# ds2y.f

          SUBROUTINE DS2Y (N, NELT, IA, JA, A, ISYM)
    C***BEGIN PROLOGUE  DS2Y
    C***PURPOSE  SLAP Triad to SLAP Column Format Converter.
    C            Routine to convert from the SLAP Triad to SLAP Column
    C            format.
    C***LIBRARY   SLATEC (SLAP)
    C***CATEGORY  D1B9
    C***TYPE      DOUBLE PRECISION (SS2Y-S, DS2Y-D)
    C***KEYWORDS  LINEAR SYSTEM, SLAP SPARSE
    C***AUTHOR  Seager, Mark K., (LLNL)
    C             Lawrence Livermore National Laboratory
    C             PO BOX 808, L-60
    C             Livermore, CA 94550 (510) 423-3141
    C             seager@llnl.gov
    C***DESCRIPTION
    C
    C *Usage:
    C     INTEGER N, NELT, IA(NELT), JA(NELT), ISYM
    C     DOUBLE PRECISION A(NELT)
    C
    C     CALL DS2Y( N, NELT, IA, JA, A, ISYM )
    C
    C *Arguments:
    C N      :IN       Integer
    C         Order of the Matrix.
    C NELT   :IN       Integer.
    C         Number of non-zeros stored in A.
    C IA     :INOUT    Integer IA(NELT).
    C JA     :INOUT    Integer JA(NELT).
    C A      :INOUT    Double Precision A(NELT).
    C         These arrays should hold the matrix A in either the SLAP
    C         Triad format or the SLAP Column format.  See "Description",
    C         below.  If the SLAP Triad format is used, this format is
    C         translated to the SLAP Column format by this routine.
    C ISYM   :IN       Integer.
    C         Flag to indicate symmetric storage format.
    C         If ISYM=0, all non-zero entries of the matrix are stored.
    C         If ISYM=1, the matrix is symmetric, and only the lower
    C         triangle of the matrix is stored.
    C
    C *Description:
    C       The Sparse Linear Algebra Package (SLAP) utilizes two matrix
    C       data structures: 1) the  SLAP Triad  format or  2)  the SLAP
    C       Column format.  The user can hand this routine either of the
    C       of these data structures.  If the SLAP Triad format is give
    C       as input then this routine transforms it into SLAP Column
    C       format.  The way this routine tells which format is given as
    C       input is to look at JA(N+1).  If JA(N+1) = NELT+1 then we
    C       have the SLAP Column format.  If that equality does not hold
    C       then it is assumed that the IA, JA, A arrays contain the
    C       SLAP Triad format.
    C
    C       =================== S L A P Triad format ===================
    C       This routine requires that the  matrix A be   stored in  the
    C       SLAP  Triad format.  In  this format only the non-zeros  are
    C       stored.  They may appear in  *ANY* order.  The user supplies
    C       three arrays of  length NELT, where  NELT is  the number  of
    C       non-zeros in the matrix: (IA(NELT), JA(NELT), A(NELT)).  For
    C       each non-zero the user puts the row and column index of that
    C       matrix element  in the IA and  JA arrays.  The  value of the
    C       non-zero   matrix  element is  placed  in  the corresponding
    C       location of the A array.   This is  an  extremely  easy data
    C       structure to generate.  On  the  other hand it   is  not too
    C       efficient on vector computers for  the iterative solution of
    C       linear systems.  Hence,   SLAP changes   this  input    data
    C       structure to the SLAP Column format  for  the iteration (but
    C       does not change it back).
    C
    C       Here is an example of the  SLAP Triad   storage format for a
    C       5x5 Matrix.  Recall that the entries may appear in any order.
    C
    C           5x5 Matrix      SLAP Triad format for 5x5 matrix on left.
    C                              1  2  3  4  5  6  7  8  9 10 11
    C       |11 12  0  0 15|   A: 51 12 11 33 15 53 55 22 35 44 21
    C       |21 22  0  0  0|  IA:  5  1  1  3  1  5  5  2  3  4  2
    C       | 0  0 33  0 35|  JA:  1  2  1  3  5  3  5  2  5  4  1
    C       | 0  0  0 44  0|
    C       |51  0 53  0 55|
    C
    C       =================== S L A P Column format ==================
    C
    C       This routine  requires that  the matrix A  be stored in  the
    C       SLAP Column format.  In this format the non-zeros are stored
    C       counting down columns (except for  the diagonal entry, which
    C       must appear first in each  "column")  and are stored  in the
    C       double precision array A.   In other words,  for each column
    C       in the matrix put the diagonal entry in  A.  Then put in the
    C       other non-zero  elements going down  the column (except  the
    C       diagonal) in order.   The  IA array holds the  row index for
    C       each non-zero.  The JA array holds the offsets  into the IA,
    C       A arrays  for  the  beginning  of each   column.   That  is,
    C       IA(JA(ICOL)),  A(JA(ICOL)) points   to the beginning  of the
    C       ICOL-th   column    in    IA and   A.      IA(JA(ICOL+1)-1),
    C       A(JA(ICOL+1)-1) points to  the  end of the   ICOL-th column.
    C       Note that we always have  JA(N+1) = NELT+1,  where N is  the
    C       number of columns in  the matrix and NELT  is the number  of
    C       non-zeros in the matrix.
    C
    C       Here is an example of the  SLAP Column  storage format for a
    C       5x5 Matrix (in the A and IA arrays '|'  denotes the end of a
    C       column):
    C
    C           5x5 Matrix      SLAP Column format for 5x5 matrix on left.
    C                              1  2  3    4  5    6  7    8    9 10 11
    C       |11 12  0  0 15|   A: 11 21 51 | 22 12 | 33 53 | 44 | 55 15 35
    C       |21 22  0  0  0|  IA:  1  2  5 |  2  1 |  3  5 |  4 |  5  1  3
    C       | 0  0 33  0 35|  JA:  1  4  6    8  9   12
    C       | 0  0  0 44  0|
    C       |51  0 53  0 55|
    C
    C***REFERENCES  (NONE)
    C***ROUTINES CALLED  QS2I1D
    C***REVISION HISTORY  (YYMMDD)
    C   871119  DATE WRITTEN
    C   881213  Previous REVISION DATE
    C   890915  Made changes requested at July 1989 CML Meeting.  (MKS)
    C   890922  Numerous changes to prologue to make closer to SLATEC
    C           standard.  (FNF)
    C   890929  Numerous changes to reduce SP/DP differences.  (FNF)
    C   910411  Prologue converted to Version 4.0 format.  (BAB)
    C   910502  Corrected C***FIRST EXECUTABLE STATEMENT line.  (FNF)
    C   920511  Added complete declaration section.  (WRB)
    C   930701  Updated CATEGORY section.  (FNF, WRB)
    C***END PROLOGUE  DS2Y