CPPEQU man page on IRIX

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CPPEQU(3F)							    CPPEQU(3F)

NAME
     CPPEQU - compute row and column scalings intended to equilibrate a
     Hermitian positive definite matrix A in packed storage and reduce its
     condition number (with respect to the two-norm)

SYNOPSIS
     SUBROUTINE CPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )

	 CHARACTER	UPLO

	 INTEGER	INFO, N

	 REAL		AMAX, SCOND

	 REAL		S( * )

	 COMPLEX	AP( * )

PURPOSE
     CPPEQU computes row and column scalings intended to equilibrate a
     Hermitian positive definite matrix A in packed storage and reduce its
     condition number (with respect to the two-norm).  S contains the scale
     factors, S(i)=1/sqrt(A(i,i)), chosen so that the scaled matrix B with
     elements B(i,j)=S(i)*A(i,j)*S(j) has ones on the diagonal.	 This choice
     of S puts the condition number of B within a factor N of the smallest
     possible condition number over all possible diagonal scalings.

ARGUMENTS
     UPLO    (input) CHARACTER*1
	     = 'U':  Upper triangle of A is stored;
	     = 'L':  Lower triangle of A is stored.

     N	     (input) INTEGER
	     The order of the matrix A.	 N >= 0.

     AP	     (input) COMPLEX array, dimension (N*(N+1)/2)
	     The upper or lower triangle of the Hermitian matrix A, packed
	     columnwise in a linear array.  The j-th column of A is stored in
	     the array AP as follows:  if UPLO = 'U', AP(i + (j-1)*j/2) =
	     A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) =
	     A(i,j) for j<=i<=n.

     S	     (output) REAL array, dimension (N)
	     If INFO = 0, S contains the scale factors for A.

     SCOND   (output) REAL
	     If INFO = 0, S contains the ratio of the smallest S(i) to the
	     largest S(i).  If SCOND >= 0.1 and AMAX is neither too large nor
	     too small, it is not worth scaling by S.

									Page 1

CPPEQU(3F)							    CPPEQU(3F)

     AMAX    (output) REAL
	     Absolute value of largest matrix element.	If AMAX is very close
	     to overflow or very close to underflow, the matrix should be
	     scaled.

     INFO    (output) INTEGER
	     = 0:  successful exit
	     < 0:  if INFO = -i, the i-th argument had an illegal value
	     > 0:  if INFO = i, the i-th diagonal element is nonpositive.

									Page 2

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