CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC           
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C                                                                   C           
C     CLUSPAC:  Computer Programs for Mixture-Model Clustering      C           
C                                                                   C           
C          COPYRIGHT (C) 1991, 1992   STANLEY LOUIS SCLOVE          C           
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CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC           
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C                                                                   C           
C       CLUSPAC LIBRARY
C       PROGRAM  MIX1CMA                                            C           
C                                                                   C           
C       THE PROGRAMS MIX* CLUSPAC IN ISOPAC ARE FOR CLUSTERING DATA C           
C  BY ITERATIVE MAXIMIZATION OF THE MIXTURE-MODEL LIKELIHOOD        C           
C                                                                   C           
C                 N   K                                             C           
C                --- --                                             C           
C          L  =  | | >  p(c)*f(x(i)|c),                             C           
C                | | --                                             C           
C                i=1 c=1                                            C           
C                                                                   C           
C  WHERE                                                            C           
C                                                                   C           
C       N  =  NUMBER OF OBSERVATIONS ("SAMPLE SIZE"),               C           
C       K  =  NUMBER OF CLUSTERS,                                   C           
C       x(i) = i-TH OBSERVATION, i = 1,2,...,N,                     C           
C       F(x|c) = VALUE AT x OF THE c-TH CLASS-CONDITIONAL           C           
C                DENSITY FUNCTION (c=1,2,...,K)                     C           
C  AND                                                              C           
C       p(c) = PRIOR PROBABILITY OF CLASS c.                        C           
C                                                                   C           
C                                                                   C           
C       REFERENCE FOR CLUSTERING BY MIXTURE MODEL:                  C           
C                                                                   C           
C       Wolfe, J. H. (1970).  Pattern clustering by multivariate    C           
C  mixture analysis.  Multivariate Behavioral Research 5, 329-350.  C           
C                                                                   C           
C                                                                   C           
C       THE "1" IN THE PROGRAM NAME  "MIX1CMA"  MEANS THAT          C           
C  THE PROGRAM IS FOR UNIVARIATE (1-DIMENSIONAL) DATA               C           
C  (DATA ON THE LINE); THE "CM" MEANS THAT A COMMON VARIANCE IS     C           
C  ASSUMED ACROSS CLUSTERS; AND THE "A" INDICATES THAT THERE IS     C           
C  AUTOMATIC SETTING OF NUMBERS OF CLUSTERS AND INITIAL MEANS.      C           
C                                                                   C           
C                                                                   C           
C          PROGRAMMED BY                                            C           
C              DR. STANLEY L. SCLOVE                 312/996-2681   C           
C              DEPARTMENT OF                                        C           
C                 INFORMATION & DECISION SCIENCES         M/C 294   C           
C              COLLEGE OF BUSINESS ADMINISTRATION                   C           
C              UNIVERSITY OF ILLINOIS  AT CHICAGO                   C           
C              601 S MORGAN ST           
C              CHICAGO, IL  60607-7124                              C           
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C                                                                   C           
C          VERSION 1.3   21-MAY-91                                  C           
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C     
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C                                                                   C           
C          RESTRICTIONS (CAN BE MODIFIED):                          C           
C     N, SAMPLE SIZE, AT MOST 999;                                  C           
C     K, NUMBER OF CLUSTERS, AT MOST 29;                            C           
C     ITER, MAXIMUM NUMBER OF ITERATIONS, 20.                       C           
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C                                                                   C           
C                                                                   C           
C     CONTROL CARDS:                                                            
C                                                                               
C     (1) DATASET TITLE                                                         
C     (2) N, IN FORMAT (2X,I4)                                                  
C     (3) FMT, IN FORMAT (18A4), E.G.,  (1X,F4.1).                              
C         ALLOW AT LEAST ONE BLANK IN FMT:  IT WILL ALSO BE USED                
C         FOR OUTPUT, WHERE CC1 IS FOR CARRIAGE CONTROL.                        
C         ALLOW A CC FOR THE DECIMAL POINT ON OUTPUT, WHETHER OR NOT           
C         THERE IS ONE ON INPUT.                                                
C     (4) DATA, IN FORMAT SPECIFIED BY FMT                                      
C                                                                               
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C                                                                   C           
CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC           
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      DIMENSION X(999),XMNDSQ(999),ICLUS(999),IOTA(999)                         
      DIMENSION XJ(9,9)                                                         
      DIMENSION DSQ(29),C(29),SUM(29)                                           
      DIMENSION TITLE(18)                                                       
      DIMENSION B(29),NC(29),XMEAN(29)                                          
      DIMENSION FMT(18)                                                         
      DIMENSION SS(29),SSD(29)                                                  
      DIMENSION SD(29)                                                          
      DIMENSION VAR(29)                                                         
      DIMENSION ICLSOL(999)                                                     
      DIMENSION F(999,29)                                                       
      DIMENSION P(29), XNC(29)                                                  
      DIMENSION PP(29,999)                                                      
      DIMENSION XMXPR(999)                                                      
      DIMENSION DENOM(999)                                                      
      DIMENSION AICVEC(29),SCHVEC(29),XKSVEC(29)                                
C                                                                               
      DOUBLE PRECISION SUM,SS,F,P,PP                                            
C                                                                               
C     CONTROL CARDS:                                                            
C                                                                               
C     (1) DATASET TITLE                                                         
C     (2) N, IN FORMAT (2X,I4)                                                  
C     (3) FMT, IN FORMAT (18A4), E.G.,  (1X,F4.1).                              
C         ALLOW AT LEAST ONE BLANK IN FMT:  IT WILL ALSO BE USED                
C         FOR OUTPUT, WHERE CC1 IS FOR CARRIAGE CONTROL.                        
C         ALLOW A CC FOR THE DECIMAL POINT ON OUTPUT, WHETHER OR NOR            
C         THERE IS ONE ON INPUT.                                                
C     (4) DATA, IN FORMAT SPECIFIED BY FMT