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

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

     CHARACTER UPLO

     INTEGER INFO, N

     REAL AMAX, SCOND

     REAL AP( * ), S( * )



     #include <sunperf.h>

     void sppequ(char uplo, int n, float *sap,  float  *s,  float
               *scond, float *amax, int *info) ;

PURPOSE
     SPPEQU computes row and column scalings intended to  equili-
     brate  a  symmetric  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) REAL 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) 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.

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

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

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