text: #include "cxsparse/cs.h"
  /* breadth-first search for coarse decomposition (C0,C1,R1 or R0,R3,C3) */
  static CS_INT cs_bfs (const cs *A, CS_INT n, CS_INT *wi, CS_INT *wj, CS_INT *queue,
      const CS_INT *imatch, const CS_INT *jmatch, CS_INT mark)
  {
      CS_INT *Ap, *Ai, head = 0, tail = 0, j, i, p, j2 ;
      cs *C ;
      for (j = 0 ; j < n ; j++)           /* place all unmatched nodes in queue */
      {
          if (imatch [j] >= 0) continue ; /* skip j if matched */
          wj [j] = 0 ;                    /* j in set C0 (R0 if transpose) */
          queue [tail++] = j ;            /* place unmatched col j in queue */
      }
      if (tail == 0) return (1) ;         /* quick return if no unmatched nodes */
      C = (mark == 1) ? ((cs *) A) : cs_transpose (A, 0) ;
      if (!C) return (0) ;                /* bfs of C=A' to find R3,C3 from R0 */
      Ap = C->p ; Ai = C->i ;
      while (head < tail)                 /* while queue is not empty */
      {
          j = queue [head++] ;            /* get the head of the queue */
          for (p = Ap [j] ; p < Ap [j+1] ; p++)
          {
              i = Ai [p] ;
              if (wi [i] >= 0) continue ; /* skip if i is marked */
              wi [i] = mark ;             /* i in set R1 (C3 if transpose) */
              j2 = jmatch [i] ;           /* traverse alternating path to j2 */
              if (wj [j2] >= 0) continue ;/* skip j2 if it is marked */
              wj [j2] = mark ;            /* j2 in set C1 (R3 if transpose) */
              queue [tail++] = j2 ;       /* add j2 to queue */
          }
      }
      if (mark != 1) cs_spfree (C) ;      /* free A' if it was created */
      return (1) ;
  }
  
  /* collect matched rows and columns into p and q */
  static void cs_matched (CS_INT n, const CS_INT *wj, const CS_INT *imatch, CS_INT *p, CS_INT *q,
      CS_INT *cc, CS_INT *rr, CS_INT set, CS_INT mark)
  {
      CS_INT kc = cc [set], j ;
      CS_INT kr = rr [set-1] ;
      for (j = 0 ; j < n ; j++)
      {
          if (wj [j] != mark) continue ;      /* skip if j is not in C set */
          p [kr++] = imatch [j] ;
          q [kc++] = j ;
      }
      cc [set+1] = kc ;
      rr [set] = kr ;
  }
  
  /* collect unmatched rows into the permutation vector p */
  static void cs_unmatched (CS_INT m, const CS_INT *wi, CS_INT *p, CS_INT *rr, CS_INT set)
  {
      CS_INT i, kr = rr [set] ;
      for (i = 0 ; i < m ; i++) if (wi [i] == 0) p [kr++] = i ;
      rr [set+1] = kr ;
  }
  
  /* return 1 if row i is in R2 */
  static CS_INT cs_rprune (CS_INT i, CS_INT j, CS_ENTRY aij, void *other)
  {
      CS_INT *rr = (CS_INT *) other ;
      return (i >= rr [1] && i < rr [2]) ;
  }
  
  /* Given A, compute coarse and then fine dmperm */
  csd *cs_dmperm (const cs *A, CS_INT seed)
  {
      CS_INT m, n, i, j, k, cnz, nc, *jmatch, *imatch, *wi, *wj, *pinv, *Cp, *Ci,
          *ps, *rs, nb1, nb2, *p, *q, *cc, *rr, *r, *s, ok ;
      cs *C ;
      csd *D, *scc ;
      /* --- Maximum matching ------------------------------------------------- */
      if (!CS_CSC (A)) return (NULL) ;            /* check inputs */
      m = A->m ; n = A->n ;
      D = cs_dalloc (m, n) ;                      /* allocate result */
      if (!D) return (NULL) ;
      p = D->p ; q = D->q ; r = D->r ; s = D->s ; cc = D->cc ; rr = D->rr ;
      jmatch = cs_maxtrans (A, seed) ;            /* max transversal */
      imatch = jmatch + m ;                       /* imatch = inverse of jmatch */
      if (!jmatch) return (cs_ddone (D, NULL, jmatch, 0)) ;
      /* --- Coarse decomposition --------------------------------------------- */
      wi = r ; wj = s ;                           /* use r and s as workspace */
      for (j = 0 ; j < n ; j++) wj [j] = -1 ;     /* unmark all cols for bfs */
      for (i = 0 ; i < m ; i++) wi [i] = -1 ;     /* unmark all rows for bfs */
      cs_bfs (A, n, wi, wj, q, imatch, jmatch, 1) ;       /* find C1, R1 from C0*/
      ok = cs_bfs (A, m, wj, wi, p, jmatch, imatch, 3) ;  /* find R3, C3 from R0*/
      if (!ok) return (cs_ddone (D, NULL, jmatch, 0)) ;
      cs_unmatched (n, wj, q, cc, 0) ;                    /* unmatched set C0 */
      cs_matched (n, wj, imatch, p, q, cc, rr, 1, 1) ;    /* set R1 and C1 */
      cs_matched (n, wj, imatch, p, q, cc, rr, 2, -1) ;   /* set R2 and C2 */
      cs_matched (n, wj, imatch, p, q, cc, rr, 3, 3) ;    /* set R3 and C3 */
      cs_unmatched (m, wi, p, rr, 3) ;                    /* unmatched set R0 */
      cs_free (jmatch) ;
      /* --- Fine decomposition ----------------------------------------------- */
      pinv = cs_pinv (p, m) ;         /* pinv=p' */
      if (!pinv) return (cs_ddone (D, NULL, NULL, 0)) ;
      C = cs_permute (A, pinv, q, 0) ;/* C=A(p,q) (it will hold A(R2,C2)) */
      cs_free (pinv) ;
      if (!C) return (cs_ddone (D, NULL, NULL, 0)) ;
      Cp = C->p ;
      nc = cc [3] - cc [2] ;          /* delete cols C0, C1, and C3 from C */
      if (cc [2] > 0) for (j = cc [2] ; j <= cc [3] ; j++) Cp [j-cc[2]] = Cp [j] ;
      C->n = nc ;
      if (rr [2] - rr [1] < m)        /* delete rows R0, R1, and R3 from C */
      {
          cs_fkeep (C, cs_rprune, rr) ;
          cnz = Cp [nc] ;
          Ci = C->i ;
          if (rr [1] > 0) for (k = 0 ; k < cnz ; k++) Ci [k] -= rr [1] ;
      }
      C->m = nc ;
      scc = cs_scc (C) ;              /* find strongly connected components of C*/
      if (!scc) return (cs_ddone (D, C, NULL, 0)) ;
      /* --- Combine coarse and fine decompositions --------------------------- */
      ps = scc->p ;                   /* C(ps,ps) is the permuted matrix */
      rs = scc->r ;                   /* kth block is rs[k]..rs[k+1]-1 */
      nb1 = scc->nb  ;                /* # of blocks of A(R2,C2) */
      for (k = 0 ; k < nc ; k++) wj [k] = q [ps [k] + cc [2]] ;
      for (k = 0 ; k < nc ; k++) q [k + cc [2]] = wj [k] ;
      for (k = 0 ; k < nc ; k++) wi [k] = p [ps [k] + rr [1]] ;
      for (k = 0 ; k < nc ; k++) p [k + rr [1]] = wi [k] ;
      nb2 = 0 ;                       /* create the fine block partitions */
      r [0] = s [0] = 0 ;
      if (cc [2] > 0) nb2++ ;         /* leading coarse block A (R1, [C0 C1]) */
      for (k = 0 ; k < nb1 ; k++)     /* coarse block A (R2,C2) */
      {
          r [nb2] = rs [k] + rr [1] ; /* A (R2,C2) splits into nb1 fine blocks */
          s [nb2] = rs [k] + cc [2] ;
          nb2++ ;
      }
      if (rr [2] < m)
      {
          r [nb2] = rr [2] ;          /* trailing coarse block A ([R3 R0], C3) */
          s [nb2] = cc [3] ;
          nb2++ ;
      }
      r [nb2] = m ;
      s [nb2] = n ;
      D->nb = nb2 ;
      cs_dfree (scc) ;
      return (cs_ddone (D, C, NULL, 1)) ;
  }
  