      subroutine nroc (n, ic, ia, ja, a, jar, ar, p, flag)
clll. optimize
c
c       ----------------------------------------------------------------
c
c               yale sparse matrix package - nonsymmetric codes
c                    solving the system of equations mx = b
c
c    i.   calling sequences
c         the coefficient matrix can be processed by an ordering routine
c    (e.g., to reduce fillin or ensure numerical stability) before using
c    the remaining subroutines.  if no reordering is done, then set
c    r(i) = c(i) = ic(i) = i  for i=1,...,n.  if an ordering subroutine
c    is used, then nroc should be used to reorder the coefficient matrix
c    the calling sequence is --
c        (       (matrix ordering))
c        (nroc   (matrix reordering))
c         nsfc   (symbolic factorization to determine where fillin will
c                  occur during numeric factorization)
c         nnfc   (numeric factorization into product ldu of unit lower
c                  triangular matrix l, diagonal matrix d, and unit
c                  upper triangular matrix u, and solution of linear
c                  system)
c         nnsc   (solution of linear system for additional right-hand
c                  side using ldu factorization from nnfc)
c    (if only one system of equations is to be solved, then the
c    subroutine trk should be used.)
c
c    ii.  storage of sparse matrices
c         the nonzero entries of the coefficient matrix m are stored
c    row-by-row in the array a.  to identify the individual nonzero
c    entries in each row, we need to know in which column each entry
c    lies.  the column indices which correspond to the nonzero entries
c    of m are stored in the array ja.  i.e., if  a(k) = m(i,j),  then
c    ja(k) = j.  in addition, we need to know where each row starts and
c    how long it is.  the index positions in ja and a where the rows of
c    m begin are stored in the array ia.  i.e., if m(i,j) is the first
c    (leftmost) entry in the i-th row and  a(k) = m(i,j),  then
c    ia(i) = k.  moreover, the index in ja and a of the first location
c    following the last element in the last row is stored in ia(n+1).
c    thus, the number of entries in the i-th row is given by
c    ia(i+1) - ia(i),  the nonzero entries of the i-th row are stored
c    consecutively in
c            a(ia(i)),  a(ia(i)+1),  ..., a(ia(i+1)-1),
c    and the corresponding column indices are stored consecutively in
c            ja(ia(i)), ja(ia(i)+1), ..., ja(ia(i+1)-1).
c    for example, the 5 by 5 matrix
c                ( 1. 0. 2. 0. 0.)
c                ( 0. 3. 0. 0. 0.)
c            m = ( 0. 4. 5. 6. 0.)
c                ( 0. 0. 0. 7. 0.)
c                ( 0. 0. 0. 8. 9.)
c    would be stored as
c               - 1  2  3  4  5  6  7  8  9
c            ---+--------------------------
c            ia - 1  3  4  7  8 10
c            ja - 1  3  2  2  3  4  4  4  5
c             a - 1. 2. 3. 4. 5. 6. 7. 8. 9.         .
c
c         the strict upper (lower) triangular portion of the matrix
c    u (l) is stored in a similar fashion using the arrays  iu, ju, u
c    (il, jl, l)  except that an additional array iju (ijl) is used to
c    compress storage of ju (jl) by allowing some sequences of column
c    (row) indices to used for more than one row (column)  (n.b., l is
c    stored by columns).  iju(k) (ijl(k)) points to the starting
c    location in ju (jl) of entries for the kth row (column).
c    compression in ju (jl) occurs in two ways.  first, if a row
c    (column) i was merged into the current row (column) k, and the
c    number of elements merged in from (the tail portion of) row
c    (column) i is the same as the final length of row (column) k, then
c    the kth row (column) and the tail of row (column) i are identical
c    and iju(k) (ijl(k)) points to the start of the tail.  second, if
c    some tail portion of the (k-1)st row (column) is identical to the
c    head of the kth row (column), then iju(k) (ijl(k)) points to the
c    start of that tail portion.  for example, the nonzero structure of
c    the strict upper triangular part of the matrix
c            d 0 x x x
c            0 d 0 x x
c            0 0 d x 0
c            0 0 0 d x
c            0 0 0 0 d
c    would be represented as
c                - 1 2 3 4 5 6
c            ----+------------
c             iu - 1 4 6 7 8 8
c             ju - 3 4 5 4
c            iju - 1 2 4 3           .
c    the diagonal entries of l and u are assumed to be equal to one and
c    are not stored.  the array d contains the reciprocals of the
c    diagonal entries of the matrix d.
c
c    iii. additional storage savings
c         in nsfc, r and ic can be the same array in the calling
c    sequence if no reordering of the coefficient matrix has been done.
c         in nnfc, r, c, and ic can all be the same array if no
c    reordering has been done.  if only the rows have been reordered,
c    then c and ic can be the same array.  if the row and column
c    orderings are the same, then r and c can be the same array.  z and
c    row can be the same array.
c         in nnsc or nntc, r and c can be the same array if no
c    reordering has been done or if the row and column orderings are the
c    same.  z and b can be the same array.  however, then b will be
c    destroyed.
c
c    iv.  parameters
c         following is a list of parameters to the programs.  names are
c    uniform among the various subroutines.  class abbreviations are --
c       n - integer variable
c       f - real variable
c       v - supplies a value to a subroutine
c       r - returns a result from a subroutine
c       i - used internally by a subroutine
c       a - array
c
c class - parameter
c ------+----------
c fva   - a     - nonzero entries of the coefficient matrix m, stored
c       -           by rows.
c       -           size = number of nonzero entries in m.
c fva   - b     - right-hand side b.
c       -           size = n.
c nva   - c     - ordering of the columns of m.
c       -           size = n.
c fvra  - d     - reciprocals of the diagonal entries of the matrix d.
c       -           size = n.
c nr    - flag  - error flag.  values and their meanings are --
c       -            0     no errors detected
c       -            n+k   null row in a  --  row = k
c       -           2n+k   duplicate entry in a  --  row = k
c       -           3n+k   insufficient storage for jl  --  row = k
c       -           4n+1   insufficient storage for l
c       -           5n+k   null pivot  --  row = k
c       -           6n+k   insufficient storage for ju  --  row = k
c       -           7n+1   insufficient storage for u
c       -           8n+k   zero pivot  --  row = k
c nva   - ia    - pointers to delimit the rows of a.
c       -           size = n+1.
c nvra  - ijl   - pointers to the first element in each column in jl,
c       -           used to compress storage in jl.
c       -           size = n.
c nvra  - iju   - pointers to the first element in each row in ju, used
c       -           to compress storage in ju.
c       -           size = n.
c nvra  - il    - pointers to delimit the columns of l.
c       -           size = n+1.
c nvra  - iu    - pointers to delimit the rows of u.
c       -           size = n+1.
c nva   - ja    - column numbers corresponding to the elements of a.
c       -           size = size of a.
c nvra  - jl    - row numbers corresponding to the elements of l.
c       -           size = jlmax.
c nv    - jlmax - declared dimension of jl.  jlmax must be larger than
c       -           the number of nonzeros in the strict lower triangle
c       -           of m plus fillin minus compression.
c nvra  - ju    - column numbers corresponding to the elements of u.
c       -           size = jumax.
c nv    - jumax - declared dimension of ju.  jumax must be larger than
c       -           the number of nonzeros in the strict upper triangle
c       -           of m plus fillin minus compression.
c fvra  - l     - nonzero entries in the strict lower triangular portion
c       -           of the matrix l, stored by columns.
c       -           size = lmax.
c nv    - lmax  - declared dimension of l.  lmax must be larger than
c       -           the number of nonzeros in the strict lower triangle
c       -           of m plus fillin  (il(n+1)-1 after nsfc).
c nv    - n     - number of variables/equations.
c nva   - r     - ordering of the rows of m.
c       -           size = n.
c fvra  - u     - nonzero entries in the strict upper triangular portion
c       -           of the matrix u, stored by rows.
c       -           size = umax.
c nv    - umax  - declared dimension of u.  umax must be larger than
c       -           the number of nonzeros in the strict upper triangle
c       -           of m plus fillin  (iu(n+1)-1 after nsfc).
c fra   - z     - solution x.
c       -           size = n.
c
c       ----------------------------------------------------------------
c
c*** subroutine nroc
c*** reorders rows of a, leaving row order unchanged
c
c
c       input parameters.. n, ic, ia, ja, a
c       output parameters.. ja, a, flag
c
c       parameters used internally..
c nia   - p     - at the kth step, p is a linked list of the reordered
c       -           column indices of the kth row of a.  p(n+1) points
c       -           to the first entry in the list.
c       -           size = n+1.
c nia   - jar   - at the kth step,jar contains the elements of the
c       -           reordered column indices of a.
c       -           size = n.
c fia   - ar    - at the kth step, ar contains the elements of the
c       -           reordered row of a.
c       -           size = n.
c
      integer  ic(1), ia(1), ja(1), jar(1), p(1), flag
      real  a(1), ar(1)
c     double precision  a(1), ar(1)
c
c  ******  for each nonempty row  *******************************
      do 5 k=1,n
        jmin = ia(k)
        jmax = ia(k+1) - 1
        if(jmin .gt. jmax) go to 5
        p(n+1) = n + 1
c  ******  insert each element in the list  *********************
        do 3 j=jmin,jmax
          newj = ic(ja(j))
          i = n + 1
   1      if(p(i) .ge. newj) go to 2
            i = p(i)
            go to 1
   2      if(p(i) .eq. newj) go to 102
          p(newj) = p(i)
          p(i) = newj
          jar(newj) = ja(j)
          ar(newj) = a(j)
   3      continue
c  ******  replace old row in ja and a  *************************
        i = n + 1
        do 4 j=jmin,jmax
          i = p(i)
          ja(j) = jar(i)
   4      a(j) = ar(i)
   5    continue
      flag = 0
      return
c
c ** error.. duplicate entry in a
 102  flag = n + k
      return
      end
