/* Copyright 2004,2007 ENSEIRB, INRIA & CNRS
**
** This file is part of the Scotch software package for static mapping,
** graph partitioning and sparse matrix ordering.
**
** This software is governed by the CeCILL-C license under French law
** and abiding by the rules of distribution of free software. You can
** use, modify and/or redistribute the software under the terms of the
** CeCILL-C license as circulated by CEA, CNRS and INRIA at the following
** URL: "http://www.cecill.info".
** 
** As a counterpart to the access to the source code and rights to copy,
** modify and redistribute granted by the license, users are provided
** only with a limited warranty and the software's author, the holder of
** the economic rights, and the successive licensors have only limited
** liability.
** 
** In this respect, the user's attention is drawn to the risks associated
** with loading, using, modifying and/or developing or reproducing the
** software by the user in light of its specific status of free software,
** that may mean that it is complicated to manipulate, and that also
** therefore means that it is reserved for developers and experienced
** professionals having in-depth computer knowledge. Users are therefore
** encouraged to load and test the software's suitability as regards
** their requirements in conditions enabling the security of their
** systems and/or data to be ensured and, more generally, to use and
** operate it in the same conditions as regards security.
** 
** The fact that you are presently reading this means that you have had
** knowledge of the CeCILL-C license and that you accept its terms.
*/
/************************************************************/
/**                                                        **/
/**   NAME       : hall_order_hf.c                         **/
/**                                                        **/
/**   AUTHOR     : Patrick AMESTOY                         **/
/**                Francois PELLEGRINI                     **/
/**                                                        **/
/**   FUNCTION   : This module orders a halo graph or mesh **/
/**                structure using the block-oriented Halo **/
/**                Approximate (Multiple) Minimum Fill     **/
/**                algorithm, with super-variable          **/
/**                accounting R2HAMDf4 (v2.0).             **/
/**                                                        **/
/**   DATES      : # Version 3.4  : from : 15 may 2001     **/
/**                                 to   : 23 nov 2001     **/
/**                # Version 4.0  : from : 10 jan 2003     **/
/**                                 to   : 02 apr 2004     **/
/**                                                        **/
/**   NOTES      : # This module contains pieces of code   **/
/**                  that belong to other people; see      **/
/**                  below.                                **/
/**                                                        **/
/************************************************************/

/*
**  The defines and includes.
*/

#define HALL_ORDER_HF

#include "module.h"
#include "common.h"
#include "graph.h"
#include "hall_order_hf.h"

/*  -- translated by f2c (version 19970219). */

/** -------------------------------------------------------------------- **/
/** December 8th 2003                                                    **/
/** Unique version for both graph of variables and graphs of elements    **/
/** Let us refer to as                                                   **/
/**       Gv a graph with only variables                                 **/
/**       Ge a graph with both variables and elements                    **/
/**                                                                      **/
/** Notations used:                                                      **/
/**                                                                      **/
/**     Let V be the set of nodes                                        **/
/**       V = Ve + V0 + V1                                               **/
/**           V0 = Set of variable nodes (not in halo)                   **/
/**           V1 = Set of variable nodes (in halo)                       **/
/**           Ve = Set of element nodes                                  **/
/**                                                                      **/
/**       All 3 sets are disjoint, Ve and V1 can be empty                **/
/**                                                                      **/
/**  Modifications w.r.t. previous version :                             **/
/**                                                                      **/  
/**  New Input:                                                          **/
/**  ---------                                                           **/
/**         nbelts : integer holding size of Ve                          **/
/**                            =0 if Gv (graph of variables)             **/
/**                            >0 if Ge                                  **/
/**                                                                      **/
/**  Extension of the meaning of input entry len for nodes in Ve         **/
/**  ---------                                                           **/
/**         len(i) = | Adj(i) | if i \in V0 U Ve                         **/
/**           ( Note that in the case of a GE graph                      **/
/**              if v\in V0 then len(v) = nb of elements adjacent to v ) **/
/**         len(i) = - | Adj(i) | if i \in V1                            **/
/**                  or -N -1 if  | Adj(i) | = 0 and i \in V1            **/
/**                                                                      **/
/**  Modified the meaning of input entry elen                            **/
/**  ---------                                                           **/
/**         if e \in Ve then elen (e) = -N-1                             **/
/**         if v \in V0 then elen (v) = External degree of v             **/
/**                             Gv : elen (v) = len(v)                   **/
/**                             Ge : elen (v)                            **/
/**                                  should be computed in SCOTCH        **/
/**         if v \in V1 then elen (v) = 0                                **/
/**                                                                      **/
/**                                                                      **/
/**  Output is unchanged                                                 **/
/**  ---------                                                           **/
/**                                                                      **/
/**                                                                      **/
/** End remarks done on December 8th 2003                                **/
/** ---------------------------------------------------------------------**/
/**                                                                      **/
/**                                                                      **/
/** AMF4 (version used on newton for uns tests)                          **/
/** given to Francois on Nov 31 2000                                     **/
/** Approximation of level4 of the minimum fill heuristic                **/
/** (best approx of Min fill currently available based on collaborative  **/
/** work between P. Amestoy, T. Davis and I. Duff)                       **/
/**                                                                      **/
/** Remarks:                                                             **/
/** -------                                                              **/
/** 1/ !!!!!!!! WARNING !!!!!!!!!!                                       **/
/**    TWO additionnal parameters w.r.t HALOAMD                          **/
/**    --------------------------                                        **/
/**    NBBUCK : integer greater than 1 (advised value is 2*N)            **/
/**    HEAD   : HEAD(0:NBBUCK+1) integer array of size NBBUCK+2          **/
/**    NOTE that it start at index 0 !!                                  **/
/**                                                                      **/
/** 2/ Interface for MA41 or SCOTCH                                      **/
/**                                                                      **/
/** 3/ Nodes of V1 are amalgamated in one root supervariable             **/
/**    the complete tree (of V0+V1) is correct in the sense of           **/
/**    MC47B output interface (NV for V1 nodes is ok).                   **/
/**    Output data (PE,NV) can then be exploited by MA41LD.              **/
/**    Variable in V1 cannot be characterized on output.                 **/
/** -------------------------------------------------------------------- **/

void
hallOrderHfR2hamdf4 (
Gnum                n,                            /* Matrix order                             */
Gnum                nbelts,                       /* Number of elements                       */
Gnum                nbbuck,                       /* Number of buckets                        */
Gnum                iwlen,                        /* Length of array iw                       */
Gnum * restrict     pe /* [] */,                  /* Array of indexes in iw of start of row i */
Gnum                pfree,                        /* Useful size in iw                        */
Gnum * restrict     len /* [] */,                 /* Array of lengths of adjacency lists      */
Gnum * restrict     iw /* [] */,                  /* Adjacency list array                     */
Gnum * restrict     nv /* [] */,                  /* Array of element degrees                 */
Gnum * restrict     elen /* [] */,                /* Array that holds the inverse permutation */
Gnum * restrict     last /* [] */,                /* Array that holds the permutation         */
Gnum * restrict     ncmpa,                        /* Number of times array iw was compressed  */
Gnum * restrict     degree /* [] */,              /* Array that holds degree data             */
Gnum * restrict     wf /* [] */,                  /* Flag array                               */
Gnum * restrict     next /* [] */,                /* Linked list structure                    */
Gnum * restrict     w /* [] */,                   /* Flag array                               */
Gnum * restrict     head /* [] */)                /* Linked list structure                    */
{
  Gnum                hash, pend, hmod, lenj, dmax, wflg, dext, psrc, pdst, 
                      wnvi, e, i, j, k, p, degme, x, nelme, nreal, lastd, nleft, 
                      ilast, jlast, inext, jnext, n2, p1, nvpiv, p2, p3, me, nbflag, ln,
                      we, pj, pn, mindeg, elenme, slenme, maxmem, newmem, wf3, wf4, 
                      deg, eln, mem, nel, pme, pas, nvi, nvj, pme1, pme2, knt1, knt2, knt3;
  float               rmf, rmf1;

/** Min fill approximation one extra array of size NBBUCK+2 is needed    **/
/** INTEGER HEAD(0:NBBUCK+1)                                             **/
/** -------------------------------------------------------------------- **/
/** HALOAMD_V6: (January 1999, P. Amestoy)                               **/
/** ***********                                                          **/
/**  1/ ERROR 2 detection followed by stop statement suppressed.         **/
/**  2/ Pb 1  identified in V5 was not correctly solved.                 **/
/**                                                                      **/
/** HALOAMD_V5: (December 1998, P. Amestoy)                              **/
/** ***********                                                          **/
/**  1/ Solved problem with matrix psmigr 1, because upper bound degree  **/
/**     DEG>N was considered as a node of V1.                            **/
/**                                                                      **/
/** HALOAMD_V4: (October 1998, P. Amestoy)                               **/
/** ***********                                                          **/
/**  Only MA41 interface (ok for both scotch and MA41) is included in    **/
/**  this file.                                                          **/
/**                                                                      **/
/** HALOAMD_V3: (August 1998, P. Amestoy)                                **/
/** **********                                                           **/
/**  Solved problem in version 2: variables of V1 with len(i)=0 were not **/
/**  well processed. See modification of the input to characterize those **/
/**  variables.                                                          **/
/**  Problem detected by Jacko Koster while experimenting with C version **/
/**  2 of haloAMD in the context of multiple front method based on       **/
/**  MA27: "if for an interface variable i, row i in the matrix has only **/
/**  a nonzero entry on the diagonal, we first remove this entry and     **/
/**  len(i) is set to zero on input to HALOAMD. However, this means that **/
/**  HALOAMD will treat variable i as an interior variable (in V0)       **/
/**  instead as an interface variable (in V1). It is indeed a bit        **/
/**  strange to have such interface variables but we encountered some    **/
/**  in our debugging experiments with some random partitionings.        **/
/**  Solution:                                                           **/
/**  IF on input i \in V1 and len(i)=0 (that is adjlist(i)={}) THEN      **/
/**  len(i) must be set on input to -N-1.                                **/
/**  ENDIF                                                               **/
/**  Therefore, all variables i / len(i) < 0 and only those are in V1.   **/
/**  Variables with len(i) = -N-1 are then processed differently at the  **/
/**  beginning of the code.                                              **/
/**                                                                      **/
/** HALOAMD_V2: (April 1998)                                             **/
/** **********                                                           **/
/**  The end of the tree (including links to block of flagged indices    **/
/**  is built) . The list of flagged indices is considered as a dense    **/
/**  amalgamated node.                                                   **/
/**  Tested on rosanna: ~amestoy/MA41_NEW/SUN_RISC_dbl/SOFT              **/
/**                                                                      **/
/**  Comments on the OUTPUT:                                             **/
/**  ----------------------                                              **/
/**                                                                      **/
/**  Let V= V0 U V1 the nodes of the initial graph (|V|=n).              **/
/**  The assembly tree corresponds to the tree of the supernodes (or     **/
/**  supervariables). Each node of the assembly tree is then composed of **/
/**  one principal variable and a list of secondary variables. The list  **/
/**  of variable of a node (principal + secondary variables) then        **/
/**  describes the structure of the diagonal bloc of the supernode.      **/
/**  The elimination tree denotes the tree of all the variables(=nodes)  **/
/**  and is therefore of order n. The arrays NV(N) and PE(N) give a      **/
/**  description of the assembly tree.                                   **/
/**                                                                      **/
/**   1/ Description of array nv(N) (on OUPUT)                           **/
/**    nv(i)=0 i is a secondary variable.                                **/
/**    N+1> nv(i) >0 i is a principal variable, nv(i) holds the number   **/
/**    of elements in column i of L (true degree of i)                   **/
/**    nv(i) = N+1 then i is a flagged variable (belonging to V1)        **/
/**                                                                      **/
/**   2/ Description of array PE(N) (on OUPUT)                           **/
/**    pe(i) = -(father of variable/node i) in the elimination tree.     **/
/**    If nv (i) .gt. 0, then i represents a node in the assembly tree,  **/
/**    and the parent of i is -pe (i), or zero if i is a root.           **/
/**    If nv (i) = 0, then (i,-pe (i)) represents an edge in a           **/
/**    subtree, the root of which is a node in the assembly tree.        **/
/**                                                                      **/
/**   3/ Example:                                                        **/
/**    Let If be a root node father of Is in the assembly tree.          **/
/**    If is the principal variable of the node If and let If1, If2, If3 **/
/**    be the secondary variables of node If. Is is the principal        **/
/**    variable of the node Is and let Is1, Is2 be the secondary         **/
/**    variables of node Is.                                             **/
/**    Then:                                                             **/
/**        NV(If1)=NV(If2)=NV(If3) = 0  (secondary variables)            **/
/**        NV(Is1)=NV(Is2) = 0  (secondary variables)                    **/
/**        NV(If) > 0  (principal variable)                              **/
/**        NV(Is) > 0  (principal variable)                              **/
/**        PE(If)  = 0 (root node)                                       **/
/**        PE(Is)  = -If (If is the father of Is in the assembly tree)   **/
/**        PE(If1)=PE(If2)=PE(If3)= -If  (If is the principal variable)  **/
/**        PE(Is1)=PE(Is2)= -Is  (Is is the principal variable)          **/
/**                                                                      **/
/** HALOAMD_V1: (September 1997)                                         **/
/** **********                                                           **/
/**  Initial version designed to experiment the numerical (fill-in)      **/
/**  impact of taking into account the halo. This code should be able to **/
/**  experiment no-halo, partial halo, complete halo.                    **/
/** -------------------------------------------------------------------- **/
/** HALOAMD is designed to process a graph composed of two types         **/
/**            of nodes, V0 and V1, extracted from a larger gragh.       **/
/**            V0^V1 = {},                                               **/
/**            We used Min. degree heuristic to order only               **/
/**            nodes in V0, but the adjacency to nodes                   **/
/**            in V1 is taken into account during ordering.              **/
/**            Nodes in V1 are odered at last.                           **/
/**            Adjacency between nodes of V1 need not be provided,       **/
/**            however |len(i)| must always corresponds to the number of **/
/**            edges effectively provided in the adjacency list of i.    **/
/**          On input :                                                  **/
/**          ********                                                    **/
/**            Nodes INODE in V1 are flagged with len(INODE) = -degree   **/
/**            Update version HALO V3 (August 1998):                     **/
/**            if len(i)=0 and i \in V1 then len(i) must be set          **/
/**            on input to -N-1.                                         **/
/**          ERROR return :                                              **/
/**          ************                                                **/
/**            Negative value in ncmpa indicates an error detected       **/
/**            by HALOAMD.                                               **/
/**                                                                      **/
/**            The graph provided MUST follow the rule:                  **/
/**             if (i,j) is an edge in the gragh then                    **/
/**             j must be in the adjacency list of i AND                 **/
/**             i must be in the adjacency list of j.                    **/
/**                                                                      **/
/**    REMARKS :                                                         **/
/**    -------                                                           **/
/**        1/  Providing edges between nodes of V1 should not            **/
/**            affect the final ordering, only the amount of edges       **/
/**            of the halo should effectively affect the solution.       **/
/**            This code should work in the following cases:             **/
/**              1/ halo not provided                                    **/
/**              2/ halo partially provided                              **/
/**              3/ complete halo                                        **/
/**              4/ complete halo+interconnection between nodes of V1.   **/
/**                                                                      **/
/**             1/ should run and provide identical results (w.r.t to    **/
/**                current implementation of AMD in SCOTCH).             **/
/**             3/ and 4/ should provide identical results.              **/
/**                                                                      **/
/**        2/ All modifications of the MC47 initial code are indicated   **/
/**           with begin HALO .. end HALO                                **/
/**                                                                      **/
/** Ordering of nodes in V0 is based on Approximate Minimum Degree       **/
/** ordering algorithm, with aggressive absorption:                      **/
/** Given a representation of the nonzero pattern of a symmetric matrix, **/
/**       A, (excluding the diagonal) perform an approximate minimum     **/
/**       (UMFPACK/MA38-style) degree ordering to compute a pivot order  **/
/**       such that fill-in in the Cholesky                              **/
/**       factors A = LL^T is kept low.  At each step, the pivot         **/
/**       selected is the one with the minimum UMFPACK/MA38-style        **/
/**       upper-bound on the external degree.  Aggresive absorption is   **/
/**       used to tighten the bound on the degree.  This can result an   **/
/**       significant improvement in the quality of the ordering for     **/
/**       some matrices.                                                 **/
/**       The approximate degree algorithm implemented here is the       **/
/**       symmetric analogue of the degree update algorithm in MA38, by  **/
/**       Davis and Duff, also in the Harwell Subroutine Library.        **/
/**                                                                      **/
/** **** CAUTION:  ARGUMENTS ARE NOT CHECKED FOR ERRORS ON INPUT.  ***** **/
/** ** If you want error checking, a more versatile input format, and ** **/
/** ** a simpler user interface, then use MC47A/AD in the Harwell     ** **/
/** ** Subroutine Library, which checks for errors, transforms the    ** **/
/** ** input, and calls MC47B/BD.                                     ** **/
/** ******************************************************************** **/
/**       References:  (UF Tech Reports are available via anonymous ftp  **/
/**       to ftp.cis.ufl.edu:cis/tech-reports).                          **/
/**       [1] Timothy A. Davis and Iain Duff, "An unsymmetric-pattern    **/
/**               multifrontal method for sparse LU factorization",      **/
/**               SIAM J. Matrix Analysis and Applications, to appear.   **/
/**               also Univ. of Florida Technical Report TR-94-038.      **/
/**               Discuss UMFPACK / MA38.                                **/
/**       [2] Patrick Amestoy, Timothy A. Davis, and Iain S. Duff,       **/
/**               "An approximate minimum degree ordering algorithm,"    **/
/**               SIAM J. Matrix Analysis and Applications (to appear),  **/
/**               also Univ. of Florida Technical Report TR-94-039.      **/
/**               Discusses this routine.                                **/
/**       [3] Alan George and Joseph Liu, "The evolution of the          **/
/**               minimum degree ordering algorithm," SIAM Review, vol.  **/
/**               31, no. 1, pp. 1-19, March 1989.  We list below the    **/
/**               features mentioned in that paper that this code        **/
/**               includes:                                              **/
/**       mass elimination:                                              **/
/**               Yes.  MA27 relied on supervariable detection for mass  **/
/**               elimination.                                           **/
/**       indistinguishable nodes:                                       **/
/**               Yes (we call these "supervariables").  This was also   **/
/**               in the MA27 code - although we modified the method of  **/
/**               detecting them (the previous hash was the true degree, **/
/**               which we no longer keep track of).  A supervariable is **/
/**               a set of rows with identical nonzero pattern.  All     **/
/**               variables in a supervariable are eliminated together.  **/
/**               Each supervariable has as its numerical name that of   **/
/**               one of its variables (its principal variable).         **/
/**       quotient graph representation:                                 **/
/**               Yes.  We use the term "element" for the cliques formed **/
/**               during elimination.  This was also in the MA27 code.   **/
/**               The algorithm can operate in place, but it will work   **/
/**               more efficiently if given some "elbow room."           **/
/**       element absorption:                                            **/
/**               Yes.  This was also in the MA27 code.                  **/
/**       external degree:                                               **/
/**               Yes.  The MA27 code was based on the true degree.      **/
/**       incomplete degree update and multiple elimination:             **/
/**               No.  This was not in MA27, either.  Our method of      **/
/**               degree update within MC47B/BD is element-based, not    **/
/**               variable-based.  It is thus not well-suited for use    **/
/**               with incomplete degree update or multiple elimination. **/
/** -------------------------------------------------------------------- **/
/** Authors, and Copyright (C) 1995 by:                                  **/
/**       Timothy A. Davis, Patrick Amestoy, Iain S. Duff, &             **/
/**       John K. Reid.                                                  **/
/** Modified (V1) by P.R. Amestoy ENSEEIHT (1997)                        **/
/** Modified (V2) by P.R. Amestoy ENSEEIHT (1998)                        **/
/** Modified (V3) by P.R. Amestoy ENSEEIHT (1998)                        **/
/** Modified (V4) by P.R. Amestoy ENSEEIHT (1998)                        **/
/** Modified (V5) by P.R. Amestoy ENSEEIHT (1998)                        **/
/** Modified (V6) by P.R. Amestoy ENSEEIHT (1999)                        **/
/**                                                                      **/
/** Dates: September, 1995                                               **/
/**        September, 1997 (halo AMD V1)                                 **/
/**        April, 1998 (halo AMD V2)                                     **/
/**        August, 1998 (halo AMD V3)                                    **/

  -- w;                                           /* Parameter adjustments */
  -- next;
  -- wf;
  -- degree;
  -- last;
  -- elen;
  -- nv;
  -- len;
  -- pe;
  -- iw;
/* -- head;                                          Array head not updated since starts from 0 */

  n2 = - (nbbuck + 1);
/*  pas = n / 8; [Update F.P. 20020715 selon hamf_20020220] Distance betweeen elements of the N, ..., NBBUCK entries of HEAD */
  pas = MAX ((n / 8), 1);                         /* Distance betweeen elements of the N, ..., NBBUCK entries of HEAD        */
  wflg = 2;
  *ncmpa = 0;
  nel = 0;
  hmod = MAX (1, nbbuck - 1);
  dmax = 0;
  mem = pfree - 1;
  maxmem = mem;
  mindeg = 0;
  rmf = (float) (n) * (float) (n - 1);            /* Average sparsity of matrix; diagonal entry is not in mem */
  nbflag = 0;
  lastd = 0;

  memSet (head, 0, (nbbuck + 2) * sizeof (Gnum));
  memSet (last + 1, 0, n * sizeof (Gnum));

  if (nbelts == 0) {                              /* Patch 8/12/03 <PA> */
    memSet (elen + 1, 0, n * sizeof (Gnum));      
    for (i = 1; i <= n; i ++) {
      nv[i] = 1;
      w[i]  = 1;
      if (len[i] < 0) {
        degree[i] = n2;
        nbflag ++;
        if (len[i] == - (n + 1)) {                /* Patch 09/08/98 <PA+FP> */
          len[i] = 0;
          pe[i]  = 0;                             /* Patch 12/12/03 <PA>: Because of compress, we force skipping those entries (which are anyway empty) */
        }
        else
          len[i] = - len[i];
      }
      else
        degree[i] = len[i];
    }
  }
  else  {                                         /* Patch 08/12/03 <PA>: Duplicate part of previous loop to avoid sytematic testing for elements */
    for (i = 1; i <= n; i ++) {
      nv[i] = 1;
      w[i]  = 1;
      if (len[i] < 0) {                           /* i \in V1 */
        degree[i] = n2;
        nbflag ++;
        if (len[i] == - (n + 1)) {                /* Patch 09/08/98 <PA+FP> */
          len[i]  = 0;
          pe[i]   = 0;                            /* Patch 12/12/03 <PA>: because of compress, we force skipping those entries (which are anyway empty) */
          elen[i] = 0;                            /* Patch 16/12/03 <PA> */
        }
        else {
          len[i]  = - len[i];
          elen[i] = len[i];                       /* Patch 16/12/03 <PA>: only elements are adjacent to a variable */
        }
      }
      else {                                      /* i \in Ve or V0 */
        if (elen[i] < 0) {                        /* i \in Ve       */
          nel ++;
          degree[i] = len[i];
          elen[i]   = - nel;
          dmax      = MAX (dmax, degree[i]);      /* Patch 11/03/04 <PA> */
        }
        else {
          degree[i] = elen[i];
          elen[i]   = len[i];                     /* Patch 16/12/03 <PA>: only elements are adjacent to a variable */
        }
      }
    }
  }

/* Temporary Patch 8/12/03 <PA> TODO REMOVE */
  if (nbelts != nel)
    printf ("error 8Dec2003\n");

  nreal = n - nbflag;

  for (i = 1; i <= n; i ++) {
    if (elen[i] < 0 )                             /* Patch 16/12/03 <PA>: Skip elements */
      continue;

    deg = degree[i];
    if (deg == n2) {
      deg = nbbuck + 1;
      if (lastd == 0) {
        lastd     = i;
        head[deg] = i;
        next[i]   = 0;
        last[i]   = 0;
      }
      else {
        next[lastd] = i;
        last[i]     = lastd;
        lastd       = i;
        next[i]     = 0;
      }
    }
    else if (deg > 0) {
      if (nbelts != 0) {                          /* Patch 04/01/04 <FP+PA>           */
        Gnum                l;                    /* Size of largest adjacent element */
        Gnum                m;                    /* Current edge being visited       */

        for (m = pe[i], l = 0; m < pe[i] + elen[i]; m ++) {
          Gnum                o;                  /* Current element being visited   */

          o = iw[m];
          if (len[o] > l)
            l = len[o];
        }
        deg = (Gnum) ((float) deg * (float) (deg - 1) - (float) l * (float) (l - 1)) / 2;
        if (deg < 0)                              /* Patch 04/01/04 <FP> */
          deg = 0;
      }
      wf[i] = deg;                                /* Patch 14/01/04 <PA> */
      if (deg > n)
        deg = MIN ((deg - n) / pas + n, nbbuck);
      inext = head[deg];
      if (inext != 0)
        last[inext] = i;
      next[i]   = inext;
      head[deg] = i;
    }
    else {
      nel ++;
      elen[i] = - nel;
      pe[i]   = 0;
      w[i]    = 0;
    }
  }                                               /* L20: */

  nleft = n - nel;                                /* Patch v5 12/12/98 <PA+FP> */

  while (nel < nreal) {                           /* WHILE (selecting pivots) DO */
    for (deg = mindeg; deg <= nbbuck; deg ++) {
       me = head[deg];
       if (me > 0)
         break;                                   /* GO to 50 */
    }                                             /* L40:     */
    mindeg = deg;
    if (me <= 0) {                                /* Error 1 */
      *ncmpa = -n;
      return;
    }

    if (deg > n) {
      j = next[me];
      k = wf[me];
      while (j > 0) {
        if (wf[j] < k) {
          me = j;
          k  = wf[me];
        }
        j = next[j];
      }
      ilast = last[me];
      inext = next[me];
      if (inext != 0)
        last[inext] = ilast;
      if (ilast != 0)
        next[ilast] = inext;
      else
        head[deg] = inext;                        /* me is at the head of the degree list */
    }
    else {
      inext = next[me];
      if (inext != 0)
        last[inext] = 0;
      head[deg] = inext;
    }

    elenme   = elen[me];
    elen[me] = - (nel + 1);
    nvpiv    = nv[me];
    nel     += nvpiv;

    nv[me] = - nvpiv;
    degme  = 0;
    if (elenme == 0) {
      pme1 = pe[me];
      pme2 = pme1 - 1;

      for (p = pme1; p <= pme1 + len[me] - 1; p ++) {
        i   = iw[p];
        nvi = nv[i];
        if (nvi > 0) {
          degme +=   nvi;
          nv[i]  = - nvi;
          pme2 ++;
          iw[pme2] = i;

          if (degree[i] != n2) {
            ilast = last[i];
            inext = next[i];
            if (inext != 0)
              last[inext] = ilast;
            if (ilast != 0)
              next[ilast] = inext;
            else {
              if (wf[i] > n)
                deg = MIN ((wf[i] - n) / pas + n, nbbuck);
              else
                deg = wf[i];
              head[deg] = inext;
            }
          }
        }
      }                                           /* L60: */

      newmem = 0;
    }
    else {
      p    = pe[me];
      pme1 = pfree;
      slenme = len[me] - elenme;
      for (knt1 = 1; knt1 <= elenme + 1; knt1 ++) {
        if (knt1 > elenme) {
          e  = me;
          pj = p;
          ln = slenme;
        }
        else {
          e  = iw[p ++];
          pj = pe[e];
          ln = len[e];
        }

        for (knt2 = 1; knt2 <= ln; knt2 ++) {
          i   = iw[pj ++];
          nvi = nv[i];
          if (nvi > 0) {
            if (pfree > iwlen) {
              pe[me]   = p;
              len[me] -= knt1;
              if (len[me] == 0)
                pe[me] = 0;
              pe[e]  = pj;
              len[e] = ln - knt2;
              if (len[e] == 0)
                pe[e] = 0;
              (*ncmpa) ++;

              for (j = 1; j <= n; j ++) {
                pn = pe[j];
                if (pn > 0) {
                  pe[j]  = iw[pn];
                  iw[pn] = - j;
                }
              }                                   /* L70: */

              pdst = 1;
              psrc = 1;
              pend = pme1 - 1;

              while (psrc <= pend) {              /* L80: */
                j = - iw[psrc ++];
                if (j > 0) {
                  iw[pdst] = pe[j];
                  pe[j]    = pdst ++;
                  lenj     = len[j];
                  for (knt3 = 0; knt3 <= lenj - 2; knt3 ++)
                    iw[pdst + knt3] = iw[psrc + knt3];
                  pdst = pdst + (lenj - 1);
                  psrc = psrc + (lenj - 1);
                }
              }

              p1 = pdst;
              for (psrc = pme1; psrc <= pfree - 1; psrc ++, pdst ++) /* L100: */
                iw[pdst] = iw[psrc];
              pme1 = p1;
              pfree = pdst;
              pj = pe[e];
              p  = pe[me];
            }

            degme +=   nvi;
            nv[i]  = - nvi;
            iw[pfree] = i;
            (pfree) ++;

            if (degree[i] != n2) {
              ilast = last[i];
              inext = next[i];
              if (inext != 0)
                last[inext] = ilast;
              if (ilast != 0)
                next[ilast] = inext;
              else {
                if (wf[i] > n)
                  deg = MIN ((wf[i] - n) / pas + n, nbbuck);
                else
                  deg = wf[i];
                head[deg] = inext;
              }
            }
          }
        }                                         /* L110: */

        if (e != me) {
          pe[e] = -me;
          w[e]  = 0;
        }
      }                                           /* L120: */
      pme2 = pfree - 1;

      newmem = pfree - pme1;
      mem   += newmem;
      maxmem = MAX (maxmem, mem);
    }

    degree[me] = degme;
    pe[me]     = pme1;
    len[me]    = pme2 - pme1 + 1;

    if (wflg + n <= wflg) {
      for (x = 1; x <= n; x ++) {
        if (w[x] != 0)
          w[x] = 1;
      }                                           /* L130: */
      wflg = 2;
    }

    for (pme = pme1; pme <= pme2; pme ++) {
      i   = iw[pme];
      eln = elen[i];
      if (eln > 0) {
        nvi  = - nv[i];
        wnvi = wflg - nvi;
        for (p = pe[i]; p < pe[i] + eln; p ++) {
          e  = iw[p];
          we = w[e];
          if (we >= wflg)
            we -= nvi;
          else if (we != 0) {
            we    = degree[e] + wnvi;
            wf[e] = 0;
          }
          w[e] = we;
        }                                         /* L140: */
      }
    }                                             /* L150: */

    for (pme = pme1; pme <= pme2; pme ++) {
      i  = iw[pme];
      p1 = pe[i];
      p2 = p1 + elen[i] - 1;
      pn = p1;
      hash = 0;
      deg  = 0;
      wf3  = 0;
      wf4  = 0;
      nvi  = - nv[i];

      for (p = p1; p <= p2; p ++) {
        e    = iw[p];
        dext = w[e] - wflg;
        if (dext > 0) {
          if (wf[e] == 0)
            wf[e] = dext * ((2 * degree[e]) - dext - 1);
          wf4      += wf[e];
          deg      += dext;
          iw[pn ++] = e;
          hash     += e;
        }
        else if (dext == 0) {
          pe[e] = -me;
          w[e]  = 0;
        }
      }                                           /* L160: */
      elen[i] = pn - p1 + 1;

      p3 = pn;
      for (p = p2 + 1; p < p1 + len[i]; p ++) {
        j   = iw[p];
        nvj = nv[j];
        if (nvj > 0) {
          deg += nvj;
          wf3 += nvj;
          iw[pn ++] = j;
          hash += j;
        }
      }                                           /* L170: */

      if (degree[i] == n2)
        deg = n2;
      if (deg == 0) {
        pe[i]   = - me;
        nvi     = - nv[i];
        degme  -= nvi;
        nvpiv  += nvi;
        nel    += nvi;
        nv[i]   = 0;
        elen[i] = 0;
      }
      else {
        if (degree[i] != n2) {
          if (degree[i] < deg) {
            wf4 = 0;
            wf3 = 0;
          }
          else
            degree[i] = deg;
        }
        wf[i]  = wf4 + 2 * nvi * wf3;
        iw[pn] = iw[p3];
        iw[p3] = iw[p1];
        iw[p1] = me;
        len[i] = pn - p1 + 1;

        if (deg != n2) {
          hash = (hash % hmod) + 1;
          j = head[hash];
          if (j <= 0) {
            next[i]    = - j;
            head[hash] = - i;
          }
          else {
            next[i] = last[j];
            last[j] = i;
          }
          last[i] = hash;
        }
      }
    }                                             /* L180: */
    degree[me] = degme;

    dmax  = MAX (dmax, degme);
    wflg += dmax;

    if (wflg + n <= wflg) {
      for (x = 1; x <= n; x ++) {
        if (w[x] != 0)
          w[x] = 1;
      }
      wflg = 2;
    }

    for (pme = pme1; pme <= pme2; pme ++) {
      i = iw[pme];
      if ((nv[i] < 0) && (degree[i] != n2)) {
        hash = last[i];
        j    = head[hash];
        if (j == 0)
          continue;
        if (j < 0) {
          i = - j;
          head[hash] = 0;
        }
        else {
          i       = last[j];
          last[j] = 0;
        }
        if (i == 0)
          continue;

L200:                                             /* WHILE LOOP: */
        if (next[i] != 0) {
          ln  = len[i];
          eln = elen[i];
          for (p = pe[i] + 1; p < pe[i] + ln; p ++)
            w[iw[p]] = wflg;

          jlast = i;
          j = next[i];

L220:                                             /* WHILE LOOP: */
          if (j != 0) {
            if (len[j] != ln)
              goto L240;
            if (elen[j] != eln)
              goto L240;

            for (p = pe[j] + 1; p < pe[j] + ln; p ++) {
              if (w[iw[p]] != wflg)
                goto L240;
            }                                     /* L230: */

            pe[j]   = -i;
            if (wf[j] > wf[i])
              wf[i] = wf[j];
            nv[i]  += nv[j];
            nv[j]   = 0;
            elen[j] = 0;

            j           = next[j];
            next[jlast] = j;
            goto L220;

L240:
            jlast = j;
            j     = next[j];
            goto L220;
          }

          wflg ++;
          i = next[i];
          if (i != 0)
            goto L200;
        }
      }
    }

    p     = pme1;
    nleft = n - nel;
    for (pme = pme1; pme <= pme2; pme ++) {
      i   = iw[pme];
      nvi = - nv[i];
      if (nvi > 0) {
        nv[i] = nvi;
        if (degree[i] != n2) {
          deg = MIN (degree[i] + degme, nleft) - nvi;
          if (degree[i] + degme > nleft) {
            deg       = degree[i];
            rmf1      = (float) deg * (float) (deg - 1 + (2 * degme)) - (float) wf[i];
            degree[i] = nleft - nvi;
	    deg       = degree[i];
            rmf = (float) deg * (float) (deg - 1) - (float) (degme - nvi) * (float) (degme - nvi - 1);
            rmf = MIN (rmf, rmf1);
          }
          else {
            deg       = degree[i];
            degree[i] = degree[i] + degme - nvi;
            rmf = (float) deg * (float) (deg - 1 + (2 * degme)) - (float) wf[i];
          }

          wf[i] = (int) (rmf / (float) (nvi + 1) + 0.5);
          wf[i] = MAX (0, wf[i]);
          deg   = wf[i];
          if (deg > n)
            deg = MIN ((deg - n) / pas + n, nbbuck);
          inext = head[deg];
          if (inext != 0)
            last[inext] = i;
          next[i]   = inext;
          last[i]   = 0;
          head[deg] = i;

          mindeg    = MIN (mindeg, deg);
        }

        iw[p ++] = i;
      }
    } /* L260: */

    nv[me]  = nvpiv + degme;
    len[me] = p - pme1;
    if (len[me] == 0) {
      pe[me] = 0;
      w[me]  = 0;
    }
    if (newmem != 0) {
      pfree = p;
      mem   = mem - newmem + len[me];
    }
  }                                             /* END WHILE (selecting pivots) */

  if (nel < n) {                                /* Patch 12/12/98 <PA+FP> (old: nreal < n) */
    for (deg = mindeg; deg <= (nbbuck + 1); deg ++) {
      me = head[deg];
      if (me > 0)
        break;
    }

    mindeg = deg;
    nelme  = - (nel + 1);
    for (x = 1; x <= n; x ++) {
      if ((pe[x] > 0) && (elen[x] < 0))
        pe[x] = - me;
      else if (degree[x] == n2) {
        nel    += nv[x];
        pe[x]   = - me;
        elen[x] = 0;
        nv[x]   = 0;                              /* Patch 12/12/98 <PA+FP> (old: n + 1) */
      }
    }

    elen[me] = nelme;
    nv[me]   = n - nreal;                         /* Patch 12/12/98 <PA+FP> (old: n + 1) */
    pe[me]   = 0;
    if (nel != n) {                               /* Error 2 */
      *ncmpa = - (n + 1);
      return;
    }
  }

  for (i = 1; i <= n; i ++) {
    if (elen[i] == 0) {
      j = - pe[i];

      while (elen[j] >= 0)                        /* L270: */
        j = - pe[j];
      e = j;

      k = - elen[e];
      j = i;

      while (elen[j] >= 0) {                      /* L280: */
        jnext = - pe[j];
        pe[j] = - e;
        if (elen[j] == 0)
          elen[j] = k ++;
        j = jnext;
      }
      elen[e] = - k;
    }
  }                                               /* L290: */

#ifdef DEAD_CODE
  for (i = 1; i <= n; i ++) {                     /* Patch 19/10/98 <PA+FP>   */
    k = abs (elen[i]);
    last[k] = i;
    elen[i] = k;
  }                                               /* L300: */
#endif /* DEAD_CODE */

  pfree = maxmem;
}