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zlaqsp

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

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

          CHARACTER      EQUED, UPLO

          INTEGER        N

          DOUBLE         PRECISION AMAX, SCOND

          DOUBLE         PRECISION S( * )

          COMPLEX*16     AP( * )

 PURPOSE
      ZLAQSP 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) COMPLEX*16 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              = 'Y':  Equilibration was done, i.e., A has been
              replaced by diag(S) * A * diag(S).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.