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SUBROUTINE SSLUCS (N, B, X, NELT, IA, JA, A, ISYM, ITOL, TOL,
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+ ITMAX, ITER, ERR, IERR, IUNIT, RWORK, LENW, IWORK, LENIW)
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C***BEGIN PROLOGUE SSLUCS
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C***PURPOSE Incomplete LU BiConjugate Gradient Squared Ax=b Solver.
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C Routine to solve a linear system Ax = b using the
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C BiConjugate Gradient Squared method with Incomplete LU
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C decomposition preconditioning.
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C***LIBRARY SLATEC (SLAP)
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C***CATEGORY D2A4, D2B4
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C***TYPE SINGLE PRECISION (SSLUCS-S, DSLUCS-D)
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C***KEYWORDS ITERATIVE INCOMPLETE LU PRECONDITION,
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C NON-SYMMETRIC LINEAR SYSTEM, 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, NELT, IA(NELT), JA(NELT), ISYM, ITOL, ITMAX
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C INTEGER ITER, IERR, IUNIT, LENW, IWORK(NL+NU+4*N+2), LENIW
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C REAL B(N), X(N), A(NELT), TOL, ERR, RWORK(NL+NU+8*N)
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C CALL SSLUCS(N, B, X, NELT, IA, JA, A, ISYM, ITOL, TOL,
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C $ ITMAX, ITER, ERR, IERR, IUNIT, RWORK, LENW, IWORK, LENIW)
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C Order of the Matrix.
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C Right-hand side vector.
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C On input X is your initial guess for solution vector.
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C On output X is the final approximate solution.
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C Number of Non-Zeros stored in A.
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C IA :INOUT Integer IA(NELT).
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C JA :INOUT Integer JA(NELT).
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C A :INOUT Real A(NELT).
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C These arrays should hold the matrix A in either the SLAP
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C Triad format or the SLAP Column format. See "Description",
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C below. If the SLAP Triad format is chosen it is changed
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C internally to the SLAP Column format.
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C Flag to indicate symmetric storage format.
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C If ISYM=0, all non-zero entries of the matrix are stored.
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C If ISYM=1, the matrix is symmetric, and only the upper
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C or lower triangle of the matrix is stored.
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C Flag to indicate type of convergence criterion.
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C If ITOL=1, iteration stops when the 2-norm of the residual
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C divided by the 2-norm of the right-hand side is less than TOL.
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C This routine must calculate the residual from R = A*X - B.
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C This is unnatural and hence expensive for this type of iter-
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C ative method. ITOL=2 is *STRONGLY* recommended.
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C If ITOL=2, iteration stops when the 2-norm of M-inv times the
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C residual divided by the 2-norm of M-inv times the right hand
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C side is less than TOL, where M-inv time a vector is the pre-
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C conditioning step. This is the *NATURAL* stopping for this
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C iterative method and is *STRONGLY* recommended.
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C Convergence criterion, as described above. (Reset if IERR=4.)
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C Maximum number of iterations.
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C Number of iterations required to reach convergence, or
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C ITMAX+1 if convergence criterion could not be achieved in
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C Error estimate of error in final approximate solution, as
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C IERR = 0 => All went well.
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C IERR = 1 => Insufficient space allocated for WORK or IWORK.
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C IERR = 2 => Method failed to converge in ITMAX steps.
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C IERR = 3 => Error in user input.
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C Check input values of N, ITOL.
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C IERR = 4 => User error tolerance set too tight.
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C Reset to 500*R1MACH(3). Iteration proceeded.
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C IERR = 5 => Breakdown of the method detected.
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C (r0,r) approximately 0.
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C IERR = 6 => Stagnation of the method detected.
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C (r0,v) approximately 0.
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C IERR = 7 => Incomplete factorization broke down and was
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C fudged. Resulting preconditioning may be less
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C Unit number on which to write the error at each iteration,
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C if this is desired for monitoring convergence. If unit
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C number is 0, no writing will occur.
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C RWORK :WORK Real RWORK(LENW).
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C Real array used for workspace. NL is the number of non-
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C zeros in the lower triangle of the matrix (including the
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C diagonal). NU is the number of non-zeros in the upper
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C triangle of the matrix (including the diagonal).
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C Length of the real workspace, RWORK. LENW >= NL+NU+8*N.
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C IWORK :WORK Integer IWORK(LENIW).
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C Integer array used for workspace. NL is the number of non-
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C zeros in the lower triangle of the matrix (including the
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C diagonal). NU is the number of non-zeros in the upper
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C triangle of the matrix (including the diagonal).
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C Upon return the following locations of IWORK hold information
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C which may be of use to the user:
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C IWORK(9) Amount of Integer workspace actually used.
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C IWORK(10) Amount of Real workspace actually used.
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C Length of the integer workspace, IWORK.
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C LENIW >= NL+NU+4*N+12.
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C This routine is simply a driver for the SCGSN routine. It
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C calls the SSILUS routine to set up the preconditioning and
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C then calls SCGSN with the appropriate MATVEC, MTTVEC and
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C MSOLVE, MTSOLV routines.
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C The Sparse Linear Algebra Package (SLAP) utilizes two matrix
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C data structures: 1) the SLAP Triad format or 2) the SLAP
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C Column format. The user can hand this routine either of the
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C of these data structures and SLAP will figure out which on
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C is being used and act accordingly.
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C =================== S L A P Triad format ===================
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C This routine requires that the matrix A be stored in the
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C SLAP Triad format. In this format only the non-zeros are
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C stored. They may appear in *ANY* order. The user supplies
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C three arrays of length NELT, where NELT is the number of
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C non-zeros in the matrix: (IA(NELT), JA(NELT), A(NELT)). For
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C each non-zero the user puts the row and column index of that
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C matrix element in the IA and JA arrays. The value of the
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C non-zero matrix element is placed in the corresponding
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C location of the A array. This is an extremely easy data
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C structure to generate. On the other hand it is not too
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C efficient on vector computers for the iterative solution of
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C linear systems. Hence, SLAP changes this input data
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C structure to the SLAP Column format for the iteration (but
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C does not change it back).
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C Here is an example of the SLAP Triad storage format for a
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C 5x5 Matrix. Recall that the entries may appear in any order.
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C 5x5 Matrix SLAP Triad 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: 51 12 11 33 15 53 55 22 35 44 21
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C |21 22 0 0 0| IA: 5 1 1 3 1 5 5 2 3 4 2
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C | 0 0 33 0 35| JA: 1 2 1 3 5 3 5 2 5 4 1
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C =================== S L A P Column format ==================
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C This routine requires that the matrix A be stored in the
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C SLAP Column format. In this format the non-zeros are stored
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C counting down columns (except for the diagonal entry, which
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C must appear first in each "column") and are stored in the
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C real array A. In other words, for each column in the matrix
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C put the diagonal entry in A. Then put in the other non-zero
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C elements going down the column (except the diagonal) in
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C order. The IA array holds the row index for each non-zero.
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C The JA array holds the offsets into the IA, A arrays for the
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C beginning of each column. That is, IA(JA(ICOL)),
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C A(JA(ICOL)) points to the beginning of the ICOL-th column in
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C IA and A. IA(JA(ICOL+1)-1), A(JA(ICOL+1)-1) points to the
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C end of the ICOL-th column. Note that we always have
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C JA(N+1) = NELT+1, where N is the number of columns in the
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C matrix and NELT is the number of non-zeros in the matrix.
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C Here is an example of the SLAP Column storage format for a
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C 5x5 Matrix (in the A and IA arrays '|' denotes the end of a
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C 5x5 Matrix SLAP Column 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 21 51 | 22 12 | 33 53 | 44 | 55 15 35
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C |21 22 0 0 0| IA: 1 2 5 | 2 1 | 3 5 | 4 | 5 1 3
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C | 0 0 33 0 35| JA: 1 4 6 8 9 12
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C The SLAP Triad format (IA, JA, A) is modified internally to
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C be the SLAP Column format. See above.
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C This routine will attempt to write to the Fortran logical output
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C unit IUNIT, if IUNIT .ne. 0. Thus, the user must make sure that
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C this logical unit is attached to a file or terminal before calling
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C this routine with a non-zero value for IUNIT. This routine does
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C not check for the validity of a non-zero IUNIT unit number.
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C***SEE ALSO SCGS, SSDCGS
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C***REFERENCES 1. P. Sonneveld, CGS, a fast Lanczos-type solver
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C for nonsymmetric linear systems, Delft University
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C of Technology Report 84-16, Department of Mathe-
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C matics and Informatics, Delft, The Netherlands.
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C 2. E. F. Kaasschieter, The solution of non-symmetric
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C linear systems by biconjugate gradients or conjugate
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C gradients squared, Delft University of Technology
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C Report 86-21, Department of Mathematics and Informa-
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C tics, Delft, The Netherlands.
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C***ROUTINES CALLED SCGS, SCHKW, SS2Y, SSILUS, SSLUI, SSMV
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C***REVISION HISTORY (YYMMDD)
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C 871119 DATE WRITTEN
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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 890921 Removed TeX from comments. (FNF)
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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 920929 Corrected format of references. (FNF)
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C 921113 Corrected C***CATEGORY line. (FNF)
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C***END PROLOGUE SSLUCS
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PARAMETER (LOCRB=1, LOCIB=11)
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C .. Scalar Arguments ..
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INTEGER IERR, ISYM, ITER, ITMAX, ITOL, IUNIT, LENIW, LENW, N, NELT
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C .. Array Arguments ..
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REAL A(NELT), B(N), RWORK(LENW), X(N)
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INTEGER IA(NELT), IWORK(LENIW), JA(NELT)
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C .. Local Scalars ..
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INTEGER ICOL, J, JBGN, JEND, LOCDIN, LOCIL, LOCIU, LOCIW, LOCJL,
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+ LOCJU, LOCL, LOCNC, LOCNR, LOCP, LOCQ, LOCR, LOCR0, LOCU,
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+ LOCUU, LOCV1, LOCV2, LOCW, NL, NU
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C .. External Subroutines ..
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EXTERNAL SCGS, SCHKW, SS2Y, SSILUS, SSLUI, SSMV
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C***FIRST EXECUTABLE STATEMENT SSLUCS
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IF( N.LT.1 .OR. NELT.LT.1 ) THEN
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C Change the SLAP input matrix IA, JA, A to SLAP-Column format.
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CALL SS2Y( N, NELT, IA, JA, A, ISYM )
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C Count number of Non-Zero elements preconditioner ILU matrix.
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C Then set up the work arrays.
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C Don't count diagonal.
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IF( JBGN.LE.JEND ) THEN
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IF( IA(J).GT.ICOL ) THEN
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IF( ISYM.NE.0 ) NU = NU + 1
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C Check the workspace allocations.
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CALL SCHKW( 'SSLUCS', LOCIW, LENIW, LOCW, LENW, IERR, ITER, ERR )
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IF( IERR.NE.0 ) RETURN
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C Compute the Incomplete LU decomposition.
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CALL SSILUS( N, NELT, IA, JA, A, ISYM, NL, IWORK(LOCIL),
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$ IWORK(LOCJL), RWORK(LOCL), RWORK(LOCDIN), NU, IWORK(LOCIU),
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$ IWORK(LOCJU), RWORK(LOCUU), IWORK(LOCNR), IWORK(LOCNC) )
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C Perform the incomplete LU preconditioned
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C BiConjugate Gradient Squared algorithm.
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CALL SCGS(N, B, X, NELT, IA, JA, A, ISYM, SSMV,
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$ SSLUI, ITOL, TOL, ITMAX, ITER, ERR, IERR, IUNIT,
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$ RWORK(LOCR), RWORK(LOCR0), RWORK(LOCP),
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$ RWORK(LOCQ), RWORK(LOCU), RWORK(LOCV1),
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$ RWORK(LOCV2), RWORK, IWORK )
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C------------- LAST LINE OF SSLUCS FOLLOWS ----------------------------
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deps/openlibm/slatec/sslucs.f
