*DECK SSLI2
SUBROUTINE SSLI2 (N, B, X, NEL, IEL, JEL, EL)
C***BEGIN PROLOGUE SSLI2
C***PURPOSE SLAP Lower Triangle Matrix Backsolve.
C Routine to solve a system of the form Lx = b , where L
C is a lower triangular matrix.
C***LIBRARY SLATEC (SLAP)
C***CATEGORY D2A3
C***TYPE SINGLE PRECISION (SSLI2-S, DSLI2-D)
C***KEYWORDS ITERATIVE PRECONDITION, LINEAR SYSTEM SOLVE, SLAP, SPARSE
C***AUTHOR Greenbaum, Anne, (Courant Institute)
C 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, NEL, IEL(NEL), JEL(NEL)
C REAL B(N), X(N), EL(NEL)
C
C CALL SSLI2( N, B, X, NEL, IEL, JEL, EL )
C
C *Arguments:
C N :IN Integer
C Order of the Matrix.
C B :IN Real B(N).
C Right hand side vector.
C X :OUT Real X(N).
C Solution to Lx = b.
C NEL :IN Integer.
C Number of non-zeros in the EL array.
C IEL :IN Integer IEL(NEL).
C JEL :IN Integer JEL(NEL).
C EL :IN Real EL(NEL).
C IEL, JEL, EL contain the unit lower triangular factor of
C the incomplete decomposition of the A matrix stored in
C SLAP Row format. The diagonal of ones *IS* stored. This
C structure can be set up by the SS2LT routine. See the
C "Description", below, for more details about the SLAP Row
C format.
C
C *Description:
C This routine is supplied with the SLAP package as a routine
C to perform the MSOLVE operation in the SIR iteration routine
C for the driver routine SSGS. It must be called via the SLAP
C MSOLVE calling sequence convention interface routine SSLI.
C **** THIS ROUTINE ITSELF DOES NOT CONFORM TO THE ****
C **** SLAP MSOLVE CALLING CONVENTION ****
C
C ==================== S L A P Row format ====================
C
C This routine requires that the matrix A be stored in the
C SLAP Row format. In this format the non-zeros are stored
C counting across rows (except for the diagonal entry, which
C must appear first in each "row") and are stored in the real
C array A. In other words, for each row in the matrix put the
C diagonal entry in A. Then put in the other non-zero
C elements going across the row (except the diagonal) in
C order. The JA array holds the column index for each
C non-zero. The IA array holds the offsets into the JA, A
C arrays for the beginning of each row. That is,
C JA(IA(IROW)), A(IA(IROW)) points to the beginning of the
C IROW-th row in JA and A. JA(IA(IROW+1)-1), A(IA(IROW+1)-1)
C points to the end of the IROW-th row. Note that we always
C have IA(N+1) = NELT+1, where N is the number of rows in
C the matrix and NELT is the number of non-zeros in the
C matrix.
C
C Here is an example of the SLAP Row storage format for a 5x5
C Matrix (in the A and JA arrays '|' denotes the end of a row):
C
C 5x5 Matrix SLAP Row 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 12 15 | 22 21 | 33 35 | 44 | 55 51 53
C |21 22 0 0 0| JA: 1 2 5 | 2 1 | 3 5 | 4 | 5 1 3
C | 0 0 33 0 35| IA: 1 4 6 8 9 12
C | 0 0 0 44 0|
C |51 0 53 0 55|
C
C With the SLAP Row format the "inner loop" of this routine
C should vectorize on machines with hardware support for
C vector gather/scatter operations. Your compiler may require
C a compiler directive to convince it that there are no
C implicit vector dependencies. Compiler directives for the
C Alliant FX/Fortran and CRI CFT/CFT77 compilers are supplied
C with the standard SLAP distribution.
C
C***SEE ALSO SSLI
C***REFERENCES (NONE)
C***ROUTINES CALLED (NONE)
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 920511 Added complete declaration section. (WRB)
C 921113 Corrected C***CATEGORY line. (FNF)
C 930701 Updated CATEGORY section. (FNF, WRB)
C***END PROLOGUE SSLI2
C .. Scalar Arguments ..
INTEGER N, NEL
C .. Array Arguments ..
REAL B(N), EL(NEL), X(N)
INTEGER IEL(NEL), JEL(NEL)
C .. Local Scalars ..
INTEGER I, ICOL, J, JBGN, JEND
C***FIRST EXECUTABLE STATEMENT SSLI2
C
C Initialize the solution by copying the right hands side
C into it.
C
DO 10 I=1,N
X(I) = B(I)
10 CONTINUE
C
CVD$ NOCONCUR
DO 30 ICOL = 1, N
X(ICOL) = X(ICOL)/EL(JEL(ICOL))
JBGN = JEL(ICOL) + 1
JEND = JEL(ICOL+1) - 1
IF( JBGN.LE.JEND ) THEN
CLLL. OPTION ASSERT (NOHAZARD)
CDIR$ IVDEP
CVD$ NOCONCUR
CVD$ NODEPCHK
DO 20 J = JBGN, JEND
X(IEL(J)) = X(IEL(J)) - EL(J)*X(ICOL)
20 CONTINUE
ENDIF
30 CONTINUE
C
RETURN
C------------- LAST LINE OF SSLI2 FOLLOWS ----------------------------
END