ZLAQSP (3lapack)

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 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.

          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          = 'Y':  Equilibration was done, i.e., A has been replaced by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 scaling should be
  done based on the absolute size of the largest matrix element.  If AMAX >
  LARGE or AMAX < SMALL, scaling is done.