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Trailing-Edge - PDP-10 Archives - decuslib20-02 - decus/20-0026/dapmm.ssp
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C                                                                       DAPM  10
C     ..................................................................DAPM  20
C                                                                       DAPM  30
C        SUBROUTINE DAPMM                                               DAPM  40
C                                                                       DAPM  50
C        PURPOSE                                                        DAPM  60
C           APPROXIMATE A FUNCTION TABULATED IN N POINTS BY ANY LINEAR  DAPM  70
C           COMBINATION OF M GIVEN CONTINUOUS FUNCTIONS IN THE SENSE    DAPM  80
C           OF CHEBYSHEV.                                               DAPM  90
C                                                                       DAPM 100
C        USAGE                                                          DAPM 110
C           CALL DAPMM(FCT,N,M,TOP,IHE,PIV,T,ITER,IER)                  DAPM 120
C           PARAMETER FCT REQUIRES AN EXTERNAL STATEMENT IN THE         DAPM 130
C           CALLING PROGRAM.                                            DAPM 140
C                                                                       DAPM 150
C        DESCRIPTION OF PARAMETERS                                      DAPM 160
C           FCT    - NAME OF SUBROUTINE TO BE SUPPLIED BY THE USER.     DAPM 170
C                    IT COMPUTES VALUES OF M GIVEN FUNCTIONS FOR        DAPM 180
C                    ARGUMENT VALUE X.                                  DAPM 190
C                    USAGE                                              DAPM 200
C                       CALL FCT(Y,X,K)                                 DAPM 210
C                    DESCRIPTION OF PARAMETERS                          DAPM 220
C                       Y   - DOUBLE PRECISION RESULT VECTOR OF DIMEN-  DAPM 230
C                             SION M CONTAINING THE VALUES OF GIVEN     DAPM 240
C                             CONTINUOUS FUNCTIONS FOR GIVEN ARGUMENT X DAPM 250
C                       X   - DOUBLE PRECISON ARGUMENT VALUE            DAPM 260
C                       K   - AN INTEGER VALUE WHICH IS EQUAL TO M-1    DAPM 270
C                    REMARKS                                            DAPM 280
C                       IF APPROXIMATION BY NORMAL CHEBYSHEV, SHIFTED   DAPM 290
C                       CHEBYSHEV, LEGENDRE, LAGUERRE, HERMITE POLYNO-  DAPM 300
C                       MIALS IS DESIRED SUBROUTINES DCNP,DCSP,DLEP,    DAPM 310
C                       DLAP,DHEP, RESPECTIVELY FROM SSP COULD BE USED. DAPM 320
C           N      - NUMBER OF DATA POINTS DEFINING THE FUNCTION WHICH  DAPM 330
C                    IS TO BE APPROXIMATED                              DAPM 340
C           M      - NUMBER OF GIVEN CONTINUOUS FUNCTIONS FROM WHICH    DAPM 350
C                    THE APPROXIMATING FUNCTION IS CONSTRUCTED.         DAPM 360
C           TOP    - DOUBLE PRECISION VECTOR OF DIMENSION 3*N.          DAPM 370
C                    ON ENTRY IT MUST CONTAIN FROM TOP(1) UP TO TOP(N)  DAPM 380
C                    THE GIVEN N FUNCTION VALUES AND FROM TOP(N+1) UP   DAPM 390
C                    TO TOP(2*N) THE CORRESPONDING NODES                DAPM 400
C                    ON RETURN TOP CONTAINS FROM TOP(1) UP TO TOP(N)    DAPM 410
C                    THE ERRORS AT THOSE N NODES.                       DAPM 420
C                    OTHER VALUES OF TOP ARE SCRATCH.                   DAPM 430
C           IHE    - INTEGER VECTOR OF DIMENSION 3*M+4*N+6              DAPM 440
C           PIV    - DOUBLE PRECISION VECTOR OF DIMENSION 3*M+6.        DAPM 450
C                    ON RETURN PIV CONTAINS AT PIV(1) UP TO PIV(M) THE  DAPM 460
C                    RESULTING COEFFICIENTS OF LINEAR APPROXIMATION.    DAPM 470
C           T      - DOUBLE PRECISION AUXILIARY VECTOR OF DIMENSION     DAPM 480
C                    (M+2)*(M+2)                                        DAPM 490
C           ITER   - RESULTANT INTEGER WHICH SPECIFIES THE NUMBER OF    DAPM 500
C                    ITERATIONS NEEDED                                  DAPM 510
C           IER    - RESULTANT ERROR PARAMETER CODED IN THE FOLLOWING   DAPM 520
C                    FORM                                               DAPM 530
C                     IER=0  - NO ERROR                                 DAPM 540
C                     IER=1  - THE NUMBER OF ITERATIONS HAS REACHED     DAPM 550
C                              THE INTERNAL MAXIMUM N+M                 DAPM 560
C                     IER=-1 - NO RESULT BECAUSE OF WRONG INPUT PARA-   DAPM 570
C                              METER M OR N OR SINCE AT SOME ITERATION  DAPM 580
C                              NO SUITABLE PIVOT COULD BE FOUND         DAPM 590
C                                                                       DAPM 600
C        REMARKS                                                        DAPM 610
C           NO ACTION BESIDES ERROR MESSAGE IN CASE M LESS THAN 1 OR    DAPM 620
C           N LESS THAN 2.                                              DAPM 630
C                                                                       DAPM 640
C        SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED                  DAPM 650
C           THE EXTERNAL SUBROUTINE FCT MUST BE FURNISHED BY THE USER.  DAPM 660
C                                                                       DAPM 670
C        METHOD                                                         DAPM 680
C           THE PROBLEM OF APPROXIMATION A TABULATED FUNCTION BY ANY    DAPM 690
C           LINEAR COMBINATION OF GIVEN FUNCTIONS IN THE SENSE OF       DAPM 700
C           CHEBYSHEV (I.E. TO MINIMIZE THE MAXIMUM ERROR) IS TRANS-    DAPM 710
C           FORMED INTO A LINEAR PROGRAMMING PROBLEM. DAPMM USES A      DAPM 720
C           REVISED SIMPLEX METHOD TO SOLVE A CORRESPONDING DUAL        DAPM 730
C           PROBLEM. FOR REFERENCE, SEE                                 DAPM 740
C           I.BARRODALE/A.YOUNG, ALGORITHMS FOR BEST L-SUB-ONE AND      DAPM 750
C           L-SUB-INFINITY, LINEAR APPROXIMATIONS ON A DISCRETE SET,    DAPM 760
C           NUMERISCHE MATHEMATIK, VOL.8, ISS.3 (1966), PP.295-306.     DAPM 770
C                                                                       DAPM 780
C     ..................................................................DAPM 790
C                                                                       DAPM 800
      SUBROUTINE DAPMM(FCT,N,M,TOP,IHE,PIV,T,ITER,IER)                  DAPM 810
C                                                                       DAPM 820
C                                                                       DAPM 830
      DIMENSION TOP(1),IHE(1),PIV(1),T(1)                               DAPM 840
      DOUBLE PRECISION DSUM,TOP,PIV,T,SAVE,HELP,REPI,TOL                DAPM 850
C                                                                       DAPM 860
C        TEST ON WRONG INPUT PARAMETERS N AND M                         DAPM 870
      IER=-1                                                            DAPM 880
      IF (N-1) 81,81,1                                                  DAPM 890
    1 IF(M) 81,81,2                                                     DAPM 900
C                                                                       DAPM 910
C        INITIALIZE CHARACTERISTIC VECTORS FOR THE TABLEAU              DAPM 920
    2 IER=0                                                             DAPM 930
C                                                                       DAPM 940
C        PREPARE TOP-ROW TOP                                            DAPM 950
      DO 3 I=1,N                                                        DAPM 960
      K=I+N                                                             DAPM 970
      J=K+N                                                             DAPM 980
      TOP(J)=TOP(K)                                                     DAPM 990
    3 TOP(K)=-TOP(I)                                                    DAPM1000
C                                                                       DAPM1010
C        PREPARE INVERSE TRANSFORMATION MATRIX T                        DAPM1020
      L=M+2                                                             DAPM1030
      LL=L*L                                                            DAPM1040
      DO 4 I=1,LL                                                       DAPM1050
    4 T(I)=0.D0                                                         DAPM1060
      K=1                                                               DAPM1070
      J=L+1                                                             DAPM1080
      DO 5 I=1,L                                                        DAPM1090
      T(K)=1.D0                                                         DAPM1100
    5 K=K+J                                                             DAPM1110
C                                                                       DAPM1120
C        PREPARE INDEX-VECTOR IHE                                       DAPM1130
      DO 6 I=1,L                                                        DAPM1140
      K=I+L                                                             DAPM1150
      J=K+L                                                             DAPM1160
      IHE(I)=0                                                          DAPM1170
      IHE(K)=I                                                          DAPM1180
    6 IHE(J)=1-I                                                        DAPM1190
      NAN=N+N                                                           DAPM1200
      K=L+L+L                                                           DAPM1210
      J=K+NAN                                                           DAPM1220
      DO 7 I=1,NAN                                                      DAPM1230
      K=K+1                                                             DAPM1240
      IHE(K)=I                                                          DAPM1250
      J=J+1                                                             DAPM1260
    7 IHE(J)=I                                                          DAPM1270
C                                                                       DAPM1280
C        SET COUNTER ITER FOR ITERATION-STEPS                           DAPM1290
      ITER=-1                                                           DAPM1300
    8 ITER=ITER+1                                                       DAPM1310
C                                                                       DAPM1320
C        TEST FOR MAXIMUM ITERATION-STEPS                               DAPM1330
      IF(N+M-ITER) 9,9,10                                               DAPM1340
    9 IER=1                                                             DAPM1350
      GO TO 69                                                          DAPM1360
C                                                                       DAPM1370
C        DETERMINE THE COLUMN WITH THE MOST POSITIVE ELEMENT IN TOP     DAPM1380
   10 ISE=0                                                             DAPM1390
      IPIV=0                                                            DAPM1400
      K=L+L+L                                                           DAPM1410
      SAVE=0.D0                                                         DAPM1420
C                                                                       DAPM1430
C        START TOP-LOOP                                                 DAPM1440
      DO 14 I=1,NAN                                                     DAPM1450
      IDO=K+I                                                           DAPM1460
      HELP=TOP(I)                                                       DAPM1470
      IF(HELP-SAVE) 12,12,11                                            DAPM1480
   11 SAVE=HELP                                                         DAPM1490
      IPIV=I                                                            DAPM1500
   12 IF(IHE(IDO)) 14,13,14                                             DAPM1510
   13 ISE=I                                                             DAPM1520
   14 CONTINUE                                                          DAPM1530
C        END OF TOP-LOOP                                                DAPM1540
C                                                                       DAPM1550
C        IS OPTIMAL TABLEAU REACHED                                     DAPM1560
      IF(IPIV) 69,69,15                                                 DAPM1570
C                                                                       DAPM1580
C        DETERMINE THE PIVOT-ELEMENT FOR THE COLUMN CHOSEN UPOVE        DAPM1590
   15 ILAB=1                                                            DAPM1600
      IND=0                                                             DAPM1610
      J=ISE                                                             DAPM1620
      IF(J) 21,21,34                                                    DAPM1630
C                                                                       DAPM1640
C        TRANSFER K-TH COLUMN FROM T TO PIV                             DAPM1650
   16 K=(K-1)*L                                                         DAPM1660
      DO 17 I=1,L                                                       DAPM1670
      J=L+I                                                             DAPM1680
      K=K+1                                                             DAPM1690
   17 PIV(J)=T(K)                                                       DAPM1700
C                                                                       DAPM1710
C        IS ANOTHER COLUMN NEEDED FOR SEARCH FOR PIVOT-ELEMENT          DAPM1720
   18 IF(ISE) 22,22,19                                                  DAPM1730
   19 ISE=-ISE                                                          DAPM1740
C                                                                       DAPM1750
C        TRANSFER COLUMNS IN PIV                                        DAPM1760
      J=L+1                                                             DAPM1770
      IDO=L+L                                                           DAPM1780
      DO 20 I=J,IDO                                                     DAPM1790
      K=I+L                                                             DAPM1800
   20 PIV(K)=PIV(I)                                                     DAPM1810
   21 J=IPIV                                                            DAPM1820
      GO TO 34                                                          DAPM1830
C                                                                       DAPM1840
C        SEARCH PIVOT-ELEMENT PIV(IND)                                  DAPM1850
   22 SAVE=1.D38                                                        DAPM1860
      IDO=0                                                             DAPM1870
      K=L+1                                                             DAPM1880
      LL=L+L                                                            DAPM1890
      IND=0                                                             DAPM1900
C                                                                       DAPM1910
C        START PIVOT-LOOP                                               DAPM1920
      DO 29 I=K,LL                                                      DAPM1930
      J=I+L                                                             DAPM1940
      HELP=PIV(I)                                                       DAPM1950
      IF(HELP) 29,29,23                                                 DAPM1960
   23 HELP=-HELP                                                        DAPM1970
      IF(ISE) 26,24,26                                                  DAPM1980
   24 IF(IHE(J)) 27,25,27                                               DAPM1990
   25 IDO=I                                                             DAPM2000
      GO TO 29                                                          DAPM2010
   26 HELP=-PIV(J)/HELP                                                 DAPM2020
   27 IF(HELP-SAVE) 28,29,29                                            DAPM2030
   28 SAVE=HELP                                                         DAPM2040
      IND=I                                                             DAPM2050
   29 CONTINUE                                                          DAPM2060
C        END OF PIVOT-LOOP                                              DAPM2070
C                                                                       DAPM2080
C        TEST FOR SUITABLE PIVOT-ELEMENT                                DAPM2090
      IF(IND) 30,30,32                                                  DAPM2100
   30 IF(IDO) 68,68,31                                                  DAPM2110
   31 IND=IDO                                                           DAPM2120
C        PIVOT-ELEMENT IS STORED IN PIV(IND)                            DAPM2130
C                                                                       DAPM2140
C        COMPUTE THE RECIPROCAL OF THE PIVOT-ELEMENT REPI               DAPM2150
   32 REPI=1.D0/PIV(IND)                                                DAPM2160
      IND=IND-L                                                         DAPM2170
C                                                                       DAPM2180
C        UPDATE THE TOP-ROW TOP OF THE TABLEAU                          DAPM2190
      ILAB=0                                                            DAPM2200
      SAVE=-TOP(IPIV)*REPI                                              DAPM2210
      TOP(IPIV)=SAVE                                                    DAPM2220
C                                                                       DAPM2230
C        INITIALIZE J AS COUNTER FOR TOP-LOOP                           DAPM2240
      J=NAN                                                             DAPM2250
   33 IF(J-IPIV) 34,53,34                                               DAPM2260
   34 K=0                                                               DAPM2270
C                                                                       DAPM2280
C        SEARCH COLUMN IN TRANSFORMATION-MATRIX T                       DAPM2290
      DO 36 I=1,L                                                       DAPM2300
      IF(IHE(I)-J) 36,35,36                                             DAPM2310
   35 K=I                                                               DAPM2320
      IF(ILAB) 50,50,16                                                 DAPM2330
   36 CONTINUE                                                          DAPM2340
C                                                                       DAPM2350
C        GENERATE COLUMN USING SUBROUTINE FCT AND TRANSFORMATION-MATRIX DAPM2360
      I=L+L+L+NAN+J                                                     DAPM2370
      I=IHE(I)-N                                                        DAPM2380
      IF(I) 37,37,38                                                    DAPM2390
   37 I=I+N                                                             DAPM2400
      K=1                                                               DAPM2410
   38 I=I+NAN                                                           DAPM2420
C                                                                       DAPM2430
C        CALL SUBROUTINE FCT                                            DAPM2440
      CALL FCT(PIV,TOP(I),M-1)                                          DAPM2450
C                                                                       DAPM2460
C        PREPARE THE CALLED VECTOR PIV                                  DAPM2470
      DSUM=0.D0                                                         DAPM2480
      IDO=M                                                             DAPM2490
      DO 41 I=1,M                                                       DAPM2500
      HELP=PIV(IDO)                                                     DAPM2510
      IF(K) 39,39,40                                                    DAPM2520
   39 HELP=-HELP                                                        DAPM2530
   40 DSUM=DSUM+HELP                                                    DAPM2540
      PIV(IDO+1)=HELP                                                   DAPM2550
   41 IDO=IDO-1                                                         DAPM2560
      PIV(L)=-DSUM                                                      DAPM2570
      PIV(1)=1.D0                                                       DAPM2580
C                                                                       DAPM2590
C        TRANSFORM VECTOR PIV WITH ROWS OF MATRIX T                     DAPM2600
      IDO=IND                                                           DAPM2610
      IF(ILAB) 44,44,42                                                 DAPM2620
   42 K=1                                                               DAPM2630
   43 IDO=K                                                             DAPM2640
   44 DSUM=0.D0                                                         DAPM2650
      HELP=0.D0                                                         DAPM2660
C                                                                       DAPM2670
C        START MULTIPLICATION-LOOP                                      DAPM2680
      DO 46 I=1,L                                                       DAPM2690
      DSUM=DSUM+PIV(I)*T(IDO)                                           DAPM2700
      TOL=DABS(DSUM)                                                    DAPM2710
      IF(TOL-HELP) 46,46,45                                             DAPM2720
   45 HELP=TOL                                                          DAPM2730
   46 IDO=IDO+L                                                         DAPM2740
C        END OF MULTIPLICATION-LOOP                                     DAPM2750
C                                                                       DAPM2760
      TOL=1.D-14*HELP                                                   DAPM2770
      IF(DABS(DSUM)-TOL) 47,47,48                                       DAPM2780
   47 DSUM=0.D0                                                         DAPM2790
   48 IF(ILAB) 51,51,49                                                 DAPM2800
   49 I=K+L                                                             DAPM2810
      PIV(I)=DSUM                                                       DAPM2820
C                                                                       DAPM2830
C        TEST FOR LAST COLUMN-TERM                                      DAPM2840
      K=K+1                                                             DAPM2850
      IF(K-L) 43,43,18                                                  DAPM2860
   50 I=(K-1)*L+IND                                                     DAPM2870
      DSUM=T(I)                                                         DAPM2880
C                                                                       DAPM2890
C        COMPUTE NEW TOP-ELEMENT                                        DAPM2900
   51 DSUM=DSUM*SAVE                                                    DAPM2910
      TOL=1.D-14*DABS(DSUM)                                             DAPM2920
      TOP(J)=TOP(J)+DSUM                                                DAPM2930
      IF(DABS(TOP(J))-TOL) 52,52,53                                     DAPM2940
   52 TOP(J)=0.D0                                                       DAPM2950
C                                                                       DAPM2960
C        TEST FOR LAST TOP-TERM                                         DAPM2970
   53 J=J-1                                                             DAPM2980
      IF(J) 54,54,33                                                    DAPM2990
C        END OF TOP-LOOP                                                DAPM3000
C                                                                       DAPM3010
C        TRANSFORM PIVOT-COLUMN                                         DAPM3020
   54 I=IND+L                                                           DAPM3030
      PIV(I)=-1.D0                                                      DAPM3040
      DO 55 I=1,L                                                       DAPM3050
      J=I+L                                                             DAPM3060
   55 PIV(I)=-PIV(J)*REPI                                               DAPM3070
C                                                                       DAPM3080
C        UPDATE TRANSFORMATION-MATRIX T                                 DAPM3090
      J=0                                                               DAPM3100
      DO 57 I=1,L                                                       DAPM3110
      IDO=J+IND                                                         DAPM3120
      SAVE=T(IDO)                                                       DAPM3130
      T(IDO)=0.D0                                                       DAPM3140
      DO 56 K=1,L                                                       DAPM3150
      ISE=K+J                                                           DAPM3160
   56 T(ISE)=T(ISE)+SAVE*PIV(K)                                         DAPM3170
   57 J=J+L                                                             DAPM3180
C                                                                       DAPM3190
C        UPDATE INDEX-VECTOR IHE                                        DAPM3200
C        INITIALIZE CHARACTERISTICS                                     DAPM3210
      J=0                                                               DAPM3220
      K=0                                                               DAPM3230
      ISE=0                                                             DAPM3240
      IDO=0                                                             DAPM3250
C                                                                       DAPM3260
C        START QUESTION-LOOP                                            DAPM3270
      DO 61 I=1,L                                                       DAPM3280
      LL=I+L                                                            DAPM3290
      ILAB=IHE(LL)                                                      DAPM3300
      IF(IHE(I)-IPIV) 59,58,59                                          DAPM3310
   58 ISE=I                                                             DAPM3320
      J=ILAB                                                            DAPM3330
   59 IF(ILAB-IND) 61,60,61                                             DAPM3340
   60 IDO=I                                                             DAPM3350
      K=IHE(I)                                                          DAPM3360
   61 CONTINUE                                                          DAPM3370
C        END OF QUESTION-LOOP                                           DAPM3380
C                                                                       DAPM3390
C        START MODIFICATION                                             DAPM3400
      IF(K) 62,62,63                                                    DAPM3410
   62 IHE(IDO)=IPIV                                                     DAPM3420
      IF(ISE) 67,67,65                                                  DAPM3430
   63 IF(IND-J) 64,66,64                                                DAPM3440
   64 LL=L+L+L+NAN                                                      DAPM3450
      K=K+LL                                                            DAPM3460
      I=IPIV+LL                                                         DAPM3470
      ILAB=IHE(K)                                                       DAPM3480
      IHE(K)=IHE(I)                                                     DAPM3490
      IHE(I)=ILAB                                                       DAPM3500
      IF(ISE) 67,67,65                                                  DAPM3510
   65 IDO=IDO+L                                                         DAPM3520
      I=ISE+L                                                           DAPM3530
      IHE(IDO)=J                                                        DAPM3540
      IHE(I)=IND                                                        DAPM3550
   66 IHE(ISE)=0                                                        DAPM3560
   67 LL=L+L                                                            DAPM3570
      J=LL+IND                                                          DAPM3580
      I=LL+L+IPIV                                                       DAPM3590
      ILAB=IHE(I)                                                       DAPM3600
      IHE(I)=IHE(J)                                                     DAPM3610
      IHE(J)=ILAB                                                       DAPM3620
C        END OF MODIFICATION                                            DAPM3630
C                                                                       DAPM3640
      GO TO 8                                                           DAPM3650
C                                                                       DAPM3660
C        SET ERROR PARAMETER IER=-1 SINCE NO SUITABLE PIVOT IS FOUND    DAPM3670
   68 IER=-1                                                            DAPM3680
C                                                                       DAPM3690
C        EVALUATE FINAL TABLEAU                                         DAPM3700
C        COMPUTE SAVE AS MAXIMUM ERROR OF APPROXIMATION AND             DAPM3710
C        HELP AS ADDITIVE CONSTANCE FOR RESULTING COEFFICIENTS          DAPM3720
   69 SAVE=0.D0                                                         DAPM3730
      HELP=0.D0                                                         DAPM3740
      K=L+L+L                                                           DAPM3750
      DO 73 I=1,NAN                                                     DAPM3760
      IDO=K+I                                                           DAPM3770
      J=IHE(IDO)                                                        DAPM3780
      IF(J) 71,70,73                                                    DAPM3790
   70 SAVE=-TOP(I)                                                      DAPM3800
   71 IF(M+J+1) 73,72,73                                                DAPM3810
   72 HELP=TOP(I)                                                       DAPM3820
   73 CONTINUE                                                          DAPM3830
C                                                                       DAPM3840
C        PREPARE T,TOP,PIV                                              DAPM3850
      T(1)=SAVE                                                         DAPM3860
      IDO=NAN+1                                                         DAPM3870
      J=NAN+N                                                           DAPM3880
      DO 74 I=IDO,J                                                     DAPM3890
   74 TOP(I)=SAVE                                                       DAPM3900
      DO 75 I=1,M                                                       DAPM3910
   75 PIV(I)=HELP                                                       DAPM3920
C                                                                       DAPM3930
C        COMPUTE COEFFICIENTS OF RESULTING POLYNOMIAL IN PIV(1) UP TO PIDAPM3940
C        AND CALCULATE ERRORS AT GIVEN NODES IN TOP(1) UP TO TOP(N)     DAPM3950
      DO 79 I=1,NAN                                                     DAPM3960
      IDO=K+I                                                           DAPM3970
      J=IHE(IDO)                                                        DAPM3980
      IF(J) 76,79,77                                                    DAPM3990
   76 J=-J                                                              DAPM4000
      PIV(J)=HELP-TOP(I)                                                DAPM4010
      GO TO 79                                                          DAPM4020
   77 IF(J-N) 78,78,79                                                  DAPM4030
   78 J=J+NAN                                                           DAPM4040
      TOP(J)=SAVE+TOP(I)                                                DAPM4050
   79 CONTINUE                                                          DAPM4060
      DO 80 I=1,N                                                       DAPM4070
      IDO=NAN+I                                                         DAPM4080
   80 TOP(I)=TOP(IDO)                                                   DAPM4090
   81 RETURN                                                            DAPM4100
      END                                                               DAPM4110