*DECK SS2LT SUBROUTINE SS2LT (N, NELT, IA, JA, A, ISYM, NEL, IEL, JEL, EL) C***BEGIN PROLOGUE SS2LT C***PURPOSE Lower Triangle Preconditioner SLAP Set Up. C Routine to store the lower triangle of a matrix stored C in the SLAP Column format. C***LIBRARY SLATEC (SLAP) C***CATEGORY D2E C***TYPE SINGLE PRECISION (SS2LT-S, DS2LT-D) C***KEYWORDS LINEAR SYSTEM, LOWER TRIANGLE, 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, NELT, IA(NELT), JA(NELT), ISYM C INTEGER NEL, IEL(NEL), JEL(NEL) C REAL A(NELT), EL(NEL) C C CALL SS2LT( N, NELT, IA, JA, A, ISYM, NEL, IEL, JEL, EL ) 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 :IN Integer IA(NELT). C JA :IN Integer JA(NELT). C A :IN Real A(NELT). C These arrays should hold the matrix A in the SLAP Column C format. See "Description", below. 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 NEL :OUT Integer. C Number of non-zeros in the lower triangle of A. Also C corresponds to the length of the IEL, JEL, EL arrays. C IEL :OUT Integer IEL(NEL). C JEL :OUT Integer JEL(NEL). C EL :OUT Real EL(NEL). C IEL, JEL, EL contain the lower triangle of the A matrix C stored in SLAP Column format. See "Description", below, C for more details bout the SLAP Column format. C C *Description C =================== S L A P Column format ================== 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 (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 930701 Updated CATEGORY section. (FNF, WRB) C***END PROLOGUE SS2LT C .. Scalar Arguments .. INTEGER ISYM, N, NEL, NELT C .. Array Arguments .. REAL A(NELT), EL(NELT) INTEGER IA(NELT), IEL(NEL), JA(NELT), JEL(NEL) C .. Local Scalars .. INTEGER I, ICOL, J, JBGN, JEND C***FIRST EXECUTABLE STATEMENT SS2LT IF( ISYM.EQ.0 ) THEN C C The matrix is stored non-symmetricly. Pick out the lower C triangle. C NEL = 0 DO 20 ICOL = 1, N JEL(ICOL) = NEL+1 JBGN = JA(ICOL) JEND = JA(ICOL+1)-1 CVD$ NOVECTOR DO 10 J = JBGN, JEND IF( IA(J).GE.ICOL ) THEN NEL = NEL + 1 IEL(NEL) = IA(J) EL(NEL) = A(J) ENDIF 10 CONTINUE 20 CONTINUE JEL(N+1) = NEL+1 ELSE C C The matrix is symmetric and only the lower triangle is C stored. Copy it to IEL, JEL, EL. C NEL = NELT DO 30 I = 1, NELT IEL(I) = IA(I) EL(I) = A(I) 30 CONTINUE DO 40 I = 1, N+1 JEL(I) = JA(I) 40 CONTINUE ENDIF RETURN C------------- LAST LINE OF SS2LT FOLLOWS ---------------------------- END