ZLAQHE (3lapack)

equilibrate a Hermitian matrix A using the scaling factors in the vector S

SYNOPSIS

  SUBROUTINE ZLAQHE( UPLO, N, A, LDA, S, SCOND, AMAX, EQUED )

      CHARACTER      EQUED, UPLO

      INTEGER        LDA, N

      DOUBLE         PRECISION AMAX, SCOND

      DOUBLE         PRECISION S( * )

      COMPLEX*16     A( LDA, * )

PURPOSE

  ZLAQHE equilibrates a Hermitian 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
          Hermitian matrix A is stored.  = 'U':  Upper triangular
          = 'L':  Lower triangular

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

  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
          On entry, the Hermitian matrix A.  If UPLO = 'U', the leading n by
          n upper triangular part of A contains the upper triangular part of
          the matrix A, and the strictly lower triangular part of A is not
          referenced.  If UPLO = 'L', the leading n by n lower triangular
          part of A contains the lower triangular part of the matrix A, and
          the strictly upper triangular part of A is not referenced.

          On exit, if EQUED = 'Y', the equilibrated matrix: diag(S) * A *
          diag(S).

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

  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          = 'Y':  Equilibration was done, i.e., A has been replaced by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.