j
]))
1006 if(value_notzero_p(M
->p
[i
][j
]))
1012 void Param_Polyhedron_Print(FILE* DST
, Param_Polyhedron
*PP
, char **param_names
)
1017 for(P
=PP
->D
;P
;P
=P
->next
) {
1019 /* prints current val. dom. */
1020 fprintf(DST
, "---------------------------------------\n");
1021 fprintf(DST
, "Domain :\n");
1022 Print_Domain(DST
, P
->Domain
, param_names
);
1024 /* scan the vertices */
1025 fprintf(DST
, "Vertices :\n");
1026 FORALL_PVertex_in_ParamPolyhedron(V
,P
,PP
) {
1028 /* prints each vertex */
1029 Print_Vertex(DST
, V
->Vertex
, param_names
);
1032 END_FORALL_PVertex_in_ParamPolyhedron
;
1036 void Enumeration_Print(FILE *Dst
, Enumeration
*en
, const char * const *params
)
1038 for (; en
; en
= en
->next
) {
1039 Print_Domain(Dst
, en
->ValidityDomain
, params
);
1040 print_evalue(Dst
, &en
->EP
, params
);
1044 void Enumeration_Free(Enumeration
*en
)
1050 free_evalue_refs( &(en
->EP
) );
1051 Domain_Free( en
->ValidityDomain
);
1058 void Enumeration_mod2table(Enumeration
*en
, unsigned nparam
)
1060 for (; en
; en
= en
->next
) {
1061 evalue_mod2table(&en
->EP
, nparam
);
1062 reduce_evalue(&en
->EP
);
1066 size_t Enumeration_size(Enumeration
*en
)
1070 for (; en
; en
= en
->next
) {
1071 s
+= domain_size(en
->ValidityDomain
);
1072 s
+= evalue_size(&en
->EP
);
1077 void Free_ParamNames(char **params
, int m
)
1084 /* Check whether every set in D2 is included in some set of D1 */
1085 int DomainIncludes(Polyhedron
*D1
, Polyhedron
*D2
)
1087 for ( ; D2
; D2
= D2
->next
) {
1089 for (P1
= D1
; P1
; P1
= P1
->next
)
1090 if (PolyhedronIncludes(P1
, D2
))
1098 int line_minmax(Polyhedron
*I
, Value
*min
, Value
*max
)
1103 value_oppose(I
->Constraint
[0][2], I
->Constraint
[0][2]);
1104 /* There should never be a remainder here */
1105 if (value_pos_p(I
->Constraint
[0][1]))
1106 mpz_fdiv_q(*min
, I
->Constraint
[0][2], I
->Constraint
[0][1]);
1108 mpz_fdiv_q(*min
, I
->Constraint
[0][2], I
->Constraint
[0][1]);
1109 value_assign(*max
, *min
);
1110 } else for (i
= 0; i
< I
->NbConstraints
; ++i
) {
1111 if (value_zero_p(I
->Constraint
[i
][1])) {
1116 value_oppose(I
->Constraint
[i
][2], I
->Constraint
[i
][2]);
1117 if (value_pos_p(I
->Constraint
[i
][1]))
1118 mpz_cdiv_q(*min
, I
->Constraint
[i
][2], I
->Constraint
[i
][1]);
1120 mpz_fdiv_q(*max
, I
->Constraint
[i
][2], I
->Constraint
[i
][1]);
1128 PROCEDURES TO COMPUTE ENUMERATION. recursive procedure, recurse for
1131 @param pos index position of current loop index (1..hdim-1)
1132 @param P loop domain
1133 @param context context values for fixed indices
1134 @param exist number of existential variables
1135 @return the number of integer points in this
1139 void count_points_e (int pos
, Polyhedron
*P
, int exist
, int nparam
,
1140 Value
*context
, Value
*res
)
1145 value_set_si(*res
, 0);
1150 count_points(pos
, P
, context
, res
);
1154 value_init(LB
); value_init(UB
); value_init(k
);
1158 if (lower_upper_bounds(pos
,P
,context
,&LB
,&UB
) !=0) {
1159 /* Problem if UB or LB is INFINITY */
1160 value_clear(LB
); value_clear(UB
); value_clear(k
);
1161 if (pos
> P
->Dimension
- nparam
- exist
)
1162 value_set_si(*res
, 1);
1164 value_set_si(*res
, -1);
1171 for (value_assign(k
,LB
); value_le(k
,UB
); value_increment(k
,k
)) {
1172 fprintf(stderr
, "(");
1173 for (i
=1; i
<pos
; i
++) {
1174 value_print(stderr
,P_VALUE_FMT
,context
[i
]);
1175 fprintf(stderr
,",");
1177 value_print(stderr
,P_VALUE_FMT
,k
);
1178 fprintf(stderr
,")\n");
1183 value_set_si(context
[pos
],0);
1184 if (value_lt(UB
,LB
)) {
1185 value_clear(LB
); value_clear(UB
); value_clear(k
);
1186 value_set_si(*res
, 0);
1191 value_set_si(*res
, 1);
1193 value_subtract(k
,UB
,LB
);
1194 value_add_int(k
,k
,1);
1195 value_assign(*res
, k
);
1197 value_clear(LB
); value_clear(UB
); value_clear(k
);
1201 /*-----------------------------------------------------------------*/
1202 /* Optimization idea */
1203 /* If inner loops are not a function of k (the current index) */
1204 /* i.e. if P->Constraint[i][pos]==0 for all P following this and */
1206 /* Then CNT = (UB-LB+1)*count_points(pos+1, P->next, context) */
1207 /* (skip the for loop) */
1208 /*-----------------------------------------------------------------*/
1211 value_set_si(*res
, 0);
1212 for (value_assign(k
,LB
);value_le(k
,UB
);value_increment(k
,k
)) {
1213 /* Insert k in context */
1214 value_assign(context
[pos
],k
);
1215 count_points_e(pos
+1, P
->next
, exist
, nparam
, context
, &c
);
1216 if(value_notmone_p(c
))
1217 value_addto(*res
, *res
, c
);
1219 value_set_si(*res
, -1);
1222 if (pos
> P
->Dimension
- nparam
- exist
&&
1229 fprintf(stderr
,"%d\n",CNT
);
1233 value_set_si(context
[pos
],0);
1234 value_clear(LB
); value_clear(UB
); value_clear(k
);
1236 } /* count_points_e */
1238 int DomainContains(Polyhedron
*P
, Value
*list_args
, int len
,
1239 unsigned MaxRays
, int set
)
1244 if (P
->Dimension
== len
)
1245 return in_domain(P
, list_args
);
1247 assert(set
); // assume list_args is large enough
1248 assert((P
->Dimension
- len
) % 2 == 0);
1250 for (i
= 0; i
< P
->Dimension
- len
; i
+= 2) {
1252 for (j
= 0 ; j
< P
->NbEq
; ++j
)
1253 if (value_notzero_p(P
->Constraint
[j
][1+len
+i
]))
1255 assert(j
< P
->NbEq
);
1256 value_absolute(m
, P
->Constraint
[j
][1+len
+i
]);
1257 k
= First_Non_Zero(P
->Constraint
[j
]+1, len
);
1259 assert(First_Non_Zero(P
->Constraint
[j
]+1+k
+1, len
- k
- 1) == -1);
1260 mpz_fdiv_q(list_args
[len
+i
], list_args
[k
], m
);
1261 mpz_fdiv_r(list_args
[len
+i
+1], list_args
[k
], m
);
1265 return in_domain(P
, list_args
);
1268 Polyhedron
*DomainConcat(Polyhedron
*head
, Polyhedron
*tail
)
1273 for (S
= head
; S
->next
; S
= S
->next
)
1279 evalue
*barvinok_lexsmaller_ev(Polyhedron
*P
, Polyhedron
*D
, unsigned dim
,
1280 Polyhedron
*C
, unsigned MaxRays
)
1283 Polyhedron
*RC
, *RD
, *Q
;
1284 unsigned nparam
= dim
+ C
->Dimension
;
1288 RC
= LexSmaller(P
, D
, dim
, C
, MaxRays
);
1292 exist
= RD
->Dimension
- nparam
- dim
;
1293 CA
= align_context(RC
, RD
->Dimension
, MaxRays
);
1294 Q
= DomainIntersection(RD
, CA
, MaxRays
);
1295 Polyhedron_Free(CA
);
1297 Polyhedron_Free(RC
);
1300 for (Q
= RD
; Q
; Q
= Q
->next
) {
1302 Polyhedron
*next
= Q
->next
;
1305 t
= barvinok_enumerate_e(Q
, exist
, nparam
, MaxRays
);
1322 Enumeration
*barvinok_lexsmaller(Polyhedron
*P
, Polyhedron
*D
, unsigned dim
,
1323 Polyhedron
*C
, unsigned MaxRays
)
1325 evalue
*EP
= barvinok_lexsmaller_ev(P
, D
, dim
, C
, MaxRays
);
1327 return partition2enumeration(EP
);
1330 /* "align" matrix to have nrows by inserting
1331 * the necessary number of rows and an equal number of columns in front
1333 Matrix
*align_matrix(Matrix
*M
, int nrows
)
1336 int newrows
= nrows
- M
->NbRows
;
1337 Matrix
*M2
= Matrix_Alloc(nrows
, newrows
+ M
->NbColumns
);
1338 for (i
= 0; i
< newrows
; ++i
)
1339 value_set_si(M2
->p
[i
][i
], 1);
1340 for (i
= 0; i
< M
->NbRows
; ++i
)
1341 Vector_Copy(M
->p
[i
], M2
->p
[newrows
+i
]+newrows
, M
->NbColumns
);
1345 static void print_varlist(FILE *out
, int n
, char **names
)
1349 for (i
= 0; i
< n
; ++i
) {
1352 fprintf(out
, "%s", names
[i
]);
1357 static void print_term(FILE *out
, Value v
, int pos
, int dim
, int nparam
,
1358 char **iter_names
, char **param_names
, int *first
)
1360 if (value_zero_p(v
)) {
1361 if (first
&& *first
&& pos
>= dim
+ nparam
)
1367 if (!*first
&& value_pos_p(v
))
1371 if (pos
< dim
+ nparam
) {
1372 if (value_mone_p(v
))
1374 else if (!value_one_p(v
))
1375 value_print(out
, VALUE_FMT
, v
);
1377 fprintf(out
, "%s", iter_names
[pos
]);
1379 fprintf(out
, "%s", param_names
[pos
-dim
]);
1381 value_print(out
, VALUE_FMT
, v
);
1384 char **util_generate_names(int n
, const char *prefix
)
1387 int len
= (prefix
? strlen(prefix
) : 0) + 10;
1388 char **names
= ALLOCN(char*, n
);
1390 fprintf(stderr
, "ERROR: memory overflow.\n");
1393 for (i
= 0; i
< n
; ++i
) {
1394 names
[i
] = ALLOCN(char, len
);
1396 fprintf(stderr
, "ERROR: memory overflow.\n");
1400 snprintf(names
[i
], len
, "%d", i
);
1402 snprintf(names
[i
], len
, "%s%d", prefix
, i
);
1408 void util_free_names(int n
, char **names
)
1411 for (i
= 0; i
< n
; ++i
)
1416 void Polyhedron_pprint(FILE *out
, Polyhedron
*P
, int dim
, int nparam
,
1417 char **iter_names
, char **param_names
)
1422 assert(dim
+ nparam
== P
->Dimension
);
1428 print_varlist(out
, nparam
, param_names
);
1429 fprintf(out
, " -> ");
1431 print_varlist(out
, dim
, iter_names
);
1432 fprintf(out
, " : ");
1435 fprintf(out
, "FALSE");
1436 else for (i
= 0; i
< P
->NbConstraints
; ++i
) {
1438 int v
= First_Non_Zero(P
->Constraint
[i
]+1, P
->Dimension
);
1439 if (v
== -1 && value_pos_p(P
->Constraint
[i
][0]))
1442 fprintf(out
, " && ");
1443 if (v
== -1 && value_notzero_p(P
->Constraint
[i
][1+P
->Dimension
]))
1444 fprintf(out
, "FALSE");
1445 else if (value_pos_p(P
->Constraint
[i
][v
+1])) {
1446 print_term(out
, P
->Constraint
[i
][v
+1], v
, dim
, nparam
,
1447 iter_names
, param_names
, NULL
);
1448 if (value_zero_p(P
->Constraint
[i
][0]))
1449 fprintf(out
, " = ");
1451 fprintf(out
, " >= ");
1452 for (j
= v
+1; j
<= dim
+nparam
; ++j
) {
1453 value_oppose(tmp
, P
->Constraint
[i
][1+j
]);
1454 print_term(out
, tmp
, j
, dim
, nparam
,
1455 iter_names
, param_names
, &first
);
1458 value_oppose(tmp
, P
->Constraint
[i
][1+v
]);
1459 print_term(out
, tmp
, v
, dim
, nparam
,
1460 iter_names
, param_names
, NULL
);
1461 fprintf(out
, " <= ");
1462 for (j
= v
+1; j
<= dim
+nparam
; ++j
)
1463 print_term(out
, P
->Constraint
[i
][1+j
], j
, dim
, nparam
,
1464 iter_names
, param_names
, &first
);
1468 fprintf(out
, " }\n");
1473 /* Construct a cone over P with P placed at x_d = 1, with
1474 * x_d the coordinate of an extra dimension
1476 * It's probably a mistake to depend so much on the internal
1477 * representation. We should probably simply compute the
1478 * vertices/facets first.
1480 Polyhedron
*Cone_over_Polyhedron(Polyhedron
*P
)
1482 unsigned NbConstraints
= 0;
1483 unsigned NbRays
= 0;
1487 if (POL_HAS(P
, POL_INEQUALITIES
))
1488 NbConstraints
= P
->NbConstraints
+ 1;
1489 if (POL_HAS(P
, POL_POINTS
))
1490 NbRays
= P
->NbRays
+ 1;
1492 C
= Polyhedron_Alloc(P
->Dimension
+1, NbConstraints
, NbRays
);
1493 if (POL_HAS(P
, POL_INEQUALITIES
)) {
1495 for (i
= 0; i
< P
->NbConstraints
; ++i
)
1496 Vector_Copy(P
->Constraint
[i
], C
->Constraint
[i
], P
->Dimension
+2);
1498 value_set_si(C
->Constraint
[P
->NbConstraints
][0], 1);
1499 value_set_si(C
->Constraint
[P
->NbConstraints
][1+P
->Dimension
], 1);
1501 if (POL_HAS(P
, POL_POINTS
)) {
1502 C
->NbBid
= P
->NbBid
;
1503 for (i
= 0; i
< P
->NbRays
; ++i
)
1504 Vector_Copy(P
->Ray
[i
], C
->Ray
[i
], P
->Dimension
+2);
1506 value_set_si(C
->Ray
[P
->NbRays
][0], 1);
1507 value_set_si(C
->Ray
[P
->NbRays
][1+C
->Dimension
], 1);
1509 POL_SET(C
, POL_VALID
);
1510 if (POL_HAS(P
, POL_INEQUALITIES
))
1511 POL_SET(C
, POL_INEQUALITIES
);
1512 if (POL_HAS(P
, POL_POINTS
))
1513 POL_SET(C
, POL_POINTS
);
1514 if (POL_HAS(P
, POL_VERTICES
))
1515 POL_SET(C
, POL_VERTICES
);
1519 /* Returns a (dim+nparam+1)x((dim-n)+nparam+1) matrix
1520 * mapping the transformed subspace back to the original space.
1521 * n is the number of equalities involving the variables
1522 * (i.e., not purely the parameters).
1523 * The remaining n coordinates in the transformed space would
1524 * have constant (parametric) values and are therefore not
1525 * included in the variables of the new space.
1527 Matrix
*compress_variables(Matrix
*Equalities
, unsigned nparam
)
1529 unsigned dim
= (Equalities
->NbColumns
-2) - nparam
;
1530 Matrix
*M
, *H
, *Q
, *U
, *C
, *ratH
, *invH
, *Ul
, *T1
, *T2
, *T
;
1535 for (n
= 0; n
< Equalities
->NbRows
; ++n
)
1536 if (First_Non_Zero(Equalities
->p
[n
]+1, dim
) == -1)
1539 return Identity(dim
+nparam
+1);
1541 value_set_si(mone
, -1);
1542 M
= Matrix_Alloc(n
, dim
);
1543 C
= Matrix_Alloc(n
+1, nparam
+1);
1544 for (i
= 0; i
< n
; ++i
) {
1545 Vector_Copy(Equalities
->p
[i
]+1, M
->p
[i
], dim
);
1546 Vector_Scale(Equalities
->p
[i
]+1+dim
, C
->p
[i
], mone
, nparam
+1);
1548 value_set_si(C
->p
[n
][nparam
], 1);
1549 left_hermite(M
, &H
, &Q
, &U
);
1554 ratH
= Matrix_Alloc(n
+1, n
+1);
1555 invH
= Matrix_Alloc(n
+1, n
+1);
1556 for (i
= 0; i
< n
; ++i
)
1557 Vector_Copy(H
->p
[i
], ratH
->p
[i
], n
);
1558 value_set_si(ratH
->p
[n
][n
], 1);
1559 ok
= Matrix_Inverse(ratH
, invH
);
1563 T1
= Matrix_Alloc(n
+1, nparam
+1);
1564 Matrix_Product(invH
, C
, T1
);
1567 if (value_notone_p(T1
->p
[n
][nparam
])) {
1568 for (i
= 0; i
< n
; ++i
) {
1569 if (!mpz_divisible_p(T1
->p
[i
][nparam
], T1
->p
[n
][nparam
])) {
1574 /* compress_params should have taken care of this */
1575 for (j
= 0; j
< nparam
; ++j
)
1576 assert(mpz_divisible_p(T1
->p
[i
][j
], T1
->p
[n
][nparam
]));
1577 Vector_AntiScale(T1
->p
[i
], T1
->p
[i
], T1
->p
[n
][nparam
], nparam
+1);
1579 value_set_si(T1
->p
[n
][nparam
], 1);
1581 Ul
= Matrix_Alloc(dim
+1, n
+1);
1582 for (i
= 0; i
< dim
; ++i
)
1583 Vector_Copy(U
->p
[i
], Ul
->p
[i
], n
);
1584 value_set_si(Ul
->p
[dim
][n
], 1);
1585 T2
= Matrix_Alloc(dim
+1, nparam
+1);
1586 Matrix_Product(Ul
, T1
, T2
);
1590 T
= Matrix_Alloc(dim
+nparam
+1, (dim
-n
)+nparam
+1);
1591 for (i
= 0; i
< dim
; ++i
) {
1592 Vector_Copy(U
->p
[i
]+n
, T
->p
[i
], dim
-n
);
1593 Vector_Copy(T2
->p
[i
], T
->p
[i
]+dim
-n
, nparam
+1);
1595 for (i
= 0; i
< nparam
+1; ++i
)
1596 value_set_si(T
->p
[dim
+i
][(dim
-n
)+i
], 1);
1597 assert(value_one_p(T2
->p
[dim
][nparam
]));
1604 /* Computes the left inverse of an affine embedding M and, if Eq is not NULL,
1605 * the equalities that define the affine subspace onto which M maps
1608 Matrix
*left_inverse(Matrix
*M
, Matrix
**Eq
)
1611 Matrix
*L
, *H
, *Q
, *U
, *ratH
, *invH
, *Ut
, *inv
;
1614 if (M
->NbColumns
== 1) {
1615 inv
= Matrix_Alloc(1, M
->NbRows
);
1616 value_set_si(inv
->p
[0][M
->NbRows
-1], 1);
1618 *Eq
= Matrix_Alloc(M
->NbRows
-1, 1+(M
->NbRows
-1)+1);
1619 for (i
= 0; i
< M
->NbRows
-1; ++i
) {
1620 value_oppose((*Eq
)->p
[i
][1+i
], M
->p
[M
->NbRows
-1][0]);
1621 value_assign((*Eq
)->p
[i
][1+(M
->NbRows
-1)], M
->p
[i
][0]);
1628 L
= Matrix_Alloc(M
->NbRows
-1, M
->NbColumns
-1);
1629 for (i
= 0; i
< L
->NbRows
; ++i
)
1630 Vector_Copy(M
->p
[i
], L
->p
[i
], L
->NbColumns
);
1631 right_hermite(L
, &H
, &U
, &Q
);
1634 t
= Vector_Alloc(U
->NbColumns
);
1635 for (i
= 0; i
< U
->NbColumns
; ++i
)
1636 value_oppose(t
->p
[i
], M
->p
[i
][M
->NbColumns
-1]);
1638 *Eq
= Matrix_Alloc(H
->NbRows
- H
->NbColumns
, 2 + U
->NbColumns
);
1639 for (i
= 0; i
< H
->NbRows
- H
->NbColumns
; ++i
) {
1640 Vector_Copy(U
->p
[H
->NbColumns
+i
], (*Eq
)->p
[i
]+1, U
->NbColumns
);
1641 Inner_Product(U
->p
[H
->NbColumns
+i
], t
->p
, U
->NbColumns
,
1642 (*Eq
)->p
[i
]+1+U
->NbColumns
);
1645 ratH
= Matrix_Alloc(H
->NbColumns
+1, H
->NbColumns
+1);
1646 invH
= Matrix_Alloc(H
->NbColumns
+1, H
->NbColumns
+1);
1647 for (i
= 0; i
< H
->NbColumns
; ++i
)
1648 Vector_Copy(H
->p
[i
], ratH
->p
[i
], H
->NbColumns
);
1649 value_set_si(ratH
->p
[ratH
->NbRows
-1][ratH
->NbColumns
-1], 1);
1651 ok
= Matrix_Inverse(ratH
, invH
);
1654 Ut
= Matrix_Alloc(invH
->NbRows
, U
->NbColumns
+1);
1655 for (i
= 0; i
< Ut
->NbRows
-1; ++i
) {
1656 Vector_Copy(U
->p
[i
], Ut
->p
[i
], U
->NbColumns
);
1657 Inner_Product(U
->p
[i
], t
->p
, U
->NbColumns
, &Ut
->p
[i
][Ut
->NbColumns
-1]);
1661 value_set_si(Ut
->p
[Ut
->NbRows
-1][Ut
->NbColumns
-1], 1);
1662 inv
= Matrix_Alloc(invH
->NbRows
, Ut
->NbColumns
);
1663 Matrix_Product(invH
, Ut
, inv
);
1669 /* Check whether all rays are revlex positive in the parameters
1671 int Polyhedron_has_revlex_positive_rays(Polyhedron
*P
, unsigned nparam
)
1674 for (r
= 0; r
< P
->NbRays
; ++r
) {
1676 if (value_notzero_p(P
->Ray
[r
][P
->Dimension
+1]))
1678 for (i
= P
->Dimension
-1; i
>= P
->Dimension
-nparam
; --i
) {
1679 if (value_neg_p(P
->Ray
[r
][i
+1]))
1681 if (value_pos_p(P
->Ray
[r
][i
+1]))
1684 /* A ray independent of the parameters */
1685 if (i
< P
->Dimension
-nparam
)
1691 static Polyhedron
*Recession_Cone(Polyhedron
*P
, unsigned nparam
, unsigned MaxRays
)
1694 unsigned nvar
= P
->Dimension
- nparam
;
1695 Matrix
*M
= Matrix_Alloc(P
->NbConstraints
, 1 + nvar
+ 1);
1697 for (i
= 0; i
< P
->NbConstraints
; ++i
)
1698 Vector_Copy(P
->Constraint
[i
], M
->p
[i
], 1+nvar
);
1699 R
= Constraints2Polyhedron(M
, MaxRays
);
1704 int Polyhedron_is_unbounded(Polyhedron
*P
, unsigned nparam
, unsigned MaxRays
)
1708 Polyhedron
*R
= Recession_Cone(P
, nparam
, MaxRays
);
1709 POL_ENSURE_VERTICES(R
);
1711 for (i
= 0; i
< R
->NbRays
; ++i
)
1712 if (value_zero_p(R
->Ray
[i
][1+R
->Dimension
]))
1714 is_unbounded
= R
->NbBid
> 0 || i
< R
->NbRays
;
1716 return is_unbounded
;
1719 static void SwapColumns(Value
**V
, int n
, int i
, int j
)
1723 for (r
= 0; r
< n
; ++r
)
1724 value_swap(V
[r
][i
], V
[r
][j
]);
1727 void Polyhedron_ExchangeColumns(Polyhedron
*P
, int Column1
, int Column2
)
1729 SwapColumns(P
->Constraint
, P
->NbConstraints
, Column1
, Column2
);
1730 SwapColumns(P
->Ray
, P
->NbRays
, Column1
, Column2
);
1733 Polyhedron_Matrix_View(P
, &M
, P
->NbConstraints
);
1734 Gauss(&M
, P
->NbEq
, P
->Dimension
+1);
1738 /* perform transposition inline; assumes M is a square matrix */
1739 void Matrix_Transposition(Matrix
*M
)
1743 assert(M
->NbRows
== M
->NbColumns
);
1744 for (i
= 0; i
< M
->NbRows
; ++i
)
1745 for (j
= i
+1; j
< M
->NbColumns
; ++j
)
1746 value_swap(M
->p
[i
][j
], M
->p
[j
][i
]);
1749 /* Matrix "view" of first rows rows */
1750 void Polyhedron_Matrix_View(Polyhedron
*P
, Matrix
*M
, unsigned rows
)
1753 M
->NbColumns
= P
->Dimension
+2;
1754 M
->p_Init
= P
->p_Init
;
1755 M
->p
= P
->Constraint
;