/* glpfhv.c (LP basis factorization, FHV eta file version) */

/***********************************************************************

*  This code is part of GLPK (GNU Linear Programming Kit).

*

*  Copyright (C) 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008,

*  2009, 2010 Andrew Makhorin, Department for Applied Informatics,

*  Moscow Aviation Institute, Moscow, Russia. All rights reserved.

*  E-mail: <mao@gnu.org>.

*

*  GLPK is free software: you can redistribute it and/or modify it

*  under the terms of the GNU General Public License as published by

*  the Free Software Foundation, either version 3 of the License, or

*  (at your option) any later version.

*

*  GLPK is distributed in the hope that it will be useful, but WITHOUT

*  ANY WARRANTY; without even the implied warranty of MERCHANTABILITY

*  or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public

*  License for more details.

*

*  You should have received a copy of the GNU General Public License

*  along with GLPK. If not, see <http://www.gnu.org/licenses/>.

***********************************************************************/

#include "glpfhv.h"

#include "glpenv.h"

#define xfault xerror

/* CAUTION: DO NOT CHANGE THE LIMIT BELOW */

#define M_MAX 100000000 /* = 100*10^6 */

/* maximal order of the basis matrix */

/***********************************************************************

*  NAME

*

*  fhv_create_it - create LP basis factorization

*

*  SYNOPSIS

*

*  #include "glpfhv.h"

*  FHV *fhv_create_it(void);

*

*  DESCRIPTION

*

*  The routine fhv_create_it creates a program object, which represents

*  a factorization of LP basis.

*

*  RETURNS

*

*  The routine fhv_create_it returns a pointer to the object created. */

FHV *fhv_create_it(void)

{     FHV *fhv;

      fhv = xmalloc(sizeof(FHV));

      fhv->m_max = fhv->m = 0;

      fhv->valid = 0;

      fhv->luf = luf_create_it();

      fhv->hh_max = 50;

      fhv->hh_nfs = 0;

      fhv->hh_ind = fhv->hh_ptr = fhv->hh_len = NULL;

      fhv->p0_row = fhv->p0_col = NULL;

      fhv->cc_ind = NULL;

      fhv->cc_val = NULL;

      fhv->upd_tol = 1e-6;

      fhv->nnz_h = 0;

      return fhv;

}

/***********************************************************************

*  NAME

*

*  fhv_factorize - compute LP basis factorization

*

*  SYNOPSIS

*

*  #include "glpfhv.h"

*  int fhv_factorize(FHV *fhv, int m, int (*col)(void *info, int j,

*     int ind[], double val[]), void *info);

*

*  DESCRIPTION

*

*  The routine fhv_factorize computes the factorization of the basis

*  matrix B specified by the routine col.

*

*  The parameter fhv specified the basis factorization data structure

*  created by the routine fhv_create_it.

*

*  The parameter m specifies the order of B, m > 0.

*

*  The formal routine col specifies the matrix B to be factorized. To

*  obtain j-th column of A the routine fhv_factorize calls the routine

*  col with the parameter j (1 <= j <= n). In response the routine col

*  should store row indices and numerical values of non-zero elements

*  of j-th column of B to locations ind[1,...,len] and val[1,...,len],

*  respectively, where len is the number of non-zeros in j-th column

*  returned on exit. Neither zero nor duplicate elements are allowed.

*

*  The parameter info is a transit pointer passed to the routine col.

*

*  RETURNS

*

*  0  The factorization has been successfully computed.

*

*  FHV_ESING

*     The specified matrix is singular within the working precision.

*

*  FHV_ECOND

*     The specified matrix is ill-conditioned.

*

*  For more details see comments to the routine luf_factorize.

*

*  ALGORITHM

*

*  The routine fhv_factorize calls the routine luf_factorize (see the

*  module GLPLUF), which actually computes LU-factorization of the basis

*  matrix B in the form

*

*     [B] = (F, V, P, Q),

*

*  where F and V are such matrices that

*

*     B = F * V,

*

*  and P and Q are such permutation matrices that the matrix

*

*     L = P * F * inv(P)

*

*  is lower triangular with unity diagonal, and the matrix

*

*     U = P * V * Q

*

*  is upper triangular.

*

*  In order to build the complete representation of the factorization

*  (see formula (1) in the file glpfhv.h) the routine fhv_factorize just

*  additionally sets H = I and P0 = P. */

int fhv_factorize(FHV *fhv, int m, int (*col)(void *info, int j,

      int ind[], double val[]), void *info)

{     int ret;

      if (m < 1)

         xfault("fhv_factorize: m = %d; invalid parameter\n", m);

      if (m > M_MAX)

         xfault("fhv_factorize: m = %d; matrix too big\n", m);

      fhv->m = m;

      /* invalidate the factorization */

      fhv->valid = 0;

      /* allocate/reallocate arrays, if necessary */

      if (fhv->hh_ind == NULL)

         fhv->hh_ind = xcalloc(1+fhv->hh_max, sizeof(int));

      if (fhv->hh_ptr == NULL)

         fhv->hh_ptr = xcalloc(1+fhv->hh_max, sizeof(int));

      if (fhv->hh_len == NULL)

         fhv->hh_len = xcalloc(1+fhv->hh_max, sizeof(int));

      if (fhv->m_max < m)

      {  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);

         fhv->m_max = m + 100;

         fhv->p0_row = xcalloc(1+fhv->m_max, sizeof(int));

         fhv->p0_col = xcalloc(1+fhv->m_max, sizeof(int));

         fhv->cc_ind = xcalloc(1+fhv->m_max, sizeof(int));

         fhv->cc_val = xcalloc(1+fhv->m_max, sizeof(double));

      }

      /* try to factorize the basis matrix */

      switch (luf_factorize(fhv->luf, m, col, info))

      {  case 0:

            break;

         case LUF_ESING:

            ret = FHV_ESING;

            goto done;

         case LUF_ECOND:

            ret = FHV_ECOND;

            goto done;

         default:

            xassert(fhv != fhv);

      }

      /* the basis matrix has been successfully factorized */

      fhv->valid = 1;

      /* H := I */

      fhv->hh_nfs = 0;

      /* P0 := P */

      memcpy(&fhv->p0_row[1], &fhv->luf->pp_row[1], sizeof(int) * m);

      memcpy(&fhv->p0_col[1], &fhv->luf->pp_col[1], sizeof(int) * m);

      /* currently H has no factors */

      fhv->nnz_h = 0;

      ret = 0;

done: /* return to the calling program */

      return ret;

}

/***********************************************************************

*  NAME

*

*  fhv_h_solve - solve system H*x = b or H'*x = b

*

*  SYNOPSIS

*

*  #include "glpfhv.h"

*  void fhv_h_solve(FHV *fhv, int tr, double x[]);

*

*  DESCRIPTION

*

*  The routine fhv_h_solve solves either the system H*x = b (if the

*  flag tr is zero) or the system H'*x = b (if the flag tr is non-zero),

*  where the matrix H is a component of the factorization specified by

*  the parameter fhv, H' is a matrix transposed to H.

*

*  On entry the array x should contain elements of the right-hand side

*  vector b in locations x[1], ..., x[m], where m is the order of the

*  matrix H. On exit this array will contain elements of the solution

*  vector x in the same locations. */

void fhv_h_solve(FHV *fhv, int tr, double x[])

{     int nfs = fhv->hh_nfs;

      int *hh_ind = fhv->hh_ind;

      int *hh_ptr = fhv->hh_ptr;

      int *hh_len = fhv->hh_len;

      int *sv_ind = fhv->luf->sv_ind;

      double *sv_val = fhv->luf->sv_val;

      int i, k, beg, end, ptr;

      double temp;

      if (!fhv->valid)

         xfault("fhv_h_solve: the factorization is not valid\n");

      if (!tr)

      {  /* solve the system H*x = b */

         for (k = 1; k <= nfs; k++)

         {  i = hh_ind[k];

            temp = x[i];

            beg = hh_ptr[k];

            end = beg + hh_len[k] - 1;

            for (ptr = beg; ptr <= end; ptr++)

               temp -= sv_val[ptr] * x[sv_ind[ptr]];

            x[i] = temp;

         }

      }

      else

      {  /* solve the system H'*x = b */

         for (k = nfs; k >= 1; k--)

         {  i = hh_ind[k];

            temp = x[i];

            if (temp == 0.0) continue;

            beg = hh_ptr[k];

            end = beg + hh_len[k] - 1;

            for (ptr = beg; ptr <= end; ptr++)

               x[sv_ind[ptr]] -= sv_val[ptr] * temp;

         }

      }

      return;

}

/***********************************************************************

*  NAME

*

*  fhv_ftran - perform forward transformation (solve system B*x = b)

*

*  SYNOPSIS

*

*  #include "glpfhv.h"

*  void fhv_ftran(FHV *fhv, double x[]);

*

*  DESCRIPTION

*

*  The routine fhv_ftran performs forward transformation, i.e. solves

*  the system B*x = b, where B is the basis matrix, x is the vector of

*  unknowns to be computed, b is the vector of right-hand sides.

*

*  On entry elements of the vector b should be stored in dense format

*  in locations x[1], ..., x[m], where m is the number of rows. On exit

*  the routine stores elements of the vector x in the same locations. */

void fhv_ftran(FHV *fhv, double x[])

{     int *pp_row = fhv->luf->pp_row;

      int *pp_col = fhv->luf->pp_col;

      int *p0_row = fhv->p0_row;

      int *p0_col = fhv->p0_col;

      if (!fhv->valid)

         xfault("fhv_ftran: the factorization is not valid\n");

      /* B = F*H*V, therefore inv(B) = inv(V)*inv(H)*inv(F) */

      fhv->luf->pp_row = p0_row;

      fhv->luf->pp_col = p0_col;

      luf_f_solve(fhv->luf, 0, x);

      fhv->luf->pp_row = pp_row;

      fhv->luf->pp_col = pp_col;

      fhv_h_solve(fhv, 0, x);

      luf_v_solve(fhv->luf, 0, x);

      return;

}

/***********************************************************************

*  NAME

*

*  fhv_btran - perform backward transformation (solve system B'*x = b)

*

*  SYNOPSIS

*

*  #include "glpfhv.h"

*  void fhv_btran(FHV *fhv, double x[]);

*

*  DESCRIPTION

*

*  The routine fhv_btran performs backward transformation, i.e. solves

*  the system B'*x = b, where B' is a matrix transposed to the basis

*  matrix B, x is the vector of unknowns to be computed, b is the vector

*  of right-hand sides.

*

*  On entry elements of the vector b should be stored in dense format

*  in locations x[1], ..., x[m], where m is the number of rows. On exit

*  the routine stores elements of the vector x in the same locations. */

void fhv_btran(FHV *fhv, double x[])

{     int *pp_row = fhv->luf->pp_row;

      int *pp_col = fhv->luf->pp_col;

      int *p0_row = fhv->p0_row;

      int *p0_col = fhv->p0_col;

      if (!fhv->valid)

         xfault("fhv_btran: the factorization is not valid\n");

      /* B = F*H*V, therefore inv(B') = inv(F')*inv(H')*inv(V') */

      luf_v_solve(fhv->luf, 1, x);

      fhv_h_solve(fhv, 1, x);

      fhv->luf->pp_row = p0_row;

      fhv->luf->pp_col = p0_col;

      luf_f_solve(fhv->luf, 1, x);

      fhv->luf->pp_row = pp_row;

      fhv->luf->pp_col = pp_col;

      return;

}

/***********************************************************************

*  NAME

*

*  fhv_update_it - update LP basis factorization

*

*  SYNOPSIS

*

*  #include "glpfhv.h"

*  int fhv_update_it(FHV *fhv, int j, int len, const int ind[],

*     const double val[]);

*

*  DESCRIPTION

*

*  The routine fhv_update_it updates the factorization of the basis

*  matrix B after replacing its j-th column by a new vector.

*

*  The parameter j specifies the number of column of B, which has been

*  replaced, 1 <= j <= m, where m is the order of B.

*

*  Row indices and numerical values of non-zero elements of the new

*  column of B should be placed in locations ind[1], ..., ind[len] and

*  val[1], ..., val[len], resp., where len is the number of non-zeros

*  in the column. Neither zero nor duplicate elements are allowed.

*

*  RETURNS

*

*  0  The factorization has been successfully updated.

*

*  FHV_ESING

*     The adjacent basis matrix is structurally singular, since after

*     changing j-th column of matrix V by the new column (see algorithm

*     below) the case k1 > k2 occured.

*

*  FHV_ECHECK

*     The factorization is inaccurate, since after transforming k2-th

*     row of matrix U = P*V*Q, its diagonal element u[k2,k2] is zero or

*     close to zero,

*

*  FHV_ELIMIT

*     Maximal number of H factors has been reached.

*

*  FHV_EROOM

*     Overflow of the sparse vector area.

*

*  In case of non-zero return code the factorization becomes invalid.

*  It should not be used until it has been recomputed with the routine

*  fhv_factorize.

*

*  ALGORITHM

*

*  The routine fhv_update_it is based on the transformation proposed by

*  Forrest and Tomlin.

*

*  Let j-th column of the basis matrix B have been replaced by new

*  column B[j]. In order to keep the equality B = F*H*V j-th column of

*  matrix V should be replaced by the column inv(F*H)*B[j].

*

*  From the standpoint of matrix U = P*V*Q, replacement of j-th column

*  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 */