C @(#)progress.for	19.1 (ES0-DMD) 02/25/03 14:29:42
C===========================================================================
C Copyright (C) 1995 European Southern Observatory (ESO)
C
C This program is free software; you can redistribute it and/or 
C modify it under the terms of the GNU General Public License as 
C published by the Free Software Foundation; either version 2 of 
C the License, or (at your option) any later version.
C
C This program is distributed in the hope that it will be useful,
C but WITHOUT ANY WARRANTY; without even the implied warranty of
C MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
C GNU General Public License for more details.
C
C You should have received a copy of the GNU General Public 
C License along with this program; if not, write to the Free 
C Software Foundation, Inc., 675 Massachusetss Ave, Cambridge, 
C MA 02139, USA.
C
C Corresponding concerning ESO-MIDAS should be addressed as follows:
C	Internet e-mail: midas@eso.org
C	Postal address: European Southern Observatory
C			Data Management Division 
C			Karl-Schwarzschild-Strasse 2
C			D 85748 Garching bei Muenchen 
C			GERMANY
C===========================================================================
C
CC
CC     PROGRESS : PROGRAM FOR ROBUST REGRESSION
CC-----------------------------------------------------------------------------
CC-----LIST OF VARIABLES AND ARRAYS IN THIS PROGRAM
CC-----------------------------------------------------------------------------
CC     NDXY           = MAXIMAL NUMBER OF CASES
CC     NMXV           = MAXIMAL NUMBER OF EXPLANATORY VARIABLES
CC     NDXX           = NMXV+1 = MAXIMAL NUMBER OF COEFFICIENTS,
CC                               INCLUDING INTERCEPT
CC     JDMB           = NMXV*(NMXV+1)
CC-----------------------------------------------------------------------------
CC     X(NDXX,NDXY)   = MATRIX OF THE VALUES OF THE EXPLANATORY
CC                      VARIABLES (TRANSPOSED DESIGN MATRIX)
CC     Y(NDXY)        = VECTOR WITH THE VALUES OF
CC                      THE RESPONSE VARIABLE
CC     RESDU(NDXY)    = VECTOR FOR STORING THE RESIDUALS
CC                      (EXCEPT IN SUBROUTINE STATIS, WHERE IT IS
CC                      A WORKING VECTOR)
CC     WEIGHTS(NDXY)  = WEIGHT ASSIGNED TO EACH OBSERVATION
CC     AW(NDXY)       = WORKING VECTOR
CC     A(NMXV+1)      = VECTOR OF REGRESSION COEFFICIENTS  (LS OR RLS)
CC     DA(NMXV+1)     = VECTOR WITH THE STAND. DEVIATION OF THE COEFFICIENTS
CC     DRCTA(NMXV+1)  = VECTOR OF COEFFICIENTS FOR THE LMS
CC     XMED(NMXV+1)   = VECTOR WITH THE MEDIANS OF ALL VARIABLES
CC     XMAD(NMXV+1)   = VECTOR WITH MEDIAN ABSOLUTE DEVIATIONS
CC     UHYB(NDXY)     = VECTOR WITH THE RESISTANT DIAGNOSTICS
CC     C(NMXV,NMXV+1) = MATRIX USED FOR - STORING THE COEFFICIENTS
CC                                        OF THE LINEAR SYSTEM TO BE SOLVED
CC                                        AT EACH REPLICATION
CC                                      - STORING THE SPEARMAN
CC                                        CORRELATION COEFFICIENTS
CC     H(NMXV,NMXV+1) = MATRIX USED FOR - STORING THE VARIANCE-COVARIANCE
CC                                        MATRIX OF THE LS AND RLS COEFFICIENTS
CC                                      - STORING THE PEARSON
CC                                        CORRELATION COEFFICIENTS
CC     HVEC(JDMB)     = AUXILIARY VECTOR
CC-----------------------------------------------------------------------------
CC     NMVAL(NDXY)    = VECTOR WITH THE ORIGINAL INDEX OF THE CASES
CC     JNDVC(NMXV+1)  = VECTOR - CONTAINING THE INDEX OF THE CASES
CC                               CONSIDERED IN A RANDOM SUBSAMPLE
CC                             - COUNTING THE NUMBER OF MISSING CASES FOR
CC                               EACH VARIABLE
CC     VALMS(NMXV+1)  = VECTOR WITH THE "MISSING VALUE CODES"
CC     JNDEX(NMXV+1)  = JNDEX(J), (J=1,NVAR+1) IS 1 IF VAR(J) CONTAINS MISSING
CC                      VALUES AND IS 0 OTHERWISE
CC                      (CONSIDERED IN A RANDOM SUBSAMPLE)
CC     JNDA(NMXV)     = VECTOR CONTAINING THE INDEX OF THE CASES
CC                      WHICH YIELD THE "BEST" LMS SOLUTION
CC     JPLACE(NMXV+1) = VECTOR CONTAINING THE POSITIONS OF THE VARIABLES
CC                      USED IN THE ANALYSIS (FROM THE TOTAL DATA SET)
CC     LAB(NMXV+1)    = VECTOR WITH THE LABEL OF EACH VARIABLE
CC-----------------------------------------------------------------------------
CC-----LIST OF MOST IMPORTANT PARAMETERS:
CC-----------------------------------------------------------------------------
CC     FNAMEA         = NAME OF THE FILE WHERE THE INPUT HAS TO BE READ
CC     FNAMEB         = NAME OF THE FILE WHERE THE OUTPUT HAS TO BE WRITTEN
CC     FNAMEC         = NAME OF THE FILE WHERE THE DATA HAS TO BE SAVED
CC     LUA            = LOGICAL UNIT FOR 'FNAMEA'
CC     LUB            = LOGICAL UNIT FOR 'FNAMEB'
CC     LUC            = LOGICAL UNIT FOR 'FNAMEC'
CC     NVAR           = NUMBER OF COEFFICIENTS (INCLUDING THE CONSTANT TERM
CC                      IF THERE IS ONE)
CC     ANVAR              = REAL VALUE OF NVAR
CC     NVSB              = NVAR-1
CC     NVAD              = NVAR+1
CC     NCAS              = NUMBER OF CASES
CC     AL              = REAL VALUE OF NCAS
CC     ALGO              = CHARACTER WHICH IS 'E' FOR THE EXTENSIVE SEARCH
CC                        VERSION AND 'Q' FOR THE QUICK VERSION OF THE ALGORITHM
CC     NZWE              = NUMBER OF NON-ZERO WEIGHTS
CC     RSQ              = R SQUARED (COEFFICIENT OF DETERMINATION)
CC     AVW              = AVERAGE WEIGHT
CC     FCKW              = OBJECTIVE FUNCTION VALUE
CC     JCST              = INTEGER WHICH IS 1 IN THE CASE OF A MODEL WITH
CC                        INTERCEPT AND 0 OTHERWISE
CC     JPLT              = PLOT OPTION (0=NONE, 1=RESIDUAL, 2=INDEX, 3=BOTH)
CC     JPRT              = PRINT OPTION (0=SMALL, 1=MEDIUM-SIZED, 2=LARGE)
CC     MVAL              = OPTION FOR MISSING VALUES (0=NONE, 1=DELETE, 2=REPLACE)
CC     YNSAVE              = CHARACTER (YES OR NO) NEEDED FOR THE INTERACTIVE INPUT
CC     JHEAD              = TITLE FOR THE OUTPUT
CC     NZWE              = NUMBER OF NON-ZERO WEIGHTS
CC     PREC              = PRECISION OF THE CALCULATIONS
CC     JEY,JLP              = INTEGER VARIABLES USED FOR COUNTING THE NUMBER OF
CC                        REPLICATIONS IN THE LMS ALGORITHM
CC     JPLXY              = OPTION FOR XY PLOT (0=NO XY PLOT, 1=OTHERWISE)
CC     JREP              = NUMBER OF RANDOM SUBSAMPLES TO BE CONSIDERED
CC     JREG              = WHICH REGRESSION ? (1=LS, 2=LMS, 3=RLS)
CC     JDIAG              = OPTION FOR DIAGNOSTICS (0=NO DIAGNOSTICS, ELSE 1)
CC     JQU              = THE RANK OF THE ABSOLUTE RESIDUAL TO BE MINIMIZED
CC     NSTOP              = 1 MEANS STOP THE ANALYSIS, OTHERWISE NSTOP=0
CC-----------------------------------------------------------------------------
CC-----LIST OF SUBROUTINES AND FUNCTIONS
CC-----------------------------------------------------------------------------
CC     SUBROUTINE WRDATA  :CREATES FIRST PART OF THE OUTPUT
CC     SUBROUTINE WRDATB  :CREATES SECOND PART OF THE OUTPUT
CC     SUBROUTINE SUBHAT  :CALCULATION OF THE HAT MATRIX
CC     SUBROUTINE PRTRLS  :PRINTS THE RLS (OR LS) RESULTS
CC     SUBROUTINE SUBLMS  :ALGORITHM FOR CALCULATING THE LMS ESTIMATES
CC     SUBROUTINE PRTLMS  :PRINTS THE LMS RESULTS
CC     SUBROUTINE RDAT          :INTERACTIVE INPUT WITH READING OF THE DATA
CC     FUNCTION JNTGR          :TRANSFORMS A CHARACTER INTO AN INTEGER
CC     SUBROUTINE SMISSING:HANDLES MISSING VALUES
CC     SUBROUTINE SUBREP  :CALCULATES THE NUMBER OF REPLICATIONS
CC                           FOR THE LMS ALGORITHM
CC     SUBROUTINE STATIS  :STANDARDIZATION OF THE OBSERVATIONS
CC                           AND CALCULATION OF SOME STATISTICS
CC     SUBROUTINE CORR    :CALCULATES SPEARMAN RANK CORRELATION COEFFICIENT
CC     FUNCTION PULL      :SEARCHES THE KTH VALUE IN A VECTOR
CC     FUNCTION AMDAN     :CALCULATES THE MEDIAN
CC     FUNCTION RSQU      :CALCULATES COEFFICIENT OF DETERMINATION
CC                         OF LS AND RLS
CC     SUBROUTINE RESTT   :CALCULATES RESIDUALS AND LMS SCALE
CC     SUBROUTINE RANGS   :SORTS A VECTOR
CC     SUBROUTINE RDUAL   :GENERATES A TABLE WITH OBSERVED AND ESTIMATED
CC                         RESPONSE, RESIDUALS AND STANDARDIZED RESIDUALS
CC                         AND (IF WANTED) CALLS RESIDUAL PLOTS
CC     SUBROUTINE SHHLF   :CALCULATES LMS IN ONE DIMENSION
CC     SUBROUTINE TRC     :RETRANSFORMATION OF THE VARIANCE-COVARIANCE MATRIX
CC     SUBROUTINE SCHCV   :PRINTS THE VARIANCE-COVARIANCE MATRIX
CC     SUBROUTINE RTRAN   :RETRANSFORMATION OF THE REGRESSION COEFFICIENTS
CC     SUBROUTINE RANPN   :RANDOM NUMBER GENERATOR
CC     SUBROUTINE GENPN   :GENERATES ALL COMBINATIONS OF P POINTS OUT OF N
CC     SUBROUTINE EQUAT   :SOLVES A SYSTEM OF LINEAR EQUATIONS
CC     SUBROUTINE LSL     :LS OR RLS IN THE CASE P=1
CC     SUBROUTINE FCN     :PUTS A ROW OF THE MATRIX X IN A VECTOR
CC     SUBROUTINE LSREG   :CALCULATES LS OR RLS REGRESSION
CC     FUNCTION QLSRG     :CALCULATES LS OR RLS OBJECTIVE FUNCTION
CC     SUBROUTINE MATNV   :MATRIX INVERSION
CC     SUBROUTINE LCAT    :TREATS THE LOCATION AND SCALE ESTIMATORS
CC     SUBROUTINE SMISLOC :TREATMENT OF MISSING VALUES IN THE CASE OF LOCATION
CC     SUBROUTINE MOVE    :MOVES CHARACTERS TO THE RIGHT (IN A LABEL)
CC     FUNCTION PVAL      :CALCULATES THE P-VALUE ASSOCIATED WITH AN F-VALUE
CC     FUNCTION PTVAL     :CALCULATES THE P-VALUE ASSOCIATED WITH A T-VALUE
CC     FUNCTION SUM       :FUNCTION NEEDED IN PVAL
CC     FUNCTION ODD       :FUNCTION NEEDED IN PVAL
CC     SUBROUTINE GRAF    :MAKES A SCATTERGRAM, AND RESIDUAL AND/OR INDEX PLOTS
CC-----------------------------------------------------------------------------
CC
       PROGRAM   PROGRESS

       INCLUDE 'MID_REL_INCL:implicit.inc'

       CHARACTER YNSAVE,ALGO
       CHARACTER*30 FNAMEA,FNAMEB,FNAMEC
       CHARACTER*60 JHEAD

CC     ------------------------------------------------------------------------
CC     IF YOU LIKE TO CHANGE THE DIMENSIONS OF THE ARRAYS, THEN YOU
CC     ONLY HAVE TO ADAPT THE VALUES IN THE FOLLOWING NINE LINES:
CC     ------------------------------------------------------------------------
       DIMENSION X(21,3000),Y(3000),RESDU(3000)
       DIMENSION AW(3000),UHYB(3000)
       DIMENSION JNDVC(21),VALMS(21),JNDEX(21)
       DIMENSION NMVAL(3000),WEIGHTS(3000)
       DIMENSION A(21),DA(21),JNDA(20),JPLACE(21)
       DOUBLE PRECISION H(20,21),HVEC(420)
       DOUBLE PRECISION DTERM
       DIMENSION DRCTA(21),XMED(21),XMAD(21)
       DIMENSION C(20,21)
       CHARACTER*10 LAB(21)
       INTEGER      OUTN1,OUTN2
       INTEGER ISTAT
       CHARACTER*80 OUTEXT

       INCLUDE 'MID_INCLUDE:st_def.inc'
       COMMON  /VMR/ MADRID
       INCLUDE 'MID_INCLUDE:st_dat.inc'

       NMXV=20
       NDXY=3000

CC     ------------------------------------------------------------------------
CC     INITIALIZATIONS
CC     ------------------------------------------------------------------------

       CALL STSPRO('progress')

       LUA=1
       LUB=2
       LUC=3
       NDXX=NMXV+1
       JDMB=NMXV*NDXX
       NZWE=0
       PREC=1.0E-6
       JLP=0
       JPLXY=0
       JREG=0
       NSTOP=0
       DO 5 J=1,NMXV
       JNDA(J)=0
 5     CONTINUE
CC     ------------------------------------------------------------------------
CC     READ THE DATA
CC     ------------------------------------------------------------------------
       CALL RMIDAT(NCAS,NVAR,JCST,JPRT,NVSB,NVAD,VALMS,
     1 X,Y,JPLT,JNDEX,PREC,JPLACE,LAB,XMED,XMAD,AW,NMVAL,
     1 RESDU,WEIGHTS,NDXX,NDXY,MVAL,NMXV,LUA,LUB,LUC,JHEAD,
     1 YNSAVE,JDIAG,ALGO,NSTOP,FNAMEA,FNAMEB,FNAMEC,OUTN1,OUTN2)
       IF (NSTOP.EQ.1) GOTO 30
       AL=NCAS
       ANVAR=NVAR
CC     ------------------------------------------------------------------------
CC     CREATE THE BEGINNING OF THE OUTPUT: THE SELECTED OPTIONS
CC     ------------------------------------------------------------------------
       CALL WRDATA(NVAR,NCAS,JCST,MVAL,JPRT,ALGO,YNSAVE,FNAMEA,FNAMEB,
     1 FNAMEC,JHEAD,LUB)
CC     ------------------------------------------------------------------------
CC     IF THE DATA CONTAIN MISSING VALUES, THEN TREAT THEM
CC     ------------------------------------------------------------------------
       IF (MVAL.NE.0) THEN
       CALL SMISSING(NVAR,NCAS,NDXX,NDXY,JCST,X,Y,AW,NMVAL,MVAL,
     1 JNDEX,JNDVC,VALMS,NSTOP,LAB,JPRT,LUB)
       IF (NSTOP.EQ.1) GOTO 20
       ENDIF
CC     ------------------------------------------------------------------------
CC     CREATE SECOND PART OF THE OUTPUT: THE DATA AND AN X-Y PLOT
CC     ------------------------------------------------------------------------
       CALL WRDATB(NVAR,NCAS,NDXX,NDXY,JCST,MVAL,LAB,NMVAL,X,Y,
     1 AW,JPLT,JPRT,JREG,JHEAD,LUB)
CC     ------------------------------------------------------------------------
CC     STANDARDIZATION OF THE DATA (WITH OPTIONAL PRINTING)
CC     AND CALCULATION OF SOME STATISTICS ON THE VARIABLES
CC     (IN THIS SUBROUTINE "RESDU" IS USED AS A WORKING VECTOR)
CC     ------------------------------------------------------------------------
       CALL STATIS(X,Y,XMED,XMAD,RESDU,WEIGHTS,AW,NMVAL,C,H,JNDVC,
     1 NSTOP,NVAR,NVAD,NVSB,NCAS,JCST,JPRT,NDXX,NDXY,LUB,NMXV,
     1 PREC,LAB)
       IF (NSTOP.EQ.1) GOTO 20
CC     ------------------------------------------------------------------------
CC     CALCULATION OF THE LS ESTIMATES
CC     ------------------------------------------------------------------------
       IF (NCAS.LE.(NVAR*2)) THEN
          CALL STTPUT('TOO MANY COEFFICIENTS ACCORDING TO THE ',ISTAT)
          CALL STTPUT('NUMBER OF CASES. NUMBER OF CASES',ISTAT) 
          WRITE(OUTEXT,8050) NCAS,NVAR
          CALL STTPUT(OUTEXT,ISTAT)
          CALL STTPUT('THE NUMBER OF CASES MUST BE TWICE THE NUMBER
     1 OF COEFFICIENTS.',ISTAT)
          IF (JCST.EQ.1) CALL STTPUT(' (INCLUDING THE 
     1 CONSTANT TERM!)',ISTAT)
          GOTO 20
       ENDIF
       JREG=1
       IF (NVAR.EQ.1) THEN
       CALL LSL(NCAS,NDXY,X,Y,WEIGHTS,A,FCKW,H,NMXV,NDXX)
       ELSE
       CALL LSREG(NDXX,NDXY,NMXV,NVAR,NCAS,NVAR,A,X,Y,WEIGHTS,DA,
     1 H,FCKW,HVEC,JDMB,JNDEX)
       ENDIF
CC     ------------------------------------------------------------------------
CC     RETRANSFORMATION OF THE LS ESTIMATES
CC     ------------------------------------------------------------------------
       CALL RTRAN(NVAR,JCST,NVSB,NVAD,NDXX,XMED,XMAD,A,NVAD,FCKW)
       CALL TRC(H,DA,NMXV,NDXX,NDXY,NVAR,JCST,NVSB,NVAD,XMED,XMAD)
CC     ------------------------------------------------------------------------
CC     PRINTING THE LS RESULTS WITH THE REQUESTED OPTIONS
CC     ------------------------------------------------------------------------
       CALL PRTRLS(NVAR,NCAS,JCST,NVSB,NVAD,NDXX,NDXY,NMXV,
     1 XMED,XMAD,A,DA,H,AW,RESDU,WEIGHTS,X,Y,NMVAL,AVW,NZWE,FCKW,
     1 JREG,JPRT,JPLT,JDIAG,JHEAD,LAB,PREC,LUB)
CC     ------------------------------------------------------------------------
CC     CALCULATION OF LMS REGRESSION
CC     ------------------------------------------------------------------------  
C       CALL STTPUT('',ISTAT)
       CALL STTPUT(' ALGORITHM FOR CALCULATING THE LEAST MEDIAN
     1 OF SQUARES IS STARTED.   ',ISTAT)

       CALL SUBLMS(NVAR,NCAS,JCST,NDXX,NDXY,NMXV,PREC,X,Y,
     1 XMED,XMAD,JDIAG,ALGO,FNAMEB,JQU,JREP,DRCTA,JNDA,RESDU,WEIGHTS,
     1 UHYB,AVW,NZWE,RSQ,JHYB,JDMB,JERD,JLP,NERR,DTERM,C,HVEC,JNDVC,AW)
CC     ------------------------------------------------------------------------
CC     RETRANSFORMATION OF THE LMS ESTIMATES
CC     ------------------------------------------------------------------------
       CALL RTRAN(NVAR,JCST,NVSB,NVAD,NDXX,XMED,XMAD,DRCTA,NVAD,FCKW)
       DRCTA(NVAD)=DRCTA(NVAD)*XMAD(NVAD)
CC     ------------------------------------------------------------------------
CC     PRINTING THE LMS RESULTS WITH THE REQUESTED OPTIONS
CC     ------------------------------------------------------------------------
       CALL PRTLMS(NVAR,NCAS,JCST,NVSB,NVAD,NDXX,NDXY,NMXV,JNDVC,XMED,
     1 XMAD,DRCTA,AW,RESDU,WEIGHTS,X,Y,NMVAL,UHYB,AVW,NZWE,RSQ,JREG,
     1 JPRT,JPLT,JREP,JERD,JLP,JQU,JHYB,JDIAG,NSTOP,JHEAD,LAB,PREC,LUB)
       IF (NSTOP.NE.1) THEN
CC     ------------------------------------------------------------------------
CC     CALCULATION OF RLS REGRESSION
CC     ------------------------------------------------------------------------
       JREG=3
       CALL STTPUT('PROGRESS IS CURRENTLY CALCULATING REWEIGHTED LEAST
     1 SQUARES ...',ISTAT)
       NNUL=NZWE
       DO 10 J=1,NDXX
       A(J)=0.0
       DA(J)=0.0
       DO 10 JNC=1,NMXV
  10   H(JNC,J)=0.D0
       IF (NVAR.EQ.1) THEN
       CALL LSL(NCAS,NDXY,X,Y,WEIGHTS,A,FCKW,H,NMXV,NDXX)
       ELSE
       CALL LSREG(NDXX,NDXY,NMXV,NVAR,NCAS,NVAR,A,X,Y,WEIGHTS,DA,
     1 H,FCKW,HVEC,JDMB,JNDEX)
       ENDIF
CC     ------------------------------------------------------------------------
CC     RETRANSFORMATION OF THE RLS ESTIMATES
CC     ------------------------------------------------------------------------
       CALL RTRAN(NVAR,JCST,NVSB,NVAD,NDXX,XMED,XMAD,A,NVAD,FCKW)
       CALL TRC(H,DA,NMXV,NDXX,NDXY,NVAR,JCST,NVSB,NVAD,XMED,XMAD)
CC     ------------------------------------------------------------------------
CC     PRINTING THE RLS RESULTS WITH THE REQUESTED OPTIONS
CC     ------------------------------------------------------------------------
       CALL PRTRLS(NVAR,NCAS,JCST,NVSB,NVAD,NDXX,NDXY,NMXV,
     1 XMED,XMAD,A,DA,H,AW,RESDU,WEIGHTS,X,Y,NMVAL,AVW,NZWE,FCKW,
     1 JREG,JPRT,JPLT,JDIAG,JHEAD,LAB,PREC,LUB)

CC-----UPDATES MIDAS TABLES
       CALL MIDUAL(A,JKEUS,NVAD,NCAS,NVAR,JCST,JPRT,NVAD,LUB,PREC,JREG,
     1 X,Y,RESDU,WEIGHTS,XMED,XMAD,NZWE,AVW,JPLT,AW,NMVAL,NDXX,NDXY,
     1 JHEAD,LAB,LUA,OUTN1,OUTN2)


       ENDIF

CC     END OF THE RUN
       CALL STTPUT('                                         ',ISTAT)
       CALL STTPUT(' THE RUN HAS SUCCESSFULLY BEEN EXECUTED. ',ISTAT)
       CALL STTPUT('                                         ',ISTAT)
     
 20    IF (YNSAVE.EQ.'Y') THEN
         WRITE (OUTEXT,8020) FNAMEC
         CALL STTPUT(OUTEXT,ISTAT)
       ENDIF	 
       IF (FNAMEA.NE.'CON') THEN
         WRITE(OUTEXT,8030) FNAMEA
         CALL STTPUT(OUTEXT,ISTAT)
       ENDIF	 
       IF (FNAMEB.NE.'CON'.AND.FNAMEB.NE.'PRN') THEN
         WRITE(OUTEXT,8040)FNAMEB
         CALL STTPUT(OUTEXT,ISTAT)
       ENDIF	 
CC     -----------------------------------------------------------------
CC     FORMATS
CC     -----------------------------------------------------------------
 8020  FORMAT(' THE DATA IS SAVED IN FILE : ',A30)
 8030  FORMAT(' THE DATA HAS BEEN READ FROM FILE : ',A30)
 8040  FORMAT(' THE OUTPUT HAS BEEN WRITTEN IN FILE : ',A30)
 8050  FORMAT( 8X,'= ',I5,' NUMBER OF COEFFICIENTS = ',I5)

 30    CONTINUE
       CALL STSEPI
       END
CC     ------------------------------------------------------------------------
CC     SUBROUTINE FOR CREATING THE BEGINNING OF THE OUTPUT:
CC                      - DESCRIPTION OF THE SELECTED OPTIONS
CC     ------------------------------------------------------------------------
       SUBROUTINE WRDATA(NVAR,NCAS,JCST,MVAL,JPRT,ALGO,YNSAVE,FNAMEA,
     1 FNAMEB,FNAMEC,JHEAD,LUB)

       INCLUDE 'MID_REL_INCL:implicit.inc'

       CHARACTER ALGO,YNSAVE
       CHARACTER*30 FNAMEA,FNAMEB,FNAMEC
       CHARACTER*60 JHEAD
       WRITE(LUB,8050)
       WRITE(LUB,8040)JHEAD
       IF (JCST.EQ.0) THEN
          WRITE(LUB,8000) NCAS,NVAR	  
       ELSEIF (JCST.NE.0) THEN
          WRITE(LUB,8010) NCAS,NVAR
       ENDIF	  
       IF (ALGO.EQ.'Q') THEN
          WRITE(LUB,8020)	  
       ELSEIF (ALGO.EQ.'E') THEN
          WRITE(LUB,8030)
       ENDIF	  
       IF (FNAMEB.EQ.'CON') PAUSE ' '
CC-----TREATMENT OF MISSING VALUES
       IF (MVAL.EQ.0) THEN
          WRITE(LUB,8060)
       ELSEIF (MVAL.EQ.1) THEN
          WRITE(LUB,8070)
       ELSEIF (MVAL.EQ.2) THEN
          WRITE(LUB,8080)
       ENDIF  
       IF (JPRT.EQ.0) THEN
          WRITE(LUB,8090)
       ELSEIF (JPRT.EQ.1) THEN 
          WRITE(LUB,8100)
       ELSEIF (JPRT.EQ.2) THEN
          WRITE(LUB,8110)
       ENDIF  
       IF (YNSAVE.EQ.'Y') THEN
          WRITE(LUB,8120) FNAMEC
       ENDIF  
       IF (FNAMEA.NE.'CON') THEN
          WRITE(LUB,8130) FNAMEA
       ENDIF  
 8000  FORMAT(//' REGRESSION WITHOUT A CONSTANT TERM.'//
     1 ' NUMBER OF CASES',8X,'= ',I5/
     1 ' NUMBER OF COEFFICIENTS = ',I5)
 8010  FORMAT(/' REGRESSION WITH A CONSTANT TERM.'//
     1 ' NUMBER OF CASES',8X,'= ',I5/
     1 ' NUMBER OF COEFFICIENTS (INCLUDING CONSTANT TERM) = ',I5)
 8020  FORMAT(/' THE QUICK VERSION WILL BE USED.')
 8030  FORMAT(/' THE EXTENSIVE SEARCH VERSION WILL BE USED.')
 8040  FORMAT(/' DATA SET = ',A60)
 8050  FORMAT(//30X,19('*')/30X,'* P R O G R E S S *'/
     1 30X,19('*')///' This program performs a robust regression',
     1 ' analysis based on'/' the least median of squares',
     1 ' (LMS) method as described in'/3X,
     1 ' P. Rousseeuw (1984), Least Median of Squares Regression',/
     1 '    Journal of the American Statistical Association, 79,',
     1' 871-880.'/' A user manual to this program is the book:'/
     1 '    P. Rousseeuw and A. Leroy (1987), Robust Regression'/
     1 '    and Outlier Detection, Wiley, New York.'/)
 8060  FORMAT(/' THERE ARE NO MISSING VALUES.')
 8070  FORMAT(/' TREATMENT OF MISSING VALUES IN OPTION 1:',
     1 ' THIS MEANS THAT A CASE WITH A/14H MISSING VALUE',
     1 ' FOR AT LEAST ONE VARIABLE WILL BE DELETED.'/)
 8080  FORMAT(/' TREATMENT OF MISSING VALUES IN OPTION 2:'/
     1 ' FIRST, A CASE WITH A MISSING VALUE FOR THE RESPONSE VARIABLE'
     1 /' OR FOR ALL EXPLANATORY VARIABLES WILL BE DELETED.'/
     1 ' THEN, A MISSING VALUE FOR A VARIABLE WILL BE REPLACED BY'/
     1 ' THE MEDIAN OF THE NON-MISSING VALUES .'/)
 8090  FORMAT(/' SMALL OUTPUT IS WANTED.')
 8100  FORMAT(/' MEDIUM-SIZED OUTPUT IS WANTED.')
 8110  FORMAT(/' LARGE OUTPUT IS WANTED.')
 8120  FORMAT(//' THE DATA ARE SAVED IN FILE : ',A30/)
 8130  FORMAT(/' YOUR DATA RESIDE IN FILE',7X,': ',A30/)
       RETURN
       END
CC     ------------------------------------------------------------------------
CC     SUBROUTINE FOR CREATING THE SECOND PART OF THE OUTPUT:
CC                     - WRITING DOWN THE OBSERVATIONS
CC                     - AN X-Y PLOT
CC     ------------------------------------------------------------------------
       SUBROUTINE WRDATB(NVAR,NCAS,NDXX,NDXY,JCST,MVAL,LAB,NMVAL,X,Y,
     1 AW,JPLT,JPRT,JREG,JHEAD,LUB)

       INCLUDE 'MID_REL_INCL:implicit.inc'

       DIMENSION X(NDXX,NDXY),Y(NDXY),AW(NDXY),NMVAL(NDXY)
       CHARACTER*10 LAB(NDXX)
       CHARACTER*60 JHEAD
       NVSB=NVAR-1
       NVAD=NVAR+1
       IF ((NVAR.EQ.1.AND.JCST.EQ.0).OR.
     1 (NVAR.EQ.2.AND.JCST.EQ.1)) JPLXY=1
       IF (JPRT.EQ.2) THEN
         IF (MVAL.EQ.0) WRITE(LUB,8110)
         IF (MVAL.NE.0) WRITE(LUB,8120)
         IF (JCST.EQ.1) WRITE(LUB,8130) (LAB(J),J=1,NVSB),LAB(NVAD)
         IF (JCST.EQ.0) WRITE(LUB,8130) (LAB(J),J=1,NVAD)
       ENDIF
       DO 10 JNC=1,NCAS
       IF(JPRT.GE.2) THEN
       IF((NVAD.GT.6.AND.JCST.EQ.0).OR.(NVAD.GT.7.AND.JCST.EQ.1))
     1 GOTO 15
       IF (JCST.EQ.1) WRITE(LUB,8140) NMVAL(JNC),(X(J,JNC),J=1,NVSB),
     1 X(NVAD,JNC)
       IF (JCST.EQ.0) WRITE(LUB,8140) NMVAL(JNC),(X(J,JNC),J=1,NVAD)
       GOTO 5
 15    WRITE(LUB,8140) NMVAL(JNC),(X(J,JNC),J=1,6)
       IF (JCST.EQ.1.AND.NVSB.GE.7)
     1 WRITE(LUB,8150) (X(J,JNC),J=7,NVSB),X(NVAD,JNC)
       IF (JCST.EQ.1.AND.NVSB.LT.7) WRITE(LUB,8150) X(NVAD,JNC)
       IF (JCST.EQ.0) WRITE(LUB,8150) (X(J,JNC),J=7,NVAD)
       ENDIF
  5    IF (JPLXY.EQ.1) THEN
       AW(JNC)=X(1,JNC)
       Y(JNC)=X(NVAD,JNC)
       ENDIF
  10   CONTINUE
       IF (JPLXY.EQ.1)
     1 CALL GRAF(AW,Y,NCAS,JPLXY,0,JPLT,NMVAL,NDXY,LUB,JREG,
     1 JHEAD,NDXX,NVAD,LAB)
 8110  FORMAT(/' THE OBSERVATIONS ARE:'/)
 8120  FORMAT(/' THE OBSERVATIONS, AFTER TREATMENT'
     1 ' OF MISSING VALUES ARE:'/)
 8130  FORMAT(7X,6(A10,1X)/15X,5(A10,1X))
 8140  FORMAT(I5,2X,6(F10.4,1X))
 8150  FORMAT(15X,5(F10.4,1X))
       RETURN
       END
CC     ------------------------------------------------------------------------
CC     SUBROUTINE FOR COMPUTING THE ELEMENTS OF THE HAT MATRIX
CC     ------------------------------------------------------------------------
       SUBROUTINE SUBHAT(NVAR,NCAS,NDXX,NDXY,NMXV,X,XMED,XMAD,H,AW,
     1 WEIGHTS,NMVAL,FCKW,LUB)

       INCLUDE 'MID_REL_INCL:implicit.inc'

       DIMENSION X(NDXX,NDXY),AW(NDXY),NMVAL(NDXY),WEIGHTS(NDXY)
       DOUBLE PRECISION H(NMXV,NDXX)
       DIMENSION XMED(NDXX),XMAD(NDXX)
       DO 10 J=1,NVAR
       DO 10 J2=1,J
       H(J,J2)=H(J,J2)/DBLE(FCKW)
       H(J2,J)=H(J,J2)
 10    CONTINUE
       IF (NCAS.LE.20) WRITE (LUB,8000)
       IF (NCAS.GT.20) WRITE (LUB,8010)
       DO 20 JNA=1,NCAS
       DO 30 JNB=1,NCAS
       IF (NCAS.GT.20.AND.JNA.NE.JNB) GOTO 30
       AW(JNB)=0.0
       DO 40 J=1,NVAR
       DO 50 J2=1,NVAR
       RHJ2J=H(J2,J)
       AW(JNB)=AW(JNB)+(X(J2,JNA)*XMAD(J2)+XMED(J2))*WEIGHTS(JNA)*
     1 RHJ2J*(X(J,JNB)*XMAD(J)+XMED(J))*WEIGHTS(JNB)
 50    CONTINUE
 40    CONTINUE
 30    CONTINUE
       IF (NCAS.LE.9) THEN
         WRITE(LUB,8020) NMVAL(JNA),(AW(JNB),JNB=1,NCAS)
         GOTO 20
       ENDIF
       IF (NCAS.GT.20) THEN
         WRITE(LUB,8020) NMVAL(JNA),AW(JNA)
                       ELSE
         WRITE(LUB,8020) NMVAL(JNA),(AW(JNB),JNB=1,9)
         WRITE(LUB,8030) (AW(JNB),JNB=10,NCAS)
       ENDIF
 20    CONTINUE
 8000  FORMAT(//' --- THE HAT MATRIX ---'/1X,22('-'))
 8010  FORMAT(//' THE DIAGONAL ELEMENTS OF THE HAT MATRIX'/1X,40('-'))
 8020  FORMAT(1X,I4,1X,9(F6.3,2X))
 8030  FORMAT(4X,F8.3,F8.3,F8.3,F8.3,F8.3,F8.3,F8.3,F8.3,F8.3)
       RETURN
       END
CC     ------------------------------------------------------------------------
CC     PRINTING THE RLS ESTIMATES AND SOME OPTIONS
CC     ------------------------------------------------------------------------
       SUBROUTINE PRTRLS(NVAR,NCAS,JCST,NVSB,NVAD,NDXX,NDXY,NMXV,
     1 XMED,XMAD,A,DA,H,AW,RESDU,WEIGHTS,X,Y,NMVAL,AVW,NZWE,FCKW,
     1 JREG,JPRT,JPLT,JDIAG,JHEAD,LAB,PREC,LUB)

       INCLUDE 'MID_REL_INCL:implicit.inc'

       INTEGER   UNIT,STATUS
       DIMENSION X(NDXX,NDXY),Y(NDXY),WEIGHTS(NDXY),A(NMXV),DA(NMXV)
       DIMENSION XMED(NDXX),XMAD(NDXX),AW(NDXY),RESDU(NDXY),NMVAL(NDXY)
       DOUBLE PRECISION H(NMXV,NDXX),DS,PTVAL,DST,PVAL
       CHARACTER*10 LAB(NDXX)
       CHARACTER*60 JHEAD

       AL=NCAS
       ANVAR=NVAR
       WRITE(LUB,8000)
       IF (JREG.EQ.1) THEN
       WRITE(LUB,8010)
       NNUL=NCAS
       AVW=1
       ELSE
       WRITE(LUB,8020)
       NNUL=NZWE
       ENDIF
       NDF=NNUL-NVAR
CC-----PRINTING THE COEFFICIENTS WITH THEIR STANDARD ERROR,
CC-----AND T-VALUE
       WRITE(LUB,8030)
C       
       DO 10 J=1,NVSB
       IF (DA(J).LT.PREC) DA(J)=PREC
       STUD=A(J)/DA(J)
       DS=DBLE(STUD)
       DST=PTVAL(DS,NDF)
       RDST=DST
       WRITE(LUB,8040) LAB(J),A(J),DA(J),STUD,RDST
C----put value into MIDAS keyword OUTPUTR(1):
       CALL STKWRR('OUTPUTR',A(J),J,1,UNIT,STATUS)
C----put also error into MIDAS keyword, use OUTPUTR(3)
       CALL STKWRR('OUTPUTR',DA(J),J+2,1,UNIT,STATUS)    
C           
 10    CONTINUE
       IF(DA(NVAR).LT.PREC) DA(NVAR)=PREC
       STUD=A(NVAR)/DA(NVAR)
       DS=DBLE(STUD)
       DST=PTVAL(DS,NDF)
       RDST=DST
       IF (JCST.EQ.0) WRITE(LUB,8040) LAB(NVAR),A(NVAR),DA(NVAR),
     1 STUD,RDST
       IF (JCST.EQ.1) WRITE(LUB,8050) A(NVAR),DA(NVAR),STUD,RDST
C----put value into MIDAS keyword OUTPUTR(2):        
       CALL STKWRR('OUTPUTR',A(NVAR),NVAR,1,UNIT,STATUS)
C----put error into MIDAS keyword, use OUTPUTR(4)        
       CALL STKWRR('OUTPUTR',DA(NVAR),NVAR+2,1,UNIT,STATUS)
C              
CC-----CALCULATION OF THE COEFFICIENT OF DETERMINATION AND F-VALUE
       RSQ=RSQU(NCAS,NVAD,JCST,Y,NDXY,FCKW,FVALUE,PREC,
     1 XMAD,XMED,NDXX,WEIGHTS,NNUL)
CC-----CALCULATION OF THE SCALE ESTIMATE
       A(NVAD) = SQRT(FCKW/(AL*AVW-ANVAR))
       IF (JREG.EQ.1) THEN
       WRITE(LUB,8080) FCKW
                      ELSE
       WRITE(LUB,8090) FCKW
       ENDIF
       WRITE(LUB,8060) NDF
       WRITE(LUB,8070) A(NVAD)
CC-----PRINTING THE VARIANCE-COVARIANCE MATRIX
       CALL SCHCV(NVAR,NDXX,NMXV,H,LUB)
CC-----IF DIAGNOSTICS ARE REQUESTED, THEN PRINT THE HAT MATRIX
CC-----                              OR THE DIAGONAL ELEMENTS ONLY
       FCKW=FCKW/(AL*AVW-ANVAR)
       IF(FCKW.LT.PREC)GOTO 24
       IF (JDIAG.EQ.1) CALL SUBHAT(NVAR,NCAS,NDXX,NDXY,NMXV,X,XMED,
     1 XMAD,H,AW,WEIGHTS,NMVAL,FCKW,LUB)
CC-----PRINT COEFFICIENT OF DETERMINATION, F-VALUE, AND P-VALUE
  24   WRITE(LUB,8100) RSQ
       NDF1=NVAR-JCST
       DS=DBLE(FVALUE)
       DST=PVAL(DS,NDF1,NDF)
       RDST=DST
       WRITE(LUB,8110) FVALUE,NDF1,NDF,RDST
       IF (JREG.EQ.3) THEN
          WRITE(LUB,8200) NNUL
          WRITE(LUB,8210) AVW
          JKEUS=2
                      ELSE
          JKEUS=0
       ENDIF
CC-----GIVE RESIDUAL PLOTS IF REQUESTED
       IF(JPRT.NE.0.OR.JPLT.NE.0) THEN
       CALL RDUAL(A,JKEUS,NVAD,NCAS,NVAR,JCST,JPRT,NVAD,LUB,PREC,JREG,
     1 X,Y,RESDU,WEIGHTS,XMED,XMAD,NZWE,AVW,JPLT,AW,NMVAL,NDXX,NDXY,
     1 JHEAD,LAB)

       ENDIF

 8000  FORMAT(/1X,78('*')/)
 8010  FORMAT(' LEAST SQUARES REGRESSION '/1X,24('*')/)
 8020  FORMAT(' REWEIGHTED LEAST SQUARES BASED ON THE LMS'/
     1 1X,41('*')/)
 8030  FORMAT(/5X,'VARIABLE',5X,'COEFFICIENT',
     1 4X,'STAND. ERROR',5X,'T - VALUE',5X,'P - VALUE'/
     1 3X,70('-'))
 8040  FORMAT(3X,A10,5X,F11.5,4X,F12.5,5X,F9.5,5X,F9.5)
 8050  FORMAT(5X,'CONSTANT',5X,F11.5,4X,F12.5,5X,F9.5,5X,F9.5)
 8060  FORMAT(/' DEGREES OF FREEDOM ',5X,'= ',4X,I5)
 8070  FORMAT(/' SCALE ESTIMATE',10X,'= ',F15.5/)
 8080  FORMAT(/' SUM OF SQUARES',10X,'= ',F15.5)
 8090  FORMAT(/' WEIGHTED SUM OF SQUARES'' = ',F15.5)
 8100  FORMAT(/' COEFFICIENT OF DETERMINATION (R SQUARED) =',F15.5/)
 8110  FORMAT(' THE F-VALUE = ',F12.3,' (WITH ',I3,' AND ',
     1 I4,' DF)',3X,'P - VALUE = ',F7.5)
 8200  FORMAT(/'THERE ARE',2X,I4,
     1 ' POINTS WITH NON-ZERO WEIGHT.' )
 8210  FORMAT(/' AVERAGE WEIGHT',10X,'= ',F15.5/)
       RETURN
       END
CC     ------------------------------------------------------------------------
CC     SUBROUTINE FOR CALCULATING THE LMS REGRESSION
CC     ------------------------------------------------------------------------
       SUBROUTINE SUBLMS(NVAR,NCAS,JCST,NDXX,NDXY,NMXV,PREC,X,Y,
     1 XMED,XMAD,JDIAG,ALGO,FNAMEB,JQU,JREP,DRCTA,JNDA,RESDU,WEIGHTS,
     1 UHYB,AVW,NZWE,RSQ,JHYB,JDMB,JERD,JLP,NERR,DTERM,C,HVEC,JNDVC,AW)

       INCLUDE 'MID_REL_INCL:implicit.inc'

       DIMENSION X(NDXX,NDXY),Y(NDXY),C(NMXV,NDXX),DRCTA(NDXX)
       DIMENSION JNDA(NMXV),JNDVC(NDXX),XMED(NDXX),XMAD(NDXX)
       DIMENSION AW(NDXY),RESDU(NDXY),UHYB(NDXY),WEIGHTS(NDXY)
       DOUBLE PRECISION HVEC(JDMB)
       DOUBLE PRECISION DTERM
       CHARACTER ALGO
       CHARACTER*30 FNAMEB
       CHARACTER*80 CBUF
CC-----LIST OF VARIABLES WHICH ENTER "SUBLMS" (WITHOUT CHANGING INSIDE)
CC     NVAR, NCAS, JCST, NDXX, NDXY, NMXV, PREC,
CC     X, Y, XMED, XMAD, JDIAG, ALGO, FNAMEB
CC-----LIST OF VARIABLES THE VALUE OF WHICH IS CALCULATED IN "SUBLMS"
CC     JQU, JREP, DRCTA, JNDA, RESDU, WEIGHTS, UHYB, AVW, NZWE, RSQ,
CC     JHYB, JDMB, JERD, JLP, NERR, DTERM
CC-----LIST OF VARIABLES WHICH ARE NEEDED FOR THE CALCULATIONS
CC     C, HVEC, JNDVC, AW
CC-----LIST OF SUBROUTINES USED IN "SUBLMS"
CC     SUBROUTINE SUBREP
CC     SUBROUTINE GENPN
CC     SUBROUTINE RANPN
CC     SUBROUTINE EQUAT
CC     SUBROUTINE RESTT
CC     SUBROUTINE RANGS
CC     SUBROUTINE SHHLF
CC     FUNCTION PULL
CC-----INITIALIZATIONS
       JERD=0
       JFRST=0
       JEY=0
       AVW=0.0
       NZWE=0
       JREADZ=0
       JHYB=JDIAG
       AL=NCAS
       ANVAR=NVAR
CC-----CALCULATION OF JQU, THE RANK OF THE ABSOLUTE RESIDUAL TO BE MINIMIZED
       JQU = INT(AL/2.0) + INT( (ANVAR+1.0)/2.0 )
CC-----CALCULATE THE NUMBER OF REPLICATIONS
       CALL SUBREP(NVAR,NCAS,NDXX,ALGO,JNDVC,JREP)
CC-----MAXIMAL NUMBER OF REPLICATIONS
       MAXRP=3*JREP
       NVSB=NVAR-1
       NVAD=NVAR+1
CC-----START OF THE ALGORITHM : THE "10" LOOP PERFORMS THE REPLICATIONS
       DO 10 JJJ=1,JREP
CC-----IF (JNDVC(NVAD) = 11 THEN TAKE A COMBINATION OF NVAR POINTS
CC-----OUT OF NCAS, ELSE TAKE A RANDOM SAMPLE OF NVAR POINTS OUT OF NCAS
 20    IF(JNDVC(NVAD).EQ.11) THEN
       CALL GENPN(NCAS,NVAR,JNDVC,NDXX,JJJ)
       ELSE
           IF (JJJ.GT.2) THEN
             CALL RANPN(NCAS,NVAR,JNDVC,NDXX,JEY,JLP,MAXRP)
             IF (JLP.GT.MAXRP) GOTO 210
           ELSE
             IF (JJJ.EQ.2) THEN
             JLP=JLP+1
             DO 30 MNDX=1,NVAR
 30             JNDVC(MNDX)=NCAS-MNDX+1
                           ELSE
             JLP=JLP+1
             DO 40 MNDX=1,NVAR
 40             JNDVC(MNDX)=MNDX
             ENDIF
           ENDIF
       ENDIF
CC-----STORE THE NVAR SELECTED OBSERVATIONS IN THE MATRIX C
       DO 50 MNDX=1,NVAR
         DO 60 KJ=1,NVAD
           NDR=JNDVC(MNDX)
           C(MNDX,KJ)=X(KJ,NDR)
 60         CONTINUE
 50    CONTINUE
CC-----THE FOLLOWING FIVE LINES ARE INSTRUCTIONS FOR INFORMING
CC-----THE USER ABOUT HOW FAR THE CALCULATIONS OF THE LMS ARE ALREADY ADVANCED
CC-----(THESE LINES MAY BE DELETED IF USED ON OTHER COMPUTER)
       JREADY=(JJJ*100)/JREP
       IF (MOD(JREADY,5).EQ.0.AND.JREADY.NE.JREADZ) THEN
           WRITE(CBUF,65) JREADY
 65        FORMAT(I4,' PERCENT OF THE CALCULATIONS HAVE BEEN EXECUTED.')
           CALL STTPUT(CBUF,ISTAT)
       ENDIF	   
       IF (FNAMEB.EQ.'CON'.AND.JREADY.GE.100) PAUSE ' '
       JREADZ=JREADY
CC-----SOLVE THE SYSTEM OF EQUATIONS STORED IN C
       IF(NVAR.GT.1) THEN
         CALL EQUAT(C,NMXV,NDXX,HVEC,JDMB,NVAR,1,NERR,DTERM)
         IF(NERR.GE.0) GOTO 70
         JERD=JERD+1
         IF (JNDVC(NVAD).NE.11.AND.JJJ.GT.2) GOTO 20
         GOTO 10
                     ELSE
         IF(C(1,1).NE.0.0) C(1,1)=C(1,2)/C(1,1)
       ENDIF
CC-----CALCULATE THE RESIDUALS AND THE ASSOCIATED OBJECTIVE FUNCTION
CC-----VALUE FOR THE TRIAL ESTIMATE OBTAINED ABOVE
 70    DO 80 JNC=1,NCAS
       RESDU(JNC)=0.0
       DO 90 J=1,NVAR
       RESDU(JNC)=RESDU(JNC)+C(J,1)*X(J,JNC)
 90    CONTINUE
       RESDU(JNC)=ABS(X(NVAD,JNC)-RESDU(JNC))
 80    CONTINUE
       FCTVA=PULL(AW,NDXY,RESDU,NCAS,JQU)*1.4826
CC-----INITIALIZE THE "BEST" ESTIMATE AND OBJECTIVE FUNCTION VALUE
       IF(JFRST.NE.1) THEN
         JFRST=1
         DRCTA(NVAD)=FCTVA
         DO 100 J=1,NVAR
         JNDA(J)=JNDVC(J)
         DRCTA(J)=C(J,1)
 100         CONTINUE
         IF (FCTVA.LT.PREC) JHYB=0
CC-----IF DIAGNOSTICS ARE WANTED, THEN CALCULATE THE RDi
         IF (JHYB.EQ.0) GOTO 200
         DO 110 JNC=1,NCAS
         UHYB(JNC)=RESDU(JNC)/FCTVA*1.4826
 110         CONTINUE
                      ELSE
 120         IF(FCTVA.LT.PREC) JHYB=0
         IF (JHYB.NE.0) THEN
           DO 130 JNC=1,NCAS
           UH=RESDU(JNC)/FCTVA*1.4826
           IF(UHYB(JNC).LT.UH) UHYB(JNC)=UH
 130           CONTINUE
         ENDIF
CC-----UPDATE THE "BEST" ESTIMATE AND OBJECTIVE FUNCTION VALUE
CC-----IF NECESSARY
         IF (FCTVA.LT.DRCTA(NVAD)) THEN
           DRCTA(NVAD)=FCTVA
           DO 140 J=1,NVAR
           JNDA(J)=JNDVC(J)
 140           DRCTA(J)=C(J,1)
         ENDIF
       ENDIF
CC-----IF FCTVA IS LESS THAN PREC (A PRECISION CONSTANT) THEN ONE IS
CC-----RESORTED TO THE EXACT FIT CASE
 200   CONTINUE
C       write(6,*) 'FCTVA,PREC', FCTVA, PREC
       IF (FCTVA.LE.PREC) THEN
          DRCTA(NVAD)=FCTVA 
          CALL RESTT(DRCTA,1,0,NVAR,NCAS,NVAD,NZWE,X,Y,RESDU,WEIGHTS,
     1          XMED,XMAD,NDXX,NDXY,0,SCAL,QUAN,PREC)
          AVW=(NZWE*1.0 )/AL
C          RETURN
       ENDIF
 10    CONTINUE
 210   CONTINUE
CC-----ADJUSTING THE INTERCEPT IN THE CASE OF A MODEL WITH
CC-----CONSTANT TERM
       write(CBUF,*) 'JCST = ',JCST
       CALL STTPUT(CBUF,ISTAT)
       IF (JCST.NE.0) THEN
          CALL RESTT(DRCTA,0,0,NVSB,NCAS,NVAD,NZWE,X,Y,RESDU,
     1          WEIGHTS,XMED,XMAD,NDXX,NDXY,0,SCAL,QUAN,PREC)
          CALL RANGS(RESDU,NCAS)
          CALL SHHLF(RESDU,NCAS,JQU,SLUTN,BSTD,PREC)
          DRCTA(NVAR)=SLUTN
          DRCTA(NVAD)=BSTD*1.4826
       ENDIF
CC-----COMPUTING THE FINAL SCALE ESTIMATE OF THE LMS AND THE
CC-----RESULTING WEIGHTS
       QUAN=DRCTA(NVAD)
       QUAN=QUAN*(5.0/(AL-ANVAR)+1.0)
       CALL RESTT(DRCTA,1,0,NVAR,NCAS,NVAD,NZWE,
     1 X,Y,RESDU,WEIGHTS,XMED,XMAD,NDXX,NDXY,1,SCAL,QUAN,PREC)
       DRCTA(NVAD)=SCAL
       AVW=(NZWE*1.0)/AL
CC-----COEFFICIENT OF DETERMINATION CORRESPONDING TO THE LMS
       RSQ= DRCTA(NVAD)*XMAD(NVAD)
       DO 220 JNC=1,NCAS
 220   AW(JNC)=ABS(Y(JNC)*XMAD(NVAD))
       RSY=PULL(AW,NDXY,AW,NCAS,JQU)*1.4826
       RSQ=1.0-(RSQ/RSY)**2
       IF (RSQ.LT.0.0) RSQ=0.0
       IF (RSQ.GT.1.0) RSQ=1.0
       RETURN
       END
CC     ------------------------------------------------------------------------
CC     PRINTING  LMS ESTIMATES AND SOME OPTIONS
CC     ------------------------------------------------------------------------
       SUBROUTINE PRTLMS(NVAR,NCAS,JCST,NVSB,NVAD,NDXX,NDXY,NMXV,JNDVC,
     1 XMED,XMAD,DRCTA,AW,RESDU,WEIGHTS,X,Y,NMVAL,UHYB,AVW,NZWE,RSQ,
     1 JREG,JPRT,JPLT,JREP,JERD,JLP,JQU,JHYB,JDIAG,NSTOP,JHEAD,LAB,
     1 PREC,LUB)

       INCLUDE 'MID_REL_INCL:implicit.inc'

       DIMENSION X(NDXX,NDXY),Y(NDXY),XMED(NDXX),XMAD(NDXX),UHYB(NDXY)
       DIMENSION DRCTA(NMXV),AW(NDXY),RESDU(NDXY),NMVAL(NDXY)
       DIMENSION WEIGHTS(NDXY)
       DIMENSION JNDVC(NDXX)
       CHARACTER*10 LAB(NDXX)
       CHARACTER*60 JHEAD
       WRITE(LUB,8000)
       WRITE(LUB,8010)
       IF (JPRT.NE.0) WRITE(LUB,8020) JQU
       NSTOP=0
       IF (JERD.NE.0) THEN
       IF (JNDVC(NVAD).NE.11) THEN
          IF  (JERD.EQ.JLP) THEN
              WRITE(LUB,8030) NVAR,NCAS
              NSTOP=1
              RETURN
                            ELSE
              IF (JPRT.NE.0) WRITE(LUB,8040) JLP,NVAR,NCAS,JERD
          ENDIF
                              ELSE
          IF (JERD.EQ.JREP) THEN
             WRITE(LUB,8050) NVAR,NCAS
             NSTOP=1
             RETURN
                            ELSE
             IF (JPRT.NE.0) WRITE(LUB,8060) JERD,NVAR,NCAS,JREP
          ENDIF
       ENDIF
       ENDIF
CC-----LMS IN THE CASE OF EXACT FIT
       IF (DRCTA(NVAD).LE.PREC) THEN
          WRITE(LUB,8070)
          DO 10 J=1,NVSB
 10          WRITE(LUB,8080) LAB(J),DRCTA(J)
          IF (JCST.EQ.0) WRITE(LUB,8080) LAB(NVAR),DRCTA(NVAR)
          IF (JCST.NE.0) WRITE(LUB,8090) DRCTA(NVAR)
          WRITE(LUB,8100) DRCTA(NVAD)
          WRITE(LUB,8110) NZWE
          JREG=2
CC-----RESIDUAL PLOT FOR THE LMS IN THE CASE OF EXACT FIT
          CALL RDUAL(DRCTA,0,NVAD,NCAS,NVAR,JCST,JPRT,NVAD,LUB,PREC,
     1    JREG, X,Y,RESDU,WEIGHTS,XMED,XMAD,NZWE,AVW,JPLT,AW,NMVAL,
     1    NDXX,NDXY,JHEAD,LAB)
          NSTOP=1
          RETURN
       ENDIF
CC-----LMS IN THE GENERAL CASE
       WRITE(LUB,8130)
       DO 20 J=1,NVSB
 20    WRITE(LUB,8080) LAB(J),DRCTA(J)
       IF (JCST.EQ.0) WRITE(LUB,8080) LAB(NVAR),DRCTA(NVAR)
       IF (JCST.NE.0) WRITE(LUB,8090) DRCTA(NVAR)
       WRITE(LUB,8200) DRCTA(NVAD)
CC-----PRINT COEFFICIENT OF DETERMINATION OF THE LMS
       WRITE(LUB,8210) RSQ
       JREG=2
CC-----RESIDUAL PLOTS IF REQUESTED
       CALL RDUAL(DRCTA,1,NVAD,NCAS,NVAR,JCST,JPRT,NVAD,LUB,PREC,JREG,
     1 X,Y,RESDU,WEIGHTS,XMED,XMAD,NZWE,AVW,JPLT,AW,NMVAL,NDXX,NDXY,
     1 JHEAD,LAB)
       IF (JHYB.NE.0.AND.JDIAG.EQ.1) THEN
          WRITE(LUB,8220)
          UH=AMDAN(AW,NDXY,UHYB,NCAS)
          DO 40 JNC=1,NCAS
          RDI=UHYB(JNC)/UH
          WRITE(LUB,8230) NMVAL(JNC),UHYB(JNC),RDI
 40    CONTINUE
       ENDIF
 8000  FORMAT(/1X,78('*')/)
 8010  FORMAT(' LEAST MEDIAN OF SQUARES REGRESSION'/
     1 1X,34('*')/)
 8020  FORMAT(' THE MINIMIZATION OF THE ',I4,
     1 'TH ORDERED SQUARED RESIDUAL IS PERFORMED.')
 8030  FORMAT(//' ALL SUBSAMPLES OF ',I3,' POINTS OUT OF ',I5,
     1 ' LED TO A SINGULAR SYSTEM OF EQUATIONS.'/
     1 ' THIS MEANS THAT THERE IS AN ENORMOUS PROBLEM OF',
     1 ' COLLINEARITY IN THE DATA SET.'/
     1 ' TRY THE ANALYSIS AGAIN IN A LOWER DIMENSION.'//)
 8040  FORMAT(/' ON A TOTAL OF ',I8,' SUBSAMPLES (OF',
     1 I3,'POINTS OUT OF ',I5,')', /I7,
     1 ' SUBSAMPLES LED TO A SINGULAR SYSTEM OF EQUATIONS.'/
     1 ' THE SOLUTION IS ONLY BASED ON THE GOOD SUBSAMPLES.'//)
 8050  FORMAT(//' ALL COMBINATIONS OF ,I3,15H POINTS OUT OF ',I5,
     1 ' LED TO A SINGULAR SYSTEM OF EQUATIONS.'/
     1 ' THIS MEANS THAT THERE IS AN ENORMOUS PROBLEM OF',
     1 ' COLLINEARITY IN THE DATA SET.'/
     1 ' TRY THE ANALYSIS AGAIN IN A LOWER DIMENSION.'//)
 8060  FORMAT(/' THERE WERE ',I7,' COMBINATIONS (OF ',I3,
     1 ' POINTS OUT OF ,I5,16H) OF A TOTAL OF '/I8,' COMBINATIONS,',
     1 ' WHICH LED TO A SINGULAR SYSTEM OF EQUATIONS.'/
     1 ' THE SOLUTION IS ONLY BASED ON THE GOOD COMBINATIONS.'//)
 8070  FORMAT(/' MORE THAN THE HALF OF THE DATA LIE ON THE'
     1 /' SAME HYPERPLANE, WITH COEFFICIENTS = '//)
 8080  FORMAT(3X,A10,F20.5)
 8090  FORMAT(3X,'  CONSTANT',F20.5)
 8100  FORMAT(/' SCALE ESTIMATE',10X,'= ',F15.5/)
 8110  FORMAT(' THERE ARE',2X,I4,' POINTS ON THE HYPERPLANE')
 8130  FORMAT(/5X,'VARIABLE',9X,'COEFFICIENT'/3X,30('-'))
 8200  FORMAT(/' FINAL SCALE ESTIMATE',9X,'= ',F15.5)
 8210  FORMAT(/' COEFFICIENT OF DETERMINATION = ',F15.5/)
 8220  FORMAT(//1X,'INDEX',3X,'      Ui     ',3X,'RESISTANT '/
     1 25X,'DIAGNOSTIC'/1X,34('-'))
 8230  FORMAT(1X,I4,3X,F13.4,3X,F10.4)
       RETURN
       END






