/*
* 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_vec_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)
{
int i;
for (i = 0; i < n; ++i)
GBR_lp_get_alpha(lp, first + i, &alpha[i]);
}
/* 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->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_tab *isl_tab_compute_reduced_basis(struct isl_tab *tab)
{
unsigned dim;
struct isl_ctx *ctx;
struct isl_mat *B;
int unbounded;
int i;
GBR_LP *lp = NULL;
GBR_type F_old, alpha, F_new;
int row;
isl_int tmp;
struct isl_vec *b_tmp;
GBR_type *F = NULL;
GBR_type *alpha_buffer[2] = { NULL, NULL };
GBR_type *alpha_saved;
GBR_type F_saved;
int use_saved = 0;
isl_int mu[2];
GBR_type mu_F[2];
GBR_type two;
GBR_type one;
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;
B = tab->basis;
if (!B)
return tab;
n_bounded = dim - tab->n_unbounded;
if (n_bounded <= tab->n_zero + 1)
return tab;
isl_int_init(tmp);
isl_int_init(mu[0]);
isl_int_init(mu[1]);
GBR_init(alpha);
GBR_init(F_old);
GBR_init(F_new);
GBR_init(F_saved);
GBR_init(mu_F[0]);
GBR_init(mu_F[1]);
GBR_init(two);
GBR_init(one);
b_tmp = isl_vec_alloc(ctx, dim);
if (!b_tmp)
goto error;
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 < n_bounded; ++i) {
GBR_init(F[i]);
GBR_init(alpha_buffer[0][i]);
GBR_init(alpha_buffer[1][i]);
}
GBR_set_ui(two, 2);
GBR_set_ui(one, 1);
lp = GBR_lp_init(tab);
if (!lp)
goto error;
i = tab->n_zero;
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[i]);
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[i], 0);
}
tab->n_zero++;
}
do {
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);
GBR_lp_get_obj_val(lp, &F_new);
fixed = GBR_lp_is_fixed(lp);
GBR_set_ui(alpha, 0);
} else
if (use_saved) {
row = GBR_lp_next_row(lp);
GBR_set(F_new, F_saved);
fixed = fixed_saved;
GBR_set(alpha, alpha_saved[i]);
} else {
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);
GBR_lp_get_obj_val(lp, &F_new);
fixed = GBR_lp_is_fixed(lp);
GBR_lp_get_alpha(lp, row, &alpha);
if (i > 0)
save_alpha(lp, row-i, i, alpha_saved);
if (GBR_lp_del_row(lp) < 0)
goto error;
}
GBR_set(F[i+1], F_new);
GBR_floor(mu[0], alpha);
GBR_ceil(mu[1], alpha);
if (isl_int_eq(mu[0], mu[1]))
isl_int_set(tmp, mu[0]);
else {
int j;
for (j = 0; j <= 1; ++j) {
isl_int_set(tmp, mu[j]);
isl_seq_combine(b_tmp->el,
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);
isl_assert(ctx, !unbounded, goto error);
GBR_lp_get_obj_val(lp, &mu_F[j]);
mu_fixed[j] = GBR_lp_is_fixed(lp);
if (i > 0)
save_alpha(lp, row-i, i, alpha_buffer[j]);
}
if (GBR_lt(mu_F[0], mu_F[1]))
j = 0;
else
j = 1;
isl_int_set(tmp, mu[j]);
GBR_set(F_new, mu_F[j]);
fixed = mu_fixed[j];
alpha_saved = alpha_buffer[j];
}
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 == tab->n_zero && fixed) {
if (!GBR_is_zero(F[i+1])) {
empty = GBR_lp_cut(lp, B->row[1+i+1]+1);
if (empty)
goto done;
GBR_set_ui(F[i+1], 0);
}
tab->n_zero++;
}
GBR_set(F_old, F[i]);
use_saved = 0;
/* mu_F[0] = 4 * F_new; mu_F[1] = 3 * F_old */
GBR_set_ui(mu_F[0], 4);
GBR_mul(mu_F[0], mu_F[0], F_new);
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])) {
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;
if (GBR_lp_del_row(lp) < 0)
goto error;
--i;
} else {
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[tab->n_zero])) {
empty = GBR_lp_cut(lp, B->row[1+tab->n_zero]+1);
if (empty)
goto done;
GBR_set_ui(F[tab->n_zero], 0);
}
tab->n_zero++;
}
}
} else {
GBR_lp_add_row(lp, B->row[1+i]+1, dim);
++i;
}
} while (i < n_bounded - 1);
if (0) {
done:
if (empty < 0) {
error:
isl_mat_free(B);
B = NULL;
}
}
GBR_lp_delete(lp);
if (alpha_buffer[1])
for (i = 0; i < n_bounded; ++i) {
GBR_clear(F[i]);
GBR_clear(alpha_buffer[0][i]);
GBR_clear(alpha_buffer[1][i]);
}
free(F);
free(alpha_buffer[0]);
free(alpha_buffer[1]);
isl_vec_free(b_tmp);
GBR_clear(alpha);
GBR_clear(F_old);
GBR_clear(F_new);
GBR_clear(F_saved);
GBR_clear(mu_F[0]);
GBR_clear(mu_F[1]);
GBR_clear(two);
GBR_clear(one);
isl_int_clear(tmp);
isl_int_clear(mu[0]);
isl_int_clear(mu[1]);
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;
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;
basis = isl_mat_copy(tab->basis);
isl_tab_free(tab);
return basis;
}