basis_reduction_templ.c

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/*
 * 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 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++;
  if (GBR_lp_solve(lp) < 0)
    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++;
      if (GBR_lp_solve(lp) < 0)
        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++;
      if (GBR_lp_solve(lp) < 0)
        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++;
        if (GBR_lp_solve(lp) < 0)
          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.
 */
__isl_give isl_mat *isl_basic_set_reduced_basis(__isl_keep isl_basic_set *bset)
{
  struct isl_mat *basis;
  struct isl_tab *tab;
 
  if (isl_basic_set_check_no_locals(bset) < 0 ||
      isl_basic_set_check_no_params(bset) < 0)
    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;
    isl_size nvar = isl_basic_set_dim(bset, isl_dim_all);
    if (nvar < 0)
      goto error;
    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;
error:
  isl_tab_free(tab);
  return NULL;
}