C
C     ..................................................................
C
C        SUBROUTINE CORRE
C
C        PURPOSE
C           COMPUTE MEANS, STANDARD DEVIATIONS, SUMS OF CROSS-PRODUCTS
C           OF DEVIATIONS, AND CORRELATION COEFFICIENTS.
C
C        USAGE
C           CALL CORRE (N,M,IO,X,XBAR,STD,RX,R,B,D,T)
C
C        DESCRIPTION OF PARAMETERS
C           N     - NUMBER OF OBSERVATIONS. N MUST BE > OR = TO 2.
C           M     - NUMBER OF VARIABLES. M MUST BE > OR = TO 1.
C           IO    - OPTION CODE FOR INPUT DATA
C                   0 IF DATA ARE TO BE READ IN FROM INPUT DEVICE IN THE
C                     SPECIAL SUBROUTINE NAMED DATA.  (SEE SUBROUTINES
C                     USED BY THIS SUBROUTINE BELOW.)
C                   1 IF ALL DATA ARE ALREADY IN CORE.
C           X     - IF IO=0, THE VALUE OF X IS 0.0.
C                   IF IO=1, X IS THE INPUT MATRIX (N BY M) CONTAINING
C                            DATA.
C           XBAR  - OUTPUT VECTOR OF LENGTH M CONTAINING MEANS.
C           STD   - OUTPUT VECTOR OF LENGTH M CONTAINING STANDARD
C                   DEVIATIONS.
C           RX    - OUTPUT MATRIX (M X M) CONTAINING SUMS OF CROSS-
C                   PRODUCTS OF DEVIATIONS FROM MEANS.
C           R     - OUTPUT MATRIX (ONLY UPPER TRIANGULAR PORTION OF THE
C                   SYMMETRIC MATRIX OF M BY M) CONTAINING CORRELATION
C                   COEFFICIENTS.  (STORAGE MODE OF 1)
C           B     - OUTPUT VECTOR OF LENGTH M CONTAINING THE DIAGONAL
C                   OF THE MATRIX OF SUMS OF CROSS-PRODUCTS OF
C                   DEVIATIONS FROM MEANS.
C           D     - WORKING VECTOR OF LENGTH M.
C           T     - WORKING VECTOR OF LENGTH M.
C
C        REMARKS
C           CORRE WILL NOT ACCEPT A CONSTANT VECTOR.
C
C        SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
C           DATA(M,D) - THIS SUBROUTINE MUST BE PROVIDED BY THE USER.
C                       (1) IF IO=0, THIS SUBROUTINE IS EXPECTED TO
C                           FURNISH AN OBSERVATION IN VECTOR D FROM AN
C                           EXTERNAL INPUT DEVICE.
C                       (2) IF IO=1, THIS SUBROUTINE IS NOT USED BY
C                           CORRE BUT MUST EXIST IN JOB DECK. IF USER
C                           HAS NOT SUPPLIED A SUBROUTINE NAMED DATA,
C                           THE FOLLOWING IS SUGGESTED.
C                                SUBROUTINE DATA
C                                RETURN
C                                END
C
C        METHOD
C           PRODUCT-MOMENT CORRELATION COEFFICIENTS ARE COMPUTED.
C
C     ..................................................................
C
      SUBROUTINE CORRE (N,M,IO,X,XBAR,STD,RX,R,B,D,T)
      DIMENSION X(1),XBAR(1),STD(1),RX(1),R(1),B(1),D(1),T(1)
C
C        ...............................................................
C
C        IF A DOUBLE PRECISION VERSION OF THIS ROUTINE IS DESIRED, THE
C        C IN COLUMN 1 SHOULD BE REMOVED FROM THE DOUBLE PRECISION
C        STATEMENT WHICH FOLLOWS.
C
C     DOUBLE PRECISION XBAR,STD,RX,R,B,T
C
C        THE C MUST ALSO BE REMOVED FROM DOUBLE PRECISION STATEMENTS
C        APPEARING IN OTHER ROUTINES USED IN CONJUNCTION WITH THIS
C        ROUTINE.
C
C        THE DOUBLE PRECISION VERSION OF THIS SUBROUTINE MUST ALSO
C        CONTAIN DOUBLE PRECISION FORTRAN FUNCTIONS.  SQRT AND ABS IN
C        STATEMENT 220 MUST BE CHANGED TO DSQRT AND DABS.
C
C        ...............................................................
C
C     INITIALIZATION
C
      DO 100 J=1,M
      B(J)=0.0
  100 T(J)=0.0
      K=(M*M+M)/2
      DO 102 I=1,K
  102 R(I)=0.0
      FN=N
      L=0
C
      IF(IO) 105, 127, 105
C
C     DATA ARE ALREADY IN CORE
C
  105 DO 108 J=1,M
      DO 107 I=1,N
      L=L+1
  107 T(J)=T(J)+X(L)
      XBAR(J)=T(J)
  108 T(J)=T(J)/FN
C
      DO 115 I=1,N
      JK=0
      L=I-N
      DO 110 J=1,M
      L=L+N
      D(J)=X(L)-T(J)
  110 B(J)=B(J)+D(J)
      DO 115 J=1,M
      DO 115 K=1,J
      JK=JK+1
  115 R(JK)=R(JK)+D(J)*D(K)
      GO TO 205
C
C     READ OBSERVATIONS AND CALCULATE TEMPORARY
C     MEANS FROM THESE DATA IN T(J)
C
  127 IF(N-M) 130, 130, 135
  130 KK=N
      GO TO 137
  135 KK=M
  137 DO 140 I=1,KK
      CALL DATA (M,D)
      DO 140 J=1,M
      T(J)=T(J)+D(J)
      L=L+1
  140 RX(L)=D(J)
      FKK=KK
      DO 150 J=1,M
      XBAR(J)=T(J)
  150 T(J)=T(J)/FKK
C
C     CALCULATE SUMS OF CROSS-PRODUCTS OF DEVIATIONS
C     FROM TEMPORARY MEANS FOR M OBSERVATIONS
C
      L=0
      DO 180 I=1,KK
      JK=0
      DO 170 J=1,M
      L=L+1
  170 D(J)=RX(L)-T(J)
      DO 180 J=1,M
      B(J)=B(J)+D(J)
      DO 180 K=1,J
      JK=JK+1
  180 R(JK)=R(JK)+D(J)*D(K)
C
      IF(N-KK) 205, 205, 185
C
C     READ THE REST OF OBSERVATIONS ONE AT A TIME, SUM
C     THE OBSERVATION, AND CALCULATE SUMS OF CROSS-
C     PRODUCTS OF DEVIATIONS FROM TEMPORARY MEANS
C
  185 KK=N-KK
      DO 200 I=1,KK
      JK=0
      CALL DATA (M,D)
      DO 190 J=1,M
      XBAR(J)=XBAR(J)+D(J)
      D(J)=D(J)-T(J)
  190 B(J)=B(J)+D(J)
      DO 200 J=1,M
      DO 200 K=1,J
      JK=JK+1
  200 R(JK)=R(JK)+D(J)*D(K)
C
C     CALCULATE MEANS
C
  205 JK=0
      DO 210 J=1,M
      XBAR(J)=XBAR(J)/FN
C
C     ADJUST SUMS OF CROSS-PRODUCTS OF DEVIATIONS
C     FROM TEMPORARY MEANS
C
      DO 210 K=1,J
      JK=JK+1
  210 R(JK)=R(JK)-B(J)*B(K)/FN
C
C     CALCULATE CORRELATION COEFFICIENTS
C
      JK=0
      DO 220 J=1,M
      JK=JK+J
  220 STD(J)= SQRT( ABS(R(JK)))
      DO 230 J=1,M
      DO 230 K=J,M
      JK=J+(K*K-K)/2
      L=M*(J-1)+K
      RX(L)=R(JK)
      L=M*(K-1)+J
      RX(L)=R(JK)
      IF(STD(J)*STD(K)) 225, 222, 225
  222 R(JK)=0.0
      GO TO 230
  225 R(JK)=R(JK)/(STD(J)*STD(K))
  230 CONTINUE
C
C     CALCULATE STANDARD DEVIATIONS
C
      FN=SQRT(FN-1.0)
      DO 240 J=1,M
  240 STD(J)=STD(J)/FN
C
C     COPY THE DIAGONAL OF THE MATRIX OF SUMS OF CROSS-PRODUCTS OF
C     DEVIATIONS FROM MEANS.
C
      L=-M
      DO 250 I=1,M
      L=L+M+1
  250 B(I)=RX(L)
      RETURN
      END