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slaqsp

 NAME
      SLAQSP - equilibrate a symmetric matrix A using the scaling
      factors in the vector S

 SYNOPSIS
      SUBROUTINE SLAQSP( UPLO, N, AP, S, SCOND, AMAX, EQUED )

          CHARACTER      EQUED, UPLO

          INTEGER        N

          REAL           AMAX, SCOND

          REAL           AP( * ), S( * )

 PURPOSE
      SLAQSP 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) REAL 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) REAL array, dimension (N)
              The scale factors for A.

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

      AMAX    (input) REAL
              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              = 'Y':  Equilibration was done, i.e., A has been
              replaced by diag(S) * A * diag(S).

 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 scal-
      ing should be done based on the absolute size of the largest
      matrix element.  If AMAX > LARGE or AMAX < SMALL, scaling is
      done.