      SUBROUTINE AUTOCO(X,N,IWRITE,XAUTOC)
C
C     PURPOSE--THIS SUBROUTINE COMPUTES THE
C              SAMPLE AUTOCORRELATION COEFFICIENT 
C              OF THE DATA IN THE INPUT VECTOR X. 
C              THE SAMPLE AUTOCORRELATION COEFFICIENT =  THE CORRELATION
C              BETWEEN X(I) AND X(I+1) OVER THE ENTIRE SAMPLE.
C              THE AUTOCORRELATION COEFFICIENT COEFFICIENT WILL BE A
C              SINGLE PRECISION VALUE BETWEEN -1.0 AND 1.0
C              (INCLUSIVELY). 
C     INPUT  ARGUMENTS--X      = THE SINGLE PRECISION VECTOR OF
C                                (UNSORTED) OBSERVATIONS.
C                     --N      = THE INTEGER NUMBER OF OBSERVATIONS
C                                IN THE VECTOR X. 
C                     --IWRITE = AN INTEGER FLAG CODE WHICH 
C                                (IF SET TO 0) WILL SUPPRESS
C                                THE PRINTING OF THE
C                                SAMPLE AUTOCORRELATION COEFFICIENT
C                                AS IT IS COMPUTED;
C                                OR (IF SET TO SOME INTEGER 
C                                VALUE NOT EQUAL TO 0),
C                                LIKE, SAY, 1) WILL CAUSE
C                                THE PRINTING OF THE
C                                SAMPLE AUTOCORRELATION COEFFICIENT
C                                AT THE TIME IT IS COMPUTED.
C     OUTPUT ARGUMENTS--XAUTOC = THE SINGLE PRECISION VALUE OF THE
C                                COMPUTED SAMPLE AUTOCORRELATION
C                                COEFFICIENT.
C                                THIS SINGLE PRECISION VALUE
C                                WILL BE BETWEEN -1.0 AND 1.0
C                                (INCLUSIVELY).
C     OUTPUT--THE COMPUTED SINGLE PRECISION VALUE OF THE
C             SAMPLE AUTOCORRELATION COEFFICIENT. 
C     PRINTING--NONE, UNLESS IWRITE HAS BEEN SET TO A NON-ZERO
C               INTEGER, OR UNLESS AN INPUT ARGUMENT ERROR
C               CONDITION EXISTS.
C     RESTRICTIONS--THERE IS NO RESTRICTION ON THE MAXIMUM VALUE
C                   OF N FOR THIS SUBROUTINE.
C     OTHER DATAPAC   SUBROUTINES NEEDED--NONE.
C     FORTRAN LIBRARY SUBROUTINES NEEDED--SQRT.
C     MODE OF INTERNAL OPERATIONS--SINGLE PRECISION.
C     LANGUAGE--ANSI FORTRAN. 
C     REFERENCES--JENKINS AND WATTS, SPECTRAL ANALYSIS AND
C                 ITS APPLICATIONS, 1968, PAGES 5, 182.
C     WRITTEN BY--JAMES J. FILLIBEN
C                 STATISTICAL ENGINEERING DIVISION (714)
C                 NATIONAL BUREAU OF STANDARDS
C                 GAITHERSBURG, MD  20899
C                 PHONE:  301-921-3651
C     ORIGINAL VERSION--JUNE      1972. 
C     UPDATED         --SEPTEMBER 1975. 
C     UPDATED         --NOVEMBER  1975. 
C
C---------------------------------------------------------------------
C
      DIMENSION X(1)
C
      IPR=6
C
C     CHECK THE INPUT ARGUMENTS FOR ERRORS
C
      AN=N
      IF(N.LT.1)GOTO50
      IF(N.EQ.1)GOTO55
      HOLD=X(1)
      DO60I=2,N
      IF(X(I).NE.HOLD)GOTO90
   60 CONTINUE
      WRITE(IPR, 9)HOLD
      XAUTOC=0.0
      GOTO201
   50 WRITE(IPR,15) 
      WRITE(IPR,47)N
      RETURN
   55 WRITE(IPR,18) 
      XAUTOC=0.0
      GOTO201
   90 CONTINUE
    9 FORMAT(1H ,109H***** NON-FATAL DIAGNOSTIC--THE FIRST  INPUT ARGUME
     1NT (A VECTOR) TO THE AUTOCO SUBROUTINE HAS ALL ELEMENTS = ,E15.8,6
     1H *****)
   15 FORMAT(1H , 91H***** FATAL ERROR--THE SECOND INPUT ARGUMENT TO THE
     1 AUTOCO SUBROUTINE IS NON-POSITIVE *****)
   18 FORMAT(1H ,100H***** NON-FATAL DIAGNOSTIC--THE SECOND INPUT ARGUME
     1NT TO THE AUTOCO SUBROUTINE HAS THE VALUE 1 *****)
   47 FORMAT(1H , 35H***** THE VALUE OF THE ARGUMENT IS ,I8   ,6H *****)
C
C-----START POINT-----------------------------------------------------
C
      XBAR=0.0
      DO100I=1,N
      XBAR=XBAR+X(I)
  100 CONTINUE
      XBAR1=XBAR-X(N)
      XBAR1=XBAR1/(AN-1.0)
      XBAR2=XBAR-X(1)
      XBAR2=XBAR2/(AN-1.0)
      SUM1=0.0
      SUM2=0.0
      SUM3=0.0
      NM1=N-1
      DO200I=1,NM1
      IP1=I+1
      SUM1=SUM1+(X(I)-XBAR1)*(X(IP1)-XBAR2)
      SUM2=SUM2+(X(I)-XBAR1)**2
      SUM3=SUM3+(X(IP1)-XBAR2)**2
  200 CONTINUE
      XAUTOC=SUM1/(SQRT(SUM2*SUM3))
C
  201 IF(IWRITE.EQ.0)RETURN
      WRITE(IPR,999)
      WRITE(IPR,205)N,XAUTOC
  205 FORMAT(1H ,53HTHE LINEAR AUTOCORRELATION COEFFICIENT OF THE SET OF
     1 ,I6,17H OBSERVATIONS IS ,F14.6)
  999 FORMAT(1H )
      RETURN
      END 
