* PROGRAM TEMPLATESTESTER * * Test program for the SINGLE PRECISION iterative templates. * * The program must be driven by a short data file. The first 18 records * of the file are read using list-directed input, the last 16 records * are read using the format ( A6, L2 ). An annotated example of a data * file s a follows: * * 1.0E-8 CONVERGENCE TOLERANCE * 10 SCALED RESIDUAL TOLERANCE * CG T PUT F FOR NO TEST. ALGORITHMS TO BE TESTED * CHEBY T PUT F FOR NO TEST. * SOR T PUT F FOR NO TEST. * BICG T PUT F FOR NO TEST. * CGS T PUT F FOR NO TEST. * BICGS T PUT F FOR NO TEST. * GMRES F PUT F FOR NO TEST. * QMR T PUT F FOR NO TEST. * JACOB T PUT F FOR NO TEST. * 3 NUMBER OF SPD MATRICES TO BE GENERATED * WATH 2, 2, 1, ONES, ZERO MATRIX, NX, NY, NZ, RHS, INITIAL GUESS * F2SH 6, 6, 1, SUMR, ZERO * F3SH 3, 3, 3, ONES, ZERO * BICG T PUT F FOR NO TEST. ALGORITHMS TO BE TESTED * CGS T PUT F FOR NO TEST. * BICGS T PUT F FOR NO TEST. * GMRES F PUT F FOR NO TEST. * QMR T PUT F FOR NO TEST. * 4 NUMBER OF MATTRICES TO BE GENERATED * PDE1, 5, 5, 5, SUMR , ZERO MATRIX, NX, NY, NZ, RHS, INITIAL GUESS * PDE2, 5, 5, 5, SUMR , ZERO * PDE3, 5, 5, 5, ONES , ZERO * PDE4, 6, 6, 1, ONES , ZERO * * See: * * Barrett, Berry, Chan, Demmel, Donato, Dongarra, * Eijkhout, Pozo, Romine, and van der Vorst. * Templates for the Solution of Linear Systems: Building Blocks * for Iterative Methods, SIAM Publications, 1993. * (ftp netlib2.cs.utk.edu; cd linalg; get templates.ps). * * -- Written on 1-November-1993. * Richard Barrett, University of Tennessee * Jack Dongarra, Univ. of Tennessee and Oak Ridge National * Laboratory * * .. Parameters .. * MAXLEN must be greater than or equal to (2N**2)+3N, i.e. WORK * must have dimension N x (2N+3). This is for SOR (see StatUtils * for details). Chebyshev requires N*2. For workspace requirements * of the algorithms, see the individial template. * INTEGER MAXDIM, MAXLEN, NSUBS PARAMETER ( MAXDIM = 200, MAXLEN = 80000, NSUBS = 9) * .. * .. Scalar Declarations .. INTEGER I, LDX, LDW, SPDTESTS, NSYTESTS, SUSPSPD, $ SUSPNSY, CRITSPD, CRITNSY REAL TOL, SCALEDTOL LOGICAL LTESTT, LSAMEN, SPDRES, NSYRES CHARACTER*6 SNAMET * .. * .. Array Declarations .. REAL X( MAXDIM,NSUBS ), B( MAXDIM ), X0( MAXDIM ), $ WORK( MAXLEN ) LOGICAL LTEST( NSUBS ) CHARACTER*6 SNAMES( NSUBS ) CHARACTER*5 PFORM( 2 ) * .. * .. Common Blocks .. INTEGER N, LDA COMMON / MATDIM / N, LDA * .. * .. External Routines .. EXTERNAL MATVEC, MATVECTRANS, PSOLVE, PSOLVETRANS, $ PSOLVEQ, PSOLVETRANSQ, BACKSOLVE, SNSYCHK, $ SSPDCHK * DATA SNAMES/'CG ', 'CHEBY ', 'SOR ', 'BICG ', $ 'CGS ', 'BICGS ', 'GMRES ', 'QMR ', $ 'JACOB '/ * .. * .. Executable Statements .. * * Initializations. * LDA = MAXDIM LDX = MAXDIM LDW = MAXDIM * SPDRES = .TRUE. NSYRES = .TRUE. * PFORM( 1 ) = 'IDENT' PFORM( 2 ) = 'JACBI' * OPEN( UNIT = 9, FILE = 'test.data' ) OPEN( UNIT = 10, FILE = 'test.results' ) * * Get the convergence tolerance, the tolerance for the normalized * scaled residual, and the number of systems to be generated. * and the algorithms to be tested. * READ(9,*) TOL READ(9,*) SCALEDTOL * * Get input data for SPD testing: * Read names of subroutines and flags which indicate whether * they are to be tested. * DO 10 I = 1, NSUBS LTEST( I ) = .FALSE. 10 CONTINUE 20 READ( 9, FMT = 998 )SNAMET, LTESTT DO 30 I = 1, NSUBS IF( LSAMEN( 6, SNAMET, SNAMES( I ) ) ) GO TO 40 30 CONTINUE WRITE( *, FMT = 999 )SNAMET STOP 40 LTEST( I ) = LTESTT IF ( I.LT.NSUBS ) GO TO 20 * 50 CONTINUE * * Begin testing. * CALL HEADER( TOL ) * * Symmetric Positive Definite Routine Tester. * CALL SSPDCHK( X, LDX, B, X0, WORK, LDW, PFORM, MATVEC, $ MATVECTRANS, PSOLVE, PSOLVETRANS, PSOLVEQ, $ PSOLVETRANSQ, BACKSOLVE, TOL, SCALEDTOL, LTEST, $ SPDRES, SPDTESTS, SUSPSPD, CRITSPD ) * * Get input data for Nonsymmetric testing: * Read names of subroutines and flags which indicate whether * they are to be tested. * DO 60 I = 1, NSUBS LTEST( I ) = .FALSE. 60 CONTINUE 70 READ( 9, FMT = 998, END = 100 )SNAMET, LTESTT DO 80 I = 4, 8 IF( LSAMEN( 6, SNAMET, SNAMES( I ) ) ) GO TO 90 80 CONTINUE WRITE( *, FMT = 999 )SNAMET STOP 90 LTEST( I ) = LTESTT IF ( I.LT.8 ) GO TO 70 * 100 CONTINUE * * Nonsymmetric Routine Tester. * CALL SNSYCHK( X, LDX, B, X0, WORK, LDW, PFORM, MATVEC, $ MATVECTRANS, PSOLVE, PSOLVETRANS, PSOLVEQ, $ PSOLVETRANSQ, BACKSOLVE, TOL, SCALEDTOL, LTEST, $ NSYRES, NSYTESTS, SUSPNSY, CRITNSY ) * * End of testing. * CALL FOOTER() * CLOSE( UNIT = 9 ) CLOSE( UNIT = 10 ) * * Print overall results to screen. * WRITE(*,*) IF ( ( SPDRES ).AND.( NSYRES ) ) THEN * * All tests passed. * WRITE(*,*) 'TESTS COMPLETE:' WRITE(*,*) IF ( SPDTESTS.GT.0 ) WRITE(*,900) SPDTESTS IF ( NSYTESTS.GT.0 ) WRITE(*,901) NSYTESTS ELSE IF ( SPDRES ) THEN * IF ( SPDTESTS.GT.0 ) THEN * * SPD tests passed. * WRITE(*,*) 'TESTS COMPLETE:' WRITE(*,*) WRITE(*,910) SPDTESTS ELSE WRITE(*,*) WRITE(*,*) 'SPD TESTING NOT PERFORMED.' ENDIF ELSE * * SPD testing failed. * WRITE(*,911) SPDTESTS WRITE(*,990) CRITSPD, SUSPSPD WRITE(*,991) ENDIF WRITE(*,*) IF ( NSYRES ) THEN * IF ( SPDTESTS.GT.0 ) THEN * * Nonsymmetric tests passed. * WRITE(*,*) 'TESTS COMPLETE:' WRITE(*,*) WRITE(*,920) NSYTESTS ELSE WRITE(*,*) WRITE(*,*) 'NONSYMMETRIC TESTING NOT PERFORMED.' ENDIF ELSE * * Nonsymmetric testing failed. * WRITE(*,*) WRITE(*,921) NSYTESTS WRITE(*,990) CRITNSY, SUSPNSY WRITE(*,991) ENDIF ENDIF WRITE(*,*) * * Format statements for screen output of general test results. * 900 FORMAT(' SYMMETRIC POSITIVE DEFINITE ROUTINES PASSED. (', I3, $ ' TESTS )') 901 FORMAT(' NONSYMMETRIC ROUTINES PASSED. (', I3,' TESTS )') * 910 FORMAT(' PASSED FOR SYMMETRIC POSITIVE DEFINITE MATRICES (' ,I3,' $TESTS )') 911 FORMAT(' SYMMETRIC POSITIVE DEFINITE MATRICES: (' , I3,' TESTS )') * 920 FORMAT(' PASSED FOR NONSYMMETRIC MATRICES (' ,I3,' TESTS )') 921 FORMAT(' NONSYMMETRIC MATRICES: (' , I3,' TESTS )') * 990 FORMAT(' THERE ARE',I3,' CRITICAL ERRORS AND ' ,I3,' SUSPICIOUS RE $SULTS.') 991 FORMAT(' SEE FILE test.results FOR ADDITIONAL INFORMATION') * 998 FORMAT( A6, L2 ) 999 FORMAT( ' SUBPROGRAM NAME ', A6, ' NOT RECOGNIZED', /' ******* T', $ 'ESTS ABANDONED *******' ) * STOP * * End of Driver for Testing the Iterative Templates * END * * =============================================================== SUBROUTINE VECGEN( FORM, N, A, LDA, B, INFO ) * REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) * INTEGER I, J, N, LDA, INFO REAL A( LDA,* ), B( * ), TMP CHARACTER FORM*4 LOGICAL LSAMEN * INFO = 0 * IF ( LSAMEN( 3, FORM,'ONES' ) ) THEN DO 10 I = 1, N B( I ) = ONE 10 CONTINUE ELSE IF ( LSAMEN( 3, FORM,'ZEROS' ) ) THEN DO 20 I = 1, N B( I ) = ZERO 20 CONTINUE ELSE IF ( LSAMEN( 3, FORM,'SUMROW' ) ) THEN DO 40 I = 1, N TMP = ZERO DO 30 J = 1, N TMP = TMP + A( I,J ) 30 CONTINUE B( I ) = TMP 40 CONTINUE ELSE INFO = -1 ENDIF * RETURN * END * * =============================================================== SUBROUTINE PRECON( N, A, LDA, PFORM, M, INFO ) * * .. Scalar and Array Declarations .. * INTEGER N, LDA, INFO REAL A( LDA,* ), M( * ) CHARACTER *5 PFORM * * Purpose: * ======= * * PRECON forms a preconditioner matrix of type PROFRM for * iterative solvers of the linear system Ax = b. * * PFORM: * * IDENT identity matrix (for testing) * * JACBI diagonal scaling * * ============================================== * * .. Local Scalars .. * INTEGER I LOGICAL LSAMEN * * .. Executable Statements .. * IF ( LSAMEN( 5, PFORM,'IDENT' ) ) THEN * * Identity matrix need not be formed, since the solve involving * the preconditioner (PSolve) merely copies the right hand side * to the solution vector. * RETURN * ELSE IF ( LSAMEN( 5, PFORM,'JACBI' ) ) THEN * * Diagonal Scaling: diag(A). Note that we actually form inv(M) so that * solver can use multiplication. * DO 10 I = 1, N M( I ) = A( I,I ) 10 CONTINUE * ELSE * * Selected preconditioner not implemented * WRITE(*,*) WRITE(*,*) WRITE(*,*) 'PRECONDITIONER ',PFORM,' NOT YET IMPLEMENTED' WRITE(*,*) WRITE(*,*) WRITE(*,*) INFO = -1 * ENDIF * RETURN END * * ================================================================ REAL FUNCTION GETBREAK() * * Get breakdown parameter tolerance; for the test routine, * set to machine precision. * REAL EPS, SLAMCH * EPS = SLAMCH('EPS') GETBREAK = EPS**2 * RETURN * END * =============================================================== REAL FUNCTION SCALEDRESID( ANORM, N, X, RK, TOL ) * * Returns |B-A*X| / ( |A||X|*N*TOL ), using the infinity norm. * INTEGER N, ISAMAX REAL ANORM, TOL, XNORM, RESNORM, $ X( * ), RK( * ) * XNORM = ABS( X( ISAMAX( N, X, 1 ) ) ) RESNORM = ABS( RK( ISAMAX( N, RK, 1 ) ) ) * SCALEDRESID = RESNORM / ( TOL * N * ANORM * XNORM ) * RETURN * END * =========================================================== REAL FUNCTION MATNORM( N, A, LDA ) * * Compute infinity norm of matrix A. * INTEGER N, LDA, I, J REAL ROWSUM, ZERO, TEMP, A( LDA,* ) PARAMETER ( ZERO = 0.0E+0 ) * TEMP = ZERO DO 20 I = 1, N ROWSUM = ZERO DO 10 J = 1, N ROWSUM = ROWSUM + ABS( A( I,J ) ) 10 CONTINUE TEMP = MAX( ROWSUM, TEMP ) 20 CONTINUE * MATNORM = TEMP * RETURN * END * * =============================================================== SUBROUTINE RESULT( N, A, LDA, X, LDX, B, RK, MATTYPE, PFORM, $ ITER, RESID, TOL, INFO, AFORM, ANORM, $ LTEST, SCALEDTOL, TESTPASSED, CRITERR ) * * .. Argument Declaractions .. * INTEGER N, LDA, LDX, CRITERR, $ ITER( * ), INFO( * ) REAL TOL, ANORM, SCALEDTOL, $ A( LDA,* ), X( LDX,* ), B( * ), RK( * ), $ RESID( * ) CHARACTER MATTYPE*3, AFORM*4, PFORM*5 LOGICAL TESTPASSED, LTEST( * ) * * Purpose * ======= * * Report results of METHOD on matrix type MATTYPE. If the residual * is not directly computed by the algorithm, then the residual RESID * as returned by the algorithm is compared with the residual as * computed using the solution returned, i.e. || B-AX ||. * ======================================================= * * .. Local Declarations .. * REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) * INTEGER I, FIRSTALG, NUMALG REAL SNRM2, SCALEDRESID, SRESID( 9 ) CHARACTER*9 METHOD( 9 ) LOGICAL LSAME, LSAMEN * EXTERNAL SCOPY, SGEMV, SNRM2 * * .. Executable Statements .. * METHOD( 1 ) = 'CG ' METHOD( 2 ) = 'Chebyshev' METHOD( 3 ) = 'SOR ' METHOD( 4 ) = 'BiCG ' METHOD( 5 ) = 'CGS ' METHOD( 6 ) = 'BiCGSTAB ' METHOD( 7 ) = 'GMRESm ' METHOD( 8 ) = 'QMR ' METHOD( 9 ) = 'Jacobi ' * * Compare algorithm reported residual with |b-AX|/(|A||x|n*TOL) * IF ( LSAME( MATTYPE,'SPD' ) ) THEN FIRSTALG = 1 NUMALG = 9 ELSE FIRSTALG = 4 NUMALG = 8 ENDIF DO 10 I = FIRSTALG, NUMALG IF ( RESID( I ).NE.ZERO ) THEN CALL SCOPY( N, B, 1, RK, 1 ) CALL SGEMV('N', N, N, -ONE, A, LDA, X( 1,I ), 1, ONE, $ RK, 1 ) SRESID( I ) = SCALEDRESID( ANORM, N, X( 1,I ), RK, TOL ) ENDIF 10 CONTINUE * IF ( LSAMEN( 4, AFORM,'F2SH') ) THEN IF ( LSAMEN( 2, PFORM,'IDENT' ) ) THEN WRITE(10,900) N WRITE(*,900) N ELSE IF ( LSAMEN( 2, PFORM,'JACBI' ) ) THEN WRITE(10,901) N WRITE(*,901) N ENDIF ELSE IF ( LSAMEN( 4, AFORM,'F3SH') ) THEN IF ( LSAMEN( 2, PFORM,'IDENT' ) ) THEN WRITE(10,902) N WRITE(*,902) N ELSE IF ( LSAMEN( 2, PFORM,'JACBI' ) ) THEN WRITE(10,903) N WRITE(*,903) N ENDIF ELSE IF ( LSAMEN( 4, AFORM,'WATH' ) ) THEN IF ( LSAMEN( 2, PFORM,'IDENT' ) ) THEN WRITE(10,910) N WRITE(*,910) N ELSE IF ( LSAMEN( 2, PFORM,'JACBI' ) ) THEN WRITE(10,911) N WRITE(*,911) N ENDIF ELSE IF ( LSAMEN( 3, AFORM,'PDE' ) ) THEN IF ( LSAMEN( 2, PFORM,'IDENT' ) ) THEN WRITE(10,920) N, AFORM WRITE(*,920) N, AFORM ELSE IF ( LSAMEN( 2, PFORM,'JACBI' ) ) THEN WRITE(10,921) N, AFORM WRITE(*,921) N, AFORM ENDIF ENDIF WRITE(10,*) * * Loop over the algorithms, with a final error check. * DO 30 I = FIRSTALG, NUMALG * * Check updated residual vs. scaled residual. * IF ( LTEST( I ) ) THEN IF ( INFO( I ).EQ.0 ) THEN * * Method claims to have found solution. * Check scaled residual. * IF ( SRESID( I ).LE.SCALEDTOL ) THEN * * Scaled residual check passed. * WRITE(10,991) METHOD( I ), RESID( I ), SRESID( I ), $ ITER( I ) WRITE(*,991) METHOD( I ), RESID( I ), SRESID( I ), $ ITER( I ) ELSE CRITERR = CRITERR + 1 TESTPASSED = .FALSE. WRITE(10,992) METHOD( I ), RESID( I ), SRESID( I ), $ ITER( I ) WRITE(*,992) METHOD( I ), RESID( I ), SRESID( I ), $ ITER( I ) ENDIF ELSE IF ( INFO( I ).EQ.100 ) THEN GO TO 30 ELSE TESTPASSED = .FALSE. * * Method claims to have not found solution to tolerance, * either because the maximum number of iterations were * performed, or breakdown occured. * WRITE(10,993) METHOD( I ), RESID( I ), SRESID( I ), $ ITER( I ), INFO( I ) WRITE(*,993) METHOD( I ), RESID( I ), SRESID( I ), $ ITER( I ), INFO( I ) ENDIF * ELSE * * Method was not involved in test * GO TO 30 * ENDIF * 30 CONTINUE * WRITE(10,*) '----------------------------------------------------- $--' * * Header for each system. * 900 FORMAT('Order', I4,' SPD 2-d Poisson matrix (no preconditioning)') 901 FORMAT('Order', I4,' SPD 2-d Poisson matrix (Jacobi preconditionin $g)') 902 FORMAT('Order', I4,' SPD 3-d Poisson matrix (no preconditioning)') 903 FORMAT('Order', I4,' SPD 3-d Poisson matrix (Jacobi preconditionin $g)') 910 FORMAT('Order ', I4,' SPD Wathen matrix (no preconditioning)') 911 FORMAT('Order ', I4,' SPD Wathen matrix (Jacobi preconditioning)') 920 FORMAT('Order ', I4,' ', A4, ' nonsymmetric matrix (no preconditio $ning)') 921 FORMAT('Order ', I4,' ', A4, ' nonsymmetric matrix (Jacobi precond $itioning)') * * Reporting of results. * 991 FORMAT(' ', A9,' ',1PE8.2,' ', 1PE8.2,' ', I5 ) 992 FORMAT(' ', A9,' ',1PE8.2,' ', 1PE8.2,' ', I5, $ ' X' ) 993 FORMAT(' ', A9,' ',1PE8.2,' ', 1PE8.2,' ', I5,' ', I3 ) * RETURN * * End of Result.f * END * * ================================================================== SUBROUTINE HEADER( TOL ) * REAL TOL, EPS, SLAMCH * EPS = SLAMCH('E') * * Print header to file. * WRITE(10,*) WRITE(10,*) 'DETAILS OF ITERATIVE TEMPLATES TEST:' WRITE(10,*) WRITE(10,*) ' Univ. of Tennessee and Oak Ridge National Laborato $ry' WRITE(10,*) ' October 1, 1993' WRITE(10,*) ' Details of these algorithms are described in "Temp $lates' WRITE(10,*) ' for the Solution of Linear Systems: Building Block $s for' WRITE(10,*) ' Iterative Methods", Barrett, Berry, Chan, Demmel, $Donato,' WRITE(10,*) ' Dongarra, Eijkhout, Pozo, Romine, and van der Vors $t,' WRITE(10,*) ' SIAM Publications, 1993.' WRITE(10,*) ' (ftp netlib2.cs.utk.edu; cd linalg; get templates. $ps).' WRITE(10,*) WRITE(10,*) WRITE(10,21) EPS WRITE(10,22) TOL WRITE(10,*) WRITE(10,*) WRITE(10,*) ' For a detailed description of the following informat $ion,' WRITE(10,*) ' see the end of this file.' WRITE(10,*) WRITE(10,*) '===================================================== $=' WRITE(10,*) ' CONVERGENCE NORMALIZED NUM' WRITE(10,*) ' METHOD CRITERION RESIDUAL ITER INFO FLAG' WRITE(10,*) '===================================================== $=' WRITE(10,*) * * Print header to screen. * WRITE(*,*) WRITE(*,*) 'DETAILS OF ITERATIVE TEMPLATES TEST:' WRITE(*,*) WRITE(*,*) ' Univ. of Tennessee and Oak Ridge National Laborator $y' WRITE(*,*) ' October 1, 1993' WRITE(*,*) ' Details of these algorithms are described in "Templ $ates' WRITE(*,*) ' for the Solution of Linear Systems: Building Blocks $ for' WRITE(*,*) ' Iterative Methods", Barrett, Berry, Chan, Demmel, D $onato,' WRITE(*,*) ' Dongarra, Eijkhout, Pozo, Romine, and van der Vorst $,' WRITE(*,*) ' SIAM Publications, 1993.' WRITE(*,*) ' (ftp netlib2.cs.utk.edu; cd linalg; get templates.p $s).' WRITE(*,*) WRITE(*,*) WRITE(*,21) EPS WRITE(*,22) TOL WRITE(*,*) WRITE(*,*) WRITE(*,*) ' For a detailed description of the following informati $on,' WRITE(10,*) ' see the end of this file.' WRITE(*,*) WRITE(*,*) '=====================================================' WRITE(*,*) ' CONVERGENCE NORMALIZED NUM' WRITE(*,*) ' METHOD CRITERION RESIDUAL ITER INFO FLAG' WRITE(*,*) '=====================================================' WRITE(*,*) * 21 FORMAT( 'MACHINE PRECISION = ', 1PE8.2 ) 22 FORMAT( 'CONVERGENCE TEST TOLERANCE = ', 1PE8.2 ) * RETURN * END * * ================================================================== SUBROUTINE FOOTER() * * Puts descriptive information at bottom of results file * WRITE(10,*) WRITE(10,*) '======' WRITE(10,*) 'LEGEND:' WRITE(10,*) '======' WRITE(10,*) WRITE(10,*) ' ==================' WRITE(10,*) ' SYSTEM DESCRIPTION' WRITE(10,*) ' ==================' WRITE(10,*) WRITE(10,*) ' SPD matrices:' WRITE(10,*) WRITE(10,*) ' WATH: "Wathen Matrix": consistent mass matrix' WRITE(10,*) ' F2SH: 2-d Poisson problem' WRITE(10,*) ' F3SH: 3-d Poisson problem' WRITE(10,*) WRITE(10,*) ' PDE1: u_xx+u_yy+au_x+(a_x/2)u' WRITE(10,*) ' for a = 20exp[3.5(x**2+y**2 )]' WRITE(10,*) WRITE(10,*) ' Nonsymmetric matrices:' WRITE(10,*) WRITE(10,*) ' PDE2: u_xx+u_yy+u_zz+1000u_x' WRITE(10,*) ' PDE3 u_xx+u_yy+u_zz-10**5x**2(u_x+u_y+u_z )' WRITE(10,*) ' PDE4: u_xx+u_yy+u_zz+1000exp(xyz)(u_x+u_y-u_z)' WRITE(10,*) WRITE(10,*) ' =====================' WRITE(10,*) ' CONVERGENCE CRITERION' WRITE(10,*) ' =====================' WRITE(10,*) WRITE(10,*) ' Convergence criteria: residual as reported by the' WRITE(10,*) ' algorithm: ||AX - B|| / ||B||. Note that NaN may s $ignify' WRITE(10,*) ' divergence of the residual to the point of numeric $al overflow.' WRITE(10,*) WRITE(10,*) ' ===================' WRITE(10,*) ' NORMALIZED RESIDUAL' WRITE(10,*) ' ===================' WRITE(10,*) WRITE(10,*) ' Normalized Residual: ||AX - B|| / (||A||||X||*N*TO $L).' WRITE(10,*) ' This is an apostiori check of the iterated solutio $n.' WRITE(10,*) WRITE(10,*) ' ====' WRITE(10,*) ' INFO' WRITE(10,*) ' ====' WRITE(10,*) WRITE(10,*) ' If this column is blank, then the algorithm claims $ to have' WRITE(10,*) ' found the solution to tolerance (i.e. INFO = 0).' WRITE(10,*) ' This should be verified by checking the normalized $residual.' WRITE(10,*) WRITE(10,*) ' Otherwise:' WRITE(10,*) WRITE(10,*) ' = 1: Convergence not achieved given the maximum $ number of iterations.' WRITE(10,*) WRITE(10,*) ' Input parameter errors:' WRITE(10,*) WRITE(10,*) ' = -1: matrix dimension N < 0' WRITE(10,*) ' = -2: LDW < N' WRITE(10,*) ' = -3: Maximum number of iterations <= 0.' WRITE(10,*) ' = -4: For SOR: OMEGA not in interval (0,2)' WRITE(10,*) ' For GMRES: LDW2 < 2*RESTRT' WRITE(10,*) ' = -5: incorrect index request by uper level.' WRITE(10,*) ' = -6: incorrect job code from upper level.' WRITE(10,*) WRITE(10,*) ' <= -10: Algorithm was terminated due to breakdo $wn.' WRITE(10,*) ' See algorithm documentation for details $.' WRITE(10,*) WRITE(10,*) ' ====' WRITE(10,*) ' FLAG' WRITE(10,*) ' ====' WRITE(10,*) WRITE(10,*) ' X: Algorithm has reported convergence, but' WRITE(10,*) ' approximate solution fails scaled' WRITE(10,*) ' residual check.' WRITE(10,*) WRITE(10,*) ' =====' WRITE(10,*) ' NOTES' WRITE(10,*) ' =====' WRITE(10,*) WRITE(10,*) ' GMRES: For the symmetric test matrices, the restar $t parameter is' WRITE(10,*) ' set to N. This should, theoretically, result in no $ restarting. For' WRITE(10,*) ' nonsymmetric testing the restart parameter is set $to N / 2.' WRITE(10,*) WRITE(10,*) ' Stationary methods:' WRITE(10,*) WRITE(10,*) ' - Since the residual norm ||b-Ax|| is not availabl $e as part of' WRITE(10,*) ' the algorithm, the convergence criteria is diffe $rent from the' WRITE(10,*) ' nonstationary methods. Here we use' WRITE(10,*) WRITE(10,*) ' || X - X1 || / || X ||.' WRITE(10,*) WRITE(10,*) ' That is, we compare the current approximated sol $ution with the' WRITE(10,*) ' approximation from the previous step.' WRITE(10,*) WRITE(10,*) ' - Since Jacobi and SOR do not use preconditioning, $' WRITE(10,*) ' Jacobi is only iterated once per system, and SOR $ loops over' WRITE(10,*) ' different values for OMEGA (the first time throu $gh OMEGA = 1,' WRITE(10,*) ' i.e. the algorithm defaults to Gauss-Siedel). Th $is explains the ' WRITE(10,*) ' different residual norms for SOR with the same m $atrix.' WRITE(10,*) * RETURN * END