+/*
+ * Copyright 2006-2007 Universiteit Leiden
+ * Copyright 2008-2009 Katholieke Universiteit Leuven
+ *
+ * Use of this software is governed by the MIT license
+ *
+ * Written by Sven Verdoolaege, Leiden Institute of Advanced Computer Science,
+ * Universiteit Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands
+ * and K.U.Leuven, Departement Computerwetenschappen, Celestijnenlaan 200A,
+ * B-3001 Leuven, Belgium
+ */
+
#include <stdlib.h>
+#include <isl_ctx_private.h>
+#include <isl_map_private.h>
+#include <isl_options_private.h>
#include "isl_basis_reduction.h"
static void save_alpha(GBR_LP *lp, int first, int n, GBR_type *alpha)
GBR_lp_get_alpha(lp, first + i, &alpha[i]);
}
-/* This function implements the algorithm described in
+/* Compute a reduced basis for the set represented by the tableau "tab".
+ * tab->basis, which must be initialized by the calling function to an affine
+ * unimodular basis, is updated to reflect the reduced basis.
+ * The first tab->n_zero rows of the basis (ignoring the constant row)
+ * are assumed to correspond to equalities and are left untouched.
+ * tab->n_zero is updated to reflect any additional equalities that
+ * have been detected in the first rows of the new basis.
+ * The final tab->n_unbounded rows of the basis are assumed to correspond
+ * to unbounded directions and are also left untouched.
+ * In particular this means that the remaining rows are assumed to
+ * correspond to bounded directions.
+ *
+ * This function implements the algorithm described in
* "An Implementation of the Generalized Basis Reduction Algorithm
* for Integer Programming" of Cook el al. to compute a reduced basis.
* We use \epsilon = 1/4.
*
- * If ctx->gbr_only_first is set, the user is only interested
+ * If ctx->opt->gbr_only_first is set, the user is only interested
* in the first direction. In this case we stop the basis reduction when
* the width in the first direction becomes smaller than 2.
*/
-struct isl_mat *isl_tab_reduced_basis(struct isl_tab *tab)
+struct isl_tab *isl_tab_compute_reduced_basis(struct isl_tab *tab)
{
unsigned dim;
struct isl_ctx *ctx;
- struct isl_mat *basis;
+ struct isl_mat *B;
int unbounded;
int i;
GBR_LP *lp = NULL;
GBR_type mu_F[2];
GBR_type two;
GBR_type one;
- int n_zero = 0;
int empty = 0;
int fixed = 0;
int fixed_saved = 0;
int mu_fixed[2];
+ int n_bounded;
+ int gbr_only_first;
if (!tab)
return NULL;
+ if (tab->empty)
+ return tab;
+
ctx = tab->mat->ctx;
+ gbr_only_first = ctx->opt->gbr_only_first;
dim = tab->n_var;
- basis = isl_mat_identity(ctx, dim);
- if (!basis)
- return NULL;
+ B = tab->basis;
+ if (!B)
+ return tab;
- if (dim == 1)
- return basis;
+ n_bounded = dim - tab->n_unbounded;
+ if (n_bounded <= tab->n_zero + 1)
+ return tab;
isl_int_init(tmp);
isl_int_init(mu[0]);
if (!b_tmp)
goto error;
- F = isl_alloc_array(ctx, GBR_type, dim);
- alpha_buffer[0] = isl_alloc_array(ctx, GBR_type, dim);
- alpha_buffer[1] = isl_alloc_array(ctx, GBR_type, dim);
+ F = isl_alloc_array(ctx, GBR_type, n_bounded);
+ alpha_buffer[0] = isl_alloc_array(ctx, GBR_type, n_bounded);
+ alpha_buffer[1] = isl_alloc_array(ctx, GBR_type, n_bounded);
alpha_saved = alpha_buffer[0];
if (!F || !alpha_buffer[0] || !alpha_buffer[1])
goto error;
- for (i = 0; i < dim; ++i) {
+ for (i = 0; i < n_bounded; ++i) {
GBR_init(F[i]);
GBR_init(alpha_buffer[0][i]);
GBR_init(alpha_buffer[1][i]);
if (!lp)
goto error;
- i = 0;
+ i = tab->n_zero;
- GBR_lp_set_obj(lp, basis->row[0], dim);
+ GBR_lp_set_obj(lp, B->row[1+i]+1, dim);
ctx->stats->gbr_solved_lps++;
unbounded = GBR_lp_solve(lp);
isl_assert(ctx, !unbounded, goto error);
- GBR_lp_get_obj_val(lp, &F[0]);
+ GBR_lp_get_obj_val(lp, &F[i]);
- if (GBR_lt(F[0], one)) {
- if (!GBR_is_zero(F[0])) {
- empty = GBR_lp_cut(lp, basis->row[0]);
+ if (GBR_lt(F[i], one)) {
+ if (!GBR_is_zero(F[i])) {
+ empty = GBR_lp_cut(lp, B->row[1+i]+1);
if (empty)
goto done;
- GBR_set_ui(F[0], 0);
+ GBR_set_ui(F[i], 0);
}
- n_zero++;
+ tab->n_zero++;
}
do {
- if (i+1 == n_zero) {
- GBR_lp_set_obj(lp, basis->row[i+1], dim);
+ if (i+1 == tab->n_zero) {
+ GBR_lp_set_obj(lp, B->row[1+i+1]+1, dim);
ctx->stats->gbr_solved_lps++;
unbounded = GBR_lp_solve(lp);
isl_assert(ctx, !unbounded, goto error);
fixed = fixed_saved;
GBR_set(alpha, alpha_saved[i]);
} else {
- row = GBR_lp_add_row(lp, basis->row[i], dim);
- GBR_lp_set_obj(lp, basis->row[i+1], dim);
+ row = GBR_lp_add_row(lp, B->row[1+i]+1, dim);
+ GBR_lp_set_obj(lp, B->row[1+i+1]+1, dim);
ctx->stats->gbr_solved_lps++;
unbounded = GBR_lp_solve(lp);
isl_assert(ctx, !unbounded, goto error);
if (i > 0)
save_alpha(lp, row-i, i, alpha_saved);
- GBR_lp_del_row(lp);
+ if (GBR_lp_del_row(lp) < 0)
+ goto error;
}
GBR_set(F[i+1], F_new);
for (j = 0; j <= 1; ++j) {
isl_int_set(tmp, mu[j]);
isl_seq_combine(b_tmp->el,
- ctx->one, basis->row[i+1],
- tmp, basis->row[i], dim);
+ ctx->one, B->row[1+i+1]+1,
+ tmp, B->row[1+i]+1, dim);
GBR_lp_set_obj(lp, b_tmp->el, dim);
ctx->stats->gbr_solved_lps++;
unbounded = GBR_lp_solve(lp);
fixed = mu_fixed[j];
alpha_saved = alpha_buffer[j];
}
- isl_seq_combine(basis->row[i+1], ctx->one, basis->row[i+1],
- tmp, basis->row[i], dim);
+ isl_seq_combine(B->row[1+i+1]+1, ctx->one, B->row[1+i+1]+1,
+ tmp, B->row[1+i]+1, dim);
- if (i+1 == n_zero && fixed) {
+ if (i+1 == tab->n_zero && fixed) {
if (!GBR_is_zero(F[i+1])) {
- empty = GBR_lp_cut(lp, basis->row[i+1]);
+ empty = GBR_lp_cut(lp, B->row[1+i+1]+1);
if (empty)
goto done;
GBR_set_ui(F[i+1], 0);
}
- n_zero++;
+ tab->n_zero++;
}
GBR_set(F_old, F[i]);
GBR_set_ui(mu_F[1], 3);
GBR_mul(mu_F[1], mu_F[1], F_old);
if (GBR_lt(mu_F[0], mu_F[1])) {
- basis = isl_mat_swap_rows(basis, i, i + 1);
- if (i > 0) {
+ B = isl_mat_swap_rows(B, 1 + i, 1 + i + 1);
+ if (i > tab->n_zero) {
use_saved = 1;
GBR_set(F_saved, F_new);
fixed_saved = fixed;
- GBR_lp_del_row(lp);
+ if (GBR_lp_del_row(lp) < 0)
+ goto error;
--i;
} else {
- GBR_set(F[0], F_new);
- if (ctx->gbr_only_first && GBR_lt(F[0], two))
+ GBR_set(F[tab->n_zero], F_new);
+ if (gbr_only_first && GBR_lt(F[tab->n_zero], two))
break;
if (fixed) {
- if (!GBR_is_zero(F[0])) {
- empty = GBR_lp_cut(lp, basis->row[0]);
+ if (!GBR_is_zero(F[tab->n_zero])) {
+ empty = GBR_lp_cut(lp, B->row[1+tab->n_zero]+1);
if (empty)
goto done;
- GBR_set_ui(F[0], 0);
+ GBR_set_ui(F[tab->n_zero], 0);
}
- n_zero++;
+ tab->n_zero++;
}
}
} else {
- GBR_lp_add_row(lp, basis->row[i], dim);
+ GBR_lp_add_row(lp, B->row[1+i]+1, dim);
++i;
}
- } while (i < dim-1);
+ } while (i < n_bounded - 1);
if (0) {
done:
if (empty < 0) {
error:
- isl_mat_free(basis);
- basis = NULL;
+ isl_mat_free(B);
+ B = NULL;
}
}
GBR_lp_delete(lp);
if (alpha_buffer[1])
- for (i = 0; i < dim; ++i) {
+ for (i = 0; i < n_bounded; ++i) {
GBR_clear(F[i]);
GBR_clear(alpha_buffer[0][i]);
GBR_clear(alpha_buffer[1][i]);
isl_int_clear(mu[0]);
isl_int_clear(mu[1]);
- return basis;
+ tab->basis = B;
+
+ return tab;
}
+/* Compute an affine form of a reduced basis of the given basic
+ * non-parametric set, which is assumed to be bounded and not
+ * include any integer divisions.
+ * The first column and the first row correspond to the constant term.
+ *
+ * If the input contains any equalities, we first create an initial
+ * basis with the equalities first. Otherwise, we start off with
+ * the identity matrix.
+ */
struct isl_mat *isl_basic_set_reduced_basis(struct isl_basic_set *bset)
{
struct isl_mat *basis;
struct isl_tab *tab;
- isl_assert(bset->ctx, bset->n_eq == 0, return NULL);
+ if (!bset)
+ return NULL;
+
+ if (isl_basic_set_dim(bset, isl_dim_div) != 0)
+ isl_die(bset->ctx, isl_error_invalid,
+ "no integer division allowed", return NULL);
+ if (isl_basic_set_dim(bset, isl_dim_param) != 0)
+ isl_die(bset->ctx, isl_error_invalid,
+ "no parameters allowed", return NULL);
+
+ tab = isl_tab_from_basic_set(bset, 0);
+ if (!tab)
+ return NULL;
+
+ if (bset->n_eq == 0)
+ tab->basis = isl_mat_identity(bset->ctx, 1 + tab->n_var);
+ else {
+ isl_mat *eq;
+ unsigned nvar = isl_basic_set_total_dim(bset);
+ eq = isl_mat_sub_alloc6(bset->ctx, bset->eq, 0, bset->n_eq,
+ 1, nvar);
+ eq = isl_mat_left_hermite(eq, 0, NULL, &tab->basis);
+ tab->basis = isl_mat_lin_to_aff(tab->basis);
+ tab->n_zero = bset->n_eq;
+ isl_mat_free(eq);
+ }
+ tab = isl_tab_compute_reduced_basis(tab);
+ if (!tab)
+ return NULL;
- tab = isl_tab_from_basic_set(bset);
- basis = isl_tab_reduced_basis(tab);
+ basis = isl_mat_copy(tab->basis);
isl_tab_free(tab);
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