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SUBROUTINE SSLI2 (N, B, X, NEL, IEL, JEL, EL)
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C***BEGIN PROLOGUE SSLI2
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C***PURPOSE SLAP Lower Triangle Matrix Backsolve.
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C Routine to solve a system of the form Lx = b , where L
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C is a lower triangular matrix.
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C***LIBRARY SLATEC (SLAP)
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C***TYPE SINGLE PRECISION (SSLI2-S, DSLI2-D)
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C***KEYWORDS ITERATIVE PRECONDITION, LINEAR SYSTEM SOLVE, SLAP, SPARSE
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C***AUTHOR Greenbaum, Anne, (Courant Institute)
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C Seager, Mark K., (LLNL)
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C Lawrence Livermore National Laboratory
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C Livermore, CA 94550 (510) 423-3141
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C INTEGER N, NEL, IEL(NEL), JEL(NEL)
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C REAL B(N), X(N), EL(NEL)
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C CALL SSLI2( N, B, X, NEL, IEL, JEL, EL )
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C Order of the Matrix.
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C Right hand side vector.
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C Number of non-zeros in the EL array.
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C IEL :IN Integer IEL(NEL).
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C JEL :IN Integer JEL(NEL).
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C EL :IN Real EL(NEL).
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C IEL, JEL, EL contain the unit lower triangular factor of
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C the incomplete decomposition of the A matrix stored in
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C SLAP Row format. The diagonal of ones *IS* stored. This
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C structure can be set up by the SS2LT routine. See the
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C "Description", below, for more details about the SLAP Row
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C This routine is supplied with the SLAP package as a routine
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C to perform the MSOLVE operation in the SIR iteration routine
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C for the driver routine SSGS. It must be called via the SLAP
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C MSOLVE calling sequence convention interface routine SSLI.
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C **** THIS ROUTINE ITSELF DOES NOT CONFORM TO THE ****
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C **** SLAP MSOLVE CALLING CONVENTION ****
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C ==================== S L A P Row format ====================
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C This routine requires that the matrix A be stored in the
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C SLAP Row format. In this format the non-zeros are stored
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C counting across rows (except for the diagonal entry, which
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C must appear first in each "row") and are stored in the real
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C array A. In other words, for each row in the matrix put the
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C diagonal entry in A. Then put in the other non-zero
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C elements going across the row (except the diagonal) in
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C order. The JA array holds the column index for each
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C non-zero. The IA array holds the offsets into the JA, A
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C arrays for the beginning of each row. That is,
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C JA(IA(IROW)), A(IA(IROW)) points to the beginning of the
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C IROW-th row in JA and A. JA(IA(IROW+1)-1), A(IA(IROW+1)-1)
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C points to the end of the IROW-th row. Note that we always
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C have IA(N+1) = NELT+1, where N is the number of rows in
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C the matrix and NELT is the number of non-zeros in the
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C Here is an example of the SLAP Row storage format for a 5x5
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C Matrix (in the A and JA arrays '|' denotes the end of a row):
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C 5x5 Matrix SLAP Row format for 5x5 matrix on left.
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C 1 2 3 4 5 6 7 8 9 10 11
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C |11 12 0 0 15| A: 11 12 15 | 22 21 | 33 35 | 44 | 55 51 53
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C |21 22 0 0 0| JA: 1 2 5 | 2 1 | 3 5 | 4 | 5 1 3
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C | 0 0 33 0 35| IA: 1 4 6 8 9 12
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C With the SLAP Row format the "inner loop" of this routine
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C should vectorize on machines with hardware support for
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C vector gather/scatter operations. Your compiler may require
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C a compiler directive to convince it that there are no
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C implicit vector dependencies. Compiler directives for the
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C Alliant FX/Fortran and CRI CFT/CFT77 compilers are supplied
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C with the standard SLAP distribution.
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C***ROUTINES CALLED (NONE)
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C***REVISION HISTORY (YYMMDD)
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C 881213 Previous REVISION DATE
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C 890915 Made changes requested at July 1989 CML Meeting. (MKS)
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C 890922 Numerous changes to prologue to make closer to SLATEC
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C 890929 Numerous changes to reduce SP/DP differences. (FNF)
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C 910411 Prologue converted to Version 4.0 format. (BAB)
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C 920511 Added complete declaration section. (WRB)
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C 921113 Corrected C***CATEGORY line. (FNF)
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C 930701 Updated CATEGORY section. (FNF, WRB)
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C***END PROLOGUE SSLI2
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C .. Scalar Arguments ..
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C .. Array Arguments ..
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REAL B(N), EL(NEL), X(N)
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INTEGER IEL(NEL), JEL(NEL)
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C .. Local Scalars ..
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INTEGER I, ICOL, J, JBGN, JEND
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C***FIRST EXECUTABLE STATEMENT SSLI2
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C Initialize the solution by copying the right hands side
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X(ICOL) = X(ICOL)/EL(JEL(ICOL))
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JEND = JEL(ICOL+1) - 1
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IF( JBGN.LE.JEND ) THEN
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CLLL. OPTION ASSERT (NOHAZARD)
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X(IEL(J)) = X(IEL(J)) - EL(J)*X(ICOL)
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C------------- LAST LINE OF SSLI2 FOLLOWS ----------------------------
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deps/openlibm/slatec/ssli2.f
