C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C C C C C ISOPAC SUITE C C IMPAC LIBRARY C C PROGRAM TSSGPDTA C C VERSION 1.1 9-OCT-1982 C C C C C C C C PROGRAM TSSGPDTA WAS DEVELOPED FROM IMSGPDTA. C C C C THE "TSSGP" PROGRAMS ARE FOR SEGMENTING MULTIVARIATE C C TIME SERIES. (FOR UNIVARIATE TIME SERIES THE "TSSG1" PROGRAMS C C MAY BE USED.) C C TSPAC INCLUDES PROGRAMS USING DISTANCE IN THE METRIC OF THE C C ESTIMATED COMMON COVARIANCE MATRIX AS WELL AS PROGRAMS USING C C DIFFERENT COVARIANCE MATRICES, WITH ADJUSTMENT BY THE C C DETERMINANTS, I.E., USING ESTIMATED LOG LIKELIHOOD FOR THE C C GAUSSIAN MODEL WITH DIFFERENT COVARIANCE MATRICES. C C COVARIANCE MATRICES. C C THERE ARE PROGRAMS IN MANUAL MODE, IN WHICH THE NUMBER OF C C CLASSES AND INITIAL MEANS ARE INPUT AND PROGRAMS IN AUTOMATIC C C MODE, WHICH TRY A RANGE OF NUMBERS OF CLASSES, WITH AUTOMATIC C C SETTING OF INITIAL MEANS. C C C C C C PROGRAMMED BY: C C DR. STANLEY L. SCLOVE 312/996-2681 C C INFORMATION & DECISION SCIENCES DEPT 312/996-2676 C C UNIVERSITY OF ILLINOIS AT CHICAGO C C 601 S MORGAN ST C C CHICAGO, IL 60607-7124 C C C C RESEARCH SUPPORTED IN PART BY: C C C C ONR CONTRACT N00014-80-C-0408, TASK N042-443 C C ARO CONTRACT DAAG29-82-K-0155 C C C C RESTRICTIONS (CAN BE MODIFIED): C C N, SERIES LENGTH, AT MOST 999; C C IP, NUMBER OF VARIABLES, AT MOST 20; C C K, NUMBER OF CLASSES, AT MOST 29; C C ITER, MAXIMUM NUMBER OF ITERATIONS, 20. C C C C SUBROUTINE(S) CALLED: C C MATEQ, WHICH CALLS MATDT C C C C C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C C C DIMENSION X( 999,20),SUM(29,20) DIMENSION D(29),ICLUS( 999) C DIMENSION IOTA( 999),JOTA(29) C DIMENSION TITLE(18) DIMENSION NG(29),XMEAN(29,20) DIMENSION FMT(18) DIMENSION SS(29,20,20),SSD(29,20,20) DIMENSION WGSS(20,20) DIMENSION VARHAT(20,20),WGMS(20,20) DIMENSION ICLSOL( 999) DIMENSION XMIN(20),XMAX(20) C C C NOTE THAT DATA MATRIX REQUIRES ABOUT 200 K. C DIMENSION IV(20,20) DIMENSION P(20,20) C DIMENSION A(20,20) C DIMENSION ET(29) DIMENSION PG(29,20,20) C DIMENSION NT(29,29),IRSUM(29),TP(29,29) DIMENSION PROB(29) C C DOUBLE PRECISION SS,SUM DOUBLE PRECISION WGSS,SSD DOUBLE PRECISION VARHAT DOUBLE PRECISION P DOUBLE PRECISION DET DOUBLE PRECISION D DOUBLE PRECISION XMEAN DOUBLE PRECISION TEMPIV,TEMPJV DOUBLE PRECISION F DOUBLE PRECISION CF C DOUBLE PRECISION A C DOUBLE PRECISION ET DOUBLE PRECISION PG DOUBLE PRECISION TP,PROB C C IV IS A WORK ARRAY FOR SUBROUTINE MATEQ. C C C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C C C C C CONTROL CARDS: C C C C DATASET TITLE C C SERIES LENGTH, N, IN FORMAT (2X,I4) C C NUMBER OF VARIABLES, IP, IN FORMAT (3X,I2) C C FMT, IN FORMAT (18A4), E.G., (1X,F4.1) C C "FMT" WILL ALSO BE USED FOR OUTPUT: ALLOW AT LEAST ONE BLANK C C AT THE BEGINNING FOR CARRIAGE CONTROL. C C DATA, BY TIME POINT, IN FORMAT SPECIFIED BY FMT C C DATA IS INDEXED BY TIME POINT AND VARIABLE. C C VARIABLE CHANGES FIRST, THEN TIME. C C C C KL, MIN NUMBER OF CLASSES, IN FORMAT (3X,I2) C C KU, MAX NUMBER OF CLASSES, IN FORMAT (2X,I2) C C C C C CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC C C READ (5,28000) TITLE C C WRITE PROGRAM INFORMATION. WRITE (6,17000) WRITE (6,53000) WRITE (6,35000) TITLE C C READ SERIES LENGTH, N. READ (5,16000) N C WRITE (6,33000) N C C READ NUMBER OF VARIABLES, IP. READ (5,29000) IP WRITE (6,14000) IP C C READ DATA FORMAT. READ (5,28000) FMT WRITE (6,11000) FMT C C C READ DATA. C DO 300 I = 1,N C READ (5,FMT) (X(I,IVAR), IVAR=1,IP) IF (I .EQ. 1) GO TO 100 GO TO 200 100 CONTINUE DO 200 IVAR = 1,IP XMAX(IVAR) = X(1,IVAR) XMIN(IVAR) = X(1,IVAR) 200 CONTINUE DO 300 IVAR = 1,IP IF (X(I,IVAR) .LT. XMIN(IVAR)) XMIN(IVAR)= X X(I,IVAR) IF (X(I,IVAR) .GT. XMAX(IVAR)) XMAX(IVAR)= X X(I,IVAR) 300 CONTINUE WRITE (6,54000) WRITE (6,FMT) (XMIN(IVAR),IVAR=1,IP) WRITE (6,55000) WRITE (6,FMT) (XMAX(IVAR),IVAR=1,IP) C C READ KL AND KU, THE MIN AND MAX NUMBER OF CLASSES TO BE TRIED. READ (5,15000) KL READ (5,15000) KU WRITE (6,18000) KL,KU C C SET CONSTANTS. C PI = 3.1415927 C C XN = N DO 400 INTEG=1,N IOTA(INTEG) = INTEG 400 CONTINUE C DO 6500 K = KL,KU C K IS THE NUMBER OF CLASSES. C C COMPUTE INITIAL MEANS: DO 500 IG=1,K DO 500 IVAR = 1,IP XMEAN(IG,IVAR) = XMIN(IVAR) + IG*(XMAX(IVAR)- X XMIN(IVAR))/(K+1) 500 CONTINUE C WRITE (6,19000) K C WRITE INITIAL MEANS C DO 600 IG = 1,K WRITE (6,20000) IG,(XMEAN(IG,IVAR),IVAR=1,IP) 600 CONTINUE C C SET CONSTANTS FOR THIS VALUE OF K. C DO 700 J = 1,K JOTA(J) = J 700 CONTINUE C C PARAMETERS FOR MODEL WITH COMMON COVARIANCE MATRIX ARE C K MEAN VECTORS AND ONE COVARIANCE MATRIX. NOPARM = K*IP + IP*(IP+1)/2 C PARAMETERS FOR MODEL WITH DIFFERENT COVARIANCE MATRICES ARE C K MEAN VECTORS AND K COVARIANCE MATRICES. NPRMDF = K*IP + K*IP*(IP+1)/2 C C NON-DISTRIBUTIONAL PARAMETERS: C K-BY-K TRANSITION PROB. MATRIX C GIVES K(K-1) FREE TRANSITION PROBABILITIES C NOPARM = NOPARM + K*(K-1) NPRMDF = NPRMDF + K*(K-1) C C C FOR FIRST ITERATION, MARGINAL DISTRIBUTION OF LABELS, PROB, C IS TAKEN TO BE UNIFORM. C DO 800 IG=1,K 800 PROB(IG) = 1.0/K C C ITER = 1 C ITERATIONS BEGIN HERE C 900 CONTINUE IF (ITER .EQ. 1) GO TO 1100 DO 1000 I = 1,N C ICLSOL(I) = ICLUS(I) 1000 CONTINUE C SAVE PREVIOUS VALUE OF -2 LOG MAX LIKELIHOOD: XMN20L = XMN2LL 1100 CONTINUE C C COMMENCE DISTANCE COMPUTATIONS. C DO 2400 I = 1,N C C INITIALIZE DISTANCES (TO BE ACCUMULATED) AT ZERO. DO 1200 L = 1,K D(L) = 0.0 1200 CONTINUE C FOR FIRST ITERATION, EUCLIDEAN DISTANCE IS USED BECAUSE C NO COVARIANCE MATRIX IS YET AVAILABLE. AFTER THE FIRST C ITERATION, DISTANCE WILL BE TAKEN IN THE METRIC OF THE C GROUP COVARIANCE MATRIX. C IF (ITER .GT. 1) GO TO 1400 DO 1300 L=1,K DO 1300 IVAR=1,IP D(L) = D(L) + ( XMEAN(L,IVAR) - X(I, X IVAR) )**2 1300 CONTINUE GO TO 1700 1400 CONTINUE DO 1600 L=1,K DO 1500 IVAR=1,IP TEMPIV = XMEAN(L,IVAR) - X(I,IVAR) DO 1500 JV=1,IP TEMPJV = XMEAN(L,JV) - X(I,JV) C D(L) = D(L) + TEMPIV*PG(L,IVAR,JV) X *TEMPJV C 1500 CONTINUE C 1600 CONTINUE 1700 CONTINUE C DO 2200 L = 1,K C FOR FIRST ITERATION, CLASSIFICATION IS SIMPLY BY C MINIMUM DISTANCE. OTHERWISE, THE TRANSITION C PROBABILITIES AND DETERMINANTS ENTER: C IF (ITER .EQ. 1) GO TO 2200 C C UP TO NOW, D(L) IS (SQUARED) DISTANCE C IT MUST NOW BE MODIFIED TO PROBABILITY, C FOR MULTIPLICATION BY THE TRANSITION PROBABILITIES. C ADD DETERMINANT OF COVARIANCE MATRIX TO DISTANCE: D(L) = D(L) + ET(L) ARG = -D(L)/2.0 IF (ARG .LT. -180.2) GO TO 1800 GO TO 1900 1800 D(L) = 0.0 GO TO 2000 1900 CONTINUE C C MOVE FROM LOG PROB SCALE TO PROB SCALE: D(L) = EXP(ARG) C D(L) IS NO LONGER A DISTANCE: C IT IS (PROPORTIONAL TO) THE BELONGING PROBABILITY 2000 CONTINUE C IF (I .EQ. 1) GO TO 2100 IG1 = ICLUS(I-1) C D(L) = -TP(IG1,L)*D(L) GO TO 2200 2100 CONTINUE C CLASSIFY FIRST OBSERVATION D(L) = -D(L)*PROB(L) 2200 CONTINUE C F = D(1) ICLUS(I) = 1 DO 2400 L = 2,K IF ( D(L) - F ) 2300,2400,2400 2300 F = D(L) ICLUS(I) = L 2400 CONTINUE WRITE (6,10000) C WRITE (6,12000) (IOTA(J), J=1,N) C WRITE (6,12000) (ICLUS(I),I=1,N) C DO 2600 IG = 1,K NG(IG) = 0 DO 2600 IVAR = 1,IP SUM(IG,IVAR) = 0.0 DO 2600 JV = 1,IP SS(IG,IVAR,JV) = 0.0 SSD(IG,IVAR,JV) = 0.0 2600 CONTINUE DO 2700 I = 1,N C IGROUP = ICLUS(I) NG(IGROUP) = NG(IGROUP) + 1 DO 2700 IVAR = 1,IP SUM(IGROUP,IVAR) = SUM(IGROUP,IVAR) + X(I, X IVAR) DO 2700 JV = 1,IP SS(IGROUP,IVAR,JV) = SS(IGROUP,IVAR,JV) + X X(I,IVAR)*X(I,JV) 2700 CONTINUE C WRITE (6,27000) (NG(IG),IG=1,K) C DO 2800 IVAR = 1,IP DO 2800 JV = 1,IP WGSS(IVAR,JV) = 0.0 2800 CONTINUE C C DO 3100 IG = 1,K IF (NG(IG) .EQ. 0) GO TO 2900 GO TO 3000 2900 WRITE (6,60000) IG GO TO 6600 3000 CONTINUE DO 3100 IVAR = 1,IP C COMPUTE MEAN VECTORS XMEAN(IG,IVAR) = SUM(IG,IVAR)/NG(IG) C COMPUTE SUM-OF-PRODUCTS MATRICES DO 3100 JV = 1,IP CF = SUM(IG,IVAR)*SUM(IG,JV)/NG(IG) SSD(IG,IVAR,JV) = SS(IG,IVAR,JV) - CF 3100 CONTINUE C C C C POOL: C DO 3200 IG = 1,K DO 3200 IVAR = 1,IP DO 3200 JV = 1,IP WGSS(IVAR,JV) = WGSS(IVAR,JV) + SSD(IG,IVAR, X JV) 3200 CONTINUE C C C COMPUTE VARHAT, MLE OF COMMON COVARIANCE MATRIX: DO 3300 IVAR = 1,IP DO 3300 JV = 1,IP VARHAT(IVAR,JV) = WGSS(IVAR,JV)/N 3300 CONTINUE C COMPUTE DET(VARHAT) IDET = 1 NSR1 = 0 DO 3400 IVAR=1,IP DO 3400 JV = 1,IP A(IVAR,JV) = VARHAT(IVAR,JV) 3400 CONTINUE CALL MATEQ(A,IP,20,JFLG,DET,IDET,IV,NRS1,P,20) C C GENERAL FORM OF CALL IS: C CALL MATEQ(A,M,N,JFLG,DET,IDET,IV,NRS1,P,LL) C SEE SUBROUTINE LISTING FOR FULLER EXPLANATION. C DET(VARHAT) = DET*10.0**IDET C (ACTUAL DET. = DET*10**IDET) C IF (JFLG .GT. 0) WRITE (6,43000) JFLG C XIDET = IDET XLGDET = DLOG(DET) + XIDET*ALOG(10.0) XMN2LL = N*(IP*ALOG(2.0*PI) + IP + XLGDET) C C IF (ITER .EQ. 1) GO TO 3600 C C COMPARE NEW SEGMENTATION WITH OLD C DO 3500 I = 1,N C IF (ICLUS(I) .EQ. ICLSOL(I)) GO TO 3500 GO TO 3600 3500 CONTINUE GO TO 6000 3600 CONTINUE C C IF NEW SEGMENTATION DIFFERS FROM OLD, C COMPUTE AND WRITE NEW STATISTICS C DO 3700 IG = 1,K WRITE (6,26000) IG, (XMEAN(IG,IVAR),IVAR=1,IP) 3700 CONTINUE C C COMPUTE TRANSITION PROBABILITY MATRIX: C DO 3800 I1 = 1,K C DO 3800 J = 1,K NT(I1,J) = 0 3800 CONTINUE DO 3900 I = 2,N C IM1 = I-1 C IBEFOR = ICLUS(IM1) C IY = ICLUS(I) NT(IBEFOR,IY) = NT(IBEFOR,IY) + 1 3900 CONTINUE DO 4000 I1 = 1,K C IRSUM(I1) = 0 4000 CONTINUE DO 4100 I1 = 1,K C DO 4100 J = 1,K IRSUM(I1) = IRSUM(I1) + NT(I1,J) 4100 CONTINUE DO 4400 I1=1,K C XDENOM=IRSUM(I1) IF (XDENOM .EQ. 0.0) GO TO 4200 GO TO 4300 4200 XDENOM = K 4300 CONTINUE C DO 4400 J = 1,K XNUM = NT(I1,J) C IF THERE ARE NO TRANSITIONS FROM I1) THEN TP(I1,J) C IS SET EQUAL TO ZERO, FOR ALL J = 1,2,...,K. C 4400 TP(I1,J) = XNUM/XDENOM 4500 CONTINUE C C COMPUTE MARGINAL DISTRIBUTION OF LABELS: DO 4600 IG = 1,K PROB(IG) = NG(IG) PROB(IG) = PROB(IG)/N 4600 CONTINUE C TRANS = 0.0 DO 4700 I1=1,K C DO 4700 J=1,K ITEST = NT(I1,J) IF (ITEST .EQ. 0) GO TO 4700 IF (TP(I1,J) .EQ. 0.) GO TO 4700 TRANS = TRANS + NT(I1,J)*DLOG(TP(I1,J)) 4700 CONTINUE C TRANS = -2.0*TRANS C C WRITE TRANSITION PROBABILITIES: WRITE (6,13000) WRITE (6,37000) (JOTA(JAY),JAY=1,K) DO 4800 I1 = 1,K C WRITE (6,38000) I1, (NT(I1,J),J=1,K) 4800 CONTINUE WRITE (6,39000) WRITE (6,37000) (JOTA(JAY),JAY=1,K) DO 4900 I1=1,K C WRITE (6,40000) I1, (TP(I1,J),J=1,K) 4900 CONTINUE WRITE (6,63000) (PROB(IG),IG=1,K) WRITE (6,32000) TRANS WRITE (6,50000) WRITE (6,22000) XMN2LL C C ACCOUNT FOR LABEL OF FIRST OBSERVATION: C C LABEL1 = ICLUS(1) PROBAB = PROB(LABEL1) FIRST = ALOG(PROBAB) C FIRST = -2.0*FIRST C C C COMPUTE MODEL SELECTION CRITERIA: C COMPUTE VALUES CORRESPONDING TO NEW SEGMENTATION AND OLD C COVARIANCE MATRIX (OMIT ON FIRST ITERATION) C IF (ITER .EQ. 1) GO TO 5200 C C FOR MODEL WITH COMMON COVARIANCE MATRIX C (NOT OPTIMIZED IN THIS PROGRAM; HOWEVER, IT IS CLEAR C THAT ONE SHOULD USE THE COMMON-COVARIANCE-MATRIX MODEL IF C THE VALUES OF THE MODEL SELECTION CRITERIA HERE FOR THAT MODEL C ARE LESS THAN THOSE FOR THE MODEL WITH DIFFERENT COVARIANCE C MATRICES): C AICOLD = XMN2OL + TRANS + FIRST + 2.0*NOPARM SCHOLD = XMN2OL + TRANS + FIRST + ALOG(XN)*NOPARM WRITE (6,59000) NOPARM WRITE (6,46000) AICOLD WRITE (6,47000) SCHOLD 5200 CONTINUE AIC = XMN2LL + TRANS + FIRST + 2.0*NOPARM WRITE (6,48000) AIC SCH = XMN2LL + TRANS + FIRST + ALOG(XN)*NOPARM WRITE (6,49000) SCH C C C COMPUTE PRECISION MATRICES FOR ALL GROUPS. C TERM=0.0 DO 5700 L=1,K IF (NG(L) .GT. IP) GO TO 5300 WRITE (6,52000) L,NG(L) GO TO 5600 5300 CONTINUE C DO 5400 IVAR=1,IP DO 5400 JV = 1,IP A(IVAR,JV) = SSD(L,IVAR,JV)/NG(L) 5400 CONTINUE IDET = 1 NRS1 = 0 CALL MATEQ(A,IP,20,JFLG,DET,IDET,IV,NRS1,P,20) DO 5500 IVAR=1,IP DO 5500 JV=1,IP PG(L,IVAR,JV) = P(IVAR,JV) 5500 CONTINUE C ET(L) = DLOG(DET*10**IDET) C 5600 CONTINUE C TERM = TERM + NG(L)*ET(L) 5700 CONTINUE C COMPUTE MODEL SELECTION CRITERIA WITH DIFFERENT COVARIANCE C MATRICES: C C PARAMETERS: C K MEAN VECTORS OF DIMENSION P AND K P-BY-P COVARIANCE MATRICES, C WHERE P IS THE NUMBER OF VARIABLES XM2LLD = N*IP*ALOG(2*PI) + N*IP + TERM XM2LLD = XM2LLD + TRANS + FIRST SCHD = XM2LLD + ALOG(XN)*NPRMDF AICD = XM2LLD + 2.0*NPRMDF WRITE (6,23000) WRITE (6,59000) NPRMDF WRITE (6,24000) XM2LLD WRITE (6,57000) AICD WRITE (6,58000) SCHD C C WRITE (6,25000) ITER DO 5800 IG = 1,K WRITE (6,21000) IG, (XMEAN(IG,IVAR),IVAR=1,IP) 5800 CONTINUE ITER = ITER + 1 IF (ITER .GE. 21) GO TO 5900 C UNLESS 20 ITERATIONS, HAVE ALREADY BEEN PERFORMED, GO BACK C AND DO ANOTHER. GO TO 900 5900 WRITE (6,44000) GO TO 6500 C C 6000 CONTINUE C C OUTPUT TO BE WRITTEN UPON CONVERGENCE: C WRITE (6,41000) ITER WRITE (6,30000) C COMPUTE AND WRITE COMMON COVARIANCE MATRIX C DO 6100 IVAR = 1,IP DO 6100 JV = 1,IP WGMS(IVAR,JV) = WGSS(IVAR,JV)/(N-K) 6100 CONTINUE DO 6200 IVAR=1,IP WRITE (6,31000) (WGMS(IVAR,JV), JV=1,IP) 6200 CONTINUE C WRITE (6,62000) C COMPUTE AND WRITE CLASS COVARIANCE MATRICES C DO 6400 L = 1,K DO 6300 IVAR=1,IP DO 6300 JV =1,IP WGMS(IVAR,JV) = SSD(L,IVAR,JV)/(NG(L)-1) 6300 CONTINUE WRITE (6,61000) L DO 6400 IVAR = 1,IP WRITE (6,31000) (WGMS(IVAR,JV),JV=1,IP) 6400 CONTINUE C C C C C C WRITE (6,45000) K C 6500 CONTINUE C WRITE (6,42000) 6600 STOP C C 10000 FORMAT(//1X,'SEGMENTATION:'/) 11000 FORMAT(/1X,'DATA READ IN UNDER FORMAT ',18A4) 12000 FORMAT(1X, (40I3/) ) 13000 FORMAT(//1X,'TRANSITIONS') 14000 FORMAT(/1X,'NUMBER OF VARIABLES = ',I2/) 15000 FORMAT(3X,I2) 16000 FORMAT(2X,I4) 17000 FORMAT('1','###################################################', X//,1X,'PROGRAM IMPAC:TSSGPDTA '/ X,1X,'FOR TIME SERIES SEGMENTATION '/ X,1X,'USING DISTANCE IN THE METRICS OF THE COVARIANCE MATRICES'/ X,1X,'ADJUSTED BY THE DETERMINANTS '/ X//,1X,'DEVELOPED AND PROGRAMMED BY '// X1X,' DR. STANLEY L. SCLOVE 312/996-2681'/ X1X,' DEPARTMENT OF QUANTITATIVE METHODS 312/996-2676'/ X1X,' UNIVERSITY OF ILLINOIS AT CHICAGO '/ X1X,' BOX 4348, CHICAGO, IL 60680 '// X//,1X,'VERSION 1.1 9-OCT-1982 '//) 18000 FORMAT('1',//,1X,'MIN AND MAX NUMBER OF CLASSES TO BE TRIED ARE ', XI2,' AND ',I2//) 19000 FORMAT(1H1,'K = ',I2,' CLASSES'//) 20000 FORMAT(/1X,'INITIAL MEAN VECTOR FOR CLASS ',I2,': ',(4E14.5/)) 21000 FORMAT(1X,'MEAN VECTOR FOR CLASS ',I2,': ',(8E13.5/)) 22000 FORMAT(/,1X,'MINUS 2 LOG LIKELIHOOD FOR MODEL WITH COMMON', X' COVARIANCE MATRIX= ', E13.5//) 23000 FORMAT(//1X,'FOR MODEL WITH DIFFERENT COVARIANCE MATRICES:'//) 24000 FORMAT(/,1X,'MINUS 2 LOG LIKELIHOOD FOR MODEL WITH DIFFERENT ', X'COVARIANCE MATRICES = ', E13.5//) 25000 FORMAT(///,1X,'ITERATION ', I2,//) 26000 FORMAT(1X,'MEAN VECTOR FOR CLASS ',I2,': ',(8E13.5/)) 27000 FORMAT(/,1X,'NUMBERS IN CLASSES:'/,(9I12/)/) 28000 FORMAT(18A4) 29000 FORMAT(3X,I2) 30000 FORMAT(///,1X,'COMMON COVARIANCE MATRIX (DIVISOR IS DF):',//) 31000 FORMAT(1X,(8E13.5/)) 32000 FORMAT(//,' CONTRIBUTION OF TRANS. PROBS. TO LOG LIKELIHOOD =', XE15.5/) 33000 FORMAT(1X,'SERIES LENGTH = ',I4) 35000 FORMAT(1X,18A4) 36000 FORMAT(/9X,(9I7/)) 37000 FORMAT(/5X,(9I7/)) 38000 FORMAT(1X, I4, (9I7/)) 39000 FORMAT(//1X,'TRANSITION PROBABILITIES') 40000 FORMAT(1X, I4,3X,(9F7.4/)) 41000 FORMAT(/1X,'CONVERGENCE: NO CASE CHANGED CLASSES AFTER ', X'ITERATION ',I2,'. SOME ADDITIONAL RESULTS ARE PRINTED BELOW.'//) 42000 FORMAT(/1X,'PROGRAM ENDED SUCCESSFULLY.') 43000 FORMAT(/,1X,'JFLG = ',I2,'. IF JFLG=0, COMPUTATION OF DET', X' WENT WELL; OTHERWISE, THERE WAS TROUBLE OR MATRIX WAS ', X'ILL-CONDITIONED.'//) 44000 FORMAT(1X,'ROUTINE HAS NOT CONVERGED IN 20 ITERATIONS. STOP') 45000 FORMAT(/,1X,'PROGRAM ENDED SUCCESSFULLY FOR THE CASE ', X'K = ',I2,'.'/) 46000 FORMAT(/1X,'AIC WITH NEW LABELS AND OLD DISTRIBUTIONAL ', X'PARAMETERS: ', E15.5) 47000 FORMAT(/1X,'SCHWARZ CRITERION WITH NEW LABELS AND OLD ', X'DISTRIBUTIONAL PARAMETERS: ', E15.5) 48000 FORMAT(/1X,'AIC WITH NEW LABELS AND NEW DISTRIBUTIONAL ', X'PARAMETERS: ',E15.5) 49000 FORMAT(/1X,'SCHWARZ CRITERION WITH NEW LABELS AND NEW ', X'DISTRIBUTIONAL PARAMETERS: ',E15.5) 50000 FORMAT(//1X,'FOR MODEL WITH COMMON COVARIANCE MATRIX ', X'(NOT OPTIMIZED IN THIS PROGRAM): '//) 51000 FORMAT(1X,'AIC FOR MODEL WITH COMMON COVARIANCE MATRIX = ',E15.5/) 52000 FORMAT(/1X,'CLASS ',I2,' CONTAINS ONLY ',I4,' OBSERVATIONS: ', X'PRECISION MATRIX FROM PREVIOUS ITERATION IS BEING RETAINED'/) 53000 FORMAT(/1X,'MODEL WITH COMMON COVARIANCE MATRIX IS NOT'/ X1X,'OPTIMIZED IN THIS PROGRAM; HOWEVER, IT IS CLEAR'/ X1X,'THAT ONE SHOULD USE IT IF HERE THE VALUES OF THE MODEL-'/ X1X,'SELECTION CRITERIA FOR THAT MODEL ARE LESS THAN THOSE '/ X1X,'FOR THE MODEL WITH DIFFERENT COVARIANCE MATRICES,'/ X1X,'WHICH IS OPTIMIZED HERE.'//) 54000 FORMAT(/1X,'MINIMUM FOR EACH VARIABLE: ',/) 55000 FORMAT(/1X,'MAXIMUM FOR EACH VARIABLE: ',/) 56000 FORMAT(1X,'SCHWARZ CRITERION FOR MODEL WITH COMMON COVARIANCE ', X'MATRIX = ',E15.5/) 57000 FORMAT(1X,'AIC FOR MODEL WITH DIFFERENT COVARIANCE MATRICES = ', XE15.5/) 58000 FORMAT(1X,'SCHWARZ CRITERION FOR MODEL WITH DIFFERENT ', X'COVARIANCE MATRICES = ', E15.5/) 59000 FORMAT(/,1X,'NUMBER OF PARAMETERS = ',I4//) 60000 FORMAT(1X,'NO OBSERVATIONS IN GROUP ',I3,'. STOP') 61000 FORMAT(//1X,'COVARIANCE MATRIX FOR CLASS ',I2/) 62000 FORMAT(///1X,'CLASS COVARIANCE MATRICES ', X' (DIVISORS ARE ONE LESS THAN NUMBER IN GROUP):'/) 63000 FORMAT(/1X,'MARGINAL PROB.VECTOR:',(9F11.4/)) END SUBROUTINE MATEQ(A,M,N,JFLG,DET,IDET,IV,NRS1,P,LL) C SUBROUTINE MATEQ IS DMATEQ FROM THE UICC SUBROUTINE LIBRARY. C C SUBROUTINE DMATEQ C ***************** C THIS ROUTINE WILL SOLVE A REAL*8 SYSTEM OF LINEAR EQUATIONS,COMPUTE C THE DETERMINANT, WITHOUT UNDERFLOW OR OVERFLOW, OF A REAL*8 MATRIX, C AND/OR INVERT A REAL*8 MATRIX. C CALLING SEQUENCE: C CALL DMATEQ(A,N,IA,JFLG,DET,IDET,IV,NRS,P,IP) WHERE; C A (INPUT) - IS THE REAL*8 MATRIX ON WHICH THE ROUTINE IS C TO WORK. IN THE PROCESS OF COMPUTATION THE C CONTENTS OF THIS MATRIX ARE DESTROYED. C N (INPUT) - IS AN INTEGER*4 VARIABLE WHICH SPECIFIES THE C ORDER OF THE A MATRIX. C IA (INPUT) - IS AN INTEGER*4 VARIABLE WHICH SPECIFIES THE C ACTUAL ROW DIMENSION OF A AS DIMENSIONED IN C THE CALLING PROGRAM. IA MUST BE GREATER THAN C OR EQUAL TO N. C JFLG (OUTPUT) - IS AN INTEGER*4 RETURN CODE VARIABLE. UPON C RETURN FROM DMATEQ IF; C JFLG=0, ALL WENT WELL. C JFLG=1, THE A MATRIX WAS SINGULAR OR NEAR C SINGULAR AND THE COMPUTATIONS COULD NOT BE C COMPLETED. THE CONTENTS OF THE VARIABLES C A, DET, IDET AND P ARE MEANINGLESS. C DET (OUTPUT) - IS A REAL*8 VARIABLE WHICH CONTAINS THE C DETERMINANT OF A. (SEE IDET) C IDET (INPUT) - IS AN INTEGER*4 VARIABLE. ON INPUT IF; C IDET=0, NO DETERMINANT IS CALCULATED. C IDET NOT 0, THE DETERMINANT OF A IS COMPUTED. C ON OUTPUT IDET CONTAINS THE POWER OF 10 C THAT DET SHOULD BE MULTIPLIED BY TO GIVE THE C CORRECT VALUE OF THE DETERMINANT. I.E. C DET(A)=DET*10.0D0**IDET. C IF DET(A) CAN BE COMPUTED WITHOUT UNDER OR C OVERFLOW, THEN IDET=0 OTHERWISE IDET IS SET C TO THE PROPER VALUE SO THAT NO UNDER OR OVER- C FLOW WILL OCCUR IN COMPUTING DET. C IV (INPUT) - IS AN INTEGER*4 WORK ARRAY WHICH SHOULD BE C DIMENSIONED AT LEAST IV(N). C C NRS (INPUT) - IS AN INTEGER*4 VARIABLE WITH THE FOLLOWING C INTERPRETATION: C NRS>0, SOLVE A SYSTEM OF LINEAR EQUATIONS C WITH NRS RIGHT HAND SIDES. C NRS=0, INVERT THE A MATRIX. C NRS<0, ONLY COMPUTE THE DETERMINANT OF A. C IN THIS CASE IDET MUST BE DIFFERENT FROM 0. C P (INPUT) - IS A REAL*8 ARRAY WITH THE FOLLOWING INTER- C PRETATION: C IF NRS>0, THEN P CONTAINS THE NRS RIGHT HAND C SIDES STORED BY COLUMNS. IN THIS CASE P MUST C BE DIMENSIONED AT LEAST P(N,NRS). ON RETURN C THE COLUMNS OF P ARE REPLACED BY THE RESPEC- C TIVE SOLUTIONS. C IF NRS=0, THEN P MUST BE DIMENSIONED AT LEAST C P(N,N). ON RETURN P WILL CONTAIN THE INVERSE C OF A. C IF NRS<0,THEN P NEED ONLY BE A DUMMY VARIABLE C IN THIS CASE P IS NEVER ACCESSED BY DMATEQ. C IP (INPUT) - IS AN INTEGER*4 VARIABLE WHICH CONTAINS THE C ACTUAL ROW DIMENSION OF P AS DIMENSIONED IN C THE CALLING PROGRAM. IP MUST BE GREATER THAN C OR EQUAL TO N. C NOTE: IMMEDIATELY ON RETURN FROM DMATEQ THE CONDITION CODE FLAG, C JFLG, SHOULD BE INTERROGATED. IF JFLG=1, THEN THE ROUTINE C COULD NOT COMPUTE A SOLUTION. C METHOD - THE ALGORITHM USED IS GAUSSIAN ELIMINATION WITH PARTIAL C -1 C PIVOTING. IN ESSENCE THE ROUTINE GENERATES A MATRIX L SUCH C -1 C THAT L *A = U, WHERE U IS AN UPPER TRIANGULAR MATRIX. THEN IT C SOLVES THE SYSTEM A*X = P BY MEANS OF THE EQUIVALENT SYSTEM C -1 -1 C U*X = L *A*X = L *P BY BACK SUBSTITUTION. C -1 C THE L MATRIX CAN BE WRITTEN AS A PRODUCT OF THE FORM C -1 C L = L *P *....*L *P WHERE EACH P IS A PERMUTATION C N-1 N-1 1 1 K C MATRIX OBTAINED BY INTERCHANGING AT MOST TWO ROWS OF THE C IDENTITY MATRIX. ( THIS REPRESENTS THE INTERCHANGING OF TWO C ROWS). THE L MATRICES ARE ELIMINATION MATRICES WHICH ARE C K C CHOSEN TO INTRODUCE ZEROS IN THE LAST N-K ENTRIES OF THE K-TH C COLUMN OF THE MATRIX. C C -1 -1 C THE CALCULATIONS OF L *A AND L *P ARE DONE BY PERFORMING C THE PERMUTATIONS ON A AND P RESPECTIVELY. THE ACTUAL L AND P C K K C ARE NOT COMPUTED. C SUBROUTINES CALLED: DMATDT C REFERENCE: C G. W. STEWART, INTRODUCTION TO MATRIX COMPUTATIONS, C ACADEMIC PRESS, 1973. REAL*8 A(N,1),DET,P(LL,1) REAL*8 DNORM,DEN,DMULT,DSUM,DISIGN DIMENSION IV(1) NRS=NRS1 IF (NRS.EQ.0) IDET=1 DISIGN=1.0D+00 DET=0.0D+00 JFLG=0 C C JFLG IS A TROUBLE FLAG.UPON EXIT IF JFLG=0 THEN THE MATRIX WAS PROCESS C WITHOUT TROUBLE.IF JFLG=1 EITHER THE MATRIX IS SINGULAR OR TROUBLE C OCCURRED.ISIGN=-ISIGN EVERY TIME A ROW IS INTERCHANGED.THIS IS USED TO C INSURE THAT THE DETERMINANT HAS THE PROPER SIGN. C M1=M-1 DO 100 I=1,M 100 IV(I)=I IF (NRS) 500,200,500 200 DO 300 I=1,M DO 300 J=1,M 300 P(I,J)=0.0D+00 DO 400 I=1,M 400 P(I,I)=1.0D+00 NRS=M C C INSTEAD OF ACTUALLY INTERCHANGING ROWS A POINTER ARRAY IS USED TO KEEP C TRACK OF THE ROW POSITIONS. C C BEGIN ELIMINATION LOOP. C 500 DO 1200 K=1,M1 ICOL=K IPCOL=K C C SEARCHING FOR LARGEST ELEMENT IN ABSOLUTE VALUE IN COLUMN K. C DNORM=A(IV(K),K) IFLG=0 KK=K+1 DO 600 J=KK,M IF (DABS(A(IV(J),K)).LE.DABS(DNORM)) GO TO 600 IFLG=1 IPCOL=IV(J) DNORM=A(IPCOL,K) 600 CONTINUE C C IF IFLG=0 NO ROW INTERCHANGE TOOK PLACE.IF IFLG=1 A ROW INTERCHANGE C TOOK PLACE AND THE POINTER ARRAY IV MUST BE UPDATED. C IF (IFLG.EQ.0) GO TO 800 ISAVE=IV(ICOL) IV(ICOL)=IPCOL ICOL1=ICOL+1 DO 700 L=ICOL1,M IF (IV(L).EQ.IPCOL) IV(L)=ISAVE 700 CONTINUE DISIGN=-DISIGN 800 IF (DNORM.EQ.0.0D+00) GO TO 1900 C C BEGIN ELIMINATION OF ROW BELOW IV(K).DEN IS THE PIVOT ELEMENT. C K1=K+1 DO 1100 IM=K1,M C C BEFORE ACTUALLY ELIMINTING WE CHECK TO SEE IF A(IV(IM),K) HAS ALREADY C BEEN ANIHILATED. C IF (A(IV(IM),K).EQ.0.0D+00) GO TO 1100 C C CACULATE ELIMINATION FACTOR. C DMULT=-A(IV(IM),K) C C WE NOW CALCULATE VALUE OF OTHER ELEMENTS IN ROW IV(IM). C DO 900 NN=K1,M 900 A(IV(IM),NN)=(DMULT*A(IV(K),NN))/DNORM+A(IV(IM),NN) IF (NRS.LE.0) GO TO 1100 DO 1000 IN=1,NRS 1000 P(IV(IM),IN)=(DMULT*P(IV(K),IN))/DNORM+P(IV(IM),IN) 1100 CONTINUE 1200 CONTINUE C C CALCULATE VALUE OF DETERMINANT. C IF (A(IV(M),M).EQ.0.0D0) GO TO 1900 DET=DISIGN IF (IDET.NE.0) CALL DMATDT(A,N,M,DET,IV,IDET) IF (DET.EQ.0.0D+00) GO TO 1900 IF (NRS.LE.0) GO TO 2000 C C WE START SOLVING RIGHT HAND SIDES.THE SOLUTION REPLACES THE RIGHT HAND C VECTOR. C 1300 N1=M-1 DO 1600 JJ=1,NRS C C BEGIN BACK SUBSTITUTION. C P(IV(M),JJ)=P(IV(M),JJ)/A(IV(M),M) DO 1500 I=1,N1 DSUM=0.0D+00 DO 1400 J=1,I 1400 DSUM=DSUM-A(IV(M-I),M-J+1)*P(IV(M-J+1),JJ) 1500 P(IV(M-I),JJ)=(P(IV(M-I),JJ)+DSUM)/A(IV(M-I),M-I) 1600 CONTINUE DO 1800 JJ=1,NRS DO 1700 IND=1,M 1700 A(IND,1)=P(IV(IND),JJ) DO 1800 IND=1,M 1800 P(IND,JJ)=A(IND,1) RETURN 1900 JFLG=1 IDET=0 2000 RETURN END SUBROUTINE MATDT(A,IA,N,DET,IV,IDET) C SUBROUTINE MATDT IS DMATDT FROM THE UICC SUBROUTINE LIBRARY. REAL*8 A(IA,1),DET,B,LOG16 INTEGER*4 IV(1),K EQUIVALENCE (B,K) NUM=16777216 LOG16=.120411998265592457D+01 IF (A(IV(N),N).EQ.0.0D+00) GO TO 300 L=0 DO 100 I=1,N B=DABS(A(IV(I),I)) K=K/NUM-64 L=L+K 100 DET=DET*(A(IV(I),I)/16.0D+00**K) B=DABS(DET) K=K/NUM-64 IW=L+K IF ((IW.LT.-64).OR.(IW.GT.63)) GO TO 200 DET=DET*16.0D+00**L IDET=0 GO TO 400 200 DET=DET*16.0D+00**(-K) IDET=L+K B=IDET*LOG16 IDET=B B=B-DFLOAT(IDET) DET=DET*1.0D+01**B GO TO 400 300 DET=0.0D+00 IDET=0 400 RETURN END