DLAQSP  - equilibrate a symmetric matrix A using the scal­
       ing factors in the vector S


SYNOPSIS

       SUBROUTINE DLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED )

           CHARACTER      EQUED, UPLO

           INTEGER        N

           DOUBLE         PRECISION AMAX, SCOND

           DOUBLE         PRECISION AP( * ), S( * )


PURPOSE

       DLAQSP equilibrates a symmetric matrix A using the scaling
       factors in the vector S.


ARGUMENTS

       UPLO    (input) CHARACTER*1
               Specifies  whether  the  upper or lower triangular
               part of the symmetric matrix A is stored.  =  'U':
               Upper triangular
               = 'L':  Lower triangular

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

       AP        (input/output)   DOUBLE   PRECISION   array,
               dimension (N*(N+1)/2)
               On  entry, the upper or lower triangle of the sym­
               metric 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.

               On exit, the equilibrated matrix:  diag(S) *  A  *
               diag(S), in the same storage format as A.

       S       (input) DOUBLE PRECISION array, dimension (N)
               The scale factors for A.

       SCOND   (input) DOUBLE PRECISION
               Ratio of the smallest S(i) to the largest S(i).

       AMAX    (input) DOUBLE PRECISION
               Absolute value of largest matrix entry.

       EQUED   (output) CHARACTER*1
               Specifies  whether  or not equilibration was done.
               = 'N':  No equilibration.
               = 'Y':  Equilibration was done, i.e., A  has  been



PARAMETERS

       THRESH  is  a  threshold  value  used to decide if scaling
       should be done based on the ratio of the scaling  factors.
       If SCOND < THRESH, scaling is done.

       LARGE  and  SMALL  are  threshold values used to decide if
       scaling should be done based on the absolute size  of  the
       largest  matrix element.  If AMAX > LARGE or AMAX < SMALL,
       scaling is done.


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