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dpoequ(3P)		    Sun Performance Library		    dpoequ(3P)

NAME
       dpoequ - compute row and column scalings intended to equilibrate a sym‐
       metric positive definite matrix A and reduce its condition number (with
       respect to the two-norm)

SYNOPSIS
       SUBROUTINE DPOEQU(N, A, LDA, SCALE, SCOND, AMAX, INFO)

       INTEGER N, LDA, INFO
       DOUBLE PRECISION SCOND, AMAX
       DOUBLE PRECISION A(LDA,*), SCALE(*)

       SUBROUTINE DPOEQU_64(N, A, LDA, SCALE, SCOND, AMAX, INFO)

       INTEGER*8 N, LDA, INFO
       DOUBLE PRECISION SCOND, AMAX
       DOUBLE PRECISION A(LDA,*), SCALE(*)

   F95 INTERFACE
       SUBROUTINE POEQU([N], A, [LDA], SCALE, SCOND, AMAX, [INFO])

       INTEGER :: N, LDA, INFO
       REAL(8) :: SCOND, AMAX
       REAL(8), DIMENSION(:) :: SCALE
       REAL(8), DIMENSION(:,:) :: A

       SUBROUTINE POEQU_64([N], A, [LDA], SCALE, SCOND, AMAX, [INFO])

       INTEGER(8) :: N, LDA, INFO
       REAL(8) :: SCOND, AMAX
       REAL(8), DIMENSION(:) :: SCALE
       REAL(8), DIMENSION(:,:) :: A

   C INTERFACE
       #include <sunperf.h>

       void  dpoequ(int	 n,  double *a, int lda, double *scale, double *scond,
		 double *amax, int *info);

       void dpoequ_64(long n, double  *a,  long	 lda,  double  *scale,	double
		 *scond, double *amax, long *info);

PURPOSE
       dpoequ  computes row and column scalings intended to equilibrate a sym‐
       metric positive definite matrix A 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 condi‐
       tion number over all possible diagonal scalings.

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

       A (input) The  N-by-N  symmetric positive definite matrix whose scaling
		 factors are to be computed.  Only the diagonal elements of  A
		 are referenced.

       LDA (input)
		 The leading dimension of the array A.	LDA >= max(1,N).

       SCALE (output)
		 If INFO = 0, SCALE contains the scale factors for A.

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

       AMAX (output)
		 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)
		 = 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.

				  6 Mar 2009			    dpoequ(3P)
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