SUBROUTINE DISCR2(X,N,NUMCLA,Y) C C PURPOSE--THIS SUBROUTINE 'DISCRETIZES' THE DATA C OF THE SINGLE PRECISION VECTOR X C INTO NUMCLA CLASSES. C ALL VALUES IN THE VECTOR X WITHIN A GIVEN CLASS C WILL BE MAPPED INTO THE MIDPOINT OF THAT CLASS. C THE SAMPLE MINIMUM AND SAMPLE MAXIMUM C ARE AUTOMATICALLY COMPUTED INTERNALLY C AND THE CLASS WIDTH (XDEL) IS COMPUTED AS C THE (SAMPLE MAX - SAMPLE MIN)/NUMCLA. C THE FIRST CLASS INTERVAL IS FROM C THE SAMPLE MIN TO THE SAMPLE MIN + XDEL; C THE SECOND CLASS INTERVAL IS FROM C THE SAMPLE MIN + XDEL TO C THE SAMPLE MIN + 2*XDEL; C ...; C THE LAST CLASS INTERVAL IS FROM C THE SAMPLE MAX - XDEL TO THE SAMPLE MAX. C THE USE OF THIS SUBROUTINE C (AND THE DISCRE AND DISCR3 SUBROUTINES) C GIVES THE DATA ANALYST THE CAPABILITY OF C CONSTRUCTING A DISCRETE VARIATE FROM C A CONTINUOUS ONE. C THE RESULTING DISCRETE VARIATE MIGHT THEN C (FOR EXAMPLE) BE ANALYZED IN ITSELF FOR C GROSS STRUCTURE, OR FOR ADHERENCE TO SOME C THEROETICAL DISCRETE PROBABILITY MODEL, C OR THE DISCRETE VARIATE MIGHT BE USED C AS A SUBSET DEFINITION VECTOR FOR SOME C OTHER VARIATE. C INPUT ARGUMENTS--X = THE SINGLE PRECISION VECTOR OF C (UNSORTED OR SORTED) OBSERVATIONS. C TO BE DISCRETIZED. C --N = THE INTEGER NUMBER OF OBSERVATIONS C IN THE VECTOR X. C --NUMLEV = THE INTEGER NUMBER OF CLASSES C DESIRED IN THE DISCRETIZATION. C OUTPUT ARGUMENTS--Y = THE SINGLE PRECISION VECTOR OF C DISCRETIZED VALUES (= THE CLASS C MIDPOINTS) CORRESPONDING TO C THE CONTINUOUS VALUES IN THE VECTOR X. C THERE WILL RESULT N SUCH DISCRETIZED C VALUES. C OUTPUT--THE SINGLE PRECISION VECTOR Y C WHICH CONTAINS N DISCRETIZED VALUES C (= THE CLASS MIDPOINTS) C CORRESPONDING TO THE N C CONTINUOUS VALUES IN THE C INPUT VECTOR X. C ALSO, (NUMCLA+5) LINES OF SUMMARY INFORMATION C WILL BE GENERATED INDICATING C 1) WHAT THE SAMPLE SIZE IS (N); C 2) WHAT THE NUMBER OF CLASSES IS (NUMCLA). C 3) WHAT THE CLASS BOUNDARIES AND C THE NUMBER OF OBSERVATIONS C FALLING IN EACH CLASS ARE. C PRINTING--YES C RESTRICTIONS--THERE IS NO RESTRICTION ON THE MAXIMUM VALUE C OF N FOR THIS SUBROUTINE. C --NUMCLA SHOULD BE POSITIVE AND NOT EXCEED 1000 C OTHER DATAPAC SUBROUTINES NEEDED--NONE. C FORTRAN LIBRARY SUBROUTINES NEEDED--NONE. C MODE OF INTERNAL OPERATIONS--SINGLE PRECISION. C LANGUAGE--ANSI FORTRAN. C COMMENT--THIS SUBROUTINE DIFFERS FROM THE DISCR3 C SUBROUTINE INASMUCH AS THIS SUBROUTINE C PERFORMS ITS DISCRETIZATION BY OUTPUTING C CLASS MIDPOINTS, WHEREAS THE DISCR3 C SUBROUTINE OUTPUTS CLASS NUMBERS C (1, 2, ... , NUMCLA). C COMMENT--THE INPUT VECTOR X REMAINS UNALTERED. C COMMENT--IN THE MAIN (CALLING) ROUTINE, IT IS C PERMISSABLE (IF THE ANALYST SO DESIRES) C TO USE THE SAME VARIABLE NAME C IN THE FOURTH ARGUMENT AS USED IN THE FIRST C ARGUMENT IN THE CALLING SEQUENCE TO THIS C DISCR2 SUBROUTINE--NO CONFLICT WILL RESULT C IN THE INTERNAL OPERATION OF THE DISCR2 C SUBROUTINE. FOR EXAMPLE, IT IS PERMISSIBLE C TO HAVE CALL DISCR2(X,N,10,X) C IN WHICH THE VARIABLE NAME X IS USED C AS BOTH THE FIRST AND FOURTH ARGUMENTS. C REFERENCES--NONE. C WRITTEN BY--JAMES J. FILLIBEN C STATISTICAL ENGINEERING LABORATORY (205.03) C NATIONAL BUREAU OF STANDARDS C WASHINGTON, D. C. 20234 C PHONE--301-921-2315 C ORIGINAL VERSION--NOVEMBER 1974. C UPDATED --APRIL 1975. C UPDATED --NOVEMBER 1975. C C--------------------------------------------------------------------- C DIMENSION X(1),Y(1) DIMENSION ICOUNT(1000) DIMENSION CLASSM(1000) C IPR=6 IUPNCL=1000 C C CHECK THE INPUT ARGUMENTS FOR ERRORS C IF(N.LT.1)GOTO50 IF(N.EQ.1)GOTO55 IF(NUMCLA.LT.1.OR.NUMCLA.GT.IUPNCL)GOTO70 IF(NUMCLA.EQ.1)GOTO80 HOLD=X(1) DO60I=2,N IF(X(I).NE.HOLD)GOTO90 60 CONTINUE WRITE(IPR, 9)HOLD DO65I=1,N Y(I)=X(I) 65 CONTINUE RETURN 50 WRITE(IPR,15) WRITE(IPR,47)N RETURN 55 WRITE(IPR,18) Y(1)=X(1) RETURN 70 WRITE(IPR,27)IUPNCL WRITE(IPR,47)NUMCLA DO71I=1,N Y(I)=0.0 71 CONTINUE RETURN 80 WRITE(IPR,28) 90 CONTINUE 9 FORMAT(1H ,108H***** NON-FATAL DIAGNOSTIC--THE FIRST INPUT ARGUME 1NT (A VECTOR) TO THE DISCR2 SUBROUTINE HAS ALL ELEMENTS = ,E15.8,6 1H *****) 15 FORMAT(1H , 91H***** FATAL ERROR--THE SECOND INPUT ARGUMENT TO THE 1 DISCR2 SUBROUTINE IS NON-POSITIVE *****) 18 FORMAT(1H ,100H***** NON-FATAL DIAGNOSTIC--THE SECOND INPUT ARGUME 1NT TO THE DISCR2 SUBROUTINE HAS THE VALUE 1 *****) 27 FORMAT(1H , 98H***** FATAL ERROR--THE THIRD INPUT ARGUMENT TO THE 1 DISCR2 SUBROUTINE IS OUTSIDE THE ALLOWABLE (1,,I6,16H) INTERVAL * 1****) 28 FORMAT(1H ,100H***** NON-FATAL DIAGNOSTIC--THE THIRD INPUT ARGUME 1NT TO THE DISCR2 SUBROUTINE HAS THE VALUE 1 *****) 47 FORMAT(1H , 35H***** THE VALUE OF THE ARGUMENT IS ,I8 ,6H *****) C C-----START POINT----------------------------------------------------- C ANUML=NUMCLA C C ZERO OUT THE COUNT VECTOR (ICOUNT) C DO100I=1,NUMCLA ICOUNT(I)=0 100 CONTINUE C C COMPUTE THE SAMPLE MINIMUM AND MAXIMUM, C THEN COMPUTE THE CLASS WIDTH. C XMIN=X(1) XMAX=X(1) DO200I=1,N IF(X(I).LT.XMIN)XMIN=X(I) IF(X(I).GT.XMAX)XMAX=X(I) 200 CONTINUE XDEL=(XMAX-XMIN)/ANUML C C COMPUTE THE CLASS MIDPOINT FOR EACH CLASS C DO300I=1,NUMCLA AI=I CLASSM(I)=XMIN+(AI-0.5)*XDEL 300 CONTINUE C C PERFORM THE DISCRETIZING TRANSFORMATION. C ALSO, KEEP A FREQUENCY COUNT FOR EACH CLASS. C DO400I=1,N P=(X(I)-XMIN)/(XMAX-XMIN) P=P*ANUML+1.0 IP=P IF(IP.LT.1)IP=1 IF(IP.GT.NUMCLA)IP=NUMCLA Y(I)=CLASSM(IP) ICOUNT(IP)=ICOUNT(IP)+1 400 CONTINUE C C COMPUTE CLASS LIMITS AND WRITE OUT SUMMARY INFORMATION. C WRITE(IPR,999) WRITE(IPR,501) WRITE(IPR,999) WRITE(IPR,502)N WRITE(IPR,508)NUMCLA WRITE(IPR,503)XMIN WRITE(IPR,504)XDEL WRITE(IPR,505)XMAX WRITE(IPR,999) WRITE(IPR,510) WRITE(IPR,997) DO500I=1,NUMCLA AI=I CMIN=XMIN+(AI-1.0)*XDEL CMAX=XMIN+AI*XDEL WRITE(IPR,520)I,CMIN,CLASSM(I),CMAX,ICOUNT(I) 500 CONTINUE C 501 FORMAT(1H ,35HOUTPUT FROM THE DISCR2 SUBROUTINE--) 502 FORMAT(1H ,7X,36HNUMBER OF OBSERVATIONS = ,I8) 503 FORMAT(1H ,7X,36HCOMPUTED LOWER BOUND OF INTERVAL = ,F15.7) 504 FORMAT(1H ,7X,36HCOMPUTED CLASS WIDTH = ,F15.7) 505 FORMAT(1H ,7X,36HCOMPUTED UPPER BOUND OF INTERVAL = ,F15.7) 508 FORMAT(1H ,7X,36HSPECIFIED NUMBER OF LEVELS = ,I8) 510 FORMAT(1H ,52H CLASS MINIMUM MIDPOINT MAXIMUM 1,11H COUNT) 520 FORMAT(1H ,4X,I6,2X,3F14.7,I8) 997 FORMAT(1H ,50H -------------------------------------------, 1 13H-------------) 999 FORMAT(1H ) C RETURN END