      SUBROUTINE DECOMP(NDIM,N,A,COND,IPVT,WORK)                        DEC00010
      INTEGER    NDIM,N,IPVT,NM1,I,J,K,KP1,KB,KM1,M                     DEC00020
      DOUBLE PRECISION COND,EK,T,ANORM,YNORM,ZNORM,A,WORK               DEC00030
      DIMENSION  IPVT(N),A(NDIM,N),WORK(N)                              DEC00040
C ********************************************************************  DEC00050
C * H SUBROUTINE DECOMP EINAI MIA YPOROYTINA GRAMMENH SE FORTRAN(4)  *  DEC00060
C * H OPOIA KANEI TO MEROS THS APALOIFHS TOU GAUSS POU EXARTATAI MONO*  DEC00070
C * APO TON PINAKA <A>.                                              *  DEC00080
C * DHLADH TRIGONOPOIEI TON PINAKA KAI APOTHIKEYEI TIS PLHROFORIES   *  DEC00090
C * ENALLAGHS GRAMMON.                                               *  DEC00100
C * H SUBROUTINE DECOMP EXEI TA EXHS XARAKTHRISTIKA                  *  DEC00110
C *   SUBROUTINE DECOMP(NDIM,N,A,COND,IPVT,WORK)      OPOY           *  DEC00120
C * EISODOS DECOMP                                                   *  DEC00130
C * --------------                                                   *  DEC00140
C * NDIM--->O MEGISTOS ARITHMOS GRAMMON POU MPOREI NA EXEI O PINAKAS *  DEC00150
C *         <A> SE MIA PITHANH SEIRA XRHSEON                         *  DEC00160
C *         TON SUBROUTINES DECOMP-SOLVE.                            *  DEC00170
C * N------>NDIMxN EINAI TO MEGETHOS TOU PINAKA <A> TOU SYNGEKRIMENOU*  DEC00180
C *         SYSTHMATOS POU LYNOUME.                                  *  DEC00190
C * A------>O PINAKAS POU THA TRIGONOPOIHTHH.                        *  DEC00200
C * EXODOS DECOMP                                                    *  DEC00210
C * -------------                                                    *  DEC00220
C * A------>PERIEXEI TON ANO TRIGONIKO PINAKA <U> KAI MIA            *  DEC00230
C *         METATHETHMENH MORFH TOU PINAKA <L> ETSI OSTE <PA=LU>.    *  DEC00240
C * COND--->MIA EKTIMHSH TOU DEIKTH KATASTASHS STHN NORMA <L-1>.     *  DEC00250
C *         AN <COND+1=COND> TOTE O PINAKAS EINAI PRAKTIKA           *  DEC00260
C *         MH ANTISTREPSIMOS.                                       *  DEC00270
C *           AN YPARXEI ODHGOS=0, DHLADH AN O PINAKAS EINAI AKRIBOS   *DEC00280
C *         MH ANTISTREPSIMOS TOTE <COND=1.0E+32>.                   *  DEC00290
C * IPVT--->TO ODHGO DIANYSMA.                                       *  DEC00300
C *         <IPVT(K)>=O DEIKTHS THS GRAMMHS-ODHGOU STHN <K> PHASH THS*  DEC00310
C *                   TRIGONOPOIHSHS,(1).LE.(K).LE.(N-1)             *  DEC00320
C *         <IPVT(N)>=(-1)**(OLIKOS ARITHMOS ENALAGON GRAMMON).      *  DEC00330
C * WORK--->TA STOIXEIA EISODOY TOY STO KALESMA THS SUBROUTINE DEN   *  DEC00340
C *         LAMBANONTAI YP' OPSIN. TA DE STOIXEIA EXODOY TOY EINAI   *  DEC00350
C *         SYNHTHOS XORIS SHMASIA.                                  *  DEC00360
C * PARATHRHSEIS                                                     *  DEC00370
C * ------------                                                     *  DEC00380
C * a)TA <IPVT> KAI <WORK> NA PERILAMBANONTAI STHN DIMENSION         *  DEC00390
C *   STATEMENT TOU KYRIOY PROGRAMMATOS ME THN DIASTASH <N>.         *  DEC00400
C * b)AN THELOYME NA YPOLOGISOYME THN ORIZOYSA TOY PINAKA <A>        *  DEC00410
C *   MPOROYME XROISIMOPOIONTAS TON TYPO                             *  DEC00420
C *    DET(A)=IPVT(N)*A(1,1)*A(2,2)*. . . . . *A(N,N)                *  DEC00430
C *                                                                  *  DEC00440
C * GIA PERISSOTERES PLHROFORIES BLEPE                               *  DEC00450
C * 1)B.DOUGALIS, "SHMIOSEIS ARITHMHTIKHS ANALYSHS II" (1983)        *  DEC00460
C * 2)TO PROGRAMMA EINAI APO TO BIBLIO                               *  DEC00470
C *   "COMPUTER METHODS for MATHEMATICAL COMPUTATIONS"               *  DEC00480
C *   GEORGE E. FORSYTHE                                             *  DEC00490
C *   MICHAEL A. MALCOLM                                             *  DEC00500
C *   CLEVE B.MOLER                                                  *  DEC00510
C *   ED. PRENTICE-HALL,ENGLEWOOD CLIFFS,N.J.,1977.                  *  DEC00520
C ********************************************************************  DEC00530
      IPVT(N)=1                                                         DEC00540
      IF(N.EQ.1) GO TO 80                                               DEC00550
      NM1=N-1                                                           DEC00560
C                                                                       DEC00570
C--      YPOLOGISMOS <L-1> NORMAS TOU <A>                               DEC00580
C        --------------------------------                               DEC00590
                                                                        DEC00600
      ANORM=0.0                                                         DEC00610
      DO 10 J=1,N                                                       DEC00620
          T=0.0                                                         DEC00630
        DO 5 I=1,N                                                      DEC00640
          T=T+ABS(A(I,J))                                               DEC00650
5       CONTINUE                                                        DEC00660
        IF(T.GT.ANORM) ANORM=T                                          DEC00670
10    CONTINUE                                                          DEC00680
                                                                        DEC00690
C                                                                       DEC00700
C--          APALOIFH GAUSS ME MERIKH ODHGHSH                           DEC00710
C            --------------------------------                           DEC00720
                                                                        DEC00730
      DO 35 K=1,NM1                                                     DEC00740
        KP1=K+1                                                         DEC00750
                                                                        DEC00760
C                                                                       DEC00770
C--           VRISKOUME TON ODHGO                                       DEC00780
C             -------------------                                       DEC00790
                                                                        DEC00800
        M=K                                                             DEC00810
        DO 15 I=KP1,N                                                   DEC00820
         IF(ABS(A(I,K)).GT.ABS(A(M,K))) M=I                             DEC00830
15      CONTINUE                                                        DEC00840
         IPVT(K)=M                                                      DEC00850
       IF(M.NE.K) IPVT(N)=-IPVT(N)                                      DEC00860
        T=A(M,K)                                                        DEC00870
        A(M,K)=A(K,K)                                                   DEC00880
        A(K,K)=T                                                        DEC00890
                                                                        DEC00900
C                                                                       DEC00910
C--        BHMA PARALEIPETAI AN ODHGOS=0                                DEC00920
C          -----------------------------                                DEC00930
                                                                        DEC00940
       IF(T.EQ.0.0) GO TO 35                                            DEC00950
                                                                        DEC00960
C                                                                       DEC00970
C--        YPOLOGISMOS POLLAPLASIASTON                                  DEC00980
C          ---------------------------                                  DEC00990
                                                                        DEC01000
         DO 20 I=KP1,N                                                  DEC01010
            A(I,K)=-A(I,K)/T                                            DEC01020
20      CONTINUE                                                        DEC01030
                                                                        DEC01040
C                                                                       DEC01050
C--             ENALLAGH KAI APALOIFH                                   DEC01060
C               ---------------------                                   DEC01070
                                                                        DEC01080
        DO 30 J=KP1,N                                                   DEC01090
          T=A(M,J)                                                      DEC01100
          A(M,J)=A(K,J)                                                 DEC01110
          A(K,J)=T                                                      DEC01120
           IF(T.EQ.0.0) GO TO 30                                        DEC01130
          DO 25 I=KP1,N                                                 DEC01140
          A(I,J)=A(I,J)+A(I,K)*T                                        DEC01150
25          CONTINUE                                                    DEC01160
30      CONTINUE                                                        DEC01170
35    CONTINUE                                                          DEC01180
                                                                        DEC01190
C                                                                       DEC01200
C-- EKTIMHSH TOU <COND> ME LYSH DYO SYSTHMATON  <(AT)*Y=E> KAI <A*Z=Y>  DEC01210
C-- OPOU <E> DIANYSMA ME SYNTETAGMENES +1 "H -1 EKLEGMENO ETSI OSTE     DEC01220
C-- NA PROKALEI 'MEGISTH METABOLH' STO <Y>.                             DEC01230
C-- META THETOUME <COND=(L1 NORM TOU Z)/(L1 NORM TOU X)>.               DEC01240
C   ------------------------------------------------------------------  DEC01250
                                                                        DEC01260
      DO 50 K=1,N                                                       DEC01270
        T=0.0                                                           DEC01280
        IF(K.EQ.1) GO TO 45                                             DEC01290
        KM1=K-1                                                         DEC01300
        DO 40 I=1,KM1                                                   DEC01310
          T=T+A(I,K)*WORK(I)                                            DEC01320
40      CONTINUE                                                        DEC01330
45      EK=1.0                                                          DEC01340
        IF(T.LT.0.0) EK=-1.0                                            DEC01350
        IF(A(K,K).EQ.0.0) GO TO 90                                      DEC01360
        WORK(K)=-(EK+T)/A(K,K)                                          DEC01370
50    CONTINUE                                                          DEC01380
      DO 60 KB=1,NM1                                                    DEC01390
        K=N-KB                                                          DEC01400
        T=0.0                                                           DEC01410
        KP1=K+1                                                         DEC01420
        DO 55 I=KP1,N                                                   DEC01430
          T=T+A(I,K)*WORK(I)                                            DEC01440
55      CONTINUE                                                        DEC01450
        WORK(K)=T+WORK(K)                                               DEC01460
        M=IPVT(K)                                                       DEC01470
        IF(M.EQ.K) GO TO 60                                             DEC01480
        T=WORK(M)                                                       DEC01490
        WORK(M)=WORK(K)                                                 DEC01500
        WORK(K)=T                                                       DEC01510
60    CONTINUE                                                          DEC01520
      YNORM=0.0                                                         DEC01530
      DO 65 I=1,N                                                       DEC01540
        YNORM=YNORM+ABS(WORK(I))                                        DEC01550
65     CONTINUE                                                         DEC01560
                                                                        DEC01570
C                                                                       DEC01580
C--                <A*Z=Y>                                              DEC01590
C                  -------                                              DEC01600
                                                                        DEC01610
       CALL SOLVE(NDIM,N,A,WORK,IPVT)                                   DEC01620
       ZNORM=0.0                                                        DEC01630
       DO 70 I=1,N                                                      DEC01640
         ZNORM=ZNORM+ABS(WORK(I))                                       DEC01650
70     CONTINUE                                                         DEC01660
                                                                        DEC01670
C                                                                       DEC01680
C--               EKTIMHSH <COND>                                       DEC01690
C                 ---------------                                       DEC01700
                                                                        DEC01710
       COND=ANORM*ZNORM/YNORM                                           DEC01720
       IF(COND.LT.1.0) COND=1.0                                         DEC01730
       RETURN                                                           DEC01740
                                                                        DEC01750
C                                                                       DEC01760
C--                   1x1                                               DEC01770
C                    -----                                              DEC01780
                                                                        DEC01790
80     COND=1.0                                                         DEC01800
       IF(A(1,1).NE.0.0) RETURN                                         DEC01810
                                                                        DEC01820
C                                                                       DEC01830
C--     AKRIBOS MH ANTISTREPSIMOS PINAKAS                               DEC01840
C       ---------------------------------                               DEC01850
                                                                        DEC01860
90     COND=1.0E+32                                                     DEC01870
       RETURN                                                           DEC01880
       END                                                              DEC01890
                                                                        DEC01900
       SUBROUTINE SOLVE(NDIM,N,A,B,IPVT)                                DEC01910
       INTEGER    NDIM,N,IPVT,KB,KM1,NM1,KP1,I,K,M                      DEC01920
       DOUBLE PRECISION A,B,T                                           DEC01930
       DIMENSION  A(NDIM,N),B(N),IPVT(N)                                DEC01940
C ********************************************************************  DEC01950
C * SUBROUTINE SOLVE EINAI MIA ROYTINA GRAMMENH SE FORTRAN(4) H OP0IA*  DEC01960
C * METABALLEI TO DEYTERO MELOS <B> TOU SYSTHMATOS <AX=B> KAI        *  DEC01970
C * OPISTHODROMONTAS VRISKEI THN LYSH <X> TOY SYSTHMATOSTHN OPOIA    *  DEC01980
C * APOTHHKEYEI STO DIANYSMA <B>.                                    *  DEC01990
C * H SOLVE EXEI GIA EISODO THN EXODO THS DECOMP.                    *  DEC02000
C * H SUBROUTINE SOLVE EXEI TA EXIS XARAKTHRISTIKA                   *  DEC02010
C *    SUBROUTINE SOLVE(NDIM,N,A,B,IPVT)                             *  DEC02020
C * EISODOS SOLVE                                                    *  DEC02030
C * -------------                                                    *  DEC02040
C * NDIM--->O MEGISTOS ARITHMOS GRAMMON POU MPOREI NA EXEI O PINAKAS *  DEC02050
C *         <A> SE MIA PITHANH SEIRA XRHSEON                         *  DEC02060
C *         TON SUBROUTINES DECOMP-SOLVE.                            *  DEC02070
C * N------>NxN EINAI TO MEGETHOS TOU PINAKA <A> TOU SYNGEKRIMENOU   *  DEC02080
C *         SYSTHMATOS POU LYNOUME.                                  *  DEC02090
C * A------>PERIEXEI TON ANO TRIGONIKO PINAKA <U> KAI MIA            *  DEC02100
C *         METATHETHMENH MORFH TOU PINAKA <L> ETSI OSTE <PA=LU>.    *  DEC02110
C * B------>TO DIANYSMA TON STATHERON OPON TOY SYSTHMATOPS <A*X=B>   *  DEC02120
C * IPVT--->TO ODHGO DIANYSMA TO OPOIO EINAI PROIONN THS DECOMP.     *  DEC02130
C * EXODOS SOLVE                                                     *  DEC02140
C * ------------                                                     *  DEC02150
C * B------>EINAI H LYSH TOY SYSTHMATOS <A*X=B>                      *  DEC02160
C * PARATHRHSEIS                                                     *  DEC02170
C * ------------                                                     *  DEC02180
C * a)TA <IPVT> KAI <B> NA PERILAMBANONTAI STHN DIMENSION STATEMENT  *  DEC02190
C *   TOU KYRIOY PROGRAMMATOS ME THN DIASTASH <N>.                   *  DEC02200
C * b)AN H DECOMP EXEI BGALEI PINAKA PRAKTIKA MH ANTISTREPSIMO       *  DEC02210
C *   MHN XRHSIMOPOIHTE THN SOLVE                                    *  DEC02220
C *                                                                  *  DEC02230
C * GIA PERISSOTERES PLHROFORIES BLEPE                               *  DEC02240
C * 1)B.DOUGALIS, "SHMIOSEIS ARITHMHTIKHS ANALYSHS II" (1983)        *  DEC02250
C * 2)TO PROGRAMMA EINAI APO TO BIBLIO                               *  DEC02260
C *   "COMPUTER METHODS for MATHEMATICAL COMPUTATIONS"               *  DEC02270
C *   GEORGE E. FORSYTHE                                             *  DEC02280
C *   MICHAEL A. MALCOLM                                             *  DEC02290
C *   CLEVE B.MOLER                                                  *  DEC02300
C *   ED. PRENTICE-HALL,ENGLEWOOD CLIFFS,N.J.,1977.                  *  DEC02310
C ********************************************************************  DEC02320
C                                                                       DEC02330
C--                METABOLH TOU <B>                                     DEC02340
C                  ----------------                                     DEC02350
C                                                                       DEC02360
       IF (N.EQ.1) GO TO 50                                             DEC02370
       NM1=N-1                                                          DEC02380
       DO 20 K=1,NM1                                                    DEC02390
        KP1=K+1                                                         DEC02400
        M=IPVT(K)                                                       DEC02410
        T=B(M)                                                          DEC02420
        B(M)=B(K)                                                       DEC02430
        B(K)=T                                                          DEC02440
        DO 10 I=KP1,N                                                   DEC02450
           B(I)=B(I)+A(I,K)*T                                           DEC02460
10         CONTINUE                                                     DEC02470
20     CONTINUE                                                         DEC02480
                                                                        DEC02490
C                                                                       DEC02500
C--                   OPISTHODROMHSH                                    DEC02510
C                     --------------                                    DEC02520
C                                                                       DEC02530
       DO 40 KB=1,NM1                                                   DEC02540
        KM1=N-KB                                                        DEC02550
        K=KM1+1                                                         DEC02560
        B(K)=B(K)/A(K,K)                                                DEC02570
        T=-B(K)                                                         DEC02580
        DO 30 I=1,KM1                                                   DEC02590
           B(I)=B(I)+A(I,K)*T                                           DEC02600
30        CONTINUE                                                      DEC02610
40     CONTINUE                                                         DEC02620
50     B(1)=B(1)/A(1,1)                                                 DEC02630
       RETURN                                                           DEC02640
        END                                                             DEC02650

        
