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Trailing-Edge - PDP-10 Archives - decuslib20-02 - decus/20-0026/canor.doc
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SUBROUTINE CANOR

PURPOSE
   COMPUTE THE CANONICAL CORRELATIONS BETWEEN TWO SETS OF
   VARIABLES.  CANOR IS NORMALLY PRECEDED BY A CALL TO SUBROU-
   TINE CORRE.

USAGE
   CALL CANOR (N,MP,MQ,RR,ROOTS,WLAM,CANR,CHISQ,NDF,COEFR,
	       COEFL,R)

DESCRIPTION OF PARAMETERS
   N	 - NUMBER OF OBSERVATIONS
   MP	 - NUMBER OF LEFT HAND VARIABLES
   MQ	 - NUMBER OF RIGHT HAND VARIABLES
   RR	 - INPUT MATRIX (ONLY UPPER TRIANGULAR PORTION OF THE
	   SYMMETRIC MATRIX OF M X M, WHERE M = MP + MQ)
	   CONTAINING CORRELATION COEFFICIENTS.  (STORAGE MODE
	   OF 1)
   ROOTS - OUTPUT VECTOR OF LENGTH MQ CONTAINING EIGENVALUES
	   COMPUTED IN THE NROOT SUBROUTINE.
   WLAM  - OUTPUT VECTOR OF LENGTH MQ CONTAINING LAMBDA.
   CANR  - OUTPUT VECTOR OF LENGTH MQ CONTAINING CANONICAL
	   CORRELATIONS.
   CHISQ - OUTPUT VECTOR OF LENGTH MQ CONTAINING THE
	   VALUES OF CHI-SQUARES.
   NDF	 - OUTPUT VECTOR OF LENGTH MQ CONTAINING THE DEGREES
	   OF FREEDOM ASSOCIATED WITH CHI-SQUARES.
   COEFR - OUTPUT MATRIX (MQ X MQ) CONTAINING MQ SETS OF
	   RIGHT HAND COEFFICIENTS COLUMNWISE.
   COEFL - OUTPUT MATRIX (MP X MQ) CONTAINING MQ SETS OF
	   LEFT HAND COEFFICIENTS COLUMNWISE.
   R	 - WORK MATRIX (M X M)

REMARKS
   THE NUMBER OF LEFT HAND VARIABLES (MP) SHOULD BE GREATER
   THAN OR EQUAL TO THE NUMBER OF RIGHT HAND VARIABLES (MQ).
   THE VALUES OF CANONICAL CORRELATION, LAMBDA, CHI-SQUARE,
   DEGREES OF FREEDOM, AND CANONICAL COEFFICIENTS ARE COMPUTED
   ONLY FOR THOSE EIGENVALUES IN ROOTS WHICH ARE GREATER THAN
   ZERO.

SUBROUTINES AND FUNCTION SUBPROGRAMS REQUIRED
   MINV
   NROOT  (WHICH, IN TURN, CALLS THE SUBROUTINE EIGEN.)

METHOD
   REFER TO W. W. COOLEY AND P. R. LOHNES, 'MULTIVARIATE PRO-
   CEDURES FOR THE BEHAVIORAL SCIENCES', JOHN WILEY AND SONS,
   1962, CHAPTER 3.