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Replace amos with slatec
374 lines
16 KiB
Fortran
374 lines
16 KiB
Fortran
*DECK SCGS
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SUBROUTINE SCGS (N, B, X, NELT, IA, JA, A, ISYM, MATVEC, MSOLVE,
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+ ITOL, TOL, ITMAX, ITER, ERR, IERR, IUNIT, R, R0, P, Q, U, V1,
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+ V2, RWORK, IWORK)
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C***BEGIN PROLOGUE SCGS
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C***PURPOSE Preconditioned BiConjugate Gradient Squared Ax=b Solver.
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C Routine to solve a Non-Symmetric linear system Ax = b
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C using the Preconditioned BiConjugate Gradient Squared
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C method.
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C***LIBRARY SLATEC (SLAP)
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C***CATEGORY D2A4, D2B4
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C***TYPE SINGLE PRECISION (SCGS-S, DCGS-D)
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C***KEYWORDS BICONJUGATE GRADIENT, ITERATIVE 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 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, ITOL, ITMAX
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C INTEGER ITER, IERR, IUNIT, IWORK(USER DEFINED)
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C REAL B(N), X(N), A(NELT), TOL, ERR, R(N), R0(N), P(N)
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C REAL Q(N), U(N), V1(N), V2(N), RWORK(USER DEFINED)
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C EXTERNAL MATVEC, MSOLVE
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C
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C CALL SCGS(N, B, X, NELT, IA, JA, A, ISYM, MATVEC,
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C $ MSOLVE, ITOL, TOL, ITMAX, ITER, ERR, IERR, IUNIT,
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C $ R, R0, P, Q, U, V1, V2, RWORK, IWORK)
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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 Real B(N).
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C Right-hand side vector.
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C X :INOUT Real 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 Real A(NELT).
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C These arrays contain the matrix data structure for A.
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C It could take any form. See "Description", below,
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C for more details.
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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 MATVEC :EXT External.
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C Name of a routine which performs the matrix vector multiply
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C operation Y = A*X given A and X. The name of the MATVEC
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C routine must be declared external in the calling program.
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C The calling sequence of MATVEC is:
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C CALL MATVEC( N, X, Y, NELT, IA, JA, A, ISYM )
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C Where N is the number of unknowns, Y is the product A*X upon
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C return, X is an input vector. NELT, IA, JA, A and ISYM
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C define the SLAP matrix data structure: see Description,below.
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C MSOLVE :EXT External.
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C Name of a routine which solves a linear system MZ = R for Z
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C given R with the preconditioning matrix M (M is supplied via
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C RWORK and IWORK arrays). The name of the MSOLVE routine
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C must be declared external in the calling program. The
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C calling sequence of MSOLVE is:
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C CALL MSOLVE(N, R, Z, NELT, IA, JA, A, ISYM, RWORK, IWORK)
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C Where N is the number of unknowns, R is the right-hand side
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C vector, and Z is the solution upon return. NELT, IA, JA, A
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C and ISYM define the SLAP matrix data structure: see
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C Description, below. RWORK is a real array that can be used
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C to pass necessary preconditioning information and/or
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C workspace to MSOLVE. IWORK is an integer work array for the
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C same purpose as RWORK.
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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 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 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 /SSLBLK/ 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 Real.
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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 Real.
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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*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 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 R :WORK Real R(N).
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C R0 :WORK Real R0(N).
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C P :WORK Real P(N).
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C Q :WORK Real Q(N).
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C U :WORK Real U(N).
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C V1 :WORK Real V1(N).
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C V2 :WORK Real V2(N).
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C Real arrays used for workspace.
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C RWORK :WORK Real RWORK(USER DEFINED).
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C Real array that can be used for workspace in MSOLVE.
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C IWORK :WORK Integer IWORK(USER DEFINED).
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C Integer array that can be used for workspace in MSOLVE.
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C
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C *Description
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C This routine does not care what matrix data structure is
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C used for A and M. It simply calls the MATVEC and MSOLVE
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C routines, with the arguments as described above. The user
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C could write any type of structure and the appropriate MATVEC
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C and MSOLVE routines. It is assumed that A is stored in the
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C IA, JA, A arrays in some fashion and that M (or INV(M)) is
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C stored in IWORK and RWORK in some fashion. The SLAP
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C routines SSDBCG and SSLUCS are examples of this procedure.
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C
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C Two examples of matrix data structures are the: 1) SLAP
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C Triad format and 2) SLAP Column format.
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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 real array A.
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C In other words, for each column 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 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 JA(N+1)
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C = NELT+1, where N is the number of columns in the matrix and
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C NELT is the number of non-zeros in the 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 *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 SSDCGS, SSLUCS
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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 3. Mark K. Seager, A SLAP for the Masses, in
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C G. F. Carey, Ed., Parallel Supercomputing: Methods,
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C Algorithms and Applications, Wiley, 1989, pp.135-155.
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C***ROUTINES CALLED ISSCGS, R1MACH, SAXPY, SDOT
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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 standard. (FNF)
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C 890929 Numerous changes to reduce SP/DP differences. (FNF)
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C 891004 Added new reference.
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C 910411 Prologue converted to Version 4.0 format. (BAB)
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C 910502 Removed MATVEC and MSOLVE from ROUTINES CALLED list. (FNF)
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C 920407 COMMON BLOCK renamed SSLBLK. (WRB)
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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 921019 Changed 500.0 to 500 to reduce SP/DP differences. (FNF)
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C 921113 Corrected C***CATEGORY line. (FNF)
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C***END PROLOGUE SCGS
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C .. Scalar Arguments ..
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REAL ERR, TOL
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INTEGER IERR, ISYM, ITER, ITMAX, ITOL, IUNIT, N, NELT
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C .. Array Arguments ..
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REAL A(NELT), B(N), P(N), Q(N), R(N), R0(N), RWORK(*), U(N),
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+ V1(N), V2(N), X(N)
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INTEGER IA(NELT), IWORK(*), JA(NELT)
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C .. Subroutine Arguments ..
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EXTERNAL MATVEC, MSOLVE
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C .. Local Scalars ..
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REAL AK, AKM, BK, BNRM, FUZZ, RHON, RHONM1, SIGMA, SOLNRM, TOLMIN
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INTEGER I, K
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C .. External Functions ..
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REAL R1MACH, SDOT
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INTEGER ISSCGS
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EXTERNAL R1MACH, SDOT, ISSCGS
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C .. External Subroutines ..
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EXTERNAL SAXPY
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C .. Intrinsic Functions ..
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INTRINSIC ABS
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C***FIRST EXECUTABLE STATEMENT SCGS
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C
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C Check some of the input data.
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C
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ITER = 0
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IERR = 0
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IF( N.LT.1 ) THEN
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IERR = 3
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RETURN
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ENDIF
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TOLMIN = 500*R1MACH(3)
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IF( TOL.LT.TOLMIN ) THEN
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TOL = TOLMIN
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IERR = 4
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ENDIF
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C
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C Calculate initial residual and pseudo-residual, and check
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C stopping criterion.
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CALL MATVEC(N, X, R, NELT, IA, JA, A, ISYM)
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DO 10 I = 1, N
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V1(I) = R(I) - B(I)
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10 CONTINUE
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CALL MSOLVE(N, V1, R, NELT, IA, JA, A, ISYM, RWORK, IWORK)
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C
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IF( ISSCGS(N, B, X, NELT, IA, JA, A, ISYM, MATVEC, MSOLVE,
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$ ITOL, TOL, ITMAX, ITER, ERR, IERR, IUNIT, R, R0, P, Q,
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$ U, V1, V2, RWORK, IWORK, AK, BK, BNRM, SOLNRM) .NE. 0 )
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$ GO TO 200
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IF( IERR.NE.0 ) RETURN
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C
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C Set initial values.
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C
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FUZZ = R1MACH(3)**2
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DO 20 I = 1, N
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R0(I) = R(I)
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20 CONTINUE
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RHONM1 = 1
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C
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C ***** ITERATION LOOP *****
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C
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DO 100 K=1,ITMAX
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ITER = K
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C
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C Calculate coefficient BK and direction vectors U, V and P.
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RHON = SDOT(N, R0, 1, R, 1)
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IF( ABS(RHONM1).LT.FUZZ ) GOTO 998
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BK = RHON/RHONM1
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IF( ITER.EQ.1 ) THEN
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DO 30 I = 1, N
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U(I) = R(I)
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P(I) = R(I)
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30 CONTINUE
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ELSE
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DO 40 I = 1, N
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U(I) = R(I) + BK*Q(I)
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V1(I) = Q(I) + BK*P(I)
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40 CONTINUE
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DO 50 I = 1, N
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P(I) = U(I) + BK*V1(I)
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50 CONTINUE
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ENDIF
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C
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C Calculate coefficient AK, new iterate X, Q
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CALL MATVEC(N, P, V2, NELT, IA, JA, A, ISYM)
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CALL MSOLVE(N, V2, V1, NELT, IA, JA, A, ISYM, RWORK, IWORK)
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SIGMA = SDOT(N, R0, 1, V1, 1)
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IF( ABS(SIGMA).LT.FUZZ ) GOTO 999
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AK = RHON/SIGMA
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AKM = -AK
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DO 60 I = 1, N
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Q(I) = U(I) + AKM*V1(I)
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60 CONTINUE
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DO 70 I = 1, N
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V1(I) = U(I) + Q(I)
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70 CONTINUE
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C X = X - ak*V1.
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CALL SAXPY( N, AKM, V1, 1, X, 1 )
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C -1
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C R = R - ak*M *A*V1
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CALL MATVEC(N, V1, V2, NELT, IA, JA, A, ISYM)
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CALL MSOLVE(N, V2, V1, NELT, IA, JA, A, ISYM, RWORK, IWORK)
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CALL SAXPY( N, AKM, V1, 1, R, 1 )
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C
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C check stopping criterion.
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IF( ISSCGS(N, B, X, NELT, IA, JA, A, ISYM, MATVEC, MSOLVE,
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$ ITOL, TOL, ITMAX, ITER, ERR, IERR, IUNIT, R, R0, P, Q,
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$ U, V1, V2, RWORK, IWORK, AK, BK, BNRM, SOLNRM) .NE. 0 )
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$ GO TO 200
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C
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C Update RHO.
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RHONM1 = RHON
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100 CONTINUE
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C
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C ***** end of loop *****
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C Stopping criterion not satisfied.
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ITER = ITMAX + 1
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IERR = 2
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200 RETURN
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C
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C Breakdown of method detected.
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998 IERR = 5
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RETURN
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C
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C Stagnation of method detected.
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999 IERR = 6
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RETURN
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C------------- LAST LINE OF SCGS FOLLOWS ----------------------------
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END
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