CXML
        	    
LAPACK version 3.0
slaqsb(3)

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

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

      CHARACTER	     EQUED, UPLO

      INTEGER	     KD, LDAB, N

      REAL	     AMAX, SCOND

      REAL	     AB( LDAB, * ), S( * )

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	  = 'Y':  Equilibration was done, i.e., A has been replaced by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