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

SYNOPSIS
     SUBROUTINE SPOEQU( N, A, LDA, S, SCOND, AMAX, INFO )

     INTEGER INFO, LDA, N

     REAL AMAX, SCOND

     REAL A( LDA, * ), S( * )



     #include <sunperf.h>

     void spoequ(int n, float  *sa,  int  lda,  float  *s,  float
               *scond, float *amax, int *info) ;

PURPOSE
     SPOEQU computes row and column scalings intended to  equili-
     brate  a symmetric 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  con-
     dition number over all possible diagonal scalings.


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

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