CLAQHB (3lapack)

equilibrate a symmetric band matrix A using the scaling factors in the vector S

SYNOPSIS

  SUBROUTINE CLAQHB( UPLO, N, KD, AB, LDAB, S, SCOND, AMAX, EQUED )

      CHARACTER      EQUED, UPLO

      INTEGER        KD, LDAB, N

      REAL           AMAX, SCOND

      REAL           S( * )

      COMPLEX        AB( LDAB, * )

PURPOSE

  CLAQHB equilibrates a symmetric band 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.

  KD      (input) INTEGER
          The number of super-diagonals of the matrix A if UPLO = 'U', or the
          number of sub-diagonals if UPLO = 'L'.  KD >= 0.

  AB      (input/output) COMPLEX array, dimension (LDAB,N)
          On entry, the upper or lower triangle of the symmetric band matrix
          A, stored in the first KD+1 rows of the array.  The j-th column of
          A is stored in the j-th column of the array AB as follows: if UPLO
          = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO =
          'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).

          On exit, if INFO = 0, the triangular factor U or L from the
          Cholesky factorization A = U'*U or A = L*L' of the band matrix A,
          in the same storage format as A.

  LDAB    (input) INTEGER
          The leading dimension of the array AB.  LDAB >= KD+1.

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          = 'Y':  Equilibration was done, i.e., A has been replaced by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