SSILUS(3)

SYNOPSIS
SUBROUTINE SSILUS (N, NELT, IA, JA, A, ISYM, NL, IL, JL, L, DINV, + NU, IU, JU, U, NROW, NCOL)

NAME
ssilus - Incomplete LU Decomposition Preconditioner SLAP Set Up. Routine to generate the incomplete LDU decomposition of a matrix. The unit lower triangular factor L is stored by rows and the unit upper triangular factor U is stored by columns. The inverse of the diagonal matrix D is stored. No fill in is allowed.

LIBRARY
SLATEC (SLAP)

CATEGORY
D2E

TYPE
SINGLE PRECISION (SSILUS-S, DSILUS-D)

KEYWORDS
INCOMPLETE LU FACTORIZATION, ITERATIVE PRECONDITION, NON-SYMMETRIC LINEAR SYSTEM, SLAP, SPARSE

AUTHOR
Greenbaum, Anne, (Courant Institute) Seager, Mark K., (LLNL) Lawrence Livermore National Laboratory PO BOX 808, L-60 Livermore, CA 94550 (510) 423-3141 seager@llnl.gov

DESCRIPTION
*Usage: INTEGER N, NELT, IA(NELT), JA(NELT), ISYM INTEGER NL, IL(NL), JL(NL), NU, IU(NU), JU(NU) INTEGER NROW(N), NCOL(N) REAL A(NELT), L(NL), DINV(N), U(NU) CALL SSILUS( N, NELT, IA, JA, A, ISYM, NL, IL, JL, L, $ DINV, NU, IU, JU, U, NROW, NCOL ) *Arguments: N :IN Integer Order of the Matrix. NELT :IN Integer. Number of elements in arrays IA, JA, and A. IA :IN Integer IA(NELT). JA :IN Integer JA(NELT). A :IN Real A(NELT). These arrays should hold the matrix A in the SLAP Column format. See "Description", below. ISYM :IN Integer. Flag to indicate symmetric storage format. If ISYM=0, all non-zero entries of the matrix are stored. If ISYM=1, the matrix is symmetric, and only the lower triangle of the matrix is stored. NL :OUT Integer. Number of non-zeros in the L array. IL :OUT Integer IL(NL). JL :OUT Integer JL(NL). L :OUT Real L(NL). IL, JL, L contain the unit lower triangular factor of the incomplete decomposition of some matrix stored in SLAP Row format. The Diagonal of ones *IS* stored. See "DESCRIPTION", below for more details about the SLAP format. NU :OUT Integer. Number of non-zeros in the U array. IU :OUT Integer IU(NU). JU :OUT Integer JU(NU). U :OUT Real U(NU). IU, JU, U contain the unit upper triangular factor of the incomplete decomposition of some matrix stored in SLAP Column format. The Diagonal of ones *IS* stored. See "Description", below for more details about the SLAP format. NROW :WORK Integer NROW(N). NROW(I) is the number of non-zero elements in the I-th row of L. NCOL :WORK Integer NCOL(N). NCOL(I) is the number of non-zero elements in the I-th column of U. *Description IL, JL, L should contain the unit lower triangular factor of the incomplete decomposition of the A matrix stored in SLAP Row format. IU, JU, U should contain the unit upper factor of the incomplete decomposition of the A matrix stored in SLAP Column format This ILU factorization can be computed by the SSILUS routine. The diagonals (which are all one's) are stored. =================== S L A P Column format ================== This routine requires that the matrix A be stored in the SLAP Column format. In this format the non-zeros are stored counting down columns (except for the diagonal entry, which must appear first in each "column") and are stored in the real array A. In other words, for each column in the matrix put the diagonal entry in A. Then put in the other non-zero elements going down the column (except the diagonal) in order. The IA array holds the row index for each non-zero. The JA array holds the offsets into the IA, A arrays for the beginning of each column. That is, IA(JA(ICOL)), A(JA(ICOL)) points to the beginning of the ICOL-th column in IA and A. IA(JA(ICOL+1)-1), A(JA(ICOL+1)-1) points to the end of the ICOL-th column. Note that we always have JA(N+1) = NELT+1, where N is the number of columns in the matrix and NELT is the number of non-zeros in the matrix. Here is an example of the SLAP Column storage format for a 5x5 Matrix (in the A and IA arrays '|' denotes the end of a column): 5x5 Matrix SLAP Column format for 5x5 matrix on left. 1 2 3 4 5 6 7 8 9 10 11 |11 12 0 0 15| A: 11 21 51 | 22 12 | 33 53 | 44 | 55 15 35 |21 22 0 0 0| IA: 1 2 5 | 2 1 | 3 5 | 4 | 5 1 3 | 0 0 33 0 35| JA: 1 4 6 8 9 12 | 0 0 0 44 0| |51 0 53 0 55| ==================== S L A P Row format ==================== This routine requires that the matrix A be stored in the SLAP Row format. In this format the non-zeros are stored counting across rows (except for the diagonal entry, which must appear first in each "row") and are stored in the real array A. In other words, for each row in the matrix put the diagonal entry in A. Then put in the other non-zero elements going across the row (except the diagonal) in order. The JA array holds the column index for each non-zero. The IA array holds the offsets into the JA, A arrays for the beginning of each row. That is, JA(IA(IROW)), A(IA(IROW)) points to the beginning of the IROW-th row in JA and A. JA(IA(IROW+1)-1), A(IA(IROW+1)-1) points to the end of the IROW-th row. Note that we always have IA(N+1) = NELT+1, where N is the number of rows in the matrix and NELT is the number of non-zeros in the matrix. Here is an example of the SLAP Row storage format for a 5x5 Matrix (in the A and JA arrays '|' denotes the end of a row): 5x5 Matrix SLAP Row format for 5x5 matrix on left. 1 2 3 4 5 6 7 8 9 10 11 |11 12 0 0 15| A: 11 12 15 | 22 21 | 33 35 | 44 | 55 51 53 |21 22 0 0 0| JA: 1 2 5 | 2 1 | 3 5 | 4 | 5 1 3 | 0 0 33 0 35| IA: 1 4 6 8 9 12 | 0 0 0 44 0| |51 0 53 0 55|

SEE ALSO
SILUR

REFERENCES
1. Gene Golub and Charles Van Loan, Matrix Computations, Johns Hopkins University Press, Baltimore, Maryland, 1983.

ROUTINES CALLED
(NONE)

REVISION HISTORY (YYMMDD)
871119 DATE WRITTEN
881213 Previous REVISION DATE
890915 Made changes requested at July 1989 CML Meeting. (MKS)
890922 Numerous changes to prologue to make closer to SLATEC standard. (FNF)
890929 Numerous changes to reduce SP/DP differences. (FNF)
910411 Prologue converted to Version 4.0 format. (BAB)
920511 Added complete declaration section. (WRB)
920929 Corrected format of reference. (FNF)
930701 Updated CATEGORY section. (FNF, WRB)