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263 lines
12 KiB
Fortran
263 lines
12 KiB
Fortran
*DECK DSDOMN
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SUBROUTINE DSDOMN (N, B, X, NELT, IA, JA, A, ISYM, NSAVE, ITOL,
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+ TOL, ITMAX, ITER, ERR, IERR, IUNIT, RWORK, LENW, IWORK, LENIW)
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C***BEGIN PROLOGUE DSDOMN
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C***PURPOSE Diagonally Scaled Orthomin Sparse Iterative Ax=b Solver.
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C Routine to solve a general linear system Ax = b using
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C the Orthomin method with diagonal scaling.
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C***LIBRARY SLATEC (SLAP)
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C***CATEGORY D2A4, D2B4
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C***TYPE DOUBLE PRECISION (SSDOMN-S, DSDOMN-D)
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C***KEYWORDS ITERATIVE PRECONDITION, NON-SYMMETRIC LINEAR SYSTEM SOLVE,
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C 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 PO BOX 808, L-60
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C Livermore, CA 94550 (510) 423-3141
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C seager@llnl.gov
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C***DESCRIPTION
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C
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C *Usage:
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C INTEGER N, NELT, IA(NELT), JA(NELT), ISYM, NSAVE, ITOL, ITMAX
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C INTEGER ITER, IERR, IUNIT, LENW, IWORK(10), LENIW
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C DOUBLE PRECISION B(N), X(N), A(NELT), TOL, ERR
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C DOUBLE PRECISION RWORK(7*N+3*N*NSAVE+NSAVE)
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C
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C CALL DSDOMN(N, B, X, NELT, IA, JA, A, ISYM, NSAVE, ITOL, TOL,
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C $ ITMAX, ITER, ERR, IERR, IUNIT, RWORK, LENW, IWORK, LENIW )
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C
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C *Arguments:
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C N :IN Integer.
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C Order of the Matrix.
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C B :IN Double Precision B(N).
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C Right-hand side vector.
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C X :INOUT Double Precision X(N).
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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 NELT :IN Integer.
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C Number of Non-Zeros stored in A.
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C IA :IN Integer IA(NELT).
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C JA :IN Integer JA(NELT).
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C A :IN Double Precision 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 ISYM :IN Integer.
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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 NSAVE :IN Integer.
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C Number of direction vectors to save and orthogonalize against.
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C ITOL :IN Integer.
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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 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 is the inverse of the
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C diagonal of A.
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C ITOL=11 is often useful for checking and comparing different
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C routines. For this case, the user must supply the "exact"
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C solution or a very accurate approximation (one with an error
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C much less than TOL) through a common block,
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C COMMON /DSLBLK/ SOLN( )
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C If ITOL=11, iteration stops when the 2-norm of the difference
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C between the iterative approximation and the user-supplied
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C solution divided by the 2-norm of the user-supplied solution
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C is less than TOL.
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C TOL :INOUT Double Precision.
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C Convergence criterion, as described above. (Reset if IERR=4.)
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C ITMAX :IN Integer.
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C Maximum number of iterations.
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C ITER :OUT Integer.
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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 ITMAX iterations.
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C ERR :OUT Double Precision.
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C Error estimate of error in final approximate solution, as
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C defined by ITOL.
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C IERR :OUT Integer.
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C Return error flag.
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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*D1MACH(3). Iteration proceeded.
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C IERR = 5 => Preconditioning matrix, M, is not positive
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C definite. (r,z) < 0.
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C IERR = 6 => Breakdown of method detected.
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C (p,Ap) < epsilon**2.
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C IUNIT :IN Integer.
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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 Double Precision RWORK(LENW).
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C Double Precision array used for workspace.
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C LENW :IN Integer.
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C Length of the double precision workspace, RWORK.
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C LENW >= 7*N+NSAVE*(3*N+1).
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C IWORK :WORK Integer IWORK(LENIW).
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C Used to hold pointers into the RWORK array.
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C LENIW :IN Integer.
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C Length of the integer workspace, IWORK. LENIW >= 10.
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C
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C *Description:
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C This routine is simply a driver for the DOMN routine. It
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C calls the DSDS routine to set up the preconditioning and
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C then calls DOMN with the appropriate MATVEC and MSOLVE
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C routines.
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C
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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
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C =================== S L A P Triad format ===================
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C
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C In this format only the non-zeros are stored. They may
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C appear in *ANY* order. The user supplies three arrays of
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C length NELT, where NELT is the number of non-zeros in the
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C matrix: (IA(NELT), JA(NELT), A(NELT)). For each non-zero
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C the user puts the row and column index of that matrix
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C element in the IA and JA arrays. The value of the non-zero
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C matrix element is placed in the corresponding location of
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C the A array. This is an extremely easy data structure to
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C generate. On the other hand it is not too efficient on
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C vector computers for the iterative solution of linear
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C systems. Hence, SLAP changes this input data structure to
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C the SLAP Column format for the iteration (but does not
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C change it back).
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C
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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
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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 | 0 0 0 44 0|
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C |51 0 53 0 55|
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C
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C =================== S L A P Column format ==================
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C
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C In this format the non-zeros are stored counting down
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C columns (except for the diagonal entry, which must appear
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C first in each "column") and are stored in the double pre-
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C cision array A. In other words, for each column in the
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C matrix first put the diagonal entry in A. Then put in the
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C other non-zero elements going down the column (except the
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C diagonal) in order. The IA array holds the row index for
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C each non-zero. The JA array holds the offsets into the IA,
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C A arrays for the beginning of each column. That is,
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C IA(JA(ICOL)),A(JA(ICOL)) are the first elements of the ICOL-
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C th column in IA and A, and IA(JA(ICOL+1)-1), A(JA(ICOL+1)-1)
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C are the last elements of the ICOL-th column. Note that we
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C always have JA(N+1)=NELT+1, where N is the number of columns
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C in the matrix and NELT is the number of non-zeros in the
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C matrix.
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C
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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 column):
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C
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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 | 0 0 0 44 0|
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C |51 0 53 0 55|
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C
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C *Side Effects:
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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
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C *Cautions:
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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
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C***SEE ALSO DOMN, DSLUOM
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C***REFERENCES (NONE)
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C***ROUTINES CALLED DCHKW, DOMN, DS2Y, DSDI, DSDS, DSMV
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C***REVISION HISTORY (YYMMDD)
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C 890404 DATE WRITTEN
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C 890404 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 standard. (FNF)
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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 920407 COMMON BLOCK renamed DSLBLK. (WRB)
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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***END PROLOGUE DSDOMN
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C .. Parameters ..
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INTEGER LOCRB, LOCIB
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PARAMETER (LOCRB=1, LOCIB=11)
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C .. Scalar Arguments ..
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DOUBLE PRECISION ERR, TOL
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INTEGER IERR, ISYM, ITER, ITMAX, ITOL, IUNIT, LENIW, LENW, N,
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+ NELT, NSAVE
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C .. Array Arguments ..
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DOUBLE PRECISION A(N), 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 LOCAP, LOCCSA, LOCDIN, LOCDZ, LOCEMA, LOCIW, LOCP, LOCR,
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+ LOCW, LOCZ
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C .. External Subroutines ..
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EXTERNAL DCHKW, DOMN, DS2Y, DSDI, DSDS, DSMV
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C***FIRST EXECUTABLE STATEMENT DSDOMN
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C
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IERR = 0
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IF( N.LT.1 .OR. NELT.LT.1 ) THEN
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IERR = 3
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RETURN
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ENDIF
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C
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C Change the SLAP input matrix IA, JA, A to SLAP-Column format.
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CALL DS2Y( N, NELT, IA, JA, A, ISYM )
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C
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C Set up the workspace.
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LOCIW = LOCIB
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C
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LOCDIN = LOCRB
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LOCR = LOCDIN + N
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LOCZ = LOCR + N
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LOCP = LOCZ + N
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LOCAP = LOCP + N*(NSAVE+1)
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LOCEMA = LOCAP + N*(NSAVE+1)
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LOCDZ = LOCEMA + N*(NSAVE+1)
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LOCCSA = LOCDZ + N
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LOCW = LOCCSA + NSAVE
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C
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C Check the workspace allocations.
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CALL DCHKW( 'DSDOMN', LOCIW, LENIW, LOCW, LENW, IERR, ITER, ERR )
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IF( IERR.NE.0 ) RETURN
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C
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IWORK(4) = LOCDIN
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IWORK(9) = LOCIW
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IWORK(10) = LOCW
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C
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C Compute the inverse of the diagonal of the matrix.
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CALL DSDS(N, NELT, IA, JA, A, ISYM, RWORK(LOCDIN))
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C
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C Perform the Diagonally Scaled Orthomin iteration algorithm.
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CALL DOMN(N, B, X, NELT, IA, JA, A, ISYM, DSMV,
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$ DSDI, NSAVE, ITOL, TOL, ITMAX, ITER, ERR, IERR, IUNIT,
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$ RWORK(LOCR), RWORK(LOCZ), RWORK(LOCP), RWORK(LOCAP),
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$ RWORK(LOCEMA), RWORK(LOCDZ), RWORK(LOCCSA),
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$ RWORK, IWORK )
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RETURN
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C------------- LAST LINE OF DSDOMN FOLLOWS ----------------------------
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END
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