dppequ man page on Scientific

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DPPEQU(1)		 LAPACK routine (version 3.2)		     DPPEQU(1)

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

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

	   CHARACTER	  UPLO

	   INTEGER	  INFO, N

	   DOUBLE	  PRECISION AMAX, SCOND

	   DOUBLE	  PRECISION AP( * ), S( * )

PURPOSE
       DPPEQU  computes row and column scalings intended to equilibrate a sym‐
       metric positive definite matrix A in packed storage and reduce its con‐
       dition  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) DOUBLE PRECISION array, dimension (N*(N+1)/2)
	       The  upper  or lower triangle of the symmetric 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) DOUBLE PRECISION array, dimension (N)
	       If INFO = 0, S contains the scale factors for A.

       SCOND   (output) DOUBLE PRECISION
	       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.

       AMAX    (output) DOUBLE PRECISION
	       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.

 LAPACK routine (version 3.2)	 November 2008			     DPPEQU(1)
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