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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.