relibc_openlibm/slatec/ss2y.f

*DECK SS2Y
      SUBROUTINE SS2Y (N, NELT, IA, JA, A, ISYM)
C***BEGIN PROLOGUE  SS2Y
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      SINGLE 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     REAL    A(NELT)
C
C     CALL SS2Y( 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    Real 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       real array A.  In other words, for each column in the matrix
C       put the diagonal entry in A.  Then put in the other non-zero
C       elements going down   the  column (except  the diagonal)  in
C       order.  The IA array holds the row  index for each non-zero.
C       The JA array holds the offsets into the IA, A arrays for the
C       beginning of   each    column.    That  is,    IA(JA(ICOL)),
C       A(JA(ICOL)) points to the beginning of the ICOL-th column in
C       IA and  A.  IA(JA(ICOL+1)-1),  A(JA(ICOL+1)-1) points to the
C       end  of   the ICOL-th  column.  Note   that  we  always have
C       JA(N+1) = NELT+1, where  N  is the number of columns in  the
C       matrix and  NELT   is the number of 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  QS2I1R
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  SS2Y
C     .. Scalar Arguments ..
      INTEGER ISYM, N, NELT
C     .. Array Arguments ..
      REAL A(NELT)
      INTEGER IA(NELT), JA(NELT)
C     .. Local Scalars ..
      REAL TEMP
      INTEGER I, IBGN, ICOL, IEND, ITEMP, J
C     .. External Subroutines ..
      EXTERNAL QS2I1R
C***FIRST EXECUTABLE STATEMENT  SS2Y
C
C         Check to see if the (IA,JA,A) arrays are in SLAP Column
C         format.  If it's not then transform from SLAP Triad.
C
      IF( JA(N+1).EQ.NELT+1 ) RETURN
C
C         Sort into ascending order by COLUMN (on the ja array).
C         This will line up the columns.
C
      CALL QS2I1R( JA, IA, A, NELT, 1 )
C
C         Loop over each column to see where the column indices change
C         in the column index array ja.  This marks the beginning of the
C         next column.
C
CVD$R NOVECTOR
      JA(1) = 1
      DO 20 ICOL = 1, N-1
         DO 10 J = JA(ICOL)+1, NELT
            IF( JA(J).NE.ICOL ) THEN
               JA(ICOL+1) = J
               GOTO 20
            ENDIF
 10      CONTINUE
 20   CONTINUE
      JA(N+1) = NELT+1
C
C         Mark the n+2 element so that future calls to a SLAP routine
C         utilizing the YSMP-Column storage format will be able to tell.
C
      JA(N+2) = 0
C
C         Now loop through the IA array making sure that the diagonal
C         matrix element appears first in the column.  Then sort the
C         rest of the column in ascending order.
C
      DO 70 ICOL = 1, N
         IBGN = JA(ICOL)
         IEND = JA(ICOL+1)-1
         DO 30 I = IBGN, IEND
            IF( IA(I).EQ.ICOL ) THEN
C
C              Swap the diagonal element with the first element in the
C              column.
C
               ITEMP = IA(I)
               IA(I) = IA(IBGN)
               IA(IBGN) = ITEMP
               TEMP = A(I)
               A(I) = A(IBGN)
               A(IBGN) = TEMP
               GOTO 40
            ENDIF
 30      CONTINUE
 40      IBGN = IBGN + 1
         IF( IBGN.LT.IEND ) THEN
            DO 60 I = IBGN, IEND
               DO 50 J = I+1, IEND
                  IF( IA(I).GT.IA(J) ) THEN
                     ITEMP = IA(I)
                     IA(I) = IA(J)
                     IA(J) = ITEMP
                     TEMP = A(I)
                     A(I) = A(J)
                     A(J) = TEMP
                  ENDIF
 50            CONTINUE
 60         CONTINUE
         ENDIF
 70   CONTINUE
      RETURN
C------------- LAST LINE OF SS2Y FOLLOWS ----------------------------
      END