MAM: Multicriteria Associative Memories
for Nonlinear Estimation

Last Updated: 29 April 2017

Site maintained by:
Leigh Tesfatsion
Professor of Econ, Math, and ECpE
Heady 375
Iowa State University
Ames, Iowa 50011-1070
FAX: 515-294-0221
http://www2.econ.iastate.edu/tesfatsi/
tesfatsi@iastate.edu

About MAM:

The Fortran program MAM, developed by Robert E. Kalaba and Leigh Tesfatsion, implements the multicriteria associative memory (MAM) method for obtaining good initial estimates for nonlinear parameter estimation problems.

The MAM method was proposed by Kalaba and Tesfatsion in "Obtaining Initial Parameter Estimates for Nonlinear Systems Using Multicriteria Associative Memories" (pdf,1.3M), Computer Science in Economics and Management (now Computational Economics), 4 (1991), 237-259.

To illustrate the efficiency and reliability of the method, the above article uses the MAM program to obtain initial parameter estimates for a well-known nonlinear economic model, the Solow-Swan descriptive growth model. The MAM program code, below, implements one of these growth model experiments.

For additional articles and materials related to MAM, visit here.

The MAM Program:

Software Release Disclaimer:

The software below is provided as-is, without warranty of any kind. It is released here as free open-source software by Robert E. Kalaba and Leigh Tesfatsion (the copyright holders) under the terms of the Artistic License Agreement.
 

// EXEC FORTVCLG                                                        00000010
//FORT.SYSIN DD *                                                       00000020
C                                                                       00000030
          PROGRAM  MAM                                                  00000040
C                                                                       00000050
C         OBTAINING INITIAL PARAMETER ESTIMATES FOR NONLINEAR SYSTEMS   00000060
C         USING MULTICRITERIA ASSOCIATIVE MEMORIES, COMPUTER SCIENCE    00000070
C         IN ECONOMICS AND MANAGEMENT, VOL. 4 (1991), 237-259.          00000080
C         R. KALABA AND L. TESFATSION                                   00000090
C                                                                       00000100
C         LAST UPDATED: JUNE 13, 1992                                   00000110
C                                                                       00000120
          IMPLICIT REAL*8(A-H,O-Z)                                      00000130
          DIMENSION R(10,50),S(15,50),XMEM(10,15),RHAT(10)              00000140
C                                                                       00000150
C         THIS PROGRAM IS SET UP FOR TWO-DIMENSIONAL PARAMETER VECTORS  00000160
C         R = (KZERO,THETA) WITH NORMAL NOISE TESTING AND TIME TESTING  00000170
C                                                                       00000180
          CALL TRAIN(N,M,IQ,R,S)                                        00000190
C  THE INITIAL VALUE OF ALPHA IS ALPHAZ, THE STEPSIZE OF ALPHA IS       00000200
C  SSALPHA, AND THE NUMBER OF ALPHA VALUES TESTED IS NALPHA             00000210
           ALPHAZ = 0.10D+00                                            00000220
           SSALPHA = 0.10D+00                                           00000230
           NALPHA = 10                                                  00000240
C  THE INITIAL STANDARD DEVIATION FOR THE TEST AGAINST NOISE IS SIGMAZ, 00000250
C  THE STEPSIZE FOR SIGMA IS SSSIGMA, AND THE NUMBER OF SIGMA VALUES    00000260
C  TESTED IS NSIGMA.  FOR EACH SIGMA, THE THEORETICALLY OPTIMAL VALUE OF00000270
C  ALPHA IS AOPT = 1/(1 + (SIGMA**2)*IQ).                               00000280
          SIGMAZ = 0.00D+00                                             00000290
          SSSIGMA = 0.05D+00                                            00000300
          NSIGMA = 10                                                   00000310
          SIGMA = SIGMAZ                                                00000320
          DO 45 LL = 1,NSIGMA                                           00000330
          AOPT = 1.0D+00/(1.0D+00 + (SIGMA**2.0D+00)*DFLOAT(IQ))        00000340
          WRITE(6,700) SIGMA, AOPT                                      00000350
  700     FORMAT(3X,//2X,'THE STANDARD DEVIATION SIGMA =',F5.2,         00000360
     *    ' AND THE OPTIMAL ALPHA VALUE =',D9.4)                        00000370
C         WRITE(6,500)                                                  00000380
C 500     FORMAT(2X,'HERE IS S TRANSPOSE')                              00000390
C         DO 1000 J = 1,IQ                                              00000400
C         WRITE(6,600) (S(I,J),I = 1,M)                                 00000410
C 600     FORMAT(4X,5D15.3)                                             00000420
C1000     CONTINUE                                                      00000430
          ALPHA = ALPHAZ                                                00000440
          BETA = 1.0D+00 - ALPHA                                        00000450
          DO 10 J = 1,NALPHA                                            00000460
          CALL MEMORY(ALPHA,BETA,R,S,N,M,IQ,XMEM,CA,CZ)                 00000470
          WRITE (6,100) ALPHA,CA,CZ                                     00000480
  100     FORMAT (2X,/2X,'ALPHA =',D9.4,2X,'CA =',D12.4,2X,'CZ =',D12.4)00000490
C         TEST OF TRAINING CASE ENCODING                                00000500
          IF (J.GE.1) CALL OUTPUT(ALPHA,R,S,N,M,IQ,XMEM,SIGMA)          00000510
C         WRITE(6,1) ALPHA                                              00000520
C   1     FORMAT(2X,/1X,'HERE IS THE TRANSPOSED MEMORY MATRIX FOR ',    00000530
C    *    'ALPHA =',D9.4)                                               00000540
C         DO 40 JJ = 1,M                                                00000550
C         WRITE(6,120) (XMEM(II,JJ),II = 1,N)                           00000560
C 120     FORMAT(10X,2D25.5)                                            00000570
C  40     CONTINUE                                                      00000580
          ALPHA = ALPHA + SSALPHA                                       00000590
          BETA = 1.0D+00 - ALPHA                                        00000600
   10     CONTINUE                                                      00000610
          SIGMA = SIGMA + SSSIGMA                                       00000620
   45     CONTINUE                                                      00000630
          STOP                                                          00000640
          END                                                           00000650
C                                                                       00000660
          SUBROUTINE OUTPUT(ALPHA,R,S,N,M,IQ,XMEM,SIGMA)                00000670
          IMPLICIT REAL*8(A-H,O-Z)                                      00000680
          DIMENSION R(10,50),S(15,50),XMEM(10,15),RHAT(10),DISC(10,50)  00000690
          DIMENSION SN(15,50)                                           00000700
C         PRINT OUT OF RHAT, R, AND THE DISCREPANCIES                   00000710
C         DISC = (RHAT - R)/R FOR THE IQ TEST CASES                     00000720
C         WRITE(6,100) IQ                                               00000730
C 100     FORMAT(1X,//,2X,'HERE ARE RHAT, R = (K0,THETA), AND THE'/2X,  00000740
C    *    'DISCREPANCIES (RHAT-R)/R FOR THE',I4,' TEST CASES')          00000750
          DO 10 IC = 1,IQ                                               00000760
          DO 20 II = 1,N                                                00000770
          SUM = 0.0D+00                                                 00000780
          DO 30 JJ = 1,M                                                00000790
          XNOISE = SIGMA*0.0D+00                                        00000800
          SN(JJ,IC) = S(JJ,IC) + XNOISE                                 00000810
          SUM = SUM + XMEM(II,JJ)*SN(JJ,IC)                             00000820
   30     CONTINUE                                                      00000830
          RHAT(II) = SUM                                                00000840
          DISC(II,IC) = ((RHAT(II)-R(II,IC))/R(II,IC))*100.0D+00        00000850
   20     CONTINUE                                                      00000860
C         WRITE(6,200) IC,(RHAT(II),II=1,N),(R(II,IC),II=1,N),          00000870
C    *      (DISC(II,IC),II=1,N)                                        00000880
C 200     FORMAT(1X,I4,2X,4D12.4,2E12.3)                                00000890
   10     CONTINUE                                                      00000900
          WRITE(6,300) ALPHA,SIGMA                                      00000910
  300     FORMAT(2X,/2X,'HERE ARE THE PERCENTAGE DISCREPANCIES FOR ',   00000920
     *    'KZERO'/2X,'WHEN ALPHA =',D9.4,' AND SIGMA =',F5.2)           00000930
          WRITE(6,400) (DISC(1,IT), IT=1,IQ)                            00000940
  400     FORMAT(1X,7F11.0)                                             00000950
          WRITE(6,500) ALPHA,SIGMA                                      00000960
  500     FORMAT(2X,/2X,'HERE ARE THE PERCENTAGE DISCREPANCIES FOR ',   00000970
     *    'THETA'/2X,'WHEN ALPHA =',D9.4,' AND SIGMA =',F5.2)           00000980
          WRITE(6,600) (DISC(2,IT), IT=1,IQ)                            00000990
  600     FORMAT(1X,7F11.0)                                             00001000
          RETURN                                                        00001010
          END                                                           00001020
C                                                                       00001030
          SUBROUTINE TRAIN(N,M,IQ,R,S)                                  00001040
          IMPLICIT REAL*8(A-H,O-Z)                                      00001050
          DIMENSION R(10,50),S(15,50)                                   00001060
C         CALCULATING THE TRAINING STIMULUS AND RESPONSE MATRICES       00001070
C         FOR THE SOLOW-SWAN DESCRIPTIVE GROWTH MODEL                   00001080
C         DK = SAV*F(K) - ALAM*K WITH F(K) = K**THETA                   00001090
C         WHERE N = NUMBER OF PARAMETERS, M = NUMBER OF OBSERVATIONS,   00001100
C         AND IQ = NUMBER OF TEST CASES                                 00001110
          SAV = 0.15D+00                                                00001120
          ALAM = 0.10D+00                                               00001130
          N = 2                                                         00001140
          M = 10                                                        00001150
C  NUMBER OF TESTED KZERO AND THETA VALUES                              00001160
          NKZERO = 7                                                    00001170
          NTHETA = 7                                                    00001180
C  INITIAL VALUES FOR KZERO, THETA, AND TIME                            00001190
          XKZERZ = 4.00D+00                                             00001200
          THETAZ = 0.20D+00                                             00001210
          TINIT = 0.05D+00                                              00001220
C  STEP SIZES FOR KZERO, THETA, AND TIME                                00001230
          SSKZERO = 0.50D+00                                            00001240
          SSTHETA = 0.03D+00                                            00001250
          SSTIME = 1.0D+00                                              00001260
C  THE DO LOOPS                                                         00001270
          XKZERO = XKZERZ                                               00001280
          THETA = THETAZ                                                00001290
          T = TINIT                                                     00001300
          IQ = NKZERO*NTHETA                                            00001310
          ICASE = 1                                                     00001320
          DO 9  KK = 1,NKZERO                                           00001330
          DO 10 JJ = 1,NTHETA                                           00001340
          R(1,ICASE) = XKZERO                                           00001350
          R(2,ICASE) = THETA                                            00001360
          DO 11 II = 1,M                                                00001370
          S(II,ICASE)=((XKZERO**(1.0D+00-THETA) - SAV/ALAM)*            00001380
     &    DEXP(-(1.0D+00-THETA)*ALAM*T) + SAV/ALAM)**                   00001390
     &    (1.0D+00/(1.0D+00-THETA))                                     00001400
          T = T + SSTIME                                                00001410
  11      CONTINUE                                                      00001420
          THETA = THETA + SSTHETA                                       00001430
          ICASE = ICASE + 1                                             00001440
          T = TINIT                                                     00001450
  10      CONTINUE                                                      00001460
          XKZERO = XKZERO + SSKZERO                                     00001470
          THETA = THETAZ                                                00001480
   9      CONTINUE                                                      00001490
          RETURN                                                        00001500
          END                                                           00001510
C                                                                       00001520
          SUBROUTINE MEMORY(ALPHA,BETA,R,S,N,M,IQ,XMEM,CA,CZ)           00001530
          IMPLICIT REAL*8(A-H,O-Z)                                      00001540
          DIMENSION R(10,50),S(15,50),XMEM(10,15),ST(50,15),SST(15,15)  00001550
          DIMENSION ASST(15,15),E(15,15),F(15,15),AST(50,15),PINV(50,15)00001560
          DIMENSION XMEMS(10,50),DIF(10,50),DIFT(50,10),SQDIF(10,10)    00001570
          DIMENSION XMEMT(15,10),RST(10,15),ARST(10,15),E1(10,10)       00001580
C         CALCULATING THE ASSOCIATIVE MEMORY MATRIX                     00001590
C         XMEM = ALPHA*R*ST*(ALPHA*S*ST + (1-ALPHA)*I)-1                00001600
          CALL TRANS(M,IQ,S,ST)                                         00001610
          DO 10 I = 1,M                                                 00001620
          DO 11 J = 1,M                                                 00001630
          SUM = 0.0D+00                                                 00001640
          DO 12 K = 1,IQ                                                00001650
          SUM = SUM + S(I,K)*ST(K,J)                                    00001660
   12     CONTINUE                                                      00001670
          SST(I,J) = SUM                                                00001680
   11     CONTINUE                                                      00001690
   10     CONTINUE                                                      00001700
          CALL MULCON(M,M,ALPHA,SST,ASST)                               00001710
          CALL IDEN(M,E)                                                00001720
          CALL MULCON(M,M,BETA,E,E)                                     00001730
          CALL ADD(M,M,ASST,E,E)                                        00001740
          CALL INV(M,E,F)                                               00001750
          DO 13 I = 1,N                                                 00001760
          DO 14 J = 1,M                                                 00001770
          SUM = 0.0D+00                                                 00001780
          DO 15 K = 1,IQ                                                00001790
          SUM = SUM + R(I,K)*ST(K,J)                                    00001800
  15      CONTINUE                                                      00001810
          RST(I,J) = SUM                                                00001820
  14      CONTINUE                                                      00001830
  13      CONTINUE                                                      00001840
          DO 1 I = 1,N                                                  00001850
          DO 2 J = 1,M                                                  00001860
          ARST(I,J) = ALPHA*RST(I,J)                                    00001870
   2      CONTINUE                                                      00001880
   1      CONTINUE                                                      00001890
          DO 16 I = 1,N                                                 00001900
          DO 17 J = 1,M                                                 00001910
          SUM = 0.0D+00                                                 00001920
          DO 18 K = 1,M                                                 00001930
          SUM = SUM + ARST(I,K)*F(K,J)                                  00001940
  18      CONTINUE                                                      00001950
          XMEM(I,J) = SUM                                               00001960
  17      CONTINUE                                                      00001970
  16      CONTINUE                                                      00001980
C         CALCULATING THE COST CA = TR((XMEM*S-R)(XMEM*S-R)T)           00001990
          DO 19 I = 1,N                                                 00002000
          DO 20 J = 1,IQ                                                00002010
          SUM = 0.0D+00                                                 00002020
          DO 21 K = 1,M                                                 00002030
          SUM = SUM + XMEM(I,K)*S(K,J)                                  00002040
  21      CONTINUE                                                      00002050
          XMEMS(I,J) = SUM                                              00002060
  20      CONTINUE                                                      00002070
  19      CONTINUE                                                      00002080
          CALL SUB(N,IQ,XMEMS,R,DIF)                                    00002090
          DO 3 I = 1,IQ                                                 00002100
          DO 4 J = 1,N                                                  00002110
          DIFT(I,J) = DIF(J,I)                                          00002120
   4      CONTINUE                                                      00002130
   3      CONTINUE                                                      00002140
          DO 22 I = 1,N                                                 00002150
          DO 23 J = 1,N                                                 00002160
          SUM = 0.0D+00                                                 00002170
          DO 24 K = 1,IQ                                                00002180
          SUM = SUM + DIF(I,K)*DIFT(K,J)                                00002190
  24      CONTINUE                                                      00002200
          SQDIF(I,J) = SUM                                              00002210
  23      CONTINUE                                                      00002220
  22      CONTINUE                                                      00002230
          CALL TRACE(SQDIF,N,CA)                                        00002240
C         CALCULATING THE COST CZ = TR(XMEM*XMEMT)                      00002250
          DO 5 I = 1,M                                                  00002260
          DO 6 J = 1,N                                                  00002270
          XMEMT(I,J) = XMEM(J,I)                                        00002280
   6      CONTINUE                                                      00002290
   5      CONTINUE                                                      00002300
          DO 25 I = 1,N                                                 00002310
          DO 26 J = 1,N                                                 00002320
          SUM = 0.0D+00                                                 00002330
          DO 27 K = 1,M                                                 00002340
          SUM = SUM + XMEM(I,K)*XMEMT(K,J)                              00002350
  27      CONTINUE                                                      00002360
          E1(I,J) = SUM                                                 00002370
  26      CONTINUE                                                      00002380
  25      CONTINUE                                                      00002390
          CALL TRACE(E1,N,CZ)                                           00002400
          RETURN                                                        00002410
          END                                                           00002420
C                                                                       00002430
C  HERE ARE THE MATRIX SUBROUTINES                                      00002440
C                                                                       00002450
C     MATRIX SUBROUTINES FOR ADDITION, MULTIPLICATION, TRANSPOSITION,   00002460
C     SUBTRACTION, INVERSION, MULTIPLICATION BY A SCALAR, SHIFT, FORM   00002470
C     AN IDENTITY MATRIX, AND TAKE THE TRACE.                           00002480
C                                                                       00002490
C     CALCULATING THE SUM C=A+B OF TWO NROW X MCOL MATRICES A AND B     00002500
C                                                                       00002510
          SUBROUTINE ADD(NROW,MCOL,A,B,C)                               00002520
          IMPLICIT REAL*8(A-H,O-Z)                                      00002530
          DIMENSION A(15,15),B(15,15),C(15,15)                          00002540
          DO 10 I=1,NROW                                                00002550
          DO 20 J=1,MCOL                                                00002560
          C(I,J)=A(I,J)+B(I,J)                                          00002570
   20     CONTINUE                                                      00002580
   10     CONTINUE                                                      00002590
          RETURN                                                        00002600
          END                                                           00002610
C                                                                       00002620
C     CALCULATING THE PRODUCT C=A*B OF AN NROW X L MATRIX A AND AN      00002630
C     L X MCOL MATRIX B                                                 00002640
C                                                                       00002650
          SUBROUTINE MUL(NROW,L,MCOL,A,B,C)                             00002660
          IMPLICIT REAL*8(A-H,O-Z)                                      00002670
          DIMENSION A(15,50),B(50,15),C(15,15)                          00002680
          DO 10 I=1,NROW                                                00002690
          DO 20 J=1,MCOL                                                00002700
          SUM=0.0D+00                                                   00002710
          DO 30 K=1,L                                                   00002720
          SUM=SUM+A(I,K)*B(K,J)                                         00002730
   30     CONTINUE                                                      00002740
          C(I,J)=SUM                                                    00002750
   20     CONTINUE                                                      00002760
   10     CONTINUE                                                      00002770
          RETURN                                                        00002780
          END                                                           00002790
C                                                                       00002800
C     CALCULATING THE TRANSPOSE B OF AN NROW X MCOL MATRIX A            00002810
C                                                                       00002820
          SUBROUTINE TRANS(NROW,MCOL,A,B)                               00002830
          IMPLICIT REAL*8(A-H,O-Z)                                      00002840
          DIMENSION A(15,50),B(50,15)                                   00002850
          DO 10 I=1,NROW                                                00002860
          DO 20 J=1,MCOL                                                00002870
          B(J,I)=A(I,J)                                                 00002880
   20     CONTINUE                                                      00002890
   10     CONTINUE                                                      00002900
          RETURN                                                        00002910
          END                                                           00002920
C                                                                       00002930
C     CALCULATING THE DIFFERENCE C=A-B BETWEEN NROW X MCOL MATRICES     00002940
C     A AND B                                                           00002950
C                                                                       00002960
          SUBROUTINE SUB(NROW,MCOL,A,B,C)                               00002970
          IMPLICIT REAL*8(A-H,O-Z)                                      00002980
          DIMENSION A(10,50),B(10,50),C(10,50)                          00002990
          DO 10 I=1,NROW                                                00003000
          DO 20 J=1,MCOL                                                00003010
          C(I,J)=A(I,J)-B(I,J)                                          00003020
   20     CONTINUE                                                      00003030
   10     CONTINUE                                                      00003040
          RETURN                                                        00003050
          END                                                           00003060
C                                                                       00003070
C     CALCULATING THE INVERSE C OF A K X K MATRIX A                     00003080
C                                                                       00003090
          SUBROUTINE INV(K,A,C)                                         00003100
          IMPLICIT REAL*8(A-H,O-Z)                                      00003110
          DIMENSION A(15,15),B(15,30),C(15,15)                          00003120
          DO 5 J=1,K                                                    00003130
          DO 6 I=1,K                                                    00003140
          B(I,J)=A(I,J)                                                 00003150
    6     CONTINUE                                                      00003160
    5     CONTINUE                                                      00003170
          K2=K*2                                                        00003180
          DO 7 J=1,K                                                    00003190
          DO 8 I=1,K                                                    00003200
          B(I,K+J)=0.0D+00                                              00003210
          IF(I.EQ.J) B(I,K+J)=1.0D+00                                   00003220
    8     CONTINUE                                                      00003230
    7     CONTINUE                                                      00003240
C     THE PIVOT OPERATION STARTS HERE                                   00003250
          DO 9 L=1,K                                                    00003260
          PIVOT = B(L,L)                                                00003270
          DO 13 J=L,K2                                                  00003280
          B(L,J)=B(L,J)/PIVOT                                           00003290
   13     CONTINUE                                                      00003300
C     TO IMPROVE THE ROWS                                               00003310
          DO 14 I=1,K                                                   00003320
          IF(I.EQ.L) GO TO 14                                           00003330
          AIL=B(I,L)                                                    00003340
          DO 15 J=L,K2                                                  00003350
          B(I,J)=B(I,J)-AIL*B(L,J)                                      00003360
   15     CONTINUE                                                      00003370
   14     CONTINUE                                                      00003380
    9     CONTINUE                                                      00003390
          DO 45 I=1,K                                                   00003400
          DO 46 J=1,K                                                   00003410
          C(I,J)=B(I,K+J)                                               00003420
   46     CONTINUE                                                      00003430
   45     CONTINUE                                                      00003440
          RETURN                                                        00003450
          END                                                           00003460
C                                                                       00003470
C     CALCULATING THE PRODUCT C*A OF A SCALAR C AND AN NROW X MCOL      00003480
C     MATRIX A                                                          00003490
C                                                                       00003500
          SUBROUTINE MULCON(NROW,MCOL,C,A,CA)                           00003510
          IMPLICIT REAL*8(A-H,O-Z)                                      00003520
          DIMENSION A(15,15),CA(15,15)                                  00003530
          DO 10 I=1,NROW                                                00003540
          DO 20 J=1,MCOL                                                00003550
          CA(I,J)=C*A(I,J)                                              00003560
   20     CONTINUE                                                      00003570
   10     CONTINUE                                                      00003580
          RETURN                                                        00003590
          END                                                           00003600
C                                                                       00003610
C     PUTTING AN NROW X MCOL MATRIX A INTO AN NROW X MCOL MATRIX B      00003620
C                                                                       00003630
          SUBROUTINE SHIFT(NROW,MCOL,A,B)                               00003640
          IMPLICIT REAL*8(A-H,O-Z)                                      00003650
          DIMENSION A(15,15),B(15,15)                                   00003660
          DO 10 I=1,NROW                                                00003670
          DO 20 J=1,MCOL                                                00003680
          B(I,J)=A(I,J)                                                 00003690
   20     CONTINUE                                                      00003700
   10     CONTINUE                                                      00003710
          RETURN                                                        00003720
          END                                                           00003730
C                                                                       00003740
C     FORMING AN IDENTITY MATRIX                                        00003750
C                                                                       00003760
          SUBROUTINE IDEN(N,E)                                          00003770
          IMPLICIT REAL*8(A-H,O-Z)                                      00003780
          DIMENSION E(15,15)                                            00003790
          ZERO=0.0D+00                                                  00003800
          ONE=1.0D+00                                                   00003810
          DO 10 I=1,N                                                   00003820
          DO 20 J=1,N                                                   00003830
          E(I,J)=ZERO                                                   00003840
   20     CONTINUE                                                      00003850
   10     CONTINUE                                                      00003860
          DO 30 L=1,N                                                   00003870
          E(L,L)=ONE                                                    00003880
   30     CONTINUE                                                      00003890
          RETURN                                                        00003900
          END                                                           00003910
C                                                                       00003920
C     CALCULATING THE TRACE OF A MATRIX                                 00003930
C                                                                       00003940
          SUBROUTINE TRACE(A,N,TR)                                      00003950
          IMPLICIT REAL*8 (A-H,O-Z)                                     00003960
          DIMENSION A(10,10)                                            00003970
          SUM = 0.0D+00                                                 00003980
          DO 10 I = 1,N                                                 00003990
          SUM = SUM + A(I,I)                                            00004000
   10     CONTINUE                                                      00004010
          TR = SUM                                                      00004020
          RETURN                                                        00004030
          END                                                           00004040

Copyright © by Leigh Tesfatsion. All Rights Reserved.