2Y/*JOBPARM REGION=1024,LINES=19}// EXEC FORTGCLG //FORT.SYSIN DD *ChCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC0000~CC0PROGRAMIMPAC:IMSGPCM0C C0VERSION5.231-JAN-840CC0000~CC0000~C8CpPROGRAMIMPAC:IMSGPCMISFORSEGMENTINGMULTI-CHANNELaC\CDIGITALIMAGES.(FORSINGLE-CHANNELDATATHE"IMSG1"ACHCPROGRAMMAYBEUSED.)00CCmTHISPROGRAMUSESDISTANCEINTHEMETRICOFTHECOMMONCqC!COVARIANCEMATRIX.000CC0000~CCoMANUAL MODE:NUMBEROFCLASSESANDINITIAL MEANSARE INPUTC&CUSEIMPAC:IMSGPCMA("A"=AUTOMATIC)TOTRYA RANGEOFNUMBEROFCCCLASSES,WITHAUTOMATICSETTINGOFINITIALMEANS.0C+C0000~CC0000~C0CPROGRAMMEDBY:000CQCDR.STANLEYL.SCLOVE00JC){CPROFESSOROFQUANTITATIVEMETHODS312/996-2681C/yC%QUANTITATIVEMETHODSDEPARTMENT312/996-2676C݌CUNIVERSITYOFILLINOISATCHICAGO00CCBOX 4348,CHICAGO,IL 6068000/C_-C0000~CCyRESEARCHSUPPORTEDINPARTBY:01CC0000~C`CONRCONTRACTN00014-80-C-0408,TASKNR042-4430C' CAROCONTRACTDAAG29-82-K-015500CYC0000~Cd}C0000~ChCxPROGRAMRESTRICTIONS(CANBEMODIFIED):0/CCNR,NUMBEROFROWSOFARRAY,ATMOST256;0jChCNC,NUMBEROFCOLUMNSOFARRAY,ATMOST256;0/CmCIP,NUMBEROFCHANNELS,ATMOST20;01CqCK,NUMBEROFCLASSES,ATMOST29;00C CITER,MAXIMUMNUMBEROFITERATIONS,20.0CC0000~CuCSUBROUTINE(S)CALLED:00~Cx8CMATEQ, WHICH CALLS MATDT00C\C0000~CHC0000~CC CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCqCCĝDIMENSIONX(56,56,10)C&CCHANGENO.OFCHANNELSFROM4TO20GCANDNO.OFROWSANDCOLUMNSFROM56TO256CINDIMENSIONSTATEMENTSCWHENALLOWABLEREGIONISINCREASED.K0DIMENSION IOTA(56)OQDIMENSIONJOTA(29){DIMENSIOND(29),ICLUS(56,56)yDIMENSIONTITLE(18)SDIMENSIONNG(29),XMEAN(29,4)WDIMENSIONFMT(18)-DIMENSIONSUM(29,4),SS(29,4,4)DIMENSIONSSD(29,4,4)2DIMENSION WGSS(4,4)6 DIMENSIONVARHAT(20,20),WGMS(4,4)DIMENSIONICLSOL(56,56)YDIMENSION XMIN(4),XMAX(4)}DIMENSIONIV(20,20) DIMENSIONP(20,20)DIMENSIONNT(29,29,29),IRSUM(29,29),TP(29,29,29) hDIMENSIONPROB(29)C DOUBLEPRECISIONSS,SUM DOUBLEPRECISIONWGSS,SSDDOUBLEPRECISIONVARHATDOUBLEPRECISIONP8 DOUBLEPRECISIONDET\DOUBLEPRECISIONDHDOUBLEPRECISION XMEANDOUBLEPRECISIONTEMPIV,TEMPJVqDOUBLEPRECISIONFDOUBLEPRECISIONCFDOUBLEPRECISIONTP,PROB &CCCIVISAWORK ARRAYFORSUBROUTINEMATEQ.<C|0CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCQC0000~C{CCONTROLCARDS:000/C$yC0000~C^ CDATASET TITLE000CCNUMBEROF ROWS,NR,INFORMAT(3X,I3)0C-CNUMBEROFCOLUMNS,NC,INFORMAT(3X,I3)0C,CNUMBEROFCHANNELS,IP,INFORMAT(3X,I2)0jC?CFMT,INFORMAT(18A4), E.G.,(1X,F4.1)0ACCe"FMT"WILLALSOBEUSEDFOROUTPUT: ALLOWAT LEASTONE BLANKCCbATTHEBEGINNINGFORCARRIAGECONTROL.0jC:YCDATA,ONENUMBERATA TIME,INFORMATSPECIFIEDBYFMTC=}CdDATAISINDEXEDBYCHANNEL,ROW,ANDCOLUMN.0CbCfCOLUMNCHANGESFIRST,THENROW,THENCHANNEL.0CfC0000~ChCK,NUMBEROFCLASSES,INFORMAT(2X,I2)0CCKINITIALMEANS,INFORMATSPECIFIEDBYFMT0CkCgINITIAL MEANSAREINDEXEDBY CLASSANDCHANNEL.1Co CgCHANNELCHANGESFIRST,THENCLASS.0JCC0000~CC0000~C~8CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCv\CzHC[ READ(5,36000) TITLEqCCWRITEPROGRAMINFORMATION.WRITE(6,24000)]&WRITE(6,42000) TITLEACECREADNUMBERSOFROWSANDCOLUMNS,NRANDNC.IREAD(5,12000)NR0READ(5,12000)NC}QWRITE(6,38000)NRM{WRITE(6,40000)NCQyCREADNUMBEROFVARIABLES,IP.READ(5,62000)IP Y\WRITE(6,64000)IPU-CYCREADDATAFORMAT.READ(5,36000)FMT0C4 CREAD DATA.7YDO300 ICHAN=1,IP}0DO300I=1,NR0DO300J=1,NC0READ(5,FMT)X(I,J,ICHAN)h0IF(I.EQ.1 .AND.J.EQ.1)GOTO100 0GOTO2001000CONTINUE 0DO200IVAR=1,IP0XMAX(IVAR)=X(1,1,IVAR)0XMIN(IVAR)=X(1,1,IVAR)82000CONTINUE\0DO300IVAR=1,IPH0IF(X(I,J,IVAR).LT.XMIN(IVAR))XMIN(IVAR)=X0X(I,J,IVAR)q0IF(X(I,J,IVAR).GT.XMAX(IVAR))XMAX(IVAR)=X0X(I,J,IVAR)3000CONTINUE&WRITE(6,72000)WRITE(6,FMT)(XMIN(IVAR),IVAR=1,IP)WRITE(6,74000)WRITE(6,FMT)(XMAX(IVAR),IVAR=1,IP)0CREADK,NUMBEROFCLASSES.(QREAD(5,10000)K{WRITE(6,26000)KyCWRITE(6,20000)) CREADINITIAL MEANS/-DO400IG=1,Kݫ0DO400IVAR=1,IP0READ(5,FMT)XMEAN(IG,IVAR)_ 400CONTINUECYDO500IG=1,K}WRITE(6,22000)@WRITE(6,FMT)(XMEAN(IG,IVAR),IVAR=1,IP) 500CONTINUEdhChCSETCONSTANTS.C /N= NR*NCmXN=NqDO600INTEG=1,NC8IOTA(INTEG)= INTEG\ 600CONTINUEtHDO700J=1,Kx JOTA(J)=Jq 700CONTINUECPI=3.1415927&CC;DISTRIBUTIONALPARAMETERS:CKMEANVECTORSOFDIMENSIONIPANDANIP-BY-IPCOVARIANCEMATRIX,CCWHEREIPISTHENUMBEROFVARIABLESF0CNO.OFINDEPENDENTTRANSITIONPROB.'S=(K**2)*(K-1)QC{CNO.OFPARAMETERS=NO.OFDISTRIBUTIONALPARAMETERSKyC0A+NO.OFINDEPENDENTTRANSITIONPROB.'SONOPARM=K*IP+IP*(IP+1)/2+(K**2)*(K-1)C!INITIALIZEVARIABLES.-CSCFOR FIRSTITERATION,MARGINALDISTRIBUTIONOFLABELS, PROB,WCIS TAKENTOBEUNIFORM.DO800IG=1,K 800PROB(IG)= 1.0/K1YC5}C9ITER=1 900CONTINUEh WRITE(6,32000)ITER IF (ITER.EQ.1)GOTO1100DO1000I=1,NR 0DO1000J=1,NC1000ICLSOL(I,J)=ICLUS(I,J) CSAVEPREVIOUS VALUEOF-2LOGMAXLIKELIHOOD.8XMN2OL=XMN2LL\1100CONTINUEHCCCOMMENCEDISTANCECOMPUTATIONS.qCDO2300I=1,NR0DO2300J=1,NC&C!INITIALIZEDISTANCES(TOBEACCUMULATED)AT ZERO.0DO1200L=1,K12000D(L)=0.0 CFOR FIRSTITERATION,EUCLIDEANDISTANCEISUSEDBECAUSE0CNOCOVARIANCEMATRIXISYETAVAILABLE. AFTERTHE FIRSTQC!ITERATION,DISTANCEWILLBE TAKENINTHEMETRICOFTHE.{ C!COVARIANCEMATRIX.|y0IF (ITER.GT.1)GOTO14000DO1300 L=1,K0DO1300IVAR=1,IP$-13000D(L)=D(L)+(XMEAN(L,IVAR)-X(I,J,IVAR)^X0u)**2 0GOTO16001400CONTINUE,C(AFTER FIRSTITERATION)COMPUTEDISTANCESINMETRIC>YCOFCOVARIANCEMATRIX}0DO1500L=1,K0DO1500IVAR=1,IP:0TEMPIV=XMEAN(L,IVAR)-X(I,J,IVAR)=h00DO1500JV=1,IPb00TEMPJV=XMEAN(L,JV)-X(I,J,JV)f15000D(L)=D(L)+TEMPIV*P(IVAR,JV)*TEMPJV 1600CONTINUE0DO2100L=1,KkCFOR FIRSTITERATION,CLASSIFICATIONISSIMPLYBYn8CMINIMUMDISTANCE.OTHERWISE,THETRANSITIONr\C)PROBABILITIESENTER.H0IF (ITER.EQ.1)GOTO2100~0ARG=-D(L)/2.0vq0IF (ARG.LT.-180.2)GOTO1700z 0GOTO1800[17000D(L)=0.0& 0GOTO190018000CONTINUEC]0D(L)=EXP(ARG){019000CONTINUEDQCH{0IF(I.EQ.1.OR.J.EQ.1)GOTO2000y0IG1=ICLUS(I,J-1)}0IG2=ICLUS(I-1,J)MCQ-0D(L)=-TP(IG1,IG2,L)*D(L)C\ 0GOTO2100U20000CONTINUEYCYCCLASSIFYBOUNDARYOBSERVATIONS}0D(L)=-D(L)*PROB(L)321000CONTINUE7Ch0F=D(1)0ICLUS(I,J)=10DO2300L=2,K 0IF(D(L)-F)2200,2300,2300 22000F=D(L)0ICLUS(I,J)=L823000CONTINUE\CHWRITE(6,14000)WRITE(6,16000)(IOTA(J),J=1,NC)qDO2400I=1,NRWRITE(6,18000)I,(ICLUS(I,J),J=1,NC)2400CONTINUE&CDO2500IG=1,K NG(IG)=0 0DO2500IVAR=1,IP00SUM(IG,IVAR)=0.0Q0DO2500JV=1,IP 4{0?SSD(IG,IVAR,JV)=0.0y25000SS(IG,IVAR,JV)=0.0(DO2700I=1,NR0DO2700J=1,NC- 0IGROUP=ICLUS(I,J)0NG(IGROUP)=NG(IGROUP)+1) 0DO2600IVAR=1,IP/0?SUM(IGROUP,IVAR)=SUM(IGROUP,IVAR)+X(I,J,IVAR)0DO2600JV=1,IPY26000?SS(IGROUP,IVAR,JV)=SS(IGROUP,IVAR,JV)+X(I,%}X0J,IVAR)*X(I,J,JV)׼2700CONTINUEDO2800IVAR=1,IPh0DO2800JV=1,IP@ 0WGSS(IVAR,JV)=0.02800CONTINUEd ChCDO3100IG=1,K8IF(NG(IG).EQ.0)GOTO2900l\ GOTO3000pH2900WRITE(6,86000)IG GOTO5300q3000CONTINUEt 0DO3100IVAR=1,IPxCCOMPUTEMEANVECTORS.&0XMEAN(IG,IVAR)=SUM(IG,IVAR)/NG(IG)CCOMPUTESUM-OF-PRODUCTSMATRICES.0DO3100JV=1,IP0CF=SUM(IG,IVAR)*SUM(IG,JV)/NG(IG)00?SSD(IG,IVAR,JV)=SS(IG,IVAR,JV)-CFQ31000CONTINUEB{CFyCˌCCK-CPOOL:OCDO3200IG=1,K 0DO3200IVAR=1,IPS0DO3200JV=1,IPVY0_WGSS(IVAR,JV)=WGSS(IVAR,JV)+SSD(IG,IVAR,JV)Z}32000CONTINUEC1C5hCCOMPUTEVARHAT,MLEOFCOMMONCOVARIANCEMATRIX:9CDO3300IVAR=1,IP  0DO3300JV=1,IP 0VARHAT(IVAR,JV)=WGSS(IVAR,JV)/N 3300CONTINUE 8CPRINTVARHAT: \WRITE(6,52000) HDO3400IVAR=1,IP WRITE(6,60000)(VARHAT(IVAR,JV),JV=1,IP) q3400CONTINUE C IDET=1 &NRS1=0  NVRHT=20 NP=20 CALLMATEQ(VARHAT,IP,NVRHT,JFLG,DET,IDET,IV,NRS1,P,NP) 0C QCGENERALFORMOFCALLIS: {CCALLMATEQ(A,M,N,JFLG,DET,IDET,IV,NRS1,P,LL) yCSEELISTINGOFSUBROUTINEFORFULLEREXPLANATION. C$DET(VARHAT)=DET*10.0**IDET .C |-IF (JFLG.GT.0) WRITE(6,68000)JFLG WRITE(6,70000)DET,IDET C $WRITE(6,56000) ^DO3500IVAR=1,IP YWRITE(6,60000)(P(IVAR,JV),JV= 1,IP) }3500CONTINUE C > XIDET=IDET hXLGDET=DLOG(DET)+XIDET*ALOG(10.0) XMN2LL=N*(IP*ALOG(2.0*PI)+IP+XLGDET) :C = C bDO3600IG=1,K fWRITE(6,28000)IG,(XMEAN(IG,IVAR) ,IVAR=1,IP) i83600CONTINUE \IF (ITER.EQ.1)GOTO3800 jHDO3700I=1,NR n0DO3700J=1,NC rq0IF(ICLUS(I,J).EQ.ICLSOL(I,J))GOTO3700 0GOTO3800 ~3700CONTINUE v& GOTO5400 z3800CONTINUE [C CCOMPUTETRANSITIONPROBABILITYMATRIX: 0C QDO3900I1=1,K {0DO3900I2=1,K {y0DO3900J=1,K D0,NT(I1,I2,J)=0 H39000CONTINUE -DO4000I=2,NR }0DO4000J=2,NC M 0IM1=I-1 Q 0JM1=J-1 0INORTH=ICLUS(IM1,J) Y0 IWEST=ICLUS(I,JM1) T}0IY=ICLUS(I,J) X0NT(IWEST,INORTH,IY)=NT(IWEST,INORTH,IY)+1 4000CONTINUE hDO4100I1=1,K 30DO4100I2=1,K 70IRSUM(I1,I2)=0 4100CONTINUE DO4200I1=1,K0DO4200I2=1,K80DO4200J=1,K\0%IRSUM(I1,I2)=IRSUM(I1,I2)+NT(I1,I2,J)H42000CONTINUEDO4500I1=1,Kq0DO4500I2=1,K0XDENOM=IRSUM(I1,I2)0IF(XDENOM.EQ.0.0)GOTO4300& 0GOTO44004300XDENOM=K4400CONTINUEC00DO4500J=1,KQ0XNUM=NT(I1,I2,J){CIF THEREARENOTRANSITIONSFROM(I1,I2),THENTP(I1,I2,J)yCISSET EQUALTO ZERO,FORALLJ=1,2,...,K.C45000TP(I1,I2,J)=XNUM/XDENOM-4600CONTINUE(CCCOMPUTEMARGINALDISTRIBUTIONOFLABELS:DO4700IG=1,KPROB(IG)=NG(IG)*YPROB(IG)=PROB(IG)/N-}4700CONTINUEC TRANS=0.0%hDO4800I1=1,K0DO4800I2=1,K0DO4800 J=1,K 0ITEST=NT(I1,I2,J)@0IF(ITEST.EQ.0)GOTO4800 0IF(TP(I1,I2,J).EQ.0.)GOTO4800c80TRANS= TRANS+NT(I1,I2,J)*DLOG(TP(I1,I2,J))g\48000CONTINUEHCŵTRANS=-2.0*TRANSlqCpCACCOUNTFORLABELSOFBORDEROBSERVATIONS: FIRST=0.0&0DO5000J=1,NCt 0LABEL1=ICLUS(1,J)x0PROBAB=PROB(LABEL1)0 FIRST= FIRST+ALOG(PROBAB)05000CONTINUEQ0DO5100I=2,NR{ 0LABEL1=ICLUS(I,1)y0PROBAB=PROB(LABEL1)،0 FIRST= FIRST+ALOG(PROBAB) B5100CONTINUEF-FIRST=-2.0*FIRST˫CCKCCOMPUTE MODELSELECTIONCRITERIA:OCEXCEPTFOR FIRSTITERATION,COMPUTEAIC BASEDONRYCNEWCLUSTERINGANDOLDCOVARIANCEMATRIX.}IF (ITER.EQ.1)GOTO4900AICOLD=XMN2OL+2.0*NOPARMVWRITE(6,90000)AICOLDZhWRITE(6,90005)SCHOLD4900CONTINUE1XMN2LL=XMN2LL+ TRANS+ FIRST5 AIC=XMN2LL+2.0*NOPARM9SCH=XMN2LL+ALOG(XN)*NOPARMWRITE(6,92000)AIC8WRITE(6,92005)SCH\CHC CWRITETRANSITIONPROBABILITIES:qWRITE(6,44000) WRITE(6,48000)(JOTA(JAY),JAY=1,K)DO5010I1=1,K&0DO5010I2=1,K0 WRITE(6,46000)I1,I2,(NT(I1,I2,J),J=1,K)5010CONTINUEWRITE(6,50000)0 WRITE(6,48000)(JOTA(JAY),JAY=1,K)QDO5110I1=1,K{0DO5110I2=1,Ky0 WRITE(6,54000)I1,I2,(TP(I1,I2,J),J=1,K)5110CONTINUEWRITE(6,88000)(PROB(IG),IG=1,K)-WRITE(6,78000) TRANSITER=ITER+1.IF(ITER.GE.21)GOTO5200|GOTO900 5200 WRITE(6,76000)Y5300STOP!}C;C5400CONTINUEhC WRITE(6,66000)ITER>WRITE(6,34000)(NG(IG),IG=1,K) WRITE(6,58000)DO5500IVAR=1,IP:0DO5500JV=1,IP'80WGMS(IVAR,JV)=WGSS(IVAR,JV)/(N-K)a\5500CONTINUEeHDO5600IVAR=1,IPiWRITE(6,60000)(WGMS(IVAR,JV),JV=1,IP)q5600CONTINUEjCnCr&WRITE(6,16000)(IOTA(J),J=1,NC)DO5700I=1,NR~WRITE(6,18000)I,(ICLUS(I,J),J=1,NC)v5700CONTINUEy0CQWRITE(6,82000)NOPARM{AIC=XMN2LL+2.0*NOPARMyWRITE(6,80000)AICCC{- WRITE(6,84000)ITERD STOPH10000 FORMAT(2X,I2)12000 FORMAT(3X,I3)}14000 FORMAT(//1X,'SEGMENTATION:'/)LY 16000FORMAT(/,1X,'ROW:gCOLUMN:'/,4X,(40I3/))P}18000 FORMAT(1X, I3, (40I3/) )20000 FORMAT(//1X,'INITIAL MEANS'/)22000 FORMAT(1X, (8E13.5/)//)Th24000 FORMAT('1','#######################################*',X;X//,1X,'PROGAMIMSEGP.COMMON'/X,1X,'FOR IMAGESEGMENTATION'/ $X,1X,'USINGDISTANCEINTHEMETRICOFTHECOVARIANCEMATRIX'/3^X//,1X,'DEVELOPEDANDPROGRAMMEDBYDR.STANLEYL.SCLOVE'7^X//,1X,'VERSION5.231-JAN-84'//)826000 FORMAT('1',//,1X,'K = ',I2,' CLASSES')\ 28000FORMAT(1X,'MEANVECTORFOR CLASS',I2,':',(8E13.5/))H 30000FORMAT(/1X,'MINUS2LOGLIKELIHOOD=',E13.5//)32000 FORMAT(/,1X,'ITERATION ', I2,//)q34000 FORMAT(/,1X,'NUMBERS:',(9I13/)/)36000 FORMAT(18A4)38000 FORMAT(/1X,'NUMBER OF ROWS = ',I3/)&40000 FORMAT(/1X,'NUMBER OF COLUMNS = ',I3/) 42000 FORMAT(1X,18A4)44000 FORMAT(/1X,'TRANSITIONS'/)46000 FORMAT(1X, 2I4, (9I7/)) 048000 FORMAT(/9X,(9I7/))Q50000 FORMAT(/1X,'TRANSITION PROBABILITIES'/){52000 FORMAT(///,1X,'COMMON COVARIANCE MATRIX (MLE):',//)y54000 FORMAT(1X,2I4,3X,(9F7.4/))56000 FORMAT(///,1X,'INVERSE COVARIANCE MATRIX:',//)58000 FORMAT(///,1X,'COMMON COVARIANCE MATRIX (UNBIASED ESTIMATE):',//)-60000 FORMAT(1X,(8E13.5/))62000 FORMAT(3X,I2)64000 FORMAT(/1X,'NUMBER OF CHANNELS = ',I2/) 66000 FORMAT(/1X,'CONVERGENCE: NO CASE CHANGED CLASSES AFTER ',($X'ITERATION',I2,'.RESULTSAREPRINTEDBELOW.'//)&Y68000 FORMAT(/,1X,'JFLG = ',I2,'. IF JFLG=0, COMPUTATION OF DET',}X'WENT WELL;OTHERWISE, THEREWASTROUBLEORMATRIXWAS',^X'ILL-CONDITIONED.'//)* 70000FORMAT(/1X,'DET=',E13.5,'IDET=',I3,5X,-hX'ACTUALDET.=DET*10**IDET',//)72000 FORMAT(/1X,'MINIMUM FOR EACH CHANNEL: ',/)74000 FORMAT(/1X,'MAXIMUM FOR EACH CHANNEL: ',/)% 76000 FORMAT(1X,'ISODATA HAS NOT CONVERGED IN 20 ITERATIONS. STOP')78000 FORMAT(//,1X,'CONTRIBUTION OF TRANS. PROBS. TO LOG ',*X'LIKELIHOOD=',E15.5/)880000 FORMAT(1X,'AIC = ', E15.5///)#\82000 FORMAT(//1X,'NUMBER OF PARAMETERS = ',I4//)"H84000 FORMAT(1X,'RESULTS DID NOT CHANGE IN ITERATION NUMBER',I3,'.',cX/,1X,'PROGRAM ENDEDSUCCESSFULLY.')gq 86000FORMAT(1X,'NOOBSERVATIONSIN GROUP',I3,'.STOP') 088000 FORMAT(/1X,'MARGINAL PROB. VECTOR:',(9F11.4/))ŝ90000 FORMAT(/1X,'AIC BASED ON NEW LABELS AND OLD DISTRIBUTIONAL ',l&)X'PARAMETERS:',E15.5/)p90005 FORMAT(/1X,'SCHWARZ CRITERION BASED ON NEW LABELS AND OLD ',^X'DISTRIBUTIONALPARAMETERS:',E15.5/)92000 FORMAT(/1X,'AIC BASED ON NEW LABELS AND NEW DISTRIBUTIONAL ',s0)X'PARAMETERS:',E15.5/)wQ92005 FORMAT(/1X,'SCHWARZ CRITERION BASED ON NEW LABELS AND NEW ',{^X'DISTRIBUTIONALPARAMETERS:',E15.5/)yENDSUBROUTINEMATEQ(A,M,N,JFLG,DET,IDET,IV,NRS1,P,LL)C-C!SUBROUTINE MATEQISDMATEQFROMTHEUICCSUBROUTINELIBRARY.ثCB C0SUBROUTINEDMATEQFC0*****************CTHISROUTINEWILL SOLVEAREAL*8SYSTEMOFLINEAREQUATIONS,COMPUTEYCTHEDETERMINANT,WITHOUTUNDERFLOWOROVERFLOW,OFAREAL*8MATRIX,J}CAND/ORINVERTAREAL*8MATRIX.NCCALLINGSEQUENCE:RCCALLDMATEQ(A,N,IA,JFLG,DET,IDET,IV,NRS,P,IP)WHERE;hCjA(INPUT)-ISTHEREAL*8MATRIXON WHICHTHEROUTINEISC0TO WORK.INTHEPROCESSOFCOMPUTATIONTHEVC0CONTENTSOFTHISMATRIXAREDESTROYED.Z CjN(INPUT)-ISANINTEGER*4VARIABLE WHICHSPECIFIESTHEC0ORDEROFTHEAMATRIX.1CkIA(INPUT)-ISANINTEGER*4VARIABLE WHICHSPECIFIESTHE48C0ACTUALROWDIMENSIONOFAASDIMENSIONEDIN8\C0THECALLINGPROGRAM.IAMUSTBEGREATERTHANHC0OR EQUALTON.CmJFLG(OUTPUT)-ISANINTEGER*4RETURNCODEVARIABLE.UPONqC0RETURNFROMDMATEQIF;C0JFLG=0,ALLWENT WELL. C0JFLG=1,THEAMATRIXWASSINGULARORNEAR&C0SINGULARANDTHECOMPUTATIONS COULDNOTBEC0COMPLETED.THECONTENTSOFTHEVARIABLESC0A,DET,IDETANDPAREMEANINGLESS.ClDET(OUTPUT)-ISAREAL*8VARIABLE WHICHCONTAINSTHE0C0DETERMINANTOFA.(SEE IDET)QCmIDET(INPUT)-ISANINTEGER*4VARIABLE.ON INPUTIF;{C0IDET=0,NODETERMINANTISCALCULATED.yC0IDETNOT0,THEDETERMINANTOFAISCOMPUTED.C0KONOUTPUTIDETCONTAINSTHE POWEROF10C0THATDETSHOULDBEMULTIPLIEDBYTOGIVETHE-C0CORRECT VALUEOFTHEDETERMINANT.I.E.C0DET(A)=DET*10.0D0**IDET.C0KIFDET(A)CANBECOMPUTEDWITHOUT UNDERORC0OVERFLOW,THENIDET=0OTHERWISEIDETISSETC0TOTHEPROPER VALUESOTHATNO UNDEROR OVER-Y C0FLOWWILL OCCURINCOMPUTINGDET.+}CkIV(INPUT)-ISANINTEGER*4WORK ARRAY WHICHSHOULDBEC0DIMENSIONEDAT LEASTIV(N).C!hClNRS(INPUT)-ISANINTEGER*4VARIABLEWITHTHEFOLLOWING;C0INTERPRETATION:ߨC0NRS>0, SOLVEASYSTEMOFLINEAREQUATIONS C0WITHNRS RIGHTHANDSIDES.C0NRS=0,INVERTTHEAMATRIX.>C0NRS<0,ONLYCOMPUTETHEDETERMINANTOFA.8C0INTHISCASEIDETMUSTBEDIFFERENTFROM0.\CjP(INPUT)-ISAREAL*8 ARRAYWITHTHEFOLLOWINGINTER-`HC0PRETATION:'C0IFNRS>0,THENPCONTAINSTHENRS RIGHTHANDaqC0SIDESSTOREDBYCOLUMNS.INTHISCASEPMUSTeC0BEDIMENSIONEDAT LEASTP(N,NRS).ONRETURNiC0THECOLUMNSOFPAREREPLACEDBYTHERESPEC-&C0TIVESOLUTIONS.jC0IFNRS=0,THENPMUSTBEDIMENSIONEDAT LEASTnC0P(N,N).ONRETURNPWILLCONTAINTHEINVERSErC0OFA.0C0IFNRS<0,THENPNEEDONLYBEA DUMMYVARIABLEQC0INTHISCASEPIS NEVERACCESSEDBYDMATEQ.u{CkIP(INPUT)-ISANINTEGER*4VARIABLE WHICHCONTAINSTHEyyC0ACTUALROWDIMENSIONOFPASDIMENSIONEDINڌC0THECALLINGPROGRAM.IPMUSTBEGREATERTHANC0OR EQUALTON.-CNOTE:IMMEDIATELYONRETURNFROMDMATEQTHECONDITIONCODE FLAG,CvJFLG,SHOULDBEINTERROGATED.IFJFLG=1,THENTHEROUTINECvCOULDNOTCOMPUTEASOLUTION.{CMETHOD-THEALGORITHMUSEDISGAUSSIANELIMINATIONWITHPARTIALDC0000-1GYCrPIVOTING.INESSENCETHEROUTINEGENERATESAMATRIXLSUCH} C2-1 CmTHATL*A=U, WHEREUISAN UPPERTRIANGULARMATRIX.THENITLCoSOLVESTHESYSTEMA*X=PBY MEANSOFTHEEQUIVALENTSYSTEMPhC0-1b-1ClU*X=L*A*X=L*PBYBACKSUBSTITUTION. C2-1 ST CtTHELMATRIXCANBEWRITTENASAPRODUCTOFTHEFORMX Ck-1CaL=L*P*....*L*P WHEREEACHPISAPERMUTATION8C3N-1N-1a11JK2\CfMATRIXOBTAINEDBYINTERCHANGINGATMOSTTWOROWSOFTHE6HChIDENTITYMATRIX.(THISREPRESENTSTHEINTERCHANGINGOFTWOCfROWS).THELMATRICESAREELIMINATIONMATRICES WHICHAREq C0K CfCHOSENTOINTRODUCE ZEROSINTHELASTN-KENTRIESOFTHEK-THCfCOLUMNOFTHEMATRIX.&CC02-1b-1ClTHECALCULATIONSOFL*AANDL*PAREDONEBYPERFORMINGCTHEPERMUTATIONSONAANDPRESPECTIVELY.THEACTUALLANDP0C0000K/KQCARENOTCOMPUTED.{CSUBROUTINESCALLED:DMATDT y CREFERENCE:C G. W. STEWART, INTRODUCTION TO MATRIX COMPUTATIONS,C ACADEMIC PRESS, 1973.-REAL*8A(N,1),DET,P(LL,1)REAL*8DNORM,DEN,DMULT ,DSUM,DISIGNDIMENSION IV(1)NRS=NRS1 IF(NRS.EQ.0)IDET=1Y>DISIGN=1.0D+00} ,DET=0.0D+00<JFLG=0&ChC JFLG IS A TROUBLE FLAG.UPON EXIT IF JFLG=0 THEN THE MATRIX WAS PROCESSC WITHOUT TROUBLE.IF JFLG=1 EITHER THE MATRIX IS SINGULAR OR TROUBLE*C OCCURED.ISIGN=-ISIGN EVERY TIME A ROW IS INTERCHANGED.THIS IS USED TO- C INSURE THAT THE DETERMINANT HAS THE PROPER SIGN.CM1=M-1,8 DO100 I=1,M?\ 100IV(I)=IH IF (NRS)500,200,500ֵ200DO300 I=1,M#q0DO300 J=1,M"300P(I,J)=0.0D+00c DO400 I=1,Mg&400>P(I,I)=1.0D+00NRS=MClC INSTEAD OF ACTUALLY INTERCHANGING ROWS A POINTER ARRAY IS USED TO KEEPo0C TRACK OF THE ROW POSITIONS.QC{C BEGIN ELIMINATION LOOP.syCw500DO1200K=1,M1ICOL=K-IPCOL=KCC SEARCHING FOR LARGEST ELEMENT IN ABSOLUTE VALUE IN COLUMN K.CDNORM=A(IV(K),K)AYIFLG=0E}KK=K+1I0DO600J=KK,M0IF(DABS(A(IV(J),K)).LE.DABS(DNORM))GOTO600Jh0IFLG=1N 0IPCOL=IV(J)R0DNORM=A(IPCOL,K) 600CONTINUECVC IF IFLG=0 NO ROW INTERCHANGE TOOK PLACE.IF IFLG=1 A ROW INTERCHANGEY8C TOOK PLACE AND THE POINTER ARRAY IV MUST BE UPDATED.\C0HIF(IFLG.EQ.0)GOTO8004ISAVE=IV(ICOL)8qIV(ICOL)=IPCOL ICOL1=ICOL+1 0DO700L=ICOL1,M &0IF(IV(L).EQ.IPCOL)IV(L)=ISAVE  700CONTINUE DISIGN=-DISIGN 800IF(DNORM.EQ.0.0D+00)GOTO1900 0C Q C BEGIN ELIMINATION OF ROW BELOW IV(K).DEN IS THE PIVOT ELEMENT. {C yK1=K+1 0DO1100IM=K1,M C - C BEFORE ACTUALLY ELIMINATING WE CHECK TO SEE IF A(IV(IM),K) HAS C ALREADY BEEN ANNIHILATED. C 0IF(A(IV(IM),K).EQ.0.0D+00)GOTO1100 C YC CACULATE ELIMINATION FACTOR. }C 0DMULT=-A(IV(IM),K) C +hC WE NOW CALCULATE VALUE OF OTHER ELEMENTS IN ROW IV(IM). C 0DO900NN=K1,M ! 9000A(IV(IM),NN)=(DMULT*A(IV(K),NN))/DNORM+A(IV(IM),NN) ;0IF(NRS.LE.0)GOTO1100 0DO1000IN=1,NRS 810000P(IV(IM),IN)=(DMULT*P(IV(K),IN))/DNORM+P(IV(IM),IN) \1100CONTINUE _H1200CONTINUE C qC CALCULATE VALUE OF DETERMINANT. `C ' IF(A(IV(M),M).EQ.0.0D0)GOTO1900 a& DET=DISIGN eIF(IDET.NE.0)CALLDMATDT(A,N,M,DET,IV,IDET) iIF(DET.EQ.0.0D+00)GOTO1900 IF(NRS.LE.0)GOTO2000 0C mQC WE START SOLVING RIGHT HAND SIDES.THE SOLUTION REPLACES THE RIGHT HAND q{C VECTOR. yC Ȍ 1300N1=M-1 uDO1600JJ=1,NRS y-C ګC BEGIN BACK SUBSTITUTION. C  P(IV(M),JJ)=P(IV(M),JJ)/A(IV(M),M) 0DO1500I=1,N1 Y0DSUM=0.0D+00 }0DO1400 J=1,I C14000DSUM=DSUM-A(IV(M-I),M-J+1)*P(I V(M-J+1),JJ) G1500P(IV(M-I),JJ)=(P(IV(M-I),JJ)+DSUM)/A(IV(M-I),M-I) h1600CONTINUE DO1800JJ=1,NRS L0DO1700IND=1,M P 1700A(IND,1)=P(IV(IND),JJ) 0DO1800IND=1,M 1800P(IND,JJ)=A(IND,1) S8RETURN W\ 1900JFLG=1 HIDET=0 2000RETURN 2qEND 6SUBROUTINEMATDT(A,IA,N,DET,IV,IDET) C!SUBROUTINE MATDTISDMATDTFROMTHEUICCSUBROUTINELIBRARY. &REAL*8A(IA,1),DET,B,LOG16 INTEGER*4IV(1),K ,EQUIVALENCE (B,K)  %NUM=16777216 0?LOG16=.120411998265592457D+01 2 QIF(A(IV(N),N).EQ.0.0D+00)GOTO300 {L=0 y DO100 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 YIF((IW.LT.-64).OR .(IW.GT.63))GOTO200 } ?DET=DET*16.0D+00**L IDET=0 GOTO400 h200DET=DET*16.0D+00**(-K) <IDET=L+K & %B=IDET*LOG16 IDET=B ?B=B-DFLOAT(IDET) *?DET=DET*1.0D+01**B ^8GOTO400 \300DET=0.0D+00 HIDET=0 , 400RETURN ?qEND //GO.SYSIN DD * ֝FISHER IRIS DATA #&NR=015 "NC=010 c IP=04 g(1X,F3.1) 0 5.1VARIABLE1A1001 Q 4.9VARIABLE1A1002 k{ 4.7VARIABLE1A1003 oy 4.6VARIABLE1A1004 5.0VARIABLE1A1005 5.4VARIABLE1A1006 s- 4.6VARIABLE1A1007 w 5.0VARIABLE1A1008  4.4VARIABLE1A1009  4.9VARIABLE1A1010 5.4VARIABLE1A1011 Y 4.8VARIABLE1A1012 } 4.8VARIABLE1A1013 ] 4.3VARIABLE1A1014 A 5.8VARIABLE1A1015 Eh 5.7VARIABLE1A1016 I 5.4VARIABLE1A1017 5.1VARIABLE1A1018 J 5.7VARIABLE1A1019 N 5.1VARIABLE1A1020 R 5.4VARIABLE1A1021 8 5.1VARIABLE1A1022 \\ 4.6VARIABLE1A1023 UH 5.1VARIABLE1A1024 Y 4.8VARIABLE1A1025 q 5.0VARIABLE1A1026 0 5.0VARIABLE1A1027 4 5.2VARIABLE1A1028 8& 5.2VARIABLE1A1029  4.7VARIABLE1A1030  4.8VARIABLE1A1031  5.4VARIABLE1A1032 0 5.2VARIABLE1A1033 Q 5.5VARIABLE1A1034 { 4.9VARIABLE1A1035 y 5.0VARIABLE1A1036  5.5VARIABLE1A1037  4.9VARIABLE1A1038 - 4.4VARIABLE1A1039  5.1VARIABLE1A1040  5.0VARIABLE1A1041  4.5VARIABLE1A1042  4.4VARIABLE1A1043 Y 5.0VARIABLE1A1044 } 5.1VARIABLE1A1045  4.8VARIABLE1A1046  5.1VARIABLE1A1047 h 4.6VARIABLE1A1048 5.3VARIABLE1A1049 5.0VARIABLE1A1050 + 7.0VARIABLE1A2051  6.4VARIABLE1A2052  6.9VARIABLE1A2053 8 5.5VARIABLE1A2054 )\ 6.5VARIABLE1A2055 /H 5.7VARIABLE1A2056 ݵ 6.3VARIABLE1A2057 q 4.9VARIABLE1A2058 _ 6.6VARIABLE1A2059 5.2VARIABLE1A2060 & 5.0VARIABLE1A2061 ` 5.9VARIABLE1A2062 ' 6.0VARIABLE1A2063 a 6.1VARIABLE1A2064 d0 5.6VARIABLE1A2065 hQ 6.7VARIABLE1A2066 { 5.6VARIABLE1A2067 y 5.8VARIABLE1A2068 m 6.2VARIABLE1A2069 q 5.6VARIABLE1A2070 - 5.9VARIABLE1A2071 ȫ 6.1VARIABLE1A2072 u 6.3VARIABLE1A2073 y 6.1VARIABLE1A2074 6.4VARIABLE1A2075 Y 6.6VARIABLE1A2076 } 6.8VARIABLE1A2077 6.7VARIABLE1A2078 6.0VARIABLE1A2079 h 5.7VARIABLE1A2080 C 5.5VARIABLE1A2081 G 5.5VARIABLE1A2082 5.8VARIABLE1A2083  6.0VARIABLE1A2084 L 5.4VARIABLE1A2085 O8 6.0VARIABLE1A2086 \ 6.7VARIABLE1A2087 H 6.3VARIABLE1A2088 S 5.6VARIABLE1A2089 Wq 5.5VARIABLE1A2090 5.5VARIABLE1A2091 6.1VARIABLE1A2092 2& 5.8VARIABLE1A2093 6 5.0VARIABLE1A2094  5.6VARIABLE1A2095  5.7VARIABLE1A20960 5.7VARIABLE1A2097 Q 6.2VARIABLE1A2098{ 5.1VARIABLE1A2099 y 5.7VARIABLE1A2100 6.3VARIABLE1A3101 5.8VARIABLE1A3102- 7.1VARIABLE1A3103 6.3VARIABLE1A3104 6.5VARIABLE1A3105  7.6VARIABLE1A3106 4.9VARIABLE1A3107Y 7.3VARIABLE1A3108} 6.7VARIABLE1A3109 7.2VARIABLE1A3110 6.5VARIABLE1A3111h 6.4VARIABLE1A3112 6.8VARIABLE1A3113 5.7VARIABLE1A3114 5.8VARIABLE1A3115< 6.4VARIABLE1A3116& 6.5VARIABLE1A31178 7.7VARIABLE1A3118\ 7.7VARIABLE1A3119$H 6.0VARIABLE1A3120^ 6.9VARIABLE1A3121q 5.6VARIABLE1A3122 7.7VARIABLE1A3123, 6.3VARIABLE1A3124?& 6.7VARIABLE1A3125 7.2VARIABLE1A3126 6.2VARIABLE1A3127# 6.1VARIABLE1A3128=0 6.4VARIABLE1A3129bQ 7.2VARIABLE1A3130f{ 7.4VARIABLE1A3131y 7.9VARIABLE1A3132 6.4VARIABLE1A3133k 6.3VARIABLE1A3134 4o- 6.1VARIABLE1A3135 7.7VARIABLE1A3136 6.3VARIABLE1A3137s 6.4VARIABLE1A3138w 6.0VARIABLE1A3139zY 6.9VARIABLE1A3140[} 6.7VARIABLE1A3141 6.9VARIABLE1A3142 5.8VARIABLE1A3143h 6.8VARIABLE1A3144] 6.7VARIABLE1A3145A 6.7VARIABLE1A3146E 6.3VARIABLE1A3147I 6.5VARIABLE1A3148 6.2VARIABLE1A3149}8 5.9VARIABLE1A3150M\ 3.5VARIABLE21001QH 3.0VARIABLE21002 3.2VARIABLE21003\q 3.1VARIABLE21004U 3.6VARIABLE21005Y 3.9VARIABLE21006& 3.4VARIABLE210070 3.4VARIABLE210084 2.9VARIABLE210098 3.1VARIABLE210100 3.7VARIABLE21011Q 3.4VARIABLE21012{ 3.0VARIABLE21013y 3.0VARIABLE21014 4.0VARIABLE21015 4.4VARIABLE21016- 3.9VARIABLE21017 3.5VARIABLE21018 3.8VARIABLE21019 3.8VARIABLE21020 3.4VARIABLE21021Y 3.7VARIABLE21022} 3.6VARIABLE21023 3.3VARIABLE21024 3.4VARIABLE21025h 3.0VARIABLE21026 3.4VARIABLE21027 3.5VARIABLE21028 3.4VARIABLE21029 3.2VARIABLE21030 3.1VARIABLE21031(8 3.4VARIABLE21032\ 4.1VARIABLE21033H 4.2VARIABLE21034 3.1VARIABLE21035)q 3.2VARIABLE21036/ 3.5VARIABLE21037ݝ 3.6VARIABLE21038& 3.0VARIABLE21039_ 3.4VARIABLE21040 3.5VARIABLE21041 2.3VARIABLE210420 3.2VARIABLE21043@Q 3.5VARIABLE21044{ 3.8VARIABLE21045dy 3.0VARIABLE21046h 3.8VARIABLE21047 3.2VARIABLE21048- 3.7VARIABLE21049m 3.3VARIABLE21050q 3.2VARIABLE22051 3.2VARIABLE22052 3.1VARIABLE22053tY 2.3VARIABLE22054x} 2.8VARIABLE22055 2.8VARIABLE22056 3.3VARIABLE22057h 2.4VARIABLE22058 2.9VARIABLE22059٨ 2.7VARIABLE22060 2.0VARIABLE22061C 3.0VARIABLE22062G 2.2VARIABLE220638 2.9VARIABLE22064\ 2.9VARIABLE22065KH 3.1VARIABLE22066O 3.0VARIABLE22067q 2.7VARIABLE22068 2.2VARIABLE22069S 2.5VARIABLE22070W& 3.2VARIABLE22071 2.8VARIABLE22072 2.5VARIABLE220732 2.8VARIABLE2207450 2.9VARIABLE220759Q 3.0VARIABLE22076{ 2.8VARIABLE22077y 3.0VARIABLE22078 2.9VARIABLE22079 2.6VARIABLE22080 - 2.4VARIABLE22081 2.4VARIABLE22082  2.7VARIABLE22083 2.7VARIABLE22084 3.0VARIABLE22085Y 3.4VARIABLE22086} 3.1VARIABLE22087 2.3VARIABLE22088 3.0VARIABLE22089h 2.5VARIABLE22090 2.6VARIABLE22091 3.0VARIABLE22092 2.6VARIABLE22093  2.3VARIABLE22094 2.7VARIABLE220958 3.0VARIABLE22096.\ 2.9VARIABLE22097|H 2.9VARIABLE22098 2.5VARIABLE22099q 2.8VARIABLE22100$ 3.3VARIABLE23101^ 2.7VARIABLE23102& 3.0VARIABLE23103 2.9VARIABLE23104, 3.0VARIABLE23105? 3.0VARIABLE231060 2.5VARIABLE23107Q 2.9VARIABLE23108:{ 2.5VARIABLE23109=y 3.6VARIABLE23110b 3.2VARIABLE23111f 2.7VARIABLE23112- 3.0VARIABLE23113 2.5VARIABLE23114k 2.8VARIABLE23115o 3.2VARIABLE23116 3.0VARIABLE23117Y 3.8VARIABLE23118~} 2.6VARIABLE23119v 2.2VARIABLE23120z 3.2VARIABLE23121[h 2.8VARIABLE23122 2.8VARIABLE23123 2.7VARIABLE23124 3.3VARIABLE23125] 3.2VARIABLE23126A 2.8VARIABLE23127D8 3.0VARIABLE23128H\ 2.8VARIABLE23129H 3.0VARIABLE23130} 2.8VARIABLE23131Mq 3.8VARIABLE23132Q 2.8VARIABLE23133 2.8VARIABLE23134\& 2.6VARIABLE23135U 3.0VARIABLE23136Y 3.4VARIABLE23137 3.1VARIABLE231380 3.0VARIABLE231393Q 3.1VARIABLE231407{ 3.1VARIABLE23141 4y 3.1VARIABLE23142 2.7VARIABLE23143 3.2VARIABLE23144- 3.3VARIABLE23145 3.0VARIABLE23146 2.5VARIABLE23147 3.0VARIABLE23148 3.4VARIABLE23149Y 3.0VARIABLE23150} 1.4VARIABLE3/1001 1.4VARIABLE3/1002 1.3VARIABLE3/1003h 1.5VARIABLE3/1004 1.4VARIABLE3/1005 1.7VARIABLE3/1006 1.4VARIABLE3/1007 1.5VARIABLE3/1008 1.4VARIABLE3/10098 1.5VARIABLE3/1010\ 1.5VARIABLE3/1011H 1.6VARIABLE3/1012( 1.4VARIABLE3/1013q 1.1VARIABLE3/1014 1.2VARIABLE3/1015 1.5VARIABLE3/1016)& 1.3VARIABLE3/1017/ 1.4VARIABLE3/1018 1.7VARIABLE3/1019 1.5VARIABLE3/1020%0 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