130 IF (LEVEL.GE.2) WRITE (NOUT,140) NB         140 FORMAT (/10X,'ORDER OF BLACK SUBSYSTEM = ',I5,' (NB)')      CALL PERMAT (N,IA,JA,A,IWKSP,IWKSP(IB3),ISYM,LEVEL,NOUT,IER)        IF (IER.EQ.0) GO TO 160       IF (LEVEL.GE.0) WRITE (NOUT,150) IER        150 FORMAT ('0','*** F A T A L     E R R O R ************'/'0',   &     &   '    CALLED FROM ITPACK ROUTINE SOR '/' ',       &     &   '    ERROR DETECTED IN SUBROUTINE  PERMAT'/' ',  &     &   '    WHICH DOES THE RED-BLACK PERMUTATION'/' ','    IER = ',I5)      GO TO 360     160 CALL PERVEC (N,RHS,IWKSP)             CALL PERVEC (N,U,IWKSP) !       ! ... SCALE LINEAR SYSTEM, U, AND RHS BY THE SQUARE ROOT OF THE     ! ... DIAGONAL ELEMENTS.    !         170 CONTINUE          CALL VFILL (IPARM(8),WKSP,0.0D0)      CALL SCAL (N,IA,JA,A,RHS,U,WKSP,LEVEL,NOUT,IER)           IF (IER.EQ.0) GO TO 190       IF (LEVEL.GE.0) WRITE (NOUT,180) IER        180 FORMAT ('0','*** F A T A L     E R R O R ************'/'0',   &     &   '    CALLED FROM ITPACK ROUTINE SOR '/' ',       &     &   '    ERROR DETECTED IN SUBROUTINE  SCAL  '/' ',  &     &   '    WHICH SCALES THE SYSTEM   '/' ','    IER = ',I5)            GO TO 360     190 IF (LEVEL.LE.2) GO TO 220             IF (ADAPT) WRITE (NOUT,200)       200 FORMAT (///1X,'CME IS THE ESTIMATE OF THE LARGEST EIGENVALUE OF', &     &   ' THE JACOBI MATRIX')      WRITE (NOUT,210)        210 FORMAT (1X,'OMEGA IS THE RELAXATION FACTOR')  220 IF (IPARM(11).NE.0) GO TO 230         TIMI1 = TIMER(DUMMY)  !       ! ... ITERATION SEQUENCE    !         230 ITMAX1 = ITMAX+1            DO 240 LOOP = 1,ITMAX1         IN = LOOP-1!       ! ... CODE FOR ONE ITERATION. !       !     U           = U(IN)   !                CALL ITSOR (N,IA,JA,A,RHS,U,WKSP(IB1)) !                IF (HALT) GO TO 270  240 CONTINUE    !       ! ... ITMAX HAS BEEN REACHED!             IF (IPARM(11).NE.0) GO TO 250         TIMI2 = TIMER(DUMMY)        TIME1 = DBLE(TIMI2-TIMI1)         250 IF (LEVEL.GE.1) WRITE (NOUT,260) ITMAX      260 FORMAT ('0','*** W A R N I N G ************'/'0',   &     &   '    IN ITPACK ROUTINE SOR'/' ','    FAILURE TO CONVERGE IN',I5&     &   ,' ITERATIONS')          IER = 33          IF (IPARM(3).EQ.0) RPARM(1) = STPTST            GO TO 300   !       ! ... METHOD HAS CONVERGED  !         270 IF (IPARM(11).NE.0) GO TO 280         TIMI2 = TIMER(DUMMY)        TIME1 = DBLE(TIMI2-TIMI1)         280 IF (LEVEL.GE.1) WRITE (NOUT,290) IN         290 FORMAT (/1X,'SOR  HAS CONVERGED IN ',I5,' ITERATIONS')!       ! ... UNSCALE THE MATRIX, SOLUTION, AND RHS VECTORS.      !         300 CALL UNSCAL (N,IA,JA,A,RHS,U,WKSP)!       ! ... UN-PERMUTE MATRIX,RHS, AND SOLUTION       !             IF (IPARM(9).LT.0) GO TO 330          CALL PERMAT (N,IA,JA,A,IWKSP(IB2),IWKSP(IB3),ISYM,LEVEL,NOUT, &     &   IERPER)        IF (IERPER.EQ.0) GO TO 320            IF (LEVEL.GE.0) WRITE (NOUT,310) IERPER     310 FORMAT ('0','*** F A T A L     E R R O R ************'/'0',   &     &   '    CALLED FROM ITPACK ROUTINE SOR '/' ',       &     &   '    ERROR DETECTED IN SUBROUTINE  PERMAT'/' ',  &     &   '    WHICH UNDOES THE RED-BLACK PERMUTATION   '/' ',       &     &   '    IER = ',I5)         IF (IER.EQ.0) IER = IERPER            GO TO 360     320 CALL PERVEC (N,RHS,IWKSP(IB2))        CALL PERVEC (N,U,IWKSP(IB2))    !       ! ... OPTIONAL ERROR ANALYSIS !         330 IDGTS = IPARM(12)           IF (IDGTS.LT.0) GO TO 340             IF (IPARM(2).LE.0) IDGTS = 0          CALL PERROR5 (N,IA,JA,A,RHS,U,WKSP,DIGIT1,DIGIT2,IDGTS)!       ! ... SET RETURN PARAMETERS IN IPARM AND RPARM  !         340 IF (IPARM(11).NE.0) GO TO 350         TIMJ2 = TIMER(DUMMY)        TIME2 = DBLE(TIMJ2-TIMJ1)         350 IF (IPARM(3).NE.0) GO TO 360          IPARM(1) = IN       IPARM(9) = NB       RPARM(2) = CME      RPARM(3) = SME      RPARM(5) = OMEGA            RPARM(9) = TIME1            RPARM(10) = TIME2           RPARM(11) = DIGIT1          RPARM(12) = DIGIT2    !         360 CONTINUE          IERR = IER        IF (LEVEL.GE.3) CALL ECHALL (N,IA,JA,A,RHS,IPARM,RPARM,2)     !             RETURN            END       SUBROUTINE SSORCG (NN,IA,JA,A,RHS,U,IWKSP,NW,WKSP,IPARM,RPARM,&     &   IERR)    !       !     ITPACK 2C MAIN SUBROUTINE  SSORCG  (SYMMETRIC SUCCESSIVE OVER-!                                        RELAXATION CONJUGATE GRADIENT) !     EACH OF THE MAIN SUBROUTINES:   !           JCG, JSI, SOR, SSORCG, SSORSI, RSCG, RSSI     !     CAN BE USED INDEPENDENTLY OF THE OTHERS   !       ! ... FUNCTION:   !       !          THIS SUBROUTINE, SSORCG, DRIVES THE  SYMMETRIC SOR-CG    !          ALGORITHM.       !       ! ... PARAMETER LIST:       !       !          N      INPUT INTEGER.  DIMENSION OF THE MATRIX. (= NN)   !          IA,JA  INPUT INTEGER VECTORS.  THE TWO INTEGER ARRAYS OF !                 THE SPARSE MATRIX REPRESENTATION.       !          A      INPUT D.P. VECTOR.  THE D.P. ARRAY OF THE SPARSE  !                 MATRIX REPRESENTATION.!          RHS    INPUT D.P. VECTOR.  CONTAINS THE RIGHT HAND SIDE  !                 OF THE MATRIX PROBLEM.!          U      INPUT/OUTPUT D.P. VECTOR.  ON INPUT, U CONTAINS THE !                 INITIAL GUESS TO THE SOLUTION. ON OUTPUT, IT CONTAINS !                 THE LATEST ESTIMATE TO THE SOLUTION.    !          IWKSP  INTEGER VECTOR WORKSPACE OF LENGTH 3*N  !          NW     INPUT INTEGER.  LENGTH OF AVAILABLE WKSP.  ON OUTPUT, !                 IPARM(8) IS AMOUNT USED.      !          WKSP   D.P. VECTOR USED FOR WORKING SPACE.  SSOR-CG      !                 NEEDS TO BE IN LENGTH AT LEAST!                 6*N + 2*ITMAX,  IF IPARM(5)=0  (SYMMETRIC STORAGE)!                 6*N + 4*ITMAX,  IF IPARM(5)=1  (NONSYMMETRIC STORAGE) !          IPARM  INTEGER VECTOR OF LENGTH 12.  ALLOWS USER TO SPECIFY!                 SOME INTEGER PARAMETERS WHICH AFFECT THE METHOD.  IF!          RPARM  D.P. VECTOR OF LENGTH 12. ALLOWS USER TO SPECIFY SOME !                 D.P. PARAMETERS WHICH AFFECT THE METHOD.!          IER    OUTPUT INTEGER.  ERROR FLAG. (= IERR)   !       ! ... SSORCG SUBPROGRAM REFERENCES:   !       !          FROM ITPACK    BISRCH, CHGCON, DETERM, DFAULT, ECHALL,   !                         ECHOUT, EIGVNS, EIGVSS, EQRT1S, ITERM, TIMER, !                         ITSRCG, IVFILL, OMEG, OMGCHG, OMGSTR,     !                         PARCON, PBETA, PBSOR, PERMAT, PERROR5,     !                         PERVEC, PFSOR, PJAC, PMULT, PRBNDX, PSTOP, PVT!                         QSORT, SBELM, SCAL, DCOPY, DDOT, SUM3,    !                         UNSCAL, VEVMW, VEVPW, VFILL, VOUT, WEVMW, !                         ZBRENT      !          SYSTEM         DABS, DLOG, DLOG10, DBLE(AMAX0), DMAX1, AMIN1,!                         MOD, DSQRT  !       !     VERSION:  ITPACK 2C (MARCH 1982)!       !     CODE WRITTEN BY:  DAVID KINCAID, ROGER GRIMES, JOHN RESPESS   !                       CENTER FOR NUMERICAL ANALYSIS     !                       UNIVERSITY OF TEXAS     !                       AUSTIN, TX  78712       !                       (512) 471-1242!       !     FOR ADDITIONAL DETAILS ON THE   !          (A) SUBROUTINE SEE TOMS ARTICLE 1982 !          (B) ALGORITHM  SEE CNA REPORT 150    !       !     BASED ON THEORY BY:  DAVID YOUNG, DAVID KINCAID, LOU HAGEMAN  !       !     REFERENCE THE BOOK:  APPLIED ITERATIVE METHODS      !                          L. HAGEMAN, D. YOUNG !                          ACADEMIC PRESS, 1981 !       !     **************************************************  !     *               IMPORTANT NOTE                   *  !     *                                                *  !     *      WHEN INSTALLING ITPACK ROUTINES ON A      *  !     *  DIFFERENT COMPUTER, RESET SOME OF THE VALUES  *  !     *  IN  SUBROUTNE DFAULT.   MOST IMPORTANT ARE    *  !     *                                                *  !     *   DRELPR      MACHINE RELATIVE PRECISION       *  !     *   RPARM(1)    STOPPING CRITERION               *  !     *                                                *  !     *   ALSO CHANGE SYSTEM-DEPENDENT ROUTINE         *  !     *   SECOND USED IN TIMER                         *  !     *                                                *  !     **************************************************  !       !     SPECIFICATIONS FOR ARGUMENTS    !             INTEGER IA(1),JA(1),IWKSP(1),IPARM(12),NN,NW,IERR         DOUBLE PRECISION A(1),RHS(NN),U(NN),WKSP(NW),RPARM(12)!       !     SPECIFICATIONS FOR LOCAL VARIABLES!             INTEGER IB1,IB2,IB3,IB4,IB5,IB6,IB7,IDGTS,IER,IERPER,ITMAX1,LOOP,N&     &   ,NB,N3         DOUBLE PRECISION BETNEW,DIGIT1,DIGIT2,PBETA,TEMP,TIME1,TIME2,TOL!       ! *** BEGIN: ITPACK COMMON  !             INTEGER IN,IS,ISYM,ITMAX,LEVEL,NOUT             COMMON /ITCOM1/ IN,IS,ISYM,ITMAX,LEVEL,NOUT !             LOGICAL ADAPT,BETADT,CASEII,HALT,PARTAD         COMMON /ITCOM2/ ADAPT,BETADT,CASEII,HALT,PARTAD     !             DOUBLE PRECISION BDELNM,BETAB,CME,DELNNM,DELSNM,FF,GAMMA,OMEGA,QA,&     &   QT,RHO,RRR,SIGE,SME,SPECR,SPR,DRELPR,STPTST,UDNM,ZETA            COMMON /ITCOM3/ BDELNM,BETAB,CME,DELNNM,DELSNM,FF,GAMMA,OMEGA,QA, &     &   QT,RHO,RRR,SIGE,SME,SPECR,SPR,DRELPR,STPTST,UDNM,ZETA      !       ! *** END  : ITPACK COMMON  !       ! ... VARIABLES IN COMMON BLOCK - ITCOM1!       !     IN     - ITERATION NUMBER       !     IS     - ITERATION NUMBER WHEN PARAMETERS LAST CHANGED!     ISYM   - SYMMETRIC/NONSYMMETRIC STORAGE FORMAT SWITCH !     ITMAX  - MAXIMUM NUMBER OF ITERATIONS ALLOWED       !     LEVEL  - LEVEL OF OUTPUT CONTROL SWITCH   !     NOUT   - OUTPUT UNIT NUMBER     !       ! ... VARIABLES IN COMMON BLOCK - ITCOM2!       !     ADAPT  - FULLY ADAPTIVE PROCEDURE SWITCH  !     BETADT - SWITCH FOR ADAPTIVE DETERMINATION OF BETA  !     CASEII - ADAPTIVE PROCEDURE CASE SWITCH   !     HALT   - STOPPING TEST SWITCH   !     PARTAD - PARTIALLY ADAPTIVE PROCEDURE SWITCH!       ! ... VARIABLES IN COMMON BLOCK - ITCOM3!       !     BDELNM - TWO NORM OF B TIMES DELTA-SUPER-N!     BETAB  - ESTIMATE FOR THE SPECTRAL RADIUS OF LU MATRIX!     CME    - ESTIMATE OF LARGEST EIGENVALUE   !     DELNNM - INNER PRODUCT OF PSEUDO-RESIDUAL AT ITERATION N      !     DELSNM - INNER PRODUCT OF PSEUDO-RESIDUAL AT ITERATION S      !     FF     - ADAPTIVE PROCEDURE DAMPING FACTOR!     GAMMA  - ACCELERATION PARAMETER !     OMEGA  - OVERRELAXATION PARAMETER FOR SOR AND SSOR  !     QA     - PSEUDO-RESIDUAL RATIO  !     QT     - VIRTUAL SPECTRAL RADIUS!     RHO    - ACCELERATION PARAMETER !     RRR    - ADAPTIVE PARAMETER     !     SIGE   - PARAMETER SIGMA-SUB-E  !     SME    - ESTIMATE OF SMALLEST EIGENVALUE  !     SPECR  - SPECTRAL RADIUS ESTIMATE FOR SSOR!     DRELPR - MACHINE RELATIVE PRECISION       !     STPTST - STOPPING PARAMETER     !     UDNM   - TWO NORM OF U!     ZETA   - STOPPING CRITERION     !       ! ... INITIALIZE COMMON BLOCKS!             LEVEL = IPARM(2)            NOUT = IPARM(4)             IF (IPARM(9).GE.0) IPARM(6) = 2       IF (LEVEL.GE.1) WRITE (NOUT,10)    10 FORMAT ('0'///1X,'BEGINNING OF ITPACK SOLUTION MODULE  SSORCG')       IER = 0           IF (IPARM(1).LE.0) RETURN             N = NN            IF (IPARM(11).EQ.0) TIMJ1 = TIMER(DUMMY)        IF (LEVEL.GE.3) GO TO 20      CALL ECHOUT (IPARM,RPARM,4)           GO TO 30       20 CALL ECHALL (N,IA,JA,A,RHS,IPARM,RPARM,1)    30 TEMP = 5.0D2*DRELPR         IF (ZETA.GE.TEMP) GO TO 50            IF (LEVEL.GE.1) WRITE (NOUT,40) ZETA,DRELPR,TEMP       40 FORMAT ('0','*** W A R N I N G ************'/'0',   &     &   '    IN ITPACK ROUTINE SSORCG'/' ','    RPARM(1) =',D10.3, &     &   ' (ZETA)'/' ','    A VALUE THIS SMALL MAY HINDER CONVERGENCE '/&     &   ' ','    SINCE MACHINE PRECISION DRELPR =',D10.3/' ',      &     &   '    ZETA RESET TO ',D10.3)        ZETA = TEMP    50 CONTINUE          TIME1 = RPARM(9)            TIME2 = RPARM(10)           DIGIT1 = RPARM(11)          DIGIT2 = RPARM(12)    !       ! ... VERIFY N    !             IF (N.GT.0) GO TO 70        IER = 41          IF (LEVEL.GE.0) WRITE (NOUT,60) N    60 FORMAT ('0','*** F A T A L     E R R O R ************'/'0',   &     &   '    CALLED FROM ITPACK ROUTINE SSORCG '/' ',    &     &   '    INVALID MATRIX DIMENSION, N =',I8)      GO TO 390      70 CONTINUE    !       ! ... REMOVE ROWS AND COLUMNS IF REQUESTED      !             IF (IPARM(10).EQ.0) GO TO 90          TOL = RPARM(8)      CALL IVFILL (N,IWKSP,0)       CALL VFILL (N,WKSP,0.0D0)             CALL SBELM (N,IA,JA,A,RHS,IWKSP,WKSP,TOL,ISYM,LEVEL,NOUT,IER)       IF (IER.EQ.0) GO TO 90      IF (LEVEL.GE.0) WRITE (NOUT,80) IER,TOL      80 FORMAT ('0','*** F A T A L     E R R O R ************'/'0',   &     &   '    CALLED FROM ITPACK ROUTINE SSORCG '/' ',    &     &   '    ERROR DETECTED IN SUBROUTINE  SBELM '/' ',  &     &   '    WHICH REMOVES ROWS AND COLUMNS OF SYSTEM '/' ',       &     &   '    WHEN DIAGONAL ENTRY TOO LARGE  '/' ','    IER = ',I5,5X,&     &   ' RPARM(8) = ',D10.3,' (TOL)')       GO TO 390   !       ! ... INITIALIZE WKSP BASE ADDRESSES.