glpfhv.c

著名的大规模线性规划求解器源码GLPK.C语言版本,可以修剪.内有详细帮助文档.

*  of matrix V is equivalent to replacement of k1-th column of matrix U,
*  where k1 is determined by permutation matrix Q. Thus, matrix U loses
*  its upper triangular form and becomes the following:
*
*         1   k1       k2   m
*     1   x x * x x x x x x x
*         . x * x x x x x x x
*     k1  . . * x x x x x x x
*         . . * x x x x x x x
*         . . * . x x x x x x
*         . . * . . x x x x x
*         . . * . . . x x x x
*     k2  . . * . . . . x x x
*         . . . . . . . . x x
*     m   . . . . . . . . . x
*
*  where row index k2 corresponds to the lowest non-zero element of
*  k1-th column.
*
*  The routine moves rows and columns k1+1, k1+2, ..., k2 of matrix U
*  by one position to the left and upwards and moves k1-th row and k1-th
*  column to position k2. As the result of such symmetric permutations
*  matrix U becomes the following:
*
*         1   k1       k2   m
*     1   x x x x x x x * x x
*         . x x x x x x * x x
*     k1  . . x x x x x * x x
*         . . . x x x x * x x
*         . . . . x x x * x x
*         . . . . . x x * x x
*         . . . . . . x * x x
*     k2  . . x x x x x * x x
*         . . . . . . . . x x
*     m   . . . . . . . . . x
*
*  Then the routine performs gaussian elimination to eliminate elements
*  u[k2,k1], u[k2,k1+1], ..., u[k2,k2-1] using diagonal elements
*  u[k1,k1], u[k1+1,k1+1], ..., u[k2-1,k2-1] as pivots in the same way
*  as described in comments to the routine luf_factorize (see the module
*  GLPLUF). Note that actually all operations are performed on matrix V,
*  not on matrix U. During the elimination process the routine permutes
*  neither rows nor columns, so only k2-th row of matrix U is changed.
*
*  To keep the main equality B = F*H*V, each time when the routine
*  applies elementary gaussian transformation to the transformed row of
*  matrix V (which corresponds to k2-th row of matrix U), it also adds
*  a new element (gaussian multiplier) to the current row-like factor
*  of matrix H, which corresponds to the transformed row of matrix V. */

int fhv_update_it(FHV *fhv, int j, int len, const int ind[],
      const double val[])
{     int m = fhv->m;
      LUF *luf = fhv->luf;
      int *vr_ptr = luf->vr_ptr;
      int *vr_len = luf->vr_len;
      int *vr_cap = luf->vr_cap;
      double *vr_piv = luf->vr_piv;
      int *vc_ptr = luf->vc_ptr;
      int *vc_len = luf->vc_len;
      int *vc_cap = luf->vc_cap;
      int *pp_row = luf->pp_row;
      int *pp_col = luf->pp_col;
      int *qq_row = luf->qq_row;
      int *qq_col = luf->qq_col;
      int *sv_ind = luf->sv_ind;
      double *sv_val = luf->sv_val;
      double *work = luf->work;
      double eps_tol = luf->eps_tol;
      int *hh_ind = fhv->hh_ind;
      int *hh_ptr = fhv->hh_ptr;
      int *hh_len = fhv->hh_len;
      int *p0_row = fhv->p0_row;
      int *p0_col = fhv->p0_col;
      int *cc_ind = fhv->cc_ind;
      double *cc_val = fhv->cc_val;
      double upd_tol = fhv->upd_tol;
      int i, i_beg, i_end, i_ptr, j_beg, j_end, j_ptr, k, k1, k2, p, q,
         p_beg, p_end, p_ptr, ptr, ret;
      double f, temp;
      if (!fhv->valid)
         xfault("fhv_update_it: the factorization is not valid\n");
      if (!(1 <= j && j <= m))
         xfault("fhv_update_it: j = %d; column number out of range\n",
            j);
      /* check if the new factor of matrix H can be created */
      if (fhv->hh_nfs == fhv->hh_max)
      {  /* maximal number of updates has been reached */
         fhv->valid = 0;
         ret = FHV_ELIMIT;
         goto done;
      }
      /* convert new j-th column of B to dense format */
      for (i = 1; i <= m; i++)
         cc_val[i] = 0.0;
      for (k = 1; k <= len; k++)
      {  i = ind[k];
         if (!(1 <= i && i <= m))
            xfault("fhv_update_it: ind[%d] = %d; row number out of rang"
               "e\n", k, i);
         if (cc_val[i] != 0.0)
            xfault("fhv_update_it: ind[%d] = %d; duplicate row index no"
               "t allowed\n", k, i);
         if (val[k] == 0.0)
            xfault("fhv_update_it: val[%d] = %g; zero element not allow"
               "ed\n", k, val[k]);
         cc_val[i] = val[k];
      }
      /* new j-th column of V := inv(F * H) * (new B[j]) */
      fhv->luf->pp_row = p0_row;
      fhv->luf->pp_col = p0_col;
      luf_f_solve(fhv->luf, 0, cc_val);
      fhv->luf->pp_row = pp_row;
      fhv->luf->pp_col = pp_col;
      fhv_h_solve(fhv, 0, cc_val);
      /* convert new j-th column of V to sparse format */
      len = 0;
      for (i = 1; i <= m; i++)
      {  temp = cc_val[i];
         if (temp == 0.0 || fabs(temp) < eps_tol) continue;
         len++, cc_ind[len] = i, cc_val[len] = temp;
      }
      /* clear old content of j-th column of matrix V */
      j_beg = vc_ptr[j];
      j_end = j_beg + vc_len[j] - 1;
      for (j_ptr = j_beg; j_ptr <= j_end; j_ptr++)
      {  /* get row index of v[i,j] */
         i = sv_ind[j_ptr];
         /* find v[i,j] in the i-th row */
         i_beg = vr_ptr[i];
         i_end = i_beg + vr_len[i] - 1;
         for (i_ptr = i_beg; sv_ind[i_ptr] != j; i_ptr++) /* nop */;
         xassert(i_ptr <= i_end);
         /* remove v[i,j] from the i-th row */
         sv_ind[i_ptr] = sv_ind[i_end];
         sv_val[i_ptr] = sv_val[i_end];
         vr_len[i]--;
      }
      /* now j-th column of matrix V is empty */
      luf->nnz_v -= vc_len[j];
      vc_len[j] = 0;
      /* add new elements of j-th column of matrix V to corresponding
         row lists; determine indices k1 and k2 */
      k1 = qq_row[j], k2 = 0;
      for (ptr = 1; ptr <= len; ptr++)
      {  /* get row index of v[i,j] */
         i = cc_ind[ptr];
         /* at least one unused location is needed in i-th row */
         if (vr_len[i] + 1 > vr_cap[i])
         {  if (luf_enlarge_row(luf, i, vr_len[i] + 10))
            {  /* overflow of the sparse vector area */
               fhv->valid = 0;
               luf->new_sva = luf->sv_size + luf->sv_size;
               xassert(luf->new_sva > luf->sv_size);
               ret = FHV_EROOM;
               goto done;
            }
         }
         /* add v[i,j] to i-th row */
         i_ptr = vr_ptr[i] + vr_len[i];
         sv_ind[i_ptr] = j;
         sv_val[i_ptr] = cc_val[ptr];
         vr_len[i]++;
         /* adjust index k2 */
         if (k2 < pp_col[i]) k2 = pp_col[i];
      }
      /* capacity of j-th column (which is currently empty) should be
         not less than len locations */
      if (vc_cap[j] < len)
      {  if (luf_enlarge_col(luf, j, len))
         {  /* overflow of the sparse vector area */
            fhv->valid = 0;
            luf->new_sva = luf->sv_size + luf->sv_size;
            xassert(luf->new_sva > luf->sv_size);
            ret = FHV_EROOM;
            goto done;
         }
      }
      /* add new elements of matrix V to j-th column list */
      j_ptr = vc_ptr[j];
      memmove(&sv_ind[j_ptr], &cc_ind[1], len * sizeof(int));
      memmove(&sv_val[j_ptr], &cc_val[1], len * sizeof(double));
      vc_len[j] = len;
      luf->nnz_v += len;
      /* if k1 > k2, diagonal element u[k2,k2] of matrix U is zero and
         therefore the adjacent basis matrix is structurally singular */
      if (k1 > k2)
      {  fhv->valid = 0;
         ret = FHV_ESING;
         goto done;
      }
      /* perform implicit symmetric permutations of rows and columns of
         matrix U */
      i = pp_row[k1], j = qq_col[k1];
      for (k = k1; k < k2; k++)
      {  pp_row[k] = pp_row[k+1], pp_col[pp_row[k]] = k;
         qq_col[k] = qq_col[k+1], qq_row[qq_col[k]] = k;
      }
      pp_row[k2] = i, pp_col[i] = k2;
      qq_col[k2] = j, qq_row[j] = k2;
      /* now i-th row of the matrix V is k2-th row of matrix U; since
         no pivoting is used, only this row will be transformed */
      /* copy elements of i-th row of matrix V to the working array and
         remove these elements from matrix V */
      for (j = 1; j <= m; j++) work[j] = 0.0;
      i_beg = vr_ptr[i];
      i_end = i_beg + vr_len[i] - 1;
      for (i_ptr = i_beg; i_ptr <= i_end; i_ptr++)
      {  /* get column index of v[i,j] */
         j = sv_ind[i_ptr];
         /* store v[i,j] to the working array */
         work[j] = sv_val[i_ptr];
         /* find v[i,j] in the j-th column */
         j_beg = vc_ptr[j];
         j_end = j_beg + vc_len[j] - 1;
         for (j_ptr = j_beg; sv_ind[j_ptr] != i; j_ptr++) /* nop */;
         xassert(j_ptr <= j_end);
         /* remove v[i,j] from the j-th column */
         sv_ind[j_ptr] = sv_ind[j_end];
         sv_val[j_ptr] = sv_val[j_end];
         vc_len[j]--;
      }
      /* now i-th row of matrix V is empty */
      luf->nnz_v -= vr_len[i];
      vr_len[i] = 0;
      /* create the next row-like factor of the matrix H; this factor
         corresponds to i-th (transformed) row */
      fhv->hh_nfs++;
      hh_ind[fhv->hh_nfs] = i;
      /* hh_ptr[] will be set later */
      hh_len[fhv->hh_nfs] = 0;
      /* up to (k2 - k1) free locations are needed to add new elements
         to the non-trivial row of the row-like factor */
      if (luf->sv_end - luf->sv_beg < k2 - k1)
      {  luf_defrag_sva(luf);
         if (luf->sv_end - luf->sv_beg < k2 - k1)
         {  /* overflow of the sparse vector area */
            fhv->valid = luf->valid = 0;
            luf->new_sva = luf->sv_size + luf->sv_size;
            xassert(luf->new_sva > luf->sv_size);
            ret = FHV_EROOM;
            goto done;
         }
      }
      /* eliminate subdiagonal elements of matrix U */
      for (k = k1; k < k2; k++)
      {  /* v[p,q] = u[k,k] */
         p = pp_row[k], q = qq_col[k];
         /* this is the crucial point, where even tiny non-zeros should
            not be dropped */
         if (work[q] == 0.0) continue;
         /* compute gaussian multiplier f = v[i,q] / v[p,q] */
         f = work[q] / vr_piv[p];
         /* perform gaussian transformation:
            (i-th row) := (i-th row) - f * (p-th row)
            in order to eliminate v[i,q] = u[k2,k] */
         p_beg = vr_ptr[p];
         p_end = p_beg + vr_len[p] - 1;
         for (p_ptr = p_beg; p_ptr <= p_end; p_ptr++)
            work[sv_ind[p_ptr]] -= f * sv_val[p_ptr];
         /* store new element (gaussian multiplier that corresponds to
            p-th row) in the current row-like factor */
         luf->sv_end--;
         sv_ind[luf->sv_end] = p;
         sv_val[luf->sv_end] = f;
         hh_len[fhv->hh_nfs]++;
      }
      /* set pointer to the current row-like factor of the matrix H
         (if no elements were added to this factor, it is unity matrix
         and therefore can be discarded) */
      if (hh_len[fhv->hh_nfs] == 0)
         fhv->hh_nfs--;
      else
      {  hh_ptr[fhv->hh_nfs] = luf->sv_end;
         fhv->nnz_h += hh_len[fhv->hh_nfs];
      }
      /* store new pivot which corresponds to u[k2,k2] */
      vr_piv[i] = work[qq_col[k2]];
      /* new elements of i-th row of matrix V (which are non-diagonal
         elements u[k2,k2+1], ..., u[k2,m] of matrix U = P*V*Q) now are
         contained in the working array; add them to matrix V */
      len = 0;
      for (k = k2+1; k <= m; k++)
      {  /* get column index and value of v[i,j] = u[k2,k] */
         j = qq_col[k];
         temp = work[j];
         /* if v[i,j] is close to zero, skip it */
         if (fabs(temp) < eps_tol) continue;
         /* at least one unused location is needed in j-th column */
         if (vc_len[j] + 1 > vc_cap[j])
         {  if (luf_enlarge_col(luf, j, vc_len[j] + 10))
            {  /* overflow of the sparse vector area */
               fhv->valid = 0;
               luf->new_sva = luf->sv_size + luf->sv_size;
               xassert(luf->new_sva > luf->sv_size);
               ret = FHV_EROOM;
               goto done;
            }
         }
         /* add v[i,j] to j-th column */
         j_ptr = vc_ptr[j] + vc_len[j];
         sv_ind[j_ptr] = i;
         sv_val[j_ptr] = temp;
         vc_len[j]++;
         /* also store v[i,j] to the auxiliary array */
         len++, cc_ind[len] = j, cc_val[len] = temp;
      }
      /* capacity of i-th row (which is currently empty) should be not
         less than len locations */
      if (vr_cap[i] < len)
      {  if (luf_enlarge_row(luf, i, len))
         {  /* overflow of the sparse vector area */
            fhv->valid = 0;
            luf->new_sva = luf->sv_size + luf->sv_size;
            xassert(luf->new_sva > luf->sv_size);
            ret = FHV_EROOM;
            goto done;
         }
      }
      /* add new elements to i-th row list */
      i_ptr = vr_ptr[i];
      memmove(&sv_ind[i_ptr], &cc_ind[1], len * sizeof(int));
      memmove(&sv_val[i_ptr], &cc_val[1], len * sizeof(double));
      vr_len[i] = len;
      luf->nnz_v += len;
      /* updating is finished; check that diagonal element u[k2,k2] is
         not very small in absolute value among other elements in k2-th
         row and k2-th column of matrix U = P*V*Q */
      /* temp = max(|u[k2,*]|, |u[*,k2]|) */
      temp = 0.0;
      /* walk through k2-th row of U which is i-th row of V */
      i = pp_row[k2];
      i_beg = vr_ptr[i];
      i_end = i_beg + vr_len[i] - 1;
      for (i_ptr = i_beg; i_ptr <= i_end; i_ptr++)
         if (temp < fabs(sv_val[i_ptr])) temp = fabs(sv_val[i_ptr]);
      /* walk through k2-th column of U which is j-th column of V */
      j = qq_col[k2];
      j_beg = vc_ptr[j];
      j_end = j_beg + vc_len[j] - 1;
      for (j_ptr = j_beg; j_ptr <= j_end; j_ptr++)
         if (temp < fabs(sv_val[j_ptr])) temp = fabs(sv_val[j_ptr]);
      /* check that u[k2,k2] is not very small */
      if (fabs(vr_piv[i]) < upd_tol * temp)
      {  /* the factorization seems to be inaccurate and therefore must
            be recomputed */
         fhv->valid = 0;
         ret = FHV_ECHECK;
         goto done;
      }
      /* the factorization has been successfully updated */
      ret = 0;
done: /* return to the calling program */
      return ret;
}

/***********************************************************************
*  NAME
*
*  fhv_delete_it - delete LP basis factorization
*
*  SYNOPSIS
*
*  #include "glpfhv.h"
*  void fhv_delete_it(FHV *fhv);
*
*  DESCRIPTION
*
*  The routine fhv_delete_it deletes LP basis factorization specified
*  by the parameter fhv and frees all memory allocated to this program
*  object. */

void fhv_delete_it(FHV *fhv)
{     luf_delete_it(fhv->luf);
      if (fhv->hh_ind != NULL) xfree(fhv->hh_ind);
      if (fhv->hh_ptr != NULL) xfree(fhv->hh_ptr);
      if (fhv->hh_len != NULL) xfree(fhv->hh_len);
      if (fhv->p0_row != NULL) xfree(fhv->p0_row);
      if (fhv->p0_col != NULL) xfree(fhv->p0_col);
      if (fhv->cc_ind != NULL) xfree(fhv->cc_ind);
      if (fhv->cc_val != NULL) xfree(fhv->cc_val);
      xfree(fhv);
      return;
}

/* eof */